Gravity interpretation using Fourier transforms and simple geometrical models with exponential density contrast

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1074-1083 ◽  
Author(s):  
D. Bhaskara Rao ◽  
M. J. Prakash ◽  
N. Ramesh Babu
Keyword(s):  
Los Angeles ◽  
Fourier Transforms ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Sedimentary Basins ◽  
Density Contrast ◽  
Model Parameters ◽  
Exponential Density ◽  
Exponential Density Contrast ◽  
Gravity Interpretation

The decrease of density contrast in sedimentary basins can often be approximated by an exponential function. Theoretical Fourier transforms are derived for symmetric trapezoidal, vertical fault, vertical prism, syncline, and anticline models. This is desirable because there are no equivalent closed form solutions in the space domain for these models combined with an exponential density contrast. These transforms exhibit characteristic minima, maxima, and zero values, and hence graphical methods have been developed for interpretation of model parameters. After applying end corrections to improve the discrete transforms of observed gravity data, the transforms are interpreted for model parameters. This method is first tested on two synthetic models, then applied to gravity anomalies over the San Jacinto graben and Los Angeles basin.

Gravity inversion of an interface above which the density contrast varies exponentially with depth

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 837-845 ◽  
Author(s):  
Yufu Chai ◽  
William J. Hinze
Keyword(s):  
Los Angeles ◽  
Seismic Data ◽  
Gravity Anomalies ◽  
Sampling Technique ◽  
Sedimentary Basins ◽  
Density Contrast ◽  
Gravity Inversion ◽  
Los Angeles Basin ◽  
Deviation Equation ◽  
Basement Surface

Mapping of an interface above which the density contrast varies exponentially with depth, as is common at the basement surface of sedimentary basins, is efficiently achieved by a theoretically precise gravity method which can be applied to either profile data or twodimensional data. The contrast in mass above the interface is modeled by an array of vertical rectangular prisms with density contrasts varying exponentially with depth. Gravity anomalies due to the prisms are calculated in the wavenumber domain and then converted to the space domain. The precision of the inverse numerical Fourier transform in this procedure is significantly increased by a shift‐sampling technique based on the discrete Fourier deviation equation. Depth to the interface is determined by iterative adjustment of the vertical extent of the prisms in accordance with observed gravity anomaly data. The basement surface of the Los Angeles basin, California, calculated by this method, closely duplicates the published configuration based on drillhole data and seismic data.

Stable inversion of gravity anomalies of sedimentary basins with nonsmooth basement reliefs and arbitrary density contrast variations

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 754-764 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
A Priori ◽  
Bouguer Anomaly ◽  
Gravity Anomalies ◽  
Sedimentary Basins ◽  
Upper And Lower Bounds ◽  
Density Contrast ◽  
Good Precision ◽  
Rift Basins

We present a new, stable method for interpreting the basement relief of a sedimentary basin which delineates sharp discontinuities in the basement relief and incorporates any law known a priori for the spatial variation of the density contrast. The subsurface region containing the basin is discretized into a grid of juxtaposed elementary prisms whose density contrasts are the parameters to be estimated. Any vertical line must intersect the basement relief only once, and the mass deficiency must be concentrated near the earth’s surface, subject to the observed gravity anomaly being fitted within the experimental errors. In addition, upper and lower bounds on the density contrast of each prism are introduced a priori (one of the bounds being zero), and the method assigns to each elementary prism a density contrast which is close to either bound. The basement relief is therefore delineated by the contact between the prisms with null and nonnull estimated density contrasts, the latter occupying the upper part of the discretized region. The method is stabilized by introducing constraints favoring solutions having the attributes (shared by most sedimentary basins) of being an isolated compact source with lateral borders dipping either vertically or toward the basin center and having horizontal dimensions much greater than its largest vertical dimension. Arbitrary laws of spatial variations of the density contrast, if known a priori, may be incorporated into the problem by assigning suitable values to the nonnull bound of each prism. The proposed method differs from previous stable methods by using no smoothness constraint on the interface to be estimated. As a result, it may be applied not only to intracratonic sag basins where the basement relief is essentially smooth but also to rift basins whose basements present discontinuities caused by faults. The method’s utility in mapping such basements was demonstrated in tests using synthetic data produced by simulated rift basins. The method mapped with good precision a sequence of step faults which are close to each other and present small vertical slips, a feature particularly difficult to detect from gravity data only. The method was also able to map isolated discontinuities with large vertical throw. The method was applied to the gravity data from Reco⁁ncavo basin, Brazil. The results showed close agreement with known geological structures of the basin. It also demonstrated the method’s ability to map a sequence of alternating terraces and structural lows that could not be detected just by inspecting the gravity anomaly. To demostrate the method’s flexibility in incorporating any a priori knowledge about the density contrast variation, it was applied to the Bouguer anomaly over the San Jacinto Graben, California. Two different exponential laws for the decrease of density contrast with depth were used, leading to estimated maximum depths between 2.2 and 2.4 km.

GRAVITY INTERPRETATION USING THE FOURIER INTEGRAL

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 424-438 ◽  
Author(s):  
Mark E. Odegard ◽  
Joseph W. Berg
Keyword(s):  
Frequency Domain ◽  
Fourier Transforms ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Fourier Integral ◽  
Numerical Techniques ◽  
Functional Representations ◽  
Gravity Interpretation ◽  
Mathematical Relations ◽  
Gravitational Anomalies

The gravitational anomalies of simple bodies (sphere, cylinder, and fault) were used to develop methods for analyzing gravity data in the frequency domain. The Fourier transforms of the functional representations of the theoretical gravitational anomalies of these bodies were obtained. Mathematical relations were formulated between the transform‐versus‐frequency relationships and the depths and sizes of the bodies. Compound gravity anomalies (multiple cylinders, fault, and cylinder) were analyzed, and the transforms were reduced to transforms of anomalies due to individual simple bodies. These methods of analysis were applied to theoretical anomalies using numerical techniques, and the accuracy of both depth and size determinations was within a few percent in all cases.

A Hybrid PCG- Bat Algorithm for 2D Gravity Inversion: Applications for Ore Deposits Exploration and Interpretation of Sedimentary Basins

2020 ◽  
Author(s):  
Mohamed Abdrabou ◽  
Maha Abdelazeem ◽  
Mohamed Gobashy
Keyword(s):  
Conjugate Gradient ◽  
Hybrid Algorithm ◽  
2D Gravity ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Sedimentary Basins ◽  
Bat Algorithm ◽  
Ore Deposits ◽  
Preconditioned Conjugate Gradient ◽  
Residual Gravity

<p>Geophysical data such as gravity data can be inverted to get a subsurface image, which depicts the subsurface distribution of physical property. Consequently, inversion of geophysical data has an effective role for interpreting measured geophysical anomalies in hydrocarbons and mineral applications. Interest about ore deposits exploration and sedimentary basins interpretation is associated with their economic importance. The presence of sedimentary basins gives lower amplitude of gravity anomalies with negative signals, due to the negative density contrast as these sedimentary basins have lower density than that of the neighboring basement rocks. In prospecting ore deposits, studying the spatial distributions of densities in the subsurface is essential of significance.Two dimensional forward modelling strategy can be done via locating the rectangular cells with fixed size directly underneath the location of the observed data points using regular grid discretization. Density vector of the subsurface rectangular cells are obtained via solving the 2D gravity inverse problem by optimizing an objective function (i.e., the differences between observed and inverted residual gravity data sets). In this work, a hybrid algorithm merging a bat (BAT) algorithm with the preconditioned conjugate gradient (PCG) method is suggested as a mean for inverting surface gravity anomalies to obtain the density distribution in the subsurface. Like the hybrid, minimization algorithm has the capability to make use of the advantages of both two techniques. In this hybrid algorithm, the BAT algorithm was utilized to construct an initial solution for the PCG technique. The BAT optimizer acts as a rapid build-up of the model, whereas the second modifies the finer model approximated solution. This modern algorithm was firstly applied on a free-noise synthetic data and to a noisy data with three different levels of random noise, and good results obtained through the inversion. The validity and applicability of our algorithm are applied to real residual gravity anomalies across the San Jacinto graben in southern California, USA, and Sierra Mayor - Sierra Pinta graben, USA and prospecting of the Poshi Cu-Ni deposits, Xinjiang, northwest China. The obtained results are in excellent accordance with those produced by researchers in the published literature.</p><p> </p><p><strong>Keywords: </strong>Gravity data, 2D Inversion, BAT algorithm, Preconditioned Conjugate Gradient, Sedimentary Basins.</p>

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