SAARC Workshop on
Geophysical Techniques for Exploration of Natural Resources
18-22, October, 2010
Khalid Amin Khan [email protected]
Oil & Gas Training Institute, OGDCL Islamabad, Pakistan
This manual is a subset of my original training manual Seismic Methods K. A Khan, 2009
It is a supplement to Seismic Methods, Digital Courseware Series, 2nd Edition K. A Khan, 2009
“I do not know what I may appear to the world, but to myself I seem to have been only a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.” Isaac Newton
Training of Professionals from SAARC Countries
Geophysical Techniques for Exploration of Natural Resources By Khalid Amin Khan, Dy.Chief Geophysicist Oil & Gas Training Institute, OGDCL, Islamabad
Schedule Day-1 • Physics and Electromagnetic Spectrum • Imaging the Invisible • Overview of Geophysical Methods •
Electrical Resistivity Methods Resistivity Meter Schlumberger Configuration Wenner Configuration Vertical Electrical Sounding Curves
Day-2 • Gravity & Magnetic Methods Gravity Meter & Magnetometer Gravity Field Correction: Free Air and Bouguer Anomaly Terrain Corrections Regional and Residual Separation Gravity Modelling using Talwani Method Magnetic Data Processing 2D Grid Processing •
Seismic Waves and Rock Physics Types of Seismic Waves Seismic Velocities Engineering Properties and Rock Physics
Day-3 • Seismic Refraction Methods First Breaks: Direct and Refracted Waves Automated First Break Picking TX-Graphs and Layer Velocity and Depth Computation Low Velocity Weathered Layers and Statics Computation Interpolation and Gridding Uphole Logging Methods •
Seismic Reflection Data Acquisition Geophones as Transducers Seismic Recorder Multiplexing and De-multiplexing
Seismic Noise Coherent and Incoherent Noise Geophone Arrays Low and High Cut Filters Stacking to remove Incoherent Noise
Day-4 • Seismic Data Processing I Data Processing System Environment Processing Tasks and Job Control Language Basic Processing Flow Gains, Spherical Divergence Band Pass Filter Deconvolution •
Seismic Data Processing II Dynamic Corrections / Normal Moveout Velocity Analysis / Constant Velocity Stack Stacking: Raw, Brute Stack, Residual Statics & Migration
Day-5 • Seismic Resolution Temporal Resolution: Frequency and Bandwidth Spatial Resolution: Picket Interval and Fresnel Zone Phase Uncertainty Signal to Noise Ratio •
Seismic Interpretation Components of a Base Map Seismic Section: Display Modes, Vertical and Horizontal Scales Components of a Petroleum System Marking Horizons and Faults Auto Tracking Horizons Posting Data to Base Map Contouring 3D Seismic Cube: Inline Section, Cross-line Section & Time Slice Sonic and Bulk Density Logs for Synthetic Seismogram Seismic Modeling Seismic Velocities and Time to Depth Conversion
Contents Module 1: Physics and Electromagnetic Spectrum 1.1 Basic Foundations of Physics 1.2 Imaging Principle 1.3 Imaging the Invisible 1.4 Fundamental Laws of Wave Propagation Module 2: Electrical Resistivity Methods 2.1 Electrical Resistivity Methods 2.2 Resistivity Meter 2.3 Electrical Resistivity Surveying 2.4 Electrode Geometries 2.5 Resistivity Interpretation Module 3: Gravity & Magnetic Methods 3.1 Gravity and Magnetic Prospecting 3.2 Gravity Method 3.3 Gravimeters 3.4 Gravity Surveying and Corrections 3.5 Regional Residual Separations 3.6 Gravity Modeling 3.7 Magnetic Method 3.8 Magnetometers 3.9 Magnetic Surveying and Corrections 3.10 2D Grid Processing Module 4: Seismic Waves and Rock Physics 4.1 Seismic Waves 4.2 Types of Seismic Waves 4.3 Uses of Seismic Waves 4.4 Stress and Strain 4.5 Elasticity & Stiffness 4.6 Hooks Law of Elasticity 4.7 Elastic Moduli 4.8 Computing Density/Moduli from Seismic Velocities
Module 5: Seismic Refraction Methods 5.1 Snell’s Law 5.2 Seismic Refraction Method 5.3 Seismic Refraction Data Acquisition 5.4 First Breaks 5.5 Time-Distance Graphs 5.6 Statics Corrections 5.7 Limitations of Seismic Refraction Method Module 6: Seismic Reflection Data Acquisition 6.1 Digital Sampling and Aliasing 6.2 Seismic Recorder 6.3 Seismic Sources 6.4 Fold Coverage 6.5 Geophone Spread Geometries Module 7: Seismic Noise 7.1 Signals and Noise 7.2 Coherent Noise 7.3 Incoherent Noise 7.4 Aliased Frequencies 7.5 Multiples Module 8: Seismic Data Processing I 8.1 Propagation of Seismic Waves through Earth 8.2 Mechanical Processes 8.3 Interactive Processes 8.4 Spherical Divergence Compensation and Gains 8.5 Band Pass Filter 8.6 Deconvolution Module 9: Seismic Data Processing II 9.1 Seismic Data Processing Flow 9.2 Dynamic Corrections 9.3 Velocity Analysis 9.4 Residual Statics 9.5 Migration
Module 10: Seismic Resolution 10.1 Resolution 10.2 Seismic Resolution 10.3 Fresnel Zone 10.4 More on Seismic Resolution Module 11: Seismic Interpretation 11.1 Seismic Data Display Standards 11.2 Seismic Section Display Scales 11.3 Base Map 11.4 Seismic Interpretation 11.5 Time to Depth Conversion 11.6 2D Seismic Modeling 11.7 Synthetic Seismogram
Physics and Electromagnetic Spectrum At the end of this module you would be able to understand
Science behind Imaging the Invisible
Basic Methodology of Geophysical Exploration Techniques
1.1 Basic Foundations of Physics Physics is the science of Matter and Energy. Mater and Energy are related to each other through Einstein’s equation:
E = m c2 All Matter-Energy in the Universe has a dual nature. They exist as Particles as well as Waves. Thus Physics is the science of Particles and Waves The first question arises – What is the Size of Particles ? There is a wide range of particle size, considering the universe itself as a particle down to the elementary sub-atomic particles. Thus physics is divided into different branches on the basis of size of the particles as shown below.
Accordingly Geophysics is the physics of Earth, Space and Planets. It includes the study of solid earth, its interior, fluid envelopes (oceans) and atmospheres.
The second question arises – What is the Frequency of Waves ? This includes the whole electromagnetic spectrum (EMS). If we extend down the EMS to sound and ultra-sound waves then we have a whole range of frequencies that exist in the universe as shown below.
If we consider our human sensors (eyes and ears), we can only receive the sound and visible light frequencies, thus only a narrow window in the EMS is Visible to us; the rest is totally invisible as shown.
1.2 Imaging Principle The imaging principle considers three components; an energy source in the form of some radiation having a band of frequencies, a set of mediums through which the radiation passes and a sensor which can receive the given frequencies. This principle holds true in case of our eyes. We need a light source which transmits frequencies in the visible band. These frequencies hit the surfaces of different materials and are reflected back and finally received by our eyes which act as sensors. This produces the sensation of vision. Each material based on its physical properties (albedo) absorbs certain frequencies and reflects the remaining frequencies, which generates the impression of color on our retina. Similarly bats have no eyes, instead they use another band of frequencies, ultra-sounds to get vision. Thus different parts of the electromagnetic spectrum can be used for various types of imaging. Though most of the EMS is invisible to us, but special tools have been developed which have sensors that can receive a certain band of frequencies. The received radiation can be processed and translated into some graphical form which can be viewed and interpreted by human eye as illustrated below.
This imaging the invisible is used in medical instrumentation, geophysical methods, astrophysics and various security scanners.
1.3 Imaging the Invisible Some common imaging the invisible instruments or techniques are summarized below. • -
Medical Instrumentation X-rays Ultra Sound Magnetic resonance Imaging (MRI) Computerized Tomography Scan (CT-Scan)
• Scanning Tunnel Microscope • Astrophysics - Radio Telescope - Infrared telescope • -
Geophysics Gravity & Magnetic Electrical & Electromagnetic Ground Penetration radar (GPR) Seismic
1.4 Fundamental Laws of Wave Propagation Each imaging method is based on some contrast in a physical parameter. The physical parameter represents a potential field and therefore occupies a portion of the Electro Magnetic Spectrum (EMS). As each method uses a different frequency band of EMS, two generalized laws can be defined which can be applied to all imaging techniques. Frequency verses Resolution Resolution of a system or technique is defined as its ability to view the smallest size of an object. This purely depends on the frequency used by the system. We know the wavelength is inversely proportional to frequency. According the smallest size that can be viewed using a frequency is 1/4th of the wavelength of that frequency. Thus higher the frequency the higher would be the resolution.
- High Frequency > Small Wavelength > View Small Objects - Low Frequency > Large Wavelength > View Large Objects Frequency versus Penetration Another important concern is the wave penetration or imaging depth. In this regard the frequency is inversely proportional to depth of penetration. Thus higher the frequency the lower would be the penetration. - High Frequency > Less Penetration - Low Frequency > Deep Penetration Thus increasing the frequency increases the resolution but decreases the depth of penetration. Considering the above two principles various imaging methods have been devised according to their application and usage. In this regard, just consider the following two examples. Seismic Seismic methods use low frequencies (10-200 Hz). Thus they have low resolution but high depth of penetration. This suits us for imaging the earth. The thinnest layers are in order of several meters and may be few kilometers deep. The seismic waves can propagate down to such depths and resolve these layers. Ultrasound Ultrasound uses comparatively higher frequencies (> 20 KHz). This increases the resolution to millimeters but decreases the depth of penetration to less than a meter. It can be used successfully to image small tissues in the human body. Thus there is no need for deeper penetration.
Electrical Resistivity Methods At the end of this module you would be able to understand
Schlumberger and Wenner Configuration
Vertical Electrical Sounding Curves
2.1 Electrical Resistivity Methods The electrical resistivity method is based on resistivity (opposite of conductivity) contrast. Thus it involves measuring the apparent resistivity of soils and rock as a function of depth or position. The resistivity of soils is a complicated function of porosity, permeability, ionic content of the pore fluids, and clay mineralization. The unit of resistivity is ohm-meter. The most common electrical methods used in mineral exploration, hydrogeologic and environmental investigations are vertical electrical soundings (VES) (resistivity soundings) and resistivity profiling. The VES techniques are used to determine depth to groundwater, map clay aquitards, saltwater intrusion and vertical extent of certain types of soil and groundwater contamination, characterize subsurface hydrogeology, determine depth to bedrock/overburden thickness, map stratigraphy and estimate landfill thickness The resistivity profiling techniques are used to map lateral extent of conductive contaminant plumes, explore for sand and gravel and delineate disposal areas. Resistivities of some common rocks and mineral are given below in ohmmeter. - Igneous and Metamorphic Rocks Granite 5x103 – 106 Basalt 103 – 106 Slate 6x102 - 4x107 Marble 102 - 2.5x108 Quartzite 102 - 2x108 - Sedimentary Rocks Sandstone 8 - 4x103 Shale 20 - 2x103 Limestone 50 - 4x102 - Soils and waters Clay 1 - 100 Alluvium 10 - 800 Groundwater (fresh) 10 - 100 Sea water 0.2
2.2 Resistivity Meter The instrument used to carry out electrical resistivity surveys is called resistivity meter. It consists of the following two main units: Transmitter It includes the battery and an ammeter and sends out well defined regulated current to the ground through the current electrodes. The current can be direct current or low frequency alternating current. Receiver The receiver consists of a voltmeter and detects the transmitted signal current by measuring the potential developed between the two potential electrodes. Modern digital instruments also contain an analog to digital converter and a microprocessor which quickly takes multiple readings and averages them to get reliable results. The working of a resistivity meter is shown in the following figure. Here C1 and C2 are current electrodes, P1 and P2 are potential electrodes, A is ammeter and V is voltmeter.
2.3 Electrical Resistivity Surveying During a resistivity survey, current is injected into the earth through a pair of current electrodes, and the potential difference is measured between a pair of potential electrodes. The current and potential electrodes are generally arranged in a linear array. Common arrays include the Wenner array, Schlumberger array, dipole-dipole array and pole-Dipole array. The apparent resistivity is the bulk average resistivity of all soils and rock influencing the current. It is calculated by dividing the measured potential difference by the input current and multiplying by a geometric factor specific to the array used and electrode spacing as given below;
where ∆V is the potential difference, I is the current and k is a geometric factor depending on the geometry of the array. In vertical electrical soundings, the distance between the current electrodes and the potential electrodes is systematically increased, thereby yielding information on subsurface resistivity from successively greater depths. The variation of resistivity with depth is modeled using forward and inverse modeling computer software. Thus this technique provides a 1D vertical model of the subsurface. In resistivity profiling, the electrode spacing is fixed and measurements are taken at successive intervals by moving the entire array along a profile. This gives some information about lateral changes in the subsurface resistivity, but it cannot detect vertical changes in the resistivity. Data are generally presented as cross-section profiles or contour maps and interpreted qualitatively.
2.4 Electrode Geometries Some common electrode geometries are illustrated in the next figure along with their geometric factors. The depth of penetration of most of these configurations is half the geometry spread length.
Among these geometries Schlumberger and Wenner are the most widely used configurations. Each geometry has advantages and disadvantages. Advantages of Wenner array as compared to Schlumberger array include; large potential electrode spacing places less demand on instrument sensitivity and simplicity in geometric factor equation due to equally spaced electrodes. The main disadvantages of Wenner array are that in an expanding array all electrodes must be moved for each reading which is not the case with Schlumberger array and secondly it is more sensitive to local near-surface lateral variations.
2.5 Resistivity Interpretation Resistivity data is interpreted in the following way; Qualitative Interpretation In this type of interpretation the apparent resistivity values are directly used. For a random or gridded distribution of resistivity stations, iso-resistivity contour maps are generated for a particular depth to show the general distribution of resistivity at the given depths. Similarly resistivity stations are joined along a profile and cross-sections of apparent resistivity are generated. Such sections are also generated for resistivity profiling techniques. These sections show the cross-sectional variation of resistivity as illustrated in the next figure.
Quantitative Interpretation The main task in quantitative interpretation is to identify the subsurface layers and get their true resistivities, which in turn are translated into geological formations. The measured apparent resistivity values for 1D VES are normally plotted on a log-log graph paper. To interpret the data from such a survey, it is normally assumed that the subsurface consists of horizontal layers. In this case, the subsurface resistivity changes only with depth, but does not change in the horizontal direction. The true resistivities are obtained through a manual procedure of matching segments of field resistivity curves with a set of 2 layer master. Two layer master curves are illustrated below.
Several reverse and forward modeling techniques are also available that can interpret the apparent resistivity field curves into true resistivities and depths data as illustrated in the next figure.
Gravity & Magnetic Methods At the end of this module you would be able to understand
Gravimeter & Magnetometer
Gravity Field Correction: Free Air and Bouguer Anomaly
Regional and Residual Separation
Magnetic Data Processing
2D Grid Processing
3.1 Gravity and Magnetic Prospecting Gravity and magnetic prospecting techniques involves measuring passive potential fields of the Earth. In both these methods the measured signal is a composite contribution from all depths. On the other hand, seismic prospecting can give a detailed picture of Earth structure with different subsurface components resolved. Thus seismic method has much higher resolution as compared to these methods. Gravity and magnetic methods can be carried out on land or sea using different techniques and equipment. In addition aero-gravity and magnetic surveys can also be conducted.
3.2 Gravity Method In all gravity surveys the vertical component of g is measured. Gravity prospecting can be used where density contrasts are present in a geological structure, and the usual approach is to measure differences in gravity from place to place. In gravity prospecting we are mostly interested in lateral variations in Earth structure which in turn create lateral variations in density. Gravity method was first applied for prospecting salt domes in the Gulf of Mexico, and later for looking anticlines in continental areas. Gravity cannot detect oil directly, but if the oil is of low density and accumulated in a trap, it can give a gravity low that can be detected by gravity prospecting. Anticlines can also give gravity anomalies as they cause high or low density beds to be brought closer to the surface. Nowadays in the petroleum industry, gravity method is used for regional studies to identify large and thick enough sedimentary basins, as sedimentary rocks have lower densities than basement rocks. Gravity prospecting can also be used for mineral exploration if substantial density contrasts are expected, such as, chromite bodies have very high densities, buried channels which may contain gold or uranium can be detected because they have relatively low density. The unit of gravity is Gal, after Galileo, where 1 Gal = 1 cm/sec2. Thus g at the surface of the Earth is approximately 103 Gals. Gravity anomalies are measured in units of milliGals, where 1 mGal = 10-3 Gals = 10-5 m/sec2.
The densities of few common minerals in g/cm2 are given below - Quartz 2.65 - Felspar 2.6 - Biotite mica 2.9 - Calcite 2.6 – 2.7
3.3 Gravimeters Gravity meters, usually called gravimeters, are sensitive to 0.01 mGal = 10-8 of the Earth’s total value. Thus the specifications of gravimeters are amongst the most difficult to meet in any measuring device. It would be impossible to get the accuracy required in absolute gravity measurements quickly with any device, and thus field gravity surveying is done using relative gravimeters. There are two basic types of gravimeters: Stable Gravimeters These work on the principle of a force balancing the force of gravity on a mass, such as the Gulf gravimeter. These gravimeters take a long time to measure each point. The Gulf gravimeter comprises a flat spring wound in a helix, with a weight suspended from the lower end. An increase in g causes the mass to lower and rotate. A mirror on the mass thus rotates and it is this rotation that is measured. The sensitivity of these gravimeters is ~ 0.1 mGal. They are now obsolete, but a lot of data exist that were measured with such instruments and it is important to know that such data are not as accurate as data gathered with more modern instruments Unstable Gravimeters These are virtually universally used now. They are well devised mechanical devices where increase in g causes extension of a spring, but the extension is magnified by mechanical geometry. An example is the Wordon gravimeter, which has a sensitivity of 0.01 mGal, and is quite commonly used. Wordon gravimeter is shown in the next figure. It is housed in a thermos flask for temperature stability, but it also incorporates a mechanical temperature compensation device. It is evacuated to eliminate errors due to changes in barometric pressure. It weighs about 3 kg and the mass weighs 5 mg. Vertical movement of the mass causes rotation of a beam, and equilibrium is restored by increasing the tension of torsion fibers. Another commonly used gravity instrument is LaCost-Romberg gravimeter. The latest gravimeters are completely electronic with a software controlled
interface and a built-in GPS. They directly store data on a media floppy, which can be downloaded to a computer for further processing.
3.4 Gravity Surveying and Corrections Gravity field procedure involves measurement on a base station followed by measurements on a number of stations and finally repeating the base station. For larger surveys base station must be repeated approximately every two hours. During the survey, at each station the following information is recorded: - Time at which the measurement is taken. - Reading of the Gravity Meter in scale readings - Navigation Data: Latitude, longitude and elevation of the station. A set of corrections are applied to the observed gravity data which are discussed below. Instrument Calibration Each instrument has a scale constant (SC), provided by the manufacturer, that translates scale readings (SR) into mGal as given below. gobs = SR * SC
Drift Correction The drift correction incorporates the effects of instrument drift, uncompensated temperature effects and the gravitational attraction of the sun and moon. It is computed by taking two reading at the base station, one at start and the other at end of survey. The drift rate is computed as;
g base _ start − gbase _ end tbase _ end − tbase _ start
Now drift correction for a station is given by;
DC = DR *(tstat − tbase _ start ) Latitude Correction This correction is needed because of the ellipticity of Earth as g is reduced at low latitudes because of the Earth’s shape and rotation. It is given by;
LC = .0008122 Dist NS Sin 2φbase where DistNS is North-South Distance, φbase is latitude of base. In N-hemisphere this correction is negative if station is towards north of base and positive if station is south of base and vise versa for southern hemisphere. Free Air Correction The correction is also called elevation correction. It is required to correct for the variable heights of the stations above sea level, because g falls off with height. It is given by;
FAC = k ( Estat − Ebase ) where Estat is elevation of station, Ebase is elevation of base and k = .9406 for feet and k = .3086 for meters. Bouguer Correction This correction accounts for the mass of rock between the station and sea level. It has the effect of increasing g at the station, and thus it is subtracted.
Bouguer correction is given by;
BC = k ρ ( Estat − Ebase ) where Estat is elevation of station, Ebase is elevation of base, ρ is density of the material and k = .01276 for feet and k = .04185 for meters. Bouguer Anomaly The Bouguer anomaly is computed by apply all the above corrections to the observed gravity as given by;
BA = ( g stat − g base _ start ) + DC + LC + FAC − BC Terrain Corrections The effect of terrain always reduces the observed g. This is true for a mountain above or a valley below the station, both cause g to be reduced. Previously terrain corrections were done by hand using a transparent graticule (shown below) placed at the station, then average height of each compartment is estimated and Hammer chart was used to obtain the correction for the station. This chart gives the correction for a particular distance from the station. It has been worked out assuming a block of constant height for each compartment. This manual procedure was very time-consuming and involved a lot of repetition. With the availability of digital terrain models the same procedure has been computerized.
The figure below shows an observed gravity anomaly.
The following are the drift, latitude, free air and Bouguer corrections for the above observed anomaly.
The observed anomaly after application of above corrections is shown below.
3.5 Regional Residual Separations The processed gravity anomaly contains regional and residual effects. For regional studies we are interested in regional anomaly while for local studies we are interested in residual anomaly. There are several techniques for separation of regional and residual trend such as graphical method, moving average method with 3, 5 or 7 points operator and statistical best fir or regression techniques from first to higher orders. The figure below shows processed anomaly along with its regional and residual components.
3.6 Gravity Modeling The observed gravity anomaly gives us the trend of gravity along a profile. Forward modeling techniques, such as the Talwani method are used to create a subsurface model of geological bodies each assigned with a density. The modeling process generates a model anomaly. The shape and density of subsurface bodies are changed in such a way that the model anomaly matches the observed anomaly. Previously this was done manually through a tedious process. Currently interactive applications are available that can quickly create and fit the model.
The next figure shows a subsurface regional model with its model curve fitted to the regional trend of gravity.
3.7 Magnetic Method In magnetic prospecting precise magnetic field is measured to locate geological structures and man-made objects in the ground or under the sea. The number of possible applications of magnetic exploration is unlimited and include; oil and gas exploration, mineral exploration such as iron ore, underground pipeline detection, buried unexploded ordnance detection, and archeological prospecting. All these objects are detected as they posses an extremely weak magnetic field of their own, which is a measureable local disturbance in the Earth’s magnetic field. Such disturbance is called a magnetic anomaly. This contrast in magnetic field is called susceptibility. It is measurement in Gammas.
3.8 Magnetometers A device that measures the magnetic fields is called a magnetometer. There are several types of magnetometers among which the two most common types are;
Proton Precession Magnetometer Proton precession magnetometers, also known as proton magnetometers, measure the resonance frequency of protons (hydrogen nuclei) in the magnetic field to be measured, due to nuclear magnetic resonance (NMR). As the precession frequency depends only on atomic constants and the strength of the ambient magnetic field, the accuracy of this type of
magnetometer is very good thus it is widely used in magnetic prospecting. This magnetometer measure the total intensity (T) of the magnetic field. Fluxgate Magnetometer A fluxgate magnetometer consists of a small, magnetically susceptible, core wrapped by two coils of wire. An alternating electrical current is passed through one coil, driving the core through an alternating cycle of magnetic saturation; i.e., magnetised, unmagnetised, inversely magnetised, unmagnetised, magnetised, etc. This constantly changing field induces an electrical current in the second coil, and this output current is measured by a detector. In a magnetically neutral background, the input and output currents will match. However, when the core is exposed to a background field, it will be more easily saturated in alignment with that field and less easily saturated in opposition to it. Hence the alternating magnetic field, and the induced output current, will be out of step with the input current. The extent to which the input and output currents are out of step, will depend on the strength of the background magnetic field. Often, the current in the output coil is integrated, yielding an output analog voltage, proportional to the magnetic field. This magnetometer measures the vertical component (Z) of the magnetic field.
3.9 Magnetic Surveying and Corrections The processing of observed magnetic data is similar to gravity data, except the types of corrections are totally different. Only two corrections are applied to magnetic data which are discussed below. Diurnal Correction The suns solar activity continuously disturbs the Earth’s magnetic field. Thus we need to remove these effects from the observed data. These effects can be removed in two ways. With a single magnetometer the procedure is similar to drift correction. We start with a base station and repeat it at the end and from the difference in the two readings we compute a drift rate which is applied to observations of all stations. On the other hand if we have two instruments we fix one at the base while the other takes readings at the stations. Later the readings at the base are used as corrections that are applied to the base stations at the corresponding times.
Normal Correction The Earth’s magnetic field is not constant and changes with latitude and longitude. Global magnetic anomaly maps are published annually. They are used to apply corrections at the station locations.
3.10 2D Grid Processing In the above sections we discussed processing of gravity and magnetic data along a profile. If there is a set of parallel profiles they make up a grid. The data corrections or reductions are applied individually along a profile, but regional residual effects are separated through grid processing. In these techniques a 3 x 3 operator moves step by step through the grid to compute regional anomaly at the center of the operator. This technique is similar to Griffin’s method which used a circular operator around the grid node. The computed regional trend grid is subtracted from the input observed gravity grid to get a residual anomaly grid as shown in the next figure.
Seismic Waves and Rock Physics At the end of this module you would be able to understand
Types of Seismic Waves
Stress and Strain
Hook’s Law of Elasticity
Engineering Properties and Rock Physics
4.1 Seismic Waves Seismic waves travel through the Earth, as the result of a tectonic earthquake or an explosion. They propagate through a medium similar to sound waves. They are also called Elastic Waves.
4.2 Types of Seismic Waves Seismic waves are classified into the following types: • Body Waves - P-Waves - S-Waves • Surface Waves - Rayleigh Waves - Love Waves Body Waves Body waves travel through the interior of the Earth. They follow ray-paths bent by the varying density and modulus (stiffness) of the Earth's interior. Body waves are further classified into P and S waves. P-Waves P means Primary Waves as they are fast and arrive first. They are also called longitudinal or compressional waves, as particle motion is parallel to wave propagation. The ground is alternately compressed and dilated in the direction of propagation. These waves can travel through any type of material. P-waves have the following velocities in different mediums. Air 330 m/s (Take the form of sound waves, thus travel at the speed of sound) - Water 1450 m/s - Granite 5000 m/s (In Solids twice as fast as S Waves) -
When generated by an earthquake they are less destructive than the S waves and surface waves that follow them, due to their smaller amplitudes P Wave propagation is analogous to sound waves as shown.
S-Waves S means Secondary Waves as they arrive after the P Waves. They are also called transverse or shear waves, as particle motion is perpendicular to wave propagation. The ground is displaced perpendicularly to the direction of propagation. In the case of horizontally polarized S waves, the ground moves alternately to one side and then the other. They travel only through solids, as fluids (liquids and gases) do not support shear stresses Their speed is about 60% of that of P waves in a given material S waves are several times larger in amplitude than P waves for earthquake sources. S wave propagation is analogous to Light as shown below.
Surface Waves Surface waves are analogous to water waves and travel just under the Earth's surface. They travel more slowly than body waves. Because of their low frequency, long duration, and large amplitude, they can be the most destructive type of seismic wave.
Rayleigh Waves They travel only under the Earth’s surface. They are in the form of ripples, similar to those on the surface of water. Rayleigh waves are also called ground roll in seismic exploration data. Their speed is about 70% of that of S waves. Their existence was predicted by John William Strutt, Lord Rayleigh, in 1885. Rayleigh wave propagation is analogous to Ocean surface as shown below.
Love Waves They travel only under the Earth’s surface. They cause horizontal shearing of the ground. Their speed is about 90% of that of S waves, slightly faster than Rayleigh waves. Named after A.E.H. Love, a British mathematician who created their mathematical model in 1911 Love wave propagation is analogous to movement of Snake or Shaken Rope as shown below.
Seismic energy released during an earthquake can be recorded on a seismogram as shown below.
Surface waves P
‘Primary’ (first to arrive)
‘Surface’ (last to arrive) ‘Secondary’ (second to arrive)
4.3 Uses of Seismic Waves • P Waves are commonly used in Oil & Gas Exploration • Special 3 component (3C: P, SH, SV) Surveys are also carried out for rock physics and reservoir analysis. • P & S Waves are used to determine the engineering properties of ground. • Earth’s liquid outer core was discovered due to the fact that shear waves cannot pass through liquids (as demonstrated by Richard Dixon Oldham)
4.4 Stress and Strain Stress: The force causing the deformation in a material. Stress can be of two types. Normal stress is applied perpendicular to the face of material. Shear stress is applied parallel or tangential to the face of a material. Strain: The amount by which a material body is deformed. Strain is also of two types. Normal strain acts perpendicular to the face of a material that it is acting on. Shear strain acts parallel to the face of a material that it is acting on.
4.5 Elasticity & Stiffness Elasticity: A material is said to be elastic if it deforms under stress (applied force), but returns its original shape when the stress is removed. The amount of deformation is called the strain. Stiffness is the resistance of an elastic body to deflection or deformation by an applied force. Stress-Strain relation of rock deformation is illustrated in the following figure.
Each material has an elastic limit and a fracture point. Stress applied within the elastic limits will cause strain that will be recovered when the stress is removed. Stress greater than the elastic limit, but below the fracture point will cause a permanent strain, which will not recover when the stress is removed. If the stress is increased to or above the fracture point the material will break up. On the basis of stress stain analysis, there can be two types of deformation: Elastic Deformation: A temporary change in shape or size that is recovered when the applied stress is removed. Ductile (Plastic) Deformation: A permanent change in shape or size that is not recovered when the applied stress is removed.
4.6 Hooks Law of Elasticity The amount by which a material body is deformed (the strain) is linearly related to the force causing the deformation (the stress)
F=-kx Where X is the distance the material is stretched or compressed away from equilibrium position (Meter) F is the restoring force exerted by the material (Newton) K is Spring Constant (Newton/Meter) Hook’s law is illustrated in the following figure.
4.7 Elastic Moduli Elastic moduli for homogeneous and isotropic materials are discussed below. Bulk Modulus The bulk modulus (K) of a substance measures the substance's resistance to uniform compression. It is the ratio of volume stress to volume strain. It is defined as the pressure increase needed to affect a given relative decrease in volume. It describes the material's response to uniform pressure. For a fluid, only the bulk modulus is meaningful.
Young’s Modulus Young's modulus or modulus of elasticity (E) is a measure of the stiffness of an isotropic elastic material. It is the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds. It describes the material's response to linear strain. Lame’s Constant The Lame’s Constant (λ) has no physical interpretation, but it serves to simplify the stiffness matrix in Hooke's law. It is also called Lame’s First Parameter. Shear Modulus Shear modulus or modulus of rigidity (µ), is defined as the ratio of shear stress to the shear strain (angle of deformation). It is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force (such as friction). It describes the material's response to shearing strains.
Poisson’s Ratio Poisson's ratio (σ) is the ratio of transverse strain (normal to the applied load) to longitudinal strain (in the direction of the applied load). When a sample of material is stretched in one direction, it tends to contract (or rarely, expand) in the other two directions. Conversely, when a sample of material is compressed in one direction, it tends to expand (or rarely, contract) in the other two directions. Poisson's ratio is a measure of this tendency.
P-Wave Modulus P-wave modulus (M) or longitudinal modulus is the ratio of axial stress to axial strain in a uniaxial strain state.
4.8 Computing Density/Moduli from Seismic Velocities A seismic survey provides velocity information about sub-surface layers. Once the P or S wave velocity of a material is determined, its density and all moduli can be computed. This determination of such parameters is termed as Rock Physics or Engineering Properties.
A set of rock physics equations are listed below. P-Wave Velocity
V p = 1.16 * Vs + 1.36
Vs = (V p − 1.36) /1.16
ρ = 0.31*V p.25
Vp Vs Ratio
K = ρ (V p 2 − 43 Vs 2 )
µ = ρVs 2
σ = 0.5(V p 2 − 2Vs 2 ) / (V p 2 − Vs 2 )
P Wave Modulus
9K µ 3K + µ
Seismic Refraction Methods At the end of this module you would be able to understand
First Breaks: Direct and Refracted Waves
Automated First Break Picking
TX-Graphs, Layer Velocity and Depth Computation
Low Velocity Weathered Layers and Statics Computation
5.1 Snell’s Law Snell’s law was originally developed for light waves, but it can be equally applied to sound and seismic waves. Accordingly when a wave enters from a less dense medium (ρ1) to a denser medium ((ρ2), it bends away from the normal. Thus the angle of incidence (i) is less than angle of refraction (r). If we keep on increasing angle i, angle r will also increase, until it becomes 90º. The angle i for which angle r is 90º is called critical angle (ic).If angle i become greater than ic , the wave is reflected back into the same medium. In case of seismic the angle i increases with offset, the distance between source and receiver. Thus on the basis of angle i seismic wave is split into three components as shown below. The transmitted wave acts as a secondary source and is again split into three components at the next interface. This continues as the waves move down into deeper layers and forms the basis of seismic refraction and reflection methods.
Reflection i > ic
Transmission i < ic
Refraction i = ic
ρ2 ρ 2 > ρ2
It must be noted that the transmission, refraction and reflection of seismic waves only takes place when the velocity of each underlying layer is higher than that of above it. In Earth the general trend is increase of velocity with depth. As we move down towards deeper layers the overburden pressure increases, which increases the density and hence the velocity also increases.
5.2 Seismic Refraction Method After gravity method, seismic refraction method was developed for exploration of hydrocarbons. In 1924 it was first used for delineation of shallow salt domes. Due to some limitations it was soon replaced with seismic reflection method, which continues to be the main technique for exploration of hydrocarbons and imaging deep structures. Today the seismic refraction method is widely used to delineate the Low-Velocity Weathered Layers for computation of Statics corrections that are applied to the main reflection data. In addition it is considered as a valuable tool for near-surface geophysics & engineering, such as delineation of bed rock or basement and determining the engineering properties of ground. In the following sections the complete workflow of refraction method is discussed.
5.3 Seismic Refraction Data Acquisition A seismic refraction recorder usually consists of 24 channels each of which is connected to a geophone. The geophones are placed along a profile with variable geophone intervals. Two shots are taken at both ends of the profile, the first near geophone # 1 is called forward shooting while the second near geophone # 24 is called reverse shooting. This results in two seismic monitors each with 24 seismograms (traces) as shown below.
Forward Shooting 1
Reverse Shooting 24
5.4 First Breaks First breaks are the events that reach first at a geophone and are also called First Arrivals. They are the first prominent wave amplitude on a seismogram (trace) as shown below.
In seismic refraction techniques, we need to pick the first breaks times from the seismic traces. This time can be picked in four different modes as shown.
Zero Crossing Positive Slope Crest Zero Crossing Negative Slope Trough
First Breaks must be picked in any one of the four modes, but the selected mode must be used for the whole project. It must be noted that within a project two different modes cannot be used. Initially the seismic monitors were in the form of papers, thus first breaks were marked with a pen and their arrival times were noted. This is referred a hand picking. With the advent of digital data and computers, interactive software became available which provided a computer aided environment for picking first breaks using the mouse. This is referred as manual picking. With the increased usage of artificial intelligence in geosciences, several neural-network based techniques have been developed for automated picking of first breaks.
A seismic monitor with artificial intelligence based first break picks is shown below.
Let’s consider a three layer earth model with velocities Vo, V1 and V2 respectively and a seismic refraction spread as shown below. Now at near offset geophones the direct waves representing Vo .reach first, then at the next few geophones the refracted waves from top of V1 reach first and finally at the far offset geophones refracted waves from top of V2 reach first. The point at which the direct and refracted waves reach at the same time is called crossover distance. Distance
S = dt/dx = (t2-t1)/(x2-x1) x2,t2
V = 1/S
Refracted ρ 1 Waves
Refracted ρ 2 Waves
5.5 Time-Distance Graphs The picked first break arrival times, for both forward and reverse shooting, are plotted on a graph paper against their offsets as shown below.
For both forward and reverse shooting data, best-fit lines are passed through each segment of data, representing a subsurface layer as shown below.
Cross Over Distance
The velocities of best-fit lines (Vo, V1) are computed from their respective slope. Similarly the crossover distance (Xc), intercept time (Ti) and total time (Tt) are marked on the graph as shown on the pervious figure. The thickness of the first layer (Ho) can be computed by any one of the following equations. The first uses intercept time while the other uses crossover distance.
Ti VoV1 2 V12 − Vo 2
Xc V1 − Vo 2 V1 + Vo
Thus using the refraction method the velocities and thicknesses of near surface weathered layers are determined which are used for computation of statics corrections, for application to seismic reflection data.
5.6 Statics Corrections The Earth’s near surface is made up of weathered and sub-weathered lowvelocity layers composed of unconsolidated material. These layers induce a delay in seismic reflection data events which distort the continuity in subsurface layers geometry as seen in seismic sections. Statics are corrections applied to seismic reflection data to remove the effect of weathered layers and elevation. These corrections are applied by reducing the data with respect to a Datum Plane. The following figure illustrates the effect of weathered layers in imaging a horizontal sub-surface reflector on a seismic section. Due to variations in weather layer thickness and/or velocity, each recorded trace experiences a different delay time. Thus the horizontal reflector attains the shape of the weathered layer.
More Delay Low Velocity Layer
Similarly topographic (elevation) variations also affect the shape of the subsurface reflectors in seismic data, due to variable wave travel paths. Thus the horizontal sub-surface reflector appears as an inverted image of the topography on a seismic section as shown below. Longer Path
From the above discussion it is clear that statics corrections must be computed in order to remove the effects of weathered layers and topography as shown below.
Ho/Vo H1/V1 (Elevation - Datum) / Replacement Velocity
H o H1 H E−D + + ... + n −1 + ]*1000 Vo V1 Vn −1 VR n −1 H E−D ]*1000 Statics = −[∑ i + V V i =1 i R
Statics = −[
Weathered Layer Statics
It can be seen from the above equation that statics correction has two components; weathered layer and elevation statics. For the weathered layer statics velocity and thickness of weathered layers is provided by the refraction method. For the elevation (E) statics, we get the elevation from navigation data, the replacement velocity (VR) is selected above the highest sub-weathered velocity. Its value can be selected somewhere above 2000 m/sec and it must be kept constant throughout the project. The selection of datum (D) is arbitrary; it can be selected above or below the weathered layers. The figures below show a seismic section without (left) and with (right) statics corrections.
5.7 Limitations of Seismic Refraction Method Some limitations of refraction method are summarized below: The refraction method requires the velocity of sub-surface layers must increase with depth. If a low velocity layer under a high velocity layer is encountered, it cannot be detected by refraction method. Similarly blind zones cannot be detected by this method. If thickness of a layer is less as compared to the layers above and below it and/or the velocity contrast between it and the layer that underlies it is inadequate, such layer cannot be delineated by this method. Refraction method requires a larger spread length as compared to reflection method, for mapping the same interface (at the same depth). Thus for imaging deeper layers refraction method needs a much longer spread, which makes it impractical for such applications.
Seismic Reflection Data Acquisition At the end of this module you would be able to understand
Seismic Sensors: Geophones as Transducers
Seismic Recorder and Multiplexing
Seismic Sources: Dynamite and Vibroseis
Spread Geometries & Fold Coverage
6.1 Digital Sampling and Aliasing The initial seismic instruments recorded data on a moving paper, the next generation instruments recorded analog seismic data on magnetic tapes. With the advent of computers and digital systems, the seismic data was recorded in digital form in some standard format. Today all processing and interpretation is performed on digital seismic data, thus it is necessary to understand the difference between analog and digital data and the sampling theory. Let’s consider an analog representation of a sinusoidal function as shown below. In this form the variation of amplitude with time is recorded continuously.
Now the same sinusoidal function can be represented in digital form as shown below. It can be seen that discrete samples of amplitude values are taken after fixed interval of time called sampling interval. Joining these samples the sinusoidal function can be reconstructed.
If t is in milliseconds the Sampling frequency i.e. the number of samples per second, is given by;
Now the Nyquist frequency, which is the highest recoverable signal frequency for the given sampling frequency is given by;
f S 1000 = 2 2∆t
Thus for a given sampling interval, the recorded signal frequencies must not be greater than Nyquist frequency, otherwise they will appear as low frequencies. This is called Aliasing Effect, caused by coarse sampling (under-sampling), as shown below.
The high signal frequencies that are greater than the Nyquist frequency appear as low frequencies are called Alias frequencies given by;
f a = 2 f N − f Signal In seismic recording systems an anti-aliasing filter (fA) having a high-cut frequency equal to half of Nyquist Frequency is applied to avoid aliasing effect.
fN fA = 2
6.2 Seismic Recorder Seismic Recorder picks seismic signals (vibrations) from geophone sensors and records them on magnetic media in a digital format. It consists of multiple channels, each connected to a geophone group. It is similar to an audio tape recorder which picks audio signals from microphone and records them on a magnetic tape (cassette). A geophone is a transducer which transforms mechanical energy (seismic vibration) into electrical energy. It consists of a moving coil and a stationary magnet. The movement of the coil due to vibration creates electromagnetic flux proportional to the magnitude of vibration. The block diagram of a digital seismic recorder is given below followed by description of all main modules.
Preamplifier receives weak signals from geophones and amplifies them. Filters pass a certain range of frequencies and attenuate the rest. A seismic recorder has three types of filters. - Low Cut filter attenuates all frequencies below the cutoff frequency and passes all frequencies above it. In a seismic recorder it is set to 8-12 Hz to remove low frequency surface waves called ground roll.
- Notch filter removes only a single frequency and passes all other frequencies. In seismic it is used to remove 50/60 Hz electric power lines induction.
- High Cut filter attenuates all frequencies above the cutoff frequency and passes all frequencies below it. In a recorder it is called Antialias filter, so that all unwanted high frequencies (above 125 Hz) are removed to avoid aliasing during analog to digital conversion.
Amplifier further amplifies the signal after filtering unwanted frequencies. It enhances the gain level of the signal in decibels (db). It must be noted that the signals received from the geophone and subsequently passing through preamplifier to amplifier stages are in analog form. After final amplification the signals will be digitized.
Multiplexer: A seismic recorder consists of several channels (24 to several hundreds). Each channel is connected to a geophone and comprises of preamplifier to amplifier stages. Now the signals from all channels need to be digitized, but the recorder has a single analog to digital converter. Thus a multiplexer is used to switch one channel at a time. If a recorder has 100 channels and sampling rate is set to 2 milliseconds then the multiplexer must switch 100 channels within 2 milliseconds to get the first sample of each channel and be ready to get the next samples. The time available to scan a channel is called Skew rate given by; Skew Rate = Sampling Rate / Number of Channels The working of a multiplexer for a four channel recorder (channels labeled as A to D) is shown below. Note the multiplexer connects one channel at a time to the analog to digital converter (ADC). Time
Filters / Amp Geophone
Filters / Amp Geophone
ADC / Write Filters / Amp
Multiplexed Data A1 B1 C1 D1 SC A2 B2 C2 D2 SC A3 B3 C3 D3 SC …
Filters / Amp
SC is Scan Code after each time slice.
Analog to Digital Converter (ADC) converts the analog signals into digital form according to the specified sampling interval. The digital signal consists of discrete samples represented by a series of amplitude values as a function of time, called time series. Formatter/Writer arranges the data samples according to an industry standard format and writes it to a storage media such as tape, cartridge or DVD.
6.3 Seismic Sources A seismic source releases energy in the form of elastic waves which propagate through the earth’s medium. This energy has an amplitude and phase over a frequency band. Various types of seismic sources are classified below: • Land Sources: Used in Land Surveys - Dynamite: Several Kilograms of dynamite used to generate a short duration, high energy impulse containing a wide range of frequencies. Dynamite based seismic data is minimum phase. - Vibroseis: A truck with a base plate driven by a hydraulic system to generate a long duration, low energy sweep of defined frequency range. The vibroseis data needs to be correlated with the pilot sweep. Vibroseis based seismic data is zero phase. - Buried Primacord: Explosive extruded into rope-like form having length of several 100 ft and plowed into ground at 2-3 ft depth. When detonated at one end or center, the explosive disturbance propagates at 22,000 ft/sec, much higher than seismic velocity in near surface layer. - In addition there are several other land seismic sources such as weight dropping, hammer, wooden log hit from side to generate S waves. • Marine Sources: Used in Offshore Surveys Explosive Sources using Dynamite - Flexotir: Small pellet of dynamite embedded in a plastic cartridge. This charge is detonated at the center of a cast-iron spherical shell towed behind the ship at 40 ft depth. It pumps out water under high pressure. - MaxiPulse: Charge packed in a can, injected into the water at 40 ft depth by a delivery device trailed from the ship. On detonation it forms a bubble.
Non-Explosive Sources - Sparker: Sudden discharge of current between electrodes in water generates seismic waves. - Boomer: Current passes through Coil which moves a plate against water. - Air Gun: High pressure bubble released in water. - Aqua Pulse: Enclosed underwater chamber (elongated heavy-rubber cylinder) filled with propane and oxygen. It is detonated by electric spark. The explosion causes ballooning of the chamber which introduces a pressure pulse in water.
6.4 Fold Coverage We know that in reflection surveys the seismic waves hit the subsurface depth point and are reflected back. During multiple shots with various shot receiver combinations the same depth point may be hit multiple times and is therefore referred as common depth point (CDP). Thus for a given spread of geophones, the maximum number of times a CDP is hit by waves is called fold coverage and is computed as follows;
1 ∆x ∆x Fold = C 2 ∆g ∆s Where
C = Number of Channels ∆x=Picket Interval ∆g=Geophone Group Interval ∆s=Source Interval
6.5 Geophone Spread Geometries The positioning of geophones along a 2D seismic profile with respect to the source point is called the spread geometry. During acquisition the spread moves one or multiple picket intervals along the seismic profile. Two common spread geometries are discussed considering an 8 channel recorder.
Split Shooting In this spread the shot is at the middle with equal number of geophones at both sides. This spread remains symmetric throughout the acquisition profile as shown below along with its stacking chart and fold coverage.
According to the figure the equidistance surface points where geophones or source is placed are called pickets and the sub-surface points where the waves hit are called CDPs. It can be seen that the CDP interval is half the picket interval at the surface. End-on Shooting This spread starts in asymmetric form with the source at start of profile, followed with half number of geophones at the forward side. As the spread moves forward a geophone is added at the backward side. This is called rollin and it continues until the spread becomes symmetric. The spread continues to move forward in symmetric form until the end of the profile is reached. Finally at the end a geophone is removed from the forward side with each forward step. This is called roll-out which continues until the source reaches the end of the profile. The end-on shooting spread after rollout is shown, in the following figure along with its stacking chart.
A comparison of fold build-up, along a profile for both the above mentioned shooting geometries is illustrated below. From the figure it is clear that endone shooting provides a better fold coverage along a profile.
Seismic Noise At the end of this module you would be able to understand
Difference between Signals and Noise
Coherent and Incoherent Noise
Low and High Cut Filters
Stacking to remove Incoherent Noise
7.1 Signals and Noise All events of interest are called signals while rest is called noise. Signals and Noise are relative terms as in a certain set of analysis an event may be considered as signal, while in another analysis it is considered as noise. In seismic acquisition and processing our major emphasis is to enhance the signals and suppress the noise. Thus our aim is to increase the Signal to Noise Ratio (S/N). There can be multiple sources of noise. Noise may be due to some other source or due to the same source responsible for the signals. Seismic Noise is classified into the following two main types; - Coherent Noise - Incoherent Noise
7.2 Coherent Noise It has a periodic pattern which can be followed at substantial distances along the receiving profile. During seismic data acquisition the most common type of coherent noise is Ground Roll. Ground Roll These are surface waves primarily Rayleigh waves, having low-velocity and low-frequency with relatively higher amplitude. They override the useful reflections. In addition, refracted waves multi-reflected in a surface layer and shear refractions are also encountered. During acquisition ground roll is suppressed by two methods. As ground roll has low frequency, usually below 10 Hz and our signals are above this frequency, a low cut filter of 10-12 Hz is applied to suppress the ground roll. In addition a group of geophones spaced at half the wavelength of the noise and connected to a single channel also suppress ground roll as shown below.
Power Lines Induction If a seismic line crosses or passes close to a power line, then 50 or 60 Hz coherent noise is induced into the nearby geophone channels. This noise can be removed during recording by applying a notch filter.
7.3 Incoherent Noise It has a random pattern and therefore also called Random Noise. There can be multiple sources of random noise such as; - Scattering from near-surface irregularities. - Commonly occur when the shot point overlies or is close to gravels, boulders or vuggy limestone all of which can cause scattering of waves. - When stream banks and surface irregularities diffract energy. Incoherent noise observed at one point on the surface is entirely unrelated to that at another point. Similarly signals collected at the same point at different times contain the same signal but different random noise. Thus, addition or stacking of signals containing incoherent noise results in noise cancellation as shown below.
7.4 Aliased Frequencies If the analog signal contains frequencies higher than the Nyquist frequency then such frequencies are aliased and appear as low frequencies after digitization. Thus an anti-aliasing high cut filter of 125 Hz or above is applied before analog to digital conversion.
7.5 Multiples Sometimes seismic energy may be trapped by to and fro reflection between interfaces. Thus a reflector appears twice in a seismic section, the second time as a multiple at a greater time. The interference due to multiple reflections appears similar to primary reflections and therefore sometimes difficult to identify. Multiples are removed by predictive deconvolution. The multiples have the same stacking velocity as the primary reflections, but appear at a greater time. Thus they can be removed by avoiding them during velocity picking. There are several types of multiples as illustrated below: First Second Primary Order Order
Surface Multiples First Second Order Order
Seismic Data Processing I At the end of this module you would be able to understand
Wave propagation through Earth
Gains, Spherical Divergence
Band Pass Filter
8.1 Propagation of Seismic Waves through Earth When Seismic waves propagate through Earth’s material they undergo changes in their signature (waveform) due to the following phenomenon. Geometric Spreading Energy contained in a wave is proportional to the square of its amplitude. As body waves propagate outward from a point source they spread spherically with a constant energy. As the spherical wave front expands, the energy per unit area must decrease as rapidly as the total area of the spherical surface increases. It follows Newton’s Inverse Square Law which states: “The power per unit area in the direction of propagation, of a spherical wave front varies inversely as the square of the distance from the source, assuming there are no losses caused by absorption or scattering.”
Absorption & Attenuation: Convolution There is also loss of amplitude due to absorption caused by frictional dissipation of the elastic energy into heat. This loss from the source is found to be exponential with distance as shown below. This absorption of energy is called attenuation. Attenuation is directly proportional to frequency and therefore higher frequencies are attenuated more than the low frequencies. Thus low frequencies can penetrate further into the Earth.
Seismic energy may be absorbed due to several reasons some of which are listed below: -
Crystal phase change Compaction of porous media Fracturing within the medium Friction due to relative motions of different parts of the same rock Viscous losses through fluid flow in a porous medium Temperature change through compression and dilation of the medium.
When a Seismic Wave propagates through Earth’s material it undergoes convolution. Convolution is the term given to the mathematical technique for determining a system output given an input signal and the system impulse response. Noise Addition As a Seismic Waves from a desired source (Signal) propagate through the Earth they may get mixed with waves from other undesired sources (Noise). In addition undesired events from the desired source are also encountered. Thus the recorded seismic traces undergo the following changes, which are also illustrated below; • Amplitude decay with distance, both horizontal (offset) as well as vertical (depth) • High frequencies absorbed • Noise & unwanted events added
In seismic data processing, the main task is to enhance the amplitudes by applying suitable gains, recover the lost high frequencies through deconvolution and suppress different types of noise through band bass filter, stacking and a number of other techniques. Thus our aim is to improve the signal to noise ratio.
8.2 Mechanical Processes Seismic data processing consists of several steps among which three important steps called mechanical processes are always applied to the seismic data. They are called mechanical processes as they change the structure or form of seismic data, rather than performing some analysis to change the amplitude, frequency or phase of the data. These processes along with their input and resultant datasets are shown below.
Demultiplexing We know that seismic recorder stores data in multiplexed form, where first samples of all traces are stored first followed by second samples of all traces and so on. Samples of all traces at a constant time make a time slice. Thus the multiplexed data is in time slice order and we need to convert it into trace sequential order, i.e. all samples of first trace followed by second trace and so on. The demultiplexing of seismic data is illustrated below.
It can be seen from the previous figure that demultiplexing is simply arranging the seismic data matrix from row (time slice) to column (trace sequential) order. It must be noted that both multiplexed as well as demultiplexed data are shot ordered and all traces belong to the same shot as shown below. Modern recorders have field data units each with their own analog to digital converter, instead of the conventional centralized recording system. These systems store data in trace sequential order and thus there is no need to apply demultiplexing to such data.
Sort After performing some initial processing, the data needs to be sorted from shot order to common depth point (CDP) order. In this process traces from different shot receiver combinations that hit the same CDP are grouped together thus forming a CDP ordered data as shown below. Again it can be seen that this process is simply arrangement of data from one form to another.
Stack The number of traces in a CDP group depends on its fold coverage. For a 30 fold data the CDP order data will have 30 traces per group. After applying dynamic corrections all traces in a CDP group are stacked (added) into a single trace as shown below. This removes the random noise and enhances the reflected events. Thus stacking changes the data form, but it is not purely a mechanical process as it also improves the signal to noise ratio. It must be noted that after stacking the data volume is considerably reduced. For a 30 fold dataset the data volume is reduced 30 times.
8.3 Interactive Processes The seismic data processing workflow also includes some interactive processes, which require a lot of human interaction. With the advancements in graphics technology, computer aided interactive tools have been developed to carryout these processes. The figure below shows the sequence of these processes along with their usage application.
Trace Editing This processing step is basically quality control of the input field data. The input data may contain bad traces, reverse polarity traces and completely bad and blowout records. Using an interactive environment, the data is viewed record by record. All bad traces are muted (zeros), reverse polarity traces are converted to normal polarity and bad records are killed. Thus all bad data is removed before proceeding with further processing. First Break Picking In seismic refraction module, we discussed interactive and automated first break picking for statics correction. The statics computed from field refraction survey are referred as field statics. To further refine the data a second set of statics corrections is applied to the data by interactively picking refracted arrivals from all reflection records. This is referred as refraction statics. Velocity Picking To stack the CDP ordered data dynamic corrections or normal moveout is applied to the data. To apply dynamic corrections we need velocity information for each reflector so that they are stacked properly. As velocity changes laterally as well as vertically, velocity functions are interactively picked at selected CDP groups. The picked velocity functions are interpolated to apply dynamic corrections to all CDPs. More details about velocity analysis procedure are given in the next module. We now discuss some common processes which improve the recorded signal quality.
8.4 Spherical Divergence Compensation and Gains We know that as seismic wave front moves forward it experiences decay in amplitude. This decay takes place in all directions, both laterally with offset and vertically with depth as shown below.
In processing, the lost amplitudes must be recovered by applying some spherical diversion compensation gain and other types of time variant and trace balancing gains. Time Variant Gain (TVG) A time variant gain compensates the decay of amplitude with depth. Usually a time variant function is computed and multiplied with the corresponding samples of seismic trace. It can be a linear gain function as shown below (left). The amplitudes of the lower events have improved but they are still weaker than the top events. The slope (m) and the intercept (C) can be adjusted to get better results. Similarly we can have an exponential gain function shown below (right). Here again the value of C must be optimized to get good results otherwise for a large value of C we may get a bell-bottom type of trace with large gain applied to deeper events.
TVG compensates the vertical decay of amplitude within each trace but it does not take care of lateral decay of amplitude from near to far offset traces as shown in the next figure. It can be seen in the figure that TVG has enhanced the amplitudes of both near and far offset traces but the relative difference in amplitudes of the near and far offset traces remains the same.
Trace Balancing Certain applications, such as first break picking, require the maximum amplitudes of all near to far offset traces to be balanced at a user defined RMS amplitude (ARMS) level. This is achieved through trace balancing which compensates for lateral decay of amplitudes. Thus trace balancing is a time invariant type of gain. The procedure and application of trace balancing is illustrated in the following figure.
The following figure shows the application of trace balancing to near and far offset traces. It can be seen that the maximum amplitude of near and fat offset traces in brought to the same level.
Automatic Gain Control (AGC) The ultimate gain is a combination of TVG and trace balancing. Instead of scanning the complete trace to get AMAX , the trace is scanned within a sliding time window (operator length). Thus several gain factors (GF) are computed at the center of each window and joining them gives a time variant gain function as shown. It is called automatic gain control as no coefficient needs to set and gain factors are automatically set according to the amplitudes in a time window.
8.5 Band Pass Filter Seismic data is band limited which may range from 10 - 125 Hz. Usually the dominant frequency is 35 - 45 Hz, thus a band pass filter (BPF) of 10-80 Hz can be applied to the data to pass all useful signal frequencies and suppress the remaining frequencies. A BPF can be considered as a combination of low-cut and high-cut filters to pass a band of frequencies. Thus a BPF allows all frequencies between the low and high cut off frequencies as shown below.
The working of BPF is given in the following block diagram. A filter operator wavelet is generated according to the low-cut (fL) and high-cut frequencies (fH). The resulting wavelet contains all frequencies within these limits. This wavelet is convolved with the input trace to get the output filtered trace.
8.6 Deconvolution When seismic signals convolve with the Earth’s material, high frequencies are absorbed. These lost high frequencies are necessary for improving the temporal resolution, thus they must be recovered. Deconvolution is a mathematical process used to reverse the effects of convolution on recorded data. It is exactly what it sounds like: the undoing of undesired convolution. During convolution high frequencies are attenuated. In deconvolution we try to re-introduce these lost frequencies. Thus deconvolution can be considered as an inverse filter. Some common types of deconvolution are spiking deconvolution, predictive deconvolution and surface consistent deconvolution. The working of deconvolution is given in the following bock diagram. The input trace is converted into frequency domain using Fast Fourier transform. The inverse of amplitude spectrum is computed. Then pre-whitening is added to the inverse spectrum to avoid zeros. This is done by adding one to the amplitude of all frequencies in the spectrum. The phase spectrum is set to zero, this makes the resultant wavelet operator as zero phase. The final amplitude and phase spectrum are transformed back to time domain by using Inverse Fourier transform to get the inverse wavelet operator. Finally this operator is convolved with the input trace to get the output deconvolved trace.
Seismic Data Processing II At the end of this module you would be able to understand
Velocity Analysis / Constant Velocity Stack
Dynamic Corrections / Normal Moveout
Stacking: Raw, Brute Stack
Residual Statics and Final Stack
9.1 Seismic Data Processing Flow In the preceding module we discussed some mechanical, interactive and basic processing operations. In this module we will focus on some other important processing functions and consider the complete seismic data processing sequence. A generalized seismic data processing flow is given in the following block diagram. It also shows the mechanical, interactive and basic processing functions already discussed.
The field data is demultiplexed followed by geometry setup, where spread layout, navigation data and field statics are updated to seismic data headers. Then trace editing is performed and all basic processing such as geometric spreading compensation, filters and deconvolution are applied before sorting the data to CDP order. A copy of the geometry applied data is sub-sampled to 8 milliseconds for first break picking. Refraction statics are computed and can be applied to pre or post sorted data. Then normal moveout correction (NMO) is applied by using a regional velocity function and the data is stacked to get a raw stack. In the next stage velocity analysis comprising of constant velocity stack (CVS) and velocity picking at selected CDP locations is performed and the picked velocity functions are used in the
NMO to get a Brute stack. In the final go the velocities may be further revised and residual statics are applied to get the final stack. The structures in the final stack are migrated to their true positions to get the migrated stack.
9.2 Dynamic Corrections Dynamic corrections or Normal Moveout (NMO) are corrections applied to CDP ordered data to reduce all source receiver slant travel times (Tx) into zero offset vertical times (To) as shown below.
It can be seen in the figure, as the offset increases Tx also increases. Thus the CDP family traces represent a hyperbolic travel time curve for a reflector. As we need to stack these traces the slant travel times must be aligned along a straight line by reducing them to vertical times. Thus the NMO correction is simply reducing the data to zero offset, given by;
∆TNMO = Tx − To In the above figure Tx, To and offset x, make up a triangle. Now the problem is that two sides of the triangle have units of time while the third side, the offset, has units of distance. To solve this triangle we need to convert x into time. For this we need velocity of the reflector, called NMO velocity (VNMO), which is obtained from velocity analysis. Thus from the Pythagorean Theorem we have;
Tx 2 = To 2 + V x2
Now the NMO correction becomes; 2
∆TNMO = To 2 + V x2 − To NMO
After applying these corrections, all CDP traces are aligned and can be stacked. Like static corrections, the dynamic corrections are also in the form of a time shift. In static corrections a constant time shift is applied to all samples of a trace, thus the whole trace is moved up or down along time axis, but the relative time gap between events remains static. On the other hand, dynamic corrections are computed and applied to each reflector. As the velocity of each reflector varies, its NMO correction also varies and therefore each reflector is moved at a different rate. Thus there is a stretching or shrinking of time gap between events, therefore these corrections are called dynamic corrections. Let’s consider a reflector with NMO velocity 2250 M/Sc. If the appropriate NMO velocity is used the events are aligned, if a lower velocity is used the events in CDP gathers (traces) are stretched up, called over-corrected and if a higher velocity is used the events remain under corrected, as shown below.
9.3 Velocity Analysis From the preceding section, we know that NMO corrections require velocity information. In seismic data processing velocity analysis is an important step in which velocities are picked from seismic data at selected CDP locations. The CDP should not be selected at uniform intervals. Suitable locations are
the crests and troughs of a folded area. Zones of poor signal to noise ratio, faults and near-surface anomalies must be avoided for velocity analysis as shown below.
Constant Velocity Stack (CVS) In real Earth, the velocity generally increases with depth, thus each reflector will have a different velocity. In velocity analysis out task is to determine the appropriate velocity of each reflector. As velocity also changes laterally, we need to select several CDP locations where velocity analysis is to be performed. To view the continuity of reflectors we need a group of CDPs, thus the number of CDPs on both sides of the selected CDP location is specified. If 10 CDPs are specified on both sides, the selected location will have a group of 21 CDPs. Finally we also need to specify the minimum and maximum velocity range we expect in the region, and a velocity increment. Typical values can be 1500-5000 M/Sec with an increment of 100 M/Sec. The CVS method uses a constant velocity in NMO and stacks all CDP traces. The constant velocity is iterated from minimum to maximum range with the specified increment. In this way we get velocity panels for each selected CDP location, showing CDP group traces stacked with a range of velocities as shown in the next figure. From NMO we know that each reflector will stack with strong amplitude if its appropriate velocity is used. Higher or lower velocities will not stack the reflector properly. As velocity increases with depth the shallow reflectors will stack well at lower velocities while the deeper reflectors at increasing velocities. Thus on a velocity panel we mark a point for each reflector where it is best stacked. These points are velocity-time pairs and joining them gives us a velocity function which increases with time.
In this way we pick velocity functions for each selected CDP location. The picked velocity functions are interpolated for in between CDPs and used in NMO corrections to get a Brute stack. These velocities are referred as root mean square (RMS), NMO or Stacking velocities, as all three types have approximately same values. It must be noted that NMO/Stacking velocities can be successful if they vary within ±20% of their true value.
9.4 Residual Statics If our main horizon of interest does not show a good continuity in the Brute stack, we may need to apply residual statics. In this technique we need to mark a point on the horizon and specify its minimum and maximum times in the section. It correlates the horizon events in all traces and generates a smooth trend of the horizon. It applies a plus-minus shift to all traces, so that the horizon events are aligned according to the smooth trend. Now the horizon shows a continuous trend. It must be noted that by using this technique our horizon of interest becomes continuous while other horizons may get disturbed.
9.5 Migration The final seismic section does not represent the true geometry of the reflectors, thus migration is applied to the final stack with the following main objectives. Move Dipping reflectors to their true position Corrects for the geometric displacement of data from a dipping reflector and/or lateral velocity changes and places them in their true spatial position rather than at an assumed point in depth between the source and the receiver. Collapse Diffraction Patterns Eliminate the signal interference caused by point diffractors. To understand why seismic expression does not show the true position of events, consider the following figures. At the surface the common mid point (CMP) lies at the middle of shot and receiver positions. For a horizontal bed the common depth point (CDP) lies exactly below the CMP.
Now for a dipping bed the CDP does not lie below the CMP as shown.
The seismic section will still show the CDP below the CMP, thus we need to shift it to its true position.
Thus an anticline will appear larger with wider flanks in seismic as shown.
Similarly a syncline will appear as a bow-tie in seismic as shown.
Migration is an extremely compute intensive process. Several migration algorithms have been developed, some common types are listed below: -
Kirchhoff’s Migration Finite Difference (FD) Migration Frequency Wave number (FK) Migration Reverse Time Migration Stolt Migration
With the availability of large computing power, migration can also be applied to pre-stack data in one of the following forms: - Pre Stack Time Migration (PSTM) - Pre Stack Depth Migration (PSDM)
Seismic Resolution At the end of this module you would be able to understand
Temporal Resolution: Frequency and Bandwidth
Spatial Resolution: Picket Interval and Fresnel Zone
Signal to Noise Ratio
10.1 Resolution The smallest object that can be imaged or resolved by a system or technique is called the resolution of the system. Such as telescopes and microscopes have resolving power which decides the smallest object that can be view by these instruments. In Earth sciences resolution implies to the vertical thickness and lateral extent of a subsurface geological body that can be delineated with a geophysical method.
10.2 Seismic Resolution Seismic resolution refers to the ability of the seismic method to image the thinnest and smallest subsurface objects. Seismic resolution is of two types; Temporal Resolution It is the vertical resolution which accounts for the thickness of sub-surface beds that can be resolved. It depends on frequency of seismic waves and is 1/4th of the wavelength. Thus higher the frequency, the smaller will be the wavelength and ultimately we get a higher resolution as shown below.
To understand seismic resolution a three layer model, consisting of a thin layer sandwiched between two thick layers is given in the next figure. It can be seen that with low frequency the thin bed is not resolved, but using a higher frequency the bed is clearly resolved.
Spatial Resolution It is the lateral resolution which accounts for the lateral extent of subsurface bodies that can be resolved. It depends on spacing of sensors (geophones) on the surface. We know the CDP interval is half the picket interval. Thus the sub-surface target object must be multiple times larger then the CDP interval, if it is smaller than the CDP interval it will be missed out. Consider the following example where a small lens shaped object is shown. For large sensor spacing only one ray path hits the body and therefore its shape cannot be delineated. If the sensor spacing is reduces the CDP interval is also reduced and several ray paths hit the body at multiple CDPs thus its shape is clearly identified.
10.3 Fresnel Zone Horizontal resolution is defined in terms of Fresnel Zone which indicates how close two adjacent points in the subsurface can be, while still being distinguished from one another. We know that vertical resolution is 1/4th of the wavelength of frequency. The horizontal resolution also depends on wavelength of frequency and depth of the target. The Fresnel zone and its relationship with horizontal resolution is illustrated in the next figure.
The figure shows two wave fronts separated apart by 1/4th wavelength of the dominant frequency. The upper wave front is at a depth Z. Now AA/ is the Fresnel zone and its half is the Fresnel Zone radius, which is the horizontal resolution. Mathematically the Fresnel Zone Radius is given by;
RF = Z λ / 2 It can be seen that with the increase in depth the wave front expands and the Fresnel zone radius also increases, thus the resolution decreases.
10.4 More on Seismic Resolution Resolution is our ability to clearly interpret the nature of reflectors from a limited seismic display. The resolving power of seismic data is limited by the following: Bandwidth Previously we discussed that vertical resolution depends on frequency, but in actual it depends on bandwidth, which is a range of usable frequencies contained in seismic data. Bandwidth is not simply the difference in frequency from high to low limits. It is the logarithm of the ratio of the frequency limits given by;
Bandwidth = Log 2 ( For base 10 we have;
fh ) fl
fh ) fl Bandwidth = Log10 (2) Log10 (
The unit of bandwidth is Octave, which simply represents doubling of frequency range. 10 Hz – 20 Hz is one Octave 20 Hz – 40 Hz is second Octave 40 Hz – 80 Hz is third Octave Thus a signal containing all frequencies from 10 Hz to 80 Hz has a bandwidth of 3 Octaves. The figure below shows the effect of bandwidth on resolution. It can be seen that with the increase of upper frequency from 60 to 140 Hz the bandwidth increases and thus the resolution increases, but on increasing the lower frequency from 8 to 120 Hz the bandwidth decreases and ultimately the resolution decreases, in spite of the fact that high frequencies are present. Thus it not only the high frequency, but a range of low to high frequency called bandwidth, which improves the resolution. A minimum 2.5 Octaves is required for a good seismic resolution.
Phase Uncertainty Zero phase data provides the simplest expression of reflection events as sidelobe interactions are minimized. For interpretation purposes the data should be reduced to zero phase. It can be seen in the following figure that zero phase data shows the exact position of the reflector, while in non zero phase data we are not sure about the precise position of the reflector.
Signal to Noise Ratio (S/N) Random Noise can seriously interfere with the resolving power of data. Strong Noise can inhibit the ability to see major reflections. Thus for a better resolution, the data must have a good S/N, as shown below. When S/N decreases, the signals are masked by the noise. A S/N=1 implies that both signal and noise amplitudes are same
Seismic Interpretation At the end of this module you would be able to understand
Seismic Section: Display Modes, Vertical and Horizontal Scales
Marking Horizons and Faults
Base Map and Contouring
Seismic Velocities and Time to Depth Conversion
Sonic Log, Density Log and Synthetic Seismogram
11.1 Seismic Data Display Standards Seismic data can be displayed in a number of industry standard formats. A sample of each display type is given below in the form of an individual trace and a complete section.
Wiggle + Variable Area: Waveform with shaded crests
Wiggle: Only Waveform.
Variable Area: Only shaded crests
Color Attributes: Waveform with amplitude based colored crests
Colored Density: Crests in Red, Troughs in Blue (or other colors)
11.2 Seismic Section Display Scales Seismic sections are displayed with separate horizontal and vertical scales. Setting up of these scales is critical from interpretation point of view as sometimes gentle dips may appear as horizontal beds by using a compressed vertical scale. Similarly the dip may be exaggerated by using a large vertical scale. Setting up of both these scales is discussed below along with examples. Horizontal Scale The horizontal sale is described in the form of Traces per Inch (TPI). Increasing the number of traces per inch reduces the seismic section horizontal scale as more trace are packed within one inch as shown below.
Vertical Scale The vertical scale is described in the form of Inches per Second (IPS). In this case increasing inches per second enlarges the seismic section vertical scale as shown in the next figure. Typical setting for seismic display scales can be 24 TPI and 2.5 IPS.
11.3 Base Map In addition to seismic sections, base map is also an important component of interpretation, as it displays the spatial position of each picket of a seismic section. Its also shows the spatial relationship of all seismic sections under consideration, their tie point locations and provides the framework for contouring. Seismic base maps have also been standardized as shown below. The line is annotated on both sides in the direction of line, while pickets are annotated perpendicular to the line. Picket interval and picket annotation interval are specified before generating a map.
The base map is produced using some projection system such as Lambert Conic projection or Universal Transverse Mercator (UTM) projection. The base map also shows grids of geographic latitude-longitudes and/or projected grid coordinates. The base map is produced at a specified scale, such as 1:10000, which represents the number of real Earth units that equal 1 unit on the map.
11.4 Seismic Interpretation In interpretation our main task is to identify various reflectors or horizons as interfaces between geological formations. For this good structural and stratigraphic knowledge of the area is required. Thus during interpretation we mark the horizons and faults on the seismic section. Initially interpretation was done manually on paper sections, but with the availability of powerful computer systems with graphics support, computer aided interpretation systems are being used in the industry as shown below.
Like first break picking the horizons can also be marked in the following four modes, but the selected mode must be used throughout the project.
The complete seismic interpretation workflow is given in the following figure. Accordingly all seismic sections in the projection are interpreted by marking horizons of interest and faults. The marked horizon and fault times along with their CDP numbers and X,Y navigation coordinates for all interpreted sections are output to the gridding and contour module which generates a contour map or 3D surface of the horizon. If there is a prospective zone, a well point is marked on the respective section and the contour map.
A time contour map of a horizon, along with faults and seismic lines is given in the next figure.
Using seismic velocities this time contour map is also converted into depth map.
11.5 Time to Depth Conversion The interpreted seismic section is in time domain. In order to get a true geological picture it must be converted into a depth section. This conversion requires reliable velocity information which varies vertically as well as horizontally. The main source of velocity information is seismic velocity picked during data processing. More accurate velocities can be obtained from check shots and vertical seismic profiling (VSP) surveys. Using Dix equations, the RMS velocities, from seismic, are converted into interval and finally average velocities. These velocities are used for time to depth conversion as shown below. The horizon times are two way times (TWT) therefore they are divided by two before depth conversion.
It must be noted that the vertical axis, in the above figure, is now depth in meters. The Dix equations for conversions between RMS, interval and average velocities are given below. RMS to Interval Velocity
Vrmsi2Ti − Vrmsi2−1Ti −1 V int i = Ti − Ti −1
Interval to RMS Velocity n
(Ti − Ti −1 )
Average to Interval Velocity
V int i =
VaveiTi − Vavei −1Ti −1 Ti − Ti −1
Interval to Average Velocity n
∑V int (T − T i
11.6 2D Seismic Modeling Sometimes we have a geological cross-section and we want to know the seismic response of this section, which may be used for deciding parameters in planning a new seismic survey. Similarly, we have interpreted a seismic section in which the horizons and faults make up a geological section and we want to move back and generate its seismic section. This is done to confirm our interpretation. The generation of a seismic section from a geological section is called 2D modeling. It is the reverse of seismic interpretation as shown below.
The modeling procedure involves digital signal processing techniques. We generate a source wavelet which mathematically represents our real sources like dynamite or vibroseis. There are several techniques for generating wavelets such as Ricker wavelet, Klauder wavelet and Summed wavelet. The figure below shows a software interface to setup parameters for generating a wavelet.
To model a geological cross-section it must be in some digital format. We assign reflection coefficients to various horizons in the cross-section on the basis of their velocity and density contrasts. The acoustic impedance (I) of a layer is given by;
I =Vρ where V is the velocity and ρ is density. Now the reflection coefficient (RC) is given by;
Vi ρi − Vi −1 ρi −1 Vi ρi + Vi −1 ρi −1
After assigning the reflection coefficients to all horizons the section it is convolved with the source wavelet by specifying a CDP interval. A synthetic seismic section is generated as a result of this modeling process as shown in the next figure.
11.7 Synthetic Seismogram In the previous section we discussed 2D modeling, now synthetic seismogram is basically 1D modeling. In this procedure we also generate a source wavelet. Now instead of a 2D geological cross-section we have petrophysical logs; Sonic (DT) and Bulk Density (RHOB) logs which respectively provide the velocity and density information of subsurface layers. The DT is a delay time log and its inverse gives the velocity. These logs are acquired in the borehole. We use this velocity and density data to compute a series of reflection coefficients called reflectivity series. This series is convolved with the source wavelet to get a synthetic seismogram. In this case we have performed the convolution with only one reflectivity series (1D), thus only one seismic trace is generated. Graphically we plot multiple copies this synthetic trace so that it appears like a stack section as shown in the next figure. The synthetic seismogram vertical units are meters or feet and it can be converted into time units by using its own velocity information. Synthetic seismogram is matched with the seismic section at the well point to correlate the succession of reflectors. It may also be used to calibrate our seismic velocities.