Pseudo Gravity

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Using the pseudo-gravity functional transform to enhance deep-magnetic sources and enrich regional gravity data Stefano Panepinto*, Luciana De Luca, Marco Mantovani, and Maurizio Sfolciaghi, Schlumberger; Bruno Garcea, Edison Summary

Magnetic anomalies are difficult to analyze and interpret  because they are not always located located in the vertical direction of the perturbing bodies. Depending on the parameters of the geomagnetic field, the shape of the anomalies cannot be uniquely related to a given source. The complexity of the magnetic field and of its anomaly-to-lithology relationship often complicates interpretation. The amplitude of the anomalies is dominated by the magnetic bodies that are  present in the shallowest shallowest geologic structures. This dominant influence of shallow geologic bodies makes the detection of the deeper geological sources, which contribute to the medium and long period components of the observed magnetic signal, difficult. Conventional filtering methods smear out the shallow sources and are not capable of separating the lower amplitude magnetic anomalies associated with the deeper magnetic source rocks. Poisson’s theorem relates linearly the derivative of the gravity taken along the total magnetization vector direction and the magnetic potential due to a common, isolated source with constant density and magnetization distributions. From this theorem, two very useful functional transformations for magnetic anomalies, the reduction-to pole (RTP) and the pseudo-gravity (PSG) vertical integration, were formulated by Baranov. In this paper, a procedure to simplify the complex information of the original magnetic data is described, which consists of deriving a PSG map on which the amplitude of the displayed function is directly and simply related to a physical property of the underlying rocks. The Pseudo-Gravity transform is the vertical integration of the total magnetic intensity (TMI) grid data and uses conventional FFT tools to relate the anomalies to the vertical of the sources. The procedure was applied to a real data set and used also to enrich the low resolution of regional gravity data available for the studied area. The PSG transform demonstrates its excellent characteristics as an interpretation tool for the detection of deep-magnetic sources. Finally, the transformed PSG data set was modeled using conventional 3D modeling and inversion methods that gave a useful marker for the interpretation. Introduction

The most consolidated geophysical methodology for reservoir modelling in the oil and gas industry is seismic. Even though modern 3D acquisition techniques make more

and more focused and reliable interpretations, the intrinsic nonuniqueness principle of any geophysical solution must  be considered and minimized. All of these interpretations are equally probable without any further geological and/or geophysical information. Potential field methods are historically the first seismic “partner” to build an integrated earth model with independent geophysical information. Furthermore, considering aeromagnetic surveys as a primary tool for  providing uniform coverage of a geophysical parameter over large areas, the proposed approach is of primary interest in processing and interpreting potential field data. The following application consists of enhancing existing vintage data sets by using the PSG transform to enrich the available regional Bouguer anomaly map. The aeromagnetic and regional gravity data were provided  by Edison. The two data sets were u sed for the functional transformation of geo-potential field data. data. The first data set is a magnetic-data grid recovered from an analog anomaly map. After correcting the measurements for the temporal variations of the magnetic field, field, the TMI anomaly was produced by subtracting the theoretical geomagnetic field or international geomagnetic reference field (IGRF) (see Figure 1).

Figure 1: TMI derived by computing geomagnetic elements. The area of interest (AOI) scale is displayed by the black box.

The second data set is the complete Bouguer anomaly map obtained by using a reduction density of 2.67 g/cm3 (Figure 2). Because the data sets involve a not fully explored area of interest (AOI) in the following discussion, any geographical, positioning, or geologic references are intentionally omitted.

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aim of merging all of the available information for  producing a reliable interpretation of the basement relief. PSG functional transform: theory and results

Figure 2: Bouguer anomaly map showing mostly regional features. The black box highlights the AOI. Please note that Figure1 and 2 are not at the same scale.

Figure 2 clearly shows that the Bouguer anomaly map has only regional characteristics and no feature at the scale of the survey area is usable to assist in the local geologic interpretation. However, the Bouguer anomaly was used to scale the dynamics of the PSG result and to produce an enriched gravity image. Also, a seismic line and a well density log are available to conduct a multiparametric study of the AOI (Figure 3).

The PSG transform is an old method that has received little attention in practical exploration problems with few applications in real data. The PSG transfor m has interesting characteristics that reduce the dominance of the shallow magnetic sources and enhances the amplitude of magnetic anomalies from deeper magnetic source rocks (Pratt and Shi, 2004). Some references about this methodology clearly indicate the PSG transform can be a more useful tool than the RTP (Baronov, 1957; Fedi, 1989; Blakely, 1995). Indeed, the PSG integration, in contrast to the RTP,  provides a smoothing of the anomaly map, highlighting the deep-source contribution and reduces the degree of nonlinearity existing in the mathematical relationship  between the data and the source depth (Fedi, 1989). Thus, accurate estimates of the geometric parameters of the unknown source can be more easily and rapidly calculated  by the transformed pseudo-anomalies. For a complete discussion of the theory on which the PSG integration and the RTP are based, readers are referred to Baronov (1957). Here, only a brief description of the applied methodology is given. The PSG transformation follows from Poisson’s relation  between the magnetic potential and th e gravitational field. Considering a body with uniform magnetization and density occupying a volume v, the magnetic scalar potential is:

V ( p )   M  p



1 v

d 

dv

(1)

where p is the observation point and d  the distance from p. The gravitational potential is: 1 U ( p )  G  dv (2) v d 



Figure 3: Poststack vintage migration seismic line

To locate and outline crustal magnetic sources that could be interpreted as basement relief, the following PSG transform (Baronov, 1957-1975) is applied to the magnetic data. By using the PSG transform, the apex of the magnetic anomalies is shifted over the source body and the distortion due to the earth’s magnetic field can easily be removed. As the magnetic anomalies very rarely are centered above their source, the proposed procedure is intended to simplify the interpretation of magnetic data by treating magnetization in the same way as density. The following procedure has the

where G  is the gravitational constant and r   the density. Combining Equation 1 and Equation 2 leads to the following: 1 1 V ( p)    M  p U    Mg  M  (3) G   G    by Poisson’s relation g  M  is the component of gravity in the direction of magnetization. Thus, pseudo-gravity is defined as the gravity anomaly that would be observed if the magnetization distribution were replaced by an identical density distribution, i.e. ρ/M is a constant. However, one can consider a body to be composed of arbitrarily small

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volumes in which density and magnetization can be regarded as constant. Since potential sums, the equation (3) applies to a body which density and magnetization vary in  proportion. Because the method uses an integration of the total magnetic field grid, which produces strong edge effects beyond the boundaries of the survey area, a 10% of data grid extension was applied. The spectral analysis of the extended magnetic data set was thus performed by computing the radially averaged power spectrum (RAPS). The RAPS characterization (Figure 4) allows us to consider three different terms: i) long term; ii) intermediate term; and iii) short term.

F( ) 



G     M 

si n I a   i cos I   cos D   2  r 

, (4)



if    I a   I  , I a   I 

Where: I = geomagnetic inclination Ia = inclination for amplitude correction (never less than I). ρ = density contrast in g/cm 3 G = gravitational constant M = magnetization in Gauss D = geomagnetic declination ϴ = direction of wavenumber in degrees azimuth r  = wavenumber (radians/ground-unit). The denominator of Equation 4 is used to calculate the magnetic potential by a reduction of the magnetic pole and vertical integration, while the numerator converts magnetic potential to PSG. Figure 5 shows the PSG result. The dynamic range of the short-wavelength features that is evident in the TMI image (Figure1) is much lower in the PSG image.

Figure 4: The computed RAPS using a 10% extension for the magnetic data set. Each term revealed by the spectral analysis is related to a different depth source (see text for more explanation).

Each of these terms is linked to a different depth of the causative sources. Depending on the survey scale and geological setting of the area, the long-term interval ranges from kilometers to tens of kilometers, the intermediate-term interval from hundreds of meters to some kilometers, and the short-term interval from tens of meters to kilometers scale. Using the results of the spectral analysis, a filtering test was  performed and the best filter option was tuned to reduce the high-amplitude long wavelengths anomalies using a cutoff at the 36 km. These last anomalies are mainly due to the 10% data padding, and the effects that would dominate the PSG transform were filtered out before the vertical data integration. The pseudo-gravity transform was applied to the filtered total magnetic intensity grid using FFT. The general expression for the PSG filter includes both a reduction to the magnetic pole and vertical integration (Blakely, 1995):

Figure 5: PSG result coupled with a high-pass filter to cut out the long-wavelength term. The color bar is intentionally omitted.

The obtained PSG grid can be modelled using conventional 3D modelling and inversion methods, where the density is considered through the Poisson’s theorem as a pseudodensity defined by the relationship:   *

kM 

G

(5)

* 

where  ρ is the pseudo-density contrast, k is magnetic susceptibility, M is the total magnetic field intensity and G is the universal gravitational constant. This relationship assumes that the magnetization is induced and no remanence is present.

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To provide a reasonable marker for the seismic interpretation, an inversion test of the PSG anomaly grid has been executed by using the Parker’s algorithm (Parker, 1972; Oldenburg, 1974). Because the entire AOI is  probably characterized by a complex density distribution, the inversion test was applied to a smaller area than the available one to be able to consider a homogeneous density contrast at the inverted interface (Figure 6).

Figure 6: Selected area for the inversion experiment.

A possible source for magnetic field is identified by the Parker algorithm at a depth of approximately 6500 m.

Conclusions

The anomalies deduced from the pseudo-transform are not density related; i.e., they are still magnetic anomalies, computed on the assumption that the magnetization vector is vertical. The process does not imply that the distribution of magnetism in the Earth is necessarily related to the density distribution. The essential fact is that the deduced anomalies are as simple as Bouguer anomalies. The anomalies are located on the vertical of the magnetized masses and do not depend on the inclination of the normal field nor on the direction of the magnetization. The PSG functional transformation is useful in interpreting magnetic anomalies, not because a mass distribution actually corresponds to the magnetic distribution beneath the magnetic survey, but because gravity anomalies are easier to interpret and quantify than magnetic anomalies. The PSG transform enhances the anomalies associated with deep-magnetic sources at the expense of the dominating shallow-magnetic sources as shown in Figure 5. Finally, as demonstrated by the inversion experiment, the PSG transform is an excellent interpretation tool for the detection of deep-magnetic sources and allows the PSG data to be modeled by conventional 3D modeling methods that provide valuable results. At the resolution of the magnetic data, the method  presented provides an excellent tie with available 2D seismic, and allows for some extrapolation of the identified formation in the 3D sense where no seismic exists. Acknowledgments

The authors wish to acknowledge Edison for permission to use the aeromagnetic and gravity data and to publish the results of this research.

Figure 7: The blue curve is a legacy interpretation, while the red curve is Parker algorithm inversion result.

The amplitude and wavelength of the inverted surface appears to approximately match a sharp boundary existing in the 2D seismic line (Figures 3 and 7). This may provide a reasonable marker for interpreting the observed magnetic data and the geological source of the dominating field.

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http://dx.doi.org/10.1190/segam2014-1323.1 EDITED REFERENCES

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 Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2014 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES

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