Gravity Survey Method_31072012

Gravity Survey Method

Better understanding of Human Being over the centuries

Medieval artistic representation of a spherical Earth - with compartments representing Earth, air, and water

The Earth as seen from the Apollo 17 mission.

Three-dimensional visualization of geoid undulations, using units of Gravity

•

How Is the Gravitational Acceleration, G, Related to Geology ?

The Relevant Geologic Parameter is Not Density, But Density Contrast This simple thought experiment forms the physical basis on which gravity surveying rests.

Gravity Measurement Over a Buried Sphere

Origin of Gravity Anomaly

Principal Sources: 1.Basement Structures( Horst and Graben) 2. Basement Fault 3. Fault in Sediments 4. Sedimentary Structures 5. Salt Diapir 6. Variation in Overburden Thickness

How do we measure Gravity? Falling Body Measurement: One drops an object and directly computes the acceleration, the body undergoes, by carefully measuring the distance and the time as the body falls. Pendulum Measurement: Gravitational acceleration is estimated by measuring the period of oscillation of a pendulum. Mass on a Spring Measurement: By suspending a mass on a spring and observing a how much the spring deforms under the force of gravity, an estimate of the gravitational acceleration can be determined

Falling Body Measurement

By measuring distance and accurate time as a body falls, ‘g’ is determined.

Pendulum Measurement

Portable Pendulums were used in Oil Exploration till 1930’s.

Mass on a Spring Measurement Use started in early 1930’s and replaced the preexisting gravity surveys. These are extremely sensitive Mechanical Balances with mass supported by a spring. Small changes in gravity move the weight against the restoring force of the spring

Mass on a Spring Measurement kx = mg, where, k is spring constant, x is length of spring, m is mass of spring , g is acceleration due to gravity kΔx = mΔg (Any change in gravity i.e. Δ g should produce a proportional change Δ x in the stretch of spring)

The natural period of oscillation is T=2Π m/k •Mass = 10 gm, T < 10 second what will be length of spring.

Mass on a Spring Measurement kx = mg, where, k is spring constant, x is length of spring, m is mass of spring , g is acceleration due to gravity kΔx = mΔg (Any change in gravity i.e. Δ g should produce a proportional change Δ x in the stretch of spring) The natural period of oscillation is T = 2 Π m / k Survey requirement for portability of instrument Mass = 10 gm, T < 10 second what will be length of spring.

Data Acquisition • Instrument –Gravimeter based on mass spring balance

• Field Method –Areal coverage, –Distance between control points will decide resolution of data

Gravity Measurements in exploration For relative measurements the difference between the gravity values is determined (which is easy to measure). The instruments, which are used, for measurement are known as Gravimeters. The difference in gravity value in a particular area is due to the difference in distribution of masses. This can be attributed to variation in density of various lithological units. The relative gravity values in turn are indicative of distribution of densities in a given area.

Gravimeters

1.

All gravimeters are extremely sensitive balance in which mass is supported by a spring. 2. These spring balances carry a constant mass 3. Variation in the weight of mass is caused by variation in gravity; cause the length of spring to vary and to give a measure of change in gravity.

Static and Unstable static Equilibrium • Objects that are not moving in any way either in translation or rotation in a frame of reference , they are in static equilibrium • If a force can displace a body and end the equilibrium, the body is in unstable static equilibrium. • (An unstable equilibrium is a situation in which all forces on an object resolve to zero, but if any one of the forces is changed slightly, the object will fall over, dash off in some direction, etc., and come to rest in a different place )

Stable gravimeter This type of gravimeter has linear dependence on gravity over a large range. They require considerable amplification of the minute changes in length of the spring. This amplification may be mechanical, optical, electrical, or a combination of these. They are in state of stable equilibrium or static equilibrium. (Ref Fig.) Disadvantages:

1. Very High Period 2. Extremely sensitive to other physical factors such as pressure,

temp,

and

small

magnetic

variations. 3. Bulky and Heavy due to thermostats

and

seismic

Stable Gravimeter Working Principle

g =4* Sq. of

s / Sq. of T

Unstable gravimeter: Warden Gravimeter

A small very light Quartz element of the mass M weighs only 5 mg. Thus it is not necessary to clamp the movement between stations. The system is enclosed in vacuum flask reduces sensitivity to P & T. Automatic temperature compensating arrangement to reduce the variation of T. Warden gravimeter is small (24’ in height and 10’ in diameter) and weighs about 6 lbs. The power requirement of two cells is used to illuminate the scale.

Basic Principle of Warden Gravimeter

g

k/M)(b/a) (cos2

cos

s

Diagrammatic View of Interior of Worden Gravimeter

Lacoste-Romberg Gravimeter

g =(k/M)*(b/a)*(z/s)*(y/s)* s

Principle of Zero Length Spring • Using a ZERO LENGTH SPRING to support the beam can significantly increase the sensitivity of a system. Theoretically this spring would recoil to a length of zero when not stretched by some force. • Because of finite diameter of wire in coil, it would not recoil to zero, when not stretched by some force. But by twisting a wire at the same time as it is being coiled, a spring can be produced that behaves in the same way within the range, it can be stretched. • When no force is applied, its coils press back against one another. By twisting wire more than needed to achieve zero length, we can make inverted spring. (Pretensioning of spring) • This spring will have negative initial length. It will turn inside out when not stretched by some force. Springs made in this way can be shorter in length to achieve required sensitivity.

• For a given change in g, one can make s as large as possible by decreasing one or more factors on the right hand side; moreover the closer the spring is to zero length, smaller the z and larger s. • In operation, this is used as a null instrument, a second spring being used which can be adjusted to restore the beam to the horizontal position. The sensitivity is about 0.01 mgal.

Hinge beam and Zero Length Spring

T=2Π

mg cos (2

k a^2 cos 2

Zero Length Spring

Principle of Gravity Survey

Field Method of Gravity Survey

Record of Gravity Survey

Processing of Gravity Data • Factors that affect the ‘g’ – Temporal Variations – • These are changes in the observed acceleration that are time dependent. In other words, these factors cause variations in acceleration that would be observed even if we didn't move our gravimeter.

– Spatial Variations – • These are changes in the observed acceleration that are space dependent. That is, these change the gravitational acceleration from place to place, just like the geologic affects, but they are not related to geology.

Factors that affect the ‘g’ Instrument Drift - Changes in the observed acceleration caused by changes in the response of the gravimeter over time. Tidal Affects - Changes in the observed acceleration caused by the gravitational attraction of the sun and moon.

Factors that affect ‘g’ Latitude Variations - Changes in the observed acceleration caused by the ellipsoidal shape and the rotation of the earth. Elevation Variations - Changes in the observed acceleration caused by differences in the elevations of the observation points. Slab Effects - Changes in the observed acceleration caused by the extra mass underlying observation points at higher elevations. Topographic Effects - Changes in the observed acceleration related to topography near the observation point

1. Ocean 2. Ellipsoid 3. Local plumb 4. Continent 5. Geoid : Being an equipotential surface, the geoid is by definition a surface to which the force of gravity is everywhere perpendicular

Instrument Drift • A gradual and unintentional change in the reference value with respect to which measurements are made. • Even if the instrument is handled with great care (as it always should be - new gravimeters cost ~$30,000), the properties of the materials used to construct the spring can change with time. • These variations in spring properties with time can be due to stretching of the spring over time or to changes in spring properties related to temperature changes. To help minimize the later, gravimeters are either temperature controlled or constructed out of materials that are relatively insensitive to temperature changes. Even still, gravimeters can drift as much as 0.1 mgal per day.

Notice the general increase in the gravitational acceleration with time. This is highlighted by the green line. This line represents a least-squares, best-fit straight line to the data. This trend is caused by instrument drift. In this particular example, the instrument drifted approximately 0.12 mgal in 48 hours.

Tidal Effect • Variations in gravity observations resulting from the attraction of the moon and sun and the distortion of the earth so produced. • This component represents real changes in the gravitational acceleration. Unfortunately, these are changes that do not relate to local geology and are hence a form of noise in our observations. • The distortion of the earth varies from location to location, but it can be large enough to produce variations in gravitational acceleration as large as 0.2 mgal.

Correcting for Latitude Dependent Changes

Accounting for Elevation Variations: The Free-Air Correction

Free Air Corrected Gravity (gfa) Free Air Corrected Gravity (gfa) - The Free-Air correction accounts for gravity variations caused by elevation differences in the observation locations. The form of the Free-Air gravity anomaly, gfa, is given by; gfa = gobs - gn + 0.3086h (mgal) where h is the elevation at which the gravity station is above the elevation datum chosen for the survey (this is usually sea level).

Variations in Gravity Due to Excess Mass

Correcting for Excess Mass: The Bouguer Slab Correction

• Corrections based on simple slab approximation are referred to as the Bouguer Slab Correction. • It can be shown that the vertical gravitational acceleration associated with a flat slab can be written simply as :

.04193

h. Where the correction is given in mgal, is the

density of the slab in gm/cc, and h is the elevation difference in meters between the observation point and elevation datum. • h is positive for observation points above the datum level and negative for observation points below the datum level.

Bouguer Slab Corrected Gravity (gb) • Bouguer Slab Corrected Gravity (gb) - The Bouguer correction is a first-order correction to • account for the excess mass underlying observation points located at elevations higher than the elevation datum. Conversely, it accounts for a mass deficiency at observations points located below the elevation datum. • The form of the Bouguer gravity anomaly, gb, is given by; gb = gobs - gn + 0.3086h - 0.04193 h (mgal) where is the average density of the rocks underlying the survey area.

Correction in Gravity Due to Nearby Topography

• Terrain Corrected Bouguer Gravity (gt) - The Terrain correction accounts for variations in the • observed gravitational acceleration caused by variations in topography near each observation • point. The terrain correction is positive regardless of whether the local topography consists of a • mountain or a valley. The form of the Terrain corrected, Bouguer gravity anomaly, gt, is given by; • gt = gobs - gn + 0.3086h - 0.04193r + TC (mgal) • where TC is the value of the computed Terrain correction.

This completes the data acquisition and processing of gravity data This data is to be interpreted

Interpretation Techniques:Qualitative Methods a)

Represents a contour map, which does not bring out any anomalous feature, i.e. a homogeneous rock mass without any anomalous density distribution.

b)

c)

Profile falls from one end to another, or contour shows parallel lines of gravity, it may correspond to sloping basement. The down slope of basement will be towards decreasing gravity values.

If contours are parallel, and become more closely spacing along an axis, following possibilities exist, 1. If contour values are greater than other, it is a sharp contact or fault, If the contour values are lower on either side, 2. it may be an anticline or ridge.

Interpretation Techniques:Qualitative Methods If profile shows a high or low, or the contour contains a clear high, or low closure, the anomalous body occurs at depth.

Profile

Position Body

Symmet ric

Vertical

Symmetric

Asymme tric

Dipping

Asymmetric

Feature

Density of Anomalous body

Density of Surrounding

High

High

Low

Low

Low

High

of

Contour Pattern

Interpretation Techniques:Qualitative Methods(Contd) Depending upon Closure of Contours

Contour closures Circular

Dimension

Elliptical

2½

Highly Elliptical

2 ½ Strike Width

3

>>

Interpretation Techniques: Qualitative Methods (Contd

Sometimes anomaly may be superimposed over the other, e.g. d and f, this is due two different bodies present at different depths. The large wavelength anomaly reflects deeper bodies and small wavelength anomaly represents shallow bodies. A shallow body may give larger wavelength, but sharper fall along the edges of a body will expose its shallowness.

Quantitative Techniques Before drilling it is necessary to know the shape, size, depth of burial and geometry of a causative body . Quantitative interpretation models the dimensions of body. The gravity results are correlated with the simple geometrical shapes. Geometrical Shape

Corresponding Geological Structure

Sphere Horizontal Cylinder

Massive Sulphide Bodies, Lenses of Chromite, Mn, Ba etc. Anticlines, Ridges,

Vertical Cylinder

Domes, Salt Domes, Kimberlite Pipes

Thick vertical dipping plane

or

Dykes or other intrusive bodies

Thin vertical dipping plane

or

Fractures, veins

Anomaly over a Sphere

Thin Dipping Rod Rod having inclination α and cross section A. The gravity effect at p due to an element dl is given by δgr = g σ A dl / r2 The total effect of rod when the rod is vertical, is g = 2.03X 10-3 σ A [1/ (z2+ x2) 1/2 - 1/ {(z+L) 2 + x2}1/2] The total effect of rod when the rod is inclined, is g = 2.03X 10-3 σ A / x sin α

Faulted Horizontal Slab

T=1000 ft, h1 = 2500 ft, h2 = 4500 ft, σ=1gm /cc, α = ? What type of fault it is? For Inclined Fault with inclination α g = 4.07 X 10-3 σ t [π + tan-1{(x/h1) + cot α} - tan-1{(x/h2)+ cot α}]

Faulted Horizontal Slab

T=1000 ft, h1 = 2500 ft, h2 = 4500 ft, σ=1gm /cc, α = ? What type of fault it is? For Inclined Fault with inclination α g = 4.07 X 10-3 σ t [π + tan-1{(x/h1) + cot α} - tan-1{(x/h2)+ cot α}]

Interpretations of Gravity Profiles

The circular gravity anomaly Two Possible interpretation