Gravity Anomaly and Basement Estimation Using Spectral Analysis

Abstract

Gravity survey and interpretations play a very vital role more especially in petroleum prospecting. Spectral analysis of gravity anomaly has been successful in the estimation of sedimentary basement. Spectral analysis technique can be used in designing filter for the residual and region separation of complete Bouguer anomaly. The residual gravity anomaly which is of prime importance for applied geophysicists interested in the subsurface features is considered most useful for the interpretation of sedimentary basin. In this chapter, interpretation of the complete Bouguer gravity anomaly, the importance of the separation of the Bouguer gravity anomaly into its residual and regional component is presented. The residual component is considered for the application of the spectral analysis approach.

1. Introduction

Geophysics is a field of study that deals with the study of the physical properties of the earth’s interior generally by direct measurement on or above the earth’s surface in order to find the quantitative value of the earth attraction force on a given buried material below the subsurface on the basis of Newton's law of gravitation. Geology and geophysics appeared difficult for one to define the broader line between the two. But in a broader sense, it can be put that, geology deals with study of the physical properties of the earth by direct observations and analysis of handpicked samples from field (i.e., on the ground). While geophysics involves the study of those buried physical properties of the earth using an appropriate measuring instruments on or above the earth’s surface. It also involves the interpretation of such measured data to make inferences about the basement structures. As a matter of fact, the two branches of geoscience are interwoven. For instance, well logs are done for geological interpretation whereas borehole geophysics has to do with such measurements.

In a nutshell, geophysics provides the measuring instruments for the measurement of the composition and structures of the earth’s interior. All that comes from underneath the earth’s surface to limited certain depths to which boreholes or mine shaft penetrated come from geophysical measurements. The knowledge of the existence and properties of the earth’s crust, mantle and the core came from observations of the seismic waves by earthquakes, gravity and magnetic measurements and thermal properties of the earth.

There are practically two related aspects of all geophysical deliberations, “pure” and “applied”. First of which deals with the understanding of the dynamics of the earth whereas the second one deals with the economic applications which is of prime importance to mankind. However, for pragmatic design and execution of geophysical survey/exploitation, a perceptive understanding of the structure, evolution of the crust and the uppermost mantle and various processes operating on the earth are essential.

Gravity surveys play vital role in recognition of geological structures such as sedimentary basins, faults, caves and other archeological structures [1, 2, 3, 4, 5]. There are varieties of techniques and methods for the interpretation of gravity anomalies over or due to sedimentary basins [6, 7, 8, 9, 10, 11, 12]. The structure of the sedimentary basins is often derived from the gravity anomalies with constant density contrast throughout the section of the basins [13]. However, the density contrast of sedimentary rocks is not practically constant [9]. The gravity method for hydrocarbon exploration is firstly used in 1924 in the Gulf coast of the United States and Mexico [14]. Till date, the structures in which hydrocarbons are entrapped exhibit such large density variation when compared to the densities of the surrounding rock formations [15]. Gravity method is very useful in deciding an appropriate location for drilling. For suitable geology of an area, gravity data can provide whether the sedimentary thickness beneath the subsurface is sufficiently thick enough to justify further geophysical investigation. This can be done very easily, since the densities of different sedimentary rock formations are usually lower than those of the basement rocks. Whenever this large contrast exists, it is easier to map out and determine the depth distributions of the sedimentary basins [16].

Gravity data/method is also useful in determining the positions/locations and sizes of key source features/structures in which hydrogeological aquifers, enormous base metals, iron ores, salt domes are entrapped or hosted [17, 18]. Gravity anomaly at long wavelength usually suggests undulations possibly in the topographic interface and the lateral variations in its physical properties (densities). While, short wavelength anomaly may suggest density variations related to the nature of the basin fill. These could encompass the compaction, facies changes and basic to intermediate intrusive [17]. Gravity data can be used to study the internal tectonic and stratigraphic framework, basement and crustal structure. Thus, understanding the structural basement framework, thickness and the physical properties of crust and mantle down to lithosphere is very important more especially in hydrocarbon prospect. Moreover, gravity method is still widely used as an exploration tool to map subsurface geology and estimate ore reserves for some massive ore bodies.

In mineral exploration, gravity method plays more applicability especially in search for ores like Chromite bodies [18]. The density contrast between the chromite bodies and the material that surround them can be so large that they can easily be located through direct gravity measurement. In the same sense, buried channels beneath the earth’s subsurface containing gold or uranium can be located since the channel fill is usually less dense than the rock in which it is hosted. Regional gravity studies are also very important in delineating major geological structures like faults/lineaments in which minerals are probably accumulated [19].

2. Gravity data and regional/residual separation

The complete Bouguer airborne gravity data of part of lower Benue trough in Nigeria (Figure 1) as acquired and corrected by Fugro Airborne Surveys (FAS) in 2010. The data is issued by the Nigerian Geological Survey Agency (NGSA), Abuja office, Nigeria. The survey was at a terrain clearance of 80 m, along NE–SW oriented flight lines with 4000 m flight line spacing and gridded at 500 m grid spacing. The complete Bouguer anomaly map (Figure 1) represents geological information from both deeper crust and shallower sedimentary thicknesses. In order to outline between the two, regional/residual separation is paramount. The regional anomaly (Figure 2) with gravity values between less than −31.8 mGal and 37.8 mGal could be interpreted as gravity information due geological formations in the lower crust possibly to the mantle or even lithosphere. The anomaly map (Figure 2) is the result of the Gaussian regional filter (low pass) at 50 km cut-off wavelength in MAGMAP tool of Oasis montaj. The other component of the anomaly (residual anomaly) map (Figure 3) which is of prime importance to applied geophysicists is obtained by subtracting the regional gravity anomaly (Figure 3) from the complete Bouguer anomaly (Figure 1) using Isostatic tool menu. This anomaly map (Figure 3) shows shorter wavelengths anomalies that can account for varying depth sedimentary basins (lower gravity values) and probably volcanic structures within the sediments (higher gravity values).

Figure 1.

Complete Bouguer gravity anomaly map. Gboko as well as the basement outcrops east of Ogoja are shown. Intrusions and locations of the anticline and syncline are superimposed.

Figure 2.

Regional component of the complete Bouguer gravity anomaly map. Gboko as well as the basement outcrops east of Ogoja are shown. Intrusions and locations of the anticline and syncline are superimposed.

Figure 3.

Residual component of the complete Bouguer gravity anomaly map. Gboko as well as the basement outcrops east of Ogoja are shown. Intrusions and locations of the anticline and syncline are superimposed.

3. Spectral analysis of gravity anomaly

Spectral analysis is a much known technique for the estimation of basement depth to anomalous sources in frequency domain [20, 21, 22]. In frequency domain, the depth to the various anomalous sources can be estimated based on their frequency content. Naturally, high-frequency anomalies are due to shallow anomalous sources whereas the low-frequency anomalies are due to anomalous sources that are at greater depths. The average power spectrum of potential field data usually shows a decaying curve with increasing frequency [21]. Spector and Grant [21] method has become an important technique for top depth estimation of anomalous sources in frequency/wavenumber domain [23]. Their concept is based on an ensemble of prisms of frequency-independent randomly and uncorrelated distribution of sources equivalent to white noise distribution. According to Spector and Grant [21] method, the logarithm of the power spectrum generated from horizontal distribution of sources is always directly proportional to $\left(\mathit{-}\mathbf{2}\mathit{dw}\right)\mathit{,}$ where $\mathit{d}$ is the depth to top of sources and $\mathit{w}$ is the radial wavenumber. The depth of the anomalous sources can therefore be estimated directly from the slope of the logarithmic plot of the power spectrum against the wavenumber. The power spectrum of sources could suggest the presence of various horizontal distributions of anomalous sources in the crust pending on the number of segments defined from the power spectrum. The power spectrum is usually not straight, due to the randomly and uncorrelated distribution of anomalous sources assumed in the Spector and Grant [21] method. The random and uncorrelated distribution was assumed due to lack or little knowledge about the depth distribution of the sources. The statistical ensemble of anomalous sources is therefore determined using the following equation

$$ln\left[P\left(w\right)\right]=ln\left[C\right]-2\mathrm{dw}=ln\left[C\right]-4\mathrm{п}\mathit{df}$$E1

This equation is analogous to equation of straight line as follows

$$y=\mathit{mx}+C$$E2

Comparing the two equations, it can be shown that, the slope $\left(\mathit{m}\right)$ power spectrum is given as

$$\mathit{m}=-\mathbf{2}\mathit{d}=-\mathbf{4}\mathrm{п}\mathit{d}$$E3

$$\text{or depth},d=-\frac{m}{2}=-\frac{m}{4\mathrm{п}}$$E4

Figure 4 shown, is the residual gravity anomaly map showing the central 55 km x 55 km blocks used for the estimation of sedimentary basement. Seventeen (17) blocks labeled B1, B2, …, B17 for estimations with 50% overlapping are shown. The approach of spectral analysis for the estimation of sedimentary thickness has been done. Figures 5–7, showed the seventeen power spectra generated from the gravity anomaly. In the area, basement depth between 2.01 km and 3.73 k is calculated and interpreted the sedimentary basement and shallow sources interpreted in term of depth to top of intrusions in the area between the depths of 0.45 km and 0.76 km (Figure 8).

Figure 4.

Residual component of the complete Bouguer gravity anomaly map. Central block (B01, B02, …, B17) of 55 km x 55 km with 50% overlap are shown for the sedimentary basement estimation. Gboko as well as the basement outcrops east of Ogoja are shown. Intrusions and locations of the anticline and syncline are superimposed.

Figure 5.

Power spectra of blocks (B01, B02, …, B06), showing the depths (D1 & D2) estimated.

Figure 6.

Power spectra of blocks (B07, B02, …, B12), showing the depths (D1 & D2) estimated.

Figure 7.

Power spectra of blocks (B13, B02, …, B17), showing the depths (D1 & D2) estimated.

Figure 8.

Residual component of the complete Bouguer gravity anomaly map. Estimated depths (D1 & D2) of each block (B01, B02, …, B17) of 55 km x 55 km with 50% overlap are shown for the sedimentary basement estimation. Gboko as well as the basement outcrops east of Ogoja are shown. Intrusions and locations of the anticline and syncline are superimposed.

4. Discussion and conclusions

Gravity anomalies and depth estimation from airborne gravity data is presented. Spectral analysis approach can be used to design special filters for separation of complete Bouguer anomalies into the residual and regional components. The power spectrum from potential field data for depth interpretation using spectral analysis approach is always not straight due to randomly uncorrelated distributions of anomalous sources. The depth estimation technique using spectral analysis can be applied either in space or frequency domain. However, depth estimation of anomalous sources in frequency/wavenumber domain is simple and more reliable due to the fact that, in wavenumber domain, the convolution operator is conveniently transformed to multiplication notation using Fourier Transform. The estimation of depth from the approach is normally done from the slope of the logarithmic plot of the power spectrum against the wavenumber [12]. Geological and tectonic complexity of a region can be interpreted from the technique of spectral analysis. The drawback in using the approach of spectral analysis for depth interpretation, is that, the concept is based on an ensemble of prisms of frequency-independent randomly and uncorrelated distribution of anomalous sources equivalent to white noise distribution. That is to say, spectral analysis technique involves manually selecting a segment that correspond to certain wavenumber range from the power spectra to represents a detectable anomalous sources inside the earth.

Acknowledgments

I am thankful to geophysical Department of the Nigerian Geological Survey Agency (NGSA), Abuja office, for providing the airborne gravity data used for the present study.

Conflict of interest

I declare no conflict of interest as regards this chapter.