A least‐squares minimization approach to depth determination from moving average residual gravity anomalies

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1779-1784 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Tarek M. El‐Araby

We have developed a least‐squares minimization method to estimate the depth of a buried structure from moving average residual gravity anomalies. The method involves fitting simple models convolved with the same moving average filter as applied to the observed gravity data. As a result, our method can be applied not only to residuals but also to the Bouguer gravity data of a short profile length. The method is applied to synthetic data with and without random errors. The validity of the method is tested in detail on two field examples from the United States and Senegal.

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1105-1109 ◽  
Author(s):  
E. M. Abdelrahman ◽  
H. M. El‐Araby ◽  
T. M. El‐Araby ◽  
E. R. Abo‐Ezz

Three different least‐squares approaches are developed to determine, successively, the depth, shape (shape factor), and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly. By defining the anomaly value g(max) at the origin on the profile, the problem of depth determination is transformed into the problem of solving a nonlinear equation, [Formula: see text]. Formulas are derived for spheres and cylinders. Knowing the depth and applying the least‐squares method, the shape factor and the amplitude coefficient are determined using two simple linear equations. In this way, the depth, shape, and amplitude coefficient are determined individually from all observed gravity data. A procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources. The method is applied to synthetic data with and without random errors. In all the cases examined, the maximum error in depth, shape, and amplitude coefficient is 3%, 1.5%, and 7%, respectively. Finally, the method is tested on a field example from the United States, and the depth and shape obtained by the present method are compared with those obtained from drilling and seismic information and with those published in the literature.


2017 ◽  
Vol 47 (2) ◽  
pp. 113-132 ◽  
Author(s):  
El-Sayed Abdelrahman ◽  
Mohamed Gobashy

AbstractWe have developed a simple and fast quantitative method for depth and shape determination from residual gravity anomalies due to simple geometrical bodies (semi-infinite vertical cylinder, horizontal cylinder, and sphere). The method is based on defining the anomaly value at two characteristic points and their corresponding distances on the anomaly profile. Using all possible combinations of the two characteristic points and their corresponding distances, a statistical procedure is developed for automated determination of the best shape and depth parameters of the buried structure from gravity data. A least-squares procedure is also formulated to estimate the amplitude coefficient which is related to the radius and density contrast of the buried structure. The method is applied to synthetic data with and without random errors and tested on two field examples from the USA and Germany. In all cases examined, the estimated depths and shapes are found to be in good agreement with actual values. The present method has the capability of minimizing the effect of random noise in data points to enhance the interpretation of results.


2019 ◽  
Vol 49 (3) ◽  
pp. 229-247
Author(s):  
El-Sayed Abdelrahman ◽  
Mohamed Gobashy

Abstract We present a least-squares minimization approach to estimate simultaneously the depth to and thickness of a buried 2D thick, vertically faulted slab from gravity data using the sample spacing – curves method or simply s-curves method. The method also provides an estimate for the horizontal location of the fault and a least-squares estimate for the density contrast of the slab relative to the host. The method involves using a 2D thick vertical fault model convolved with the same finite difference second horizontal gradient filter as applied to the gravity data. The synthetic examples (noise-free and noise affected) are presented to illustrate our method. The test on the real data (Central Valley of Chile) and the obtained results were consistent with the available independent observations and the broader geological aspects of this region.


Geophysics ◽  
1995 ◽  
Vol 60 (2) ◽  
pp. 589-590 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Sharafeldin M. Sharafeldin

The gravity anomaly expression produced by most geologic structures can be represented by a continuous function of both shape (shape‐factor) and depth‐related variables with an amplitude coefficient related to mass (Abdelrahman and El‐Araby, 1993). Few methods have been developed to determine the shape of the buried geologic structure from residual gravity anomaly profiles. These methods include a Walsh transform approach (Shaw and Agarwal, 1990) and the employment of a correlation factor between successive least‐squares residuals (Abdelrahman and El‐Araby 1993). In the present note, a least‐squares minimization approach to shape‐factor determination from a residual gravity anomaly profile is presented. The problem of the shape‐factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) = 0.


Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 535-543 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Hesham M. El‐Araby ◽  
Tarek M. El‐Araby ◽  
Eid Ragab Abo‐Ezz

This paper presents two different least‐squares approaches for determining the depth and amplitude coefficient (related to the density contrast and the thickness of a buried faulted thin slab from numerical first‐, second‐, third‐, and fourth‐horizontal derivative anomalies obtained from 2D gravity data using filters of successive graticule spacings. The problem of depth determination has been transformed into the problem of finding a solution to a nonlinear equation of the form f(z) = 0. Knowing the depth and applying the least‐squares method, the amplitude coefficient is determined using a simple linear equation. In this way, the depth and amplitude coefficient are determined individually from all observed gravity data. The depths and the amplitude coefficients obtained from the first‐, second‐, third‐, and fourth‐ derivative anomaly values can be used to determine simultaneously the actual depth and amplitude coefficient of the buried fault structure and the optimum order of the regional gravity field along the profile. The method can be applied not only to residuals but also to the Bouguer anomaly profile consisting of the combined effect of a residual component due to a purely local fault structure (shallow or deep) and a regional component represented by a polynomial of any order. The method is applied to theoretical data with and without random errors and is tested on a field example from Egypt.


Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1785-1791 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Hesham M. El‐Araby

The gravity anomaly expression produced by most geologic structures can be represented by a continuous function in both shape (shape factor) and depth variables with an amplitude coefficient related to the mass. Correlation factors between successive least‐squares residual gravity anomalies from a buried vertical cylinder, horizontal cylinder, and sphere are used to determine the shape and depth of the buried geologic structure. For each shape factor value, the depth is determined automatically from the correlation value. The computed depths are plotted against the shape factor representing a continuous correlation curve. The solution for the shape and depth of the buried structure is read at the common intersection of correlation curves. This method can be applied to a Bouguer anomaly profile consisting of a residual component caused by local structure and a regional component. This is a powerful technique for automatically separating the Bouguer data into residual and regional polynomial components. This method is tested on theoretical examples and a field example. In both cases, the results obtained are in good agreement with drilling results.


2020 ◽  
Author(s):  
Mohamed Abdrabou ◽  
Maha Abdelazeem ◽  
Mohamed Gobashy

<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>


Geophysics ◽  
1957 ◽  
Vol 22 (3) ◽  
pp. 643-645 ◽  
Author(s):  
L. F. Ivanhoe

The effect of varying surface densities on gravity anomalies is a more common problem in areas of topographical relief than is generally recognized. There is an unjustified tendency to assume that gravity maps are unique and final, even though one basic assumption (density of surface rocks) is inherent in all gravity maps. The use of incorrect elevation factors will produce gravity anomalies over any topographic feature. Both positive and negative gravity anomalies can be produced by either a topographic hill or valley depending on the degree of error in the elevation factor. These “elevation factor anomalies” are especially troublesome on residual gravity maps. The interpretation of gravity data should always include an analysis of the elevation factor effect as well as a study of the surface geology.


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