Nonlinear inversion of gravity profile data for depth, radius and geometry determination of anomaly source, a case study: Aji Chai salt dome

Summary: A nonlinear inversion technique using a fast method is developed to estimate successively the depth, shape factor and amplitude coefficient of a buried structure using residual gravity anomalies along a survey line. By defining the anomaly value at the origin and the anomaly value at different points on the survey line, the problem of depth estimation is transformed into a problem of solving a nonlinear equation of the form f (z) = 0. Knowing the depth of the anomaly source, we can estimate the shape factor, and finally, the amplitude coefficient of the anomaly. Using the amplitude coefficient, we can also compute the radius of the anomaly. This technique is applicable for a class of geometrically simple anomalous bodies, including semi-infinite vertical cylinder, infinitely long horizontal cylinder, and sphere. The efficiency of this technique is demonstrated using the gravity anomaly due to a theoretical model with and without random errors. Finally, the applicability of the technique is illustrated using the residual gravity anomaly of a salt dome, situated near Miyaneh, northeast of Iran. The interpreted depth and other model parameters are in good agreement with the known actual values of the parameters. The estimated depth, radius, shape factor and the amplitude coefficient values of the salt dome are 64.63 m, 34.8 m, 1.43 and -472 mGal, respectively.
Gravity data interpretation is always subject to ambiguity. Different geometrical distributions of the subsurface mass can yield the same gravity field at the surface (Skeels, 1947). However, Roy (1962) describes how a mathematically unique solution can be achieved directly from gravity data when the density contrast is constant and the bounding surface of the body is known. Simple geometrically shaped models can be very useful in quantitative interpretation of gravity data acquired in a small area over the buried structures. The models may not be geologically realistic, but usually approximate equivalence is sufficient to determine whether the form and magnitude of the calculated gravity effects are close enough to the observed gravity data to make the geological postulate reasonable. In this paper, an inversion technique based on nonlinear equation z = f (z) is applied to analyze gravity anomalies due to simple structures. The inversion technique simultaneously estimates the depth (z), nature of the source (shape factor (q)), amplitude coefficient (A) and radius (R) of the buried structures. The accuracy of the results obtained by this procedure depends on the accuracy to which the residual anomaly can be separated from the Bouguer anomaly. Moreover, the accuracy of the results of the present method depends on the extent to which the source body conforms to one of the assumed geometries.
Methodology and Approaches: The general vertical component of the gravity anomaly expression produced by a sphere 3D), an infinite long horizontal cylinder (2D), and a semi-infinite vertical cylinder (3D) is given in Abdelrahman et al (1989). The depth of the anomaly is determined by solving a nonlinear equation for z using standard methods. Iteration form of the solution can be expressed as ( ) f j z  f z , where zj is the initial depth and zf is the revised depth; zf will be used as the zj for the next iteration. The iteration stops when |zf −zj| ≤ e, where e is a small predetermined real number close to zero. Any initial guess for z works well because there is always one global minimum. Theoretically, two different values of N and M are enough to determine the depth. In practice, more than two values of N and M are preferable because of the presence of noise in the data (xi = ± N and xi = ± M where N = 1, 2, 3, . . . and M = , , 3, . . ., and xi is the position coordinate). For each value of N and M, we compute the values of the model parameters (i.e., z, q, A and R).
Results and A simple and rapid inversion approach was formulated to use the anomaly values at the origin and two pairs of measured data points (±N and ±M). The results of the synthetic and real 2D gravity data analysis showed the proficiency the proposed method. The computed depth of the salt dome was obtained as 64.63 m and the salt dome shape was obtained as sphere approximately.