A very fast simulated annealing (VFSA) global optimization is used to interpret residual gravity anomaly Since, VFSA optimization yields a large number of best-fitted models in a vast model space; the nature of uncertainty in the interpretation is also examined simultaneously in the present study The results of VFSA optimization reveal that various parameters show a number of equivalent solutions when shape of the target body is not known and shape factor ‘q’ is also optimized together with other model parameters The study reveals that amplitude coefficient k is strongly dependent on shape factor This shows that there is a multi-model type uncertainty between these two model parameters derived from the analysis of cross-plots However, the appraised values of shape factor from various VFSA runs clearly indicate whether the subsurface structure is sphere, horizontal or vertical cylinder type structure Accordingly, the exact shape factor (15 for sphere, 10 for horizontal cylinder and 05 for vertical cylinder) is fixed and optimization process is repeated After fixing the shape factor, analysis of uncertainty and cross-plots shows a well-defined uni-model characteristic The mean model computed after fixing the shape factor gives the utmost consistent results Inversion of noise-free and noisy synthetic data as well as field data demonstrates the efficacy of the approach

Interpretation of residual gravity anomaly caused by simple shaped bodies using very fast simulated annealing global optimization

A global particle swarm optimization (GPSO) technique is developed and applied to the inversion of residual gravity anomalies caused by buried bodies with simple geometry (spheres, horizontal, and vertical cylinders). Inversion parameters, such as density contrast of geometries, radius of body, depth of body, location of anomaly, and shape factor, were optimized. The GPSO algorithm was tested on noise-free synthetic data, synthetic data with 10% Gaussian noise, and five field examples from different parts of the world. The present study shows that the GPSO method is able to determine all the model parameters accurately even when shape factor is allowed to change in the optimization problem. However, the shape was fixed a priori in order to obtain the most consistent appraisal of various model parameters. For synthetic data without noise or with 10% Gaussian noise, estimates of different parameters were very close to the actual model parameters. For the field examples, the inversion results showed excellent agreement with results from previous studies that used other inverse techniques. The computation time for the GPSO procedure is very short (less than 1 s) for a swarm size of less than 50. The advantage of the GPSO method is that it is extremely fast and does not require assumptions about the shape of the source of the residual gravity anomaly.

Application of Global Particle Swarm Optimization for Inversion of Residual Gravity Anomalies Over Geological Bodies with Idealized Geometries

We present a new method for interpreting isolated potential-field (gravity and magnetic) anomaly data. A linear equation, involving a symmetric anomalous field and its horizontal gradient, is derived to provide both the depth and nature of the buried sources. In many currently available methods, either higher order derivatives or postprocessing is necessary to extract both pieces of information; therefore, data must be of very high quality. In contrast, for gravity work with our method, only a first-order horizontal derivative is needed and the traditional data quality is sufficient. Our proposed method is similar to the Euler technique; it uses a shape factor instead of a structural index to characterize the buried sources. The method is tested using theoretical anomaly data with and without random noise. In all cases, the method adequately estimates the location and the approximate shape of the source. The practical utility of the method is demonstrated using gravity and magnetic field examples from the United States and Zimbabwe.

Linearized least‐squares method for interpretation of potential‐field data from sources of simple geometry

Model parameter estimations from residual gravity anomalies due to simple-shaped sources using Differential Evolution Algorithm☆

A Very Fast Simulated Annealing (VFSA) global optimization algorithm is developed for interpretation of gravity and magnetic anomaly over thin sheet type structure for ore exploration. The results of VFSA optimization show that it can uniquely determine all the model parameters without any uncertainty. Inversion of noise-free and noisy synthetic data for single structures as well as field data demonstrates the efficacy of the approach. The technique has been vigilantly and efficaciously applied to two real data examples from Canada with the presence of ore bodies. In both Model examples, the model parameters acquired by the present method, mostly the shape and depth of the buried structures were found to be in respectable agreement with the actual parameters. The present method has the proficiency of evading highly noisy data points and enhances the interpretation results. The technique can be extremely appropriate for mineral exploration, where the gravity and magnetic data is observed due to ore body of sheet like structure embedded in the shallow and deeper subsurface. The computation time for the whole process is very short.

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Interpretation of gravity and magnetic anomaly over thin sheet-type structure using very fast simulated annealing global optimization technique

Walsh functions are a set of complete and orthonormal functions of nonsinusoidal waveform. In contrast to sinusoidal waveforms whose amplitudes may assume any value between -1 to +1, Walsh functions assume only discrete amplitudes of + or -1 which form the kernel function of the Walsh transform. Because of this special nature of the kernel, computation of the Walsh transform of a given signal is simpler and faster than that of the Fourier transform. The properties of the Fourier transform in linear time are similar to those of the Walsh transform in dyadic time. The Fourier transform has been widely used in interpretation of geophysical problems. Considering various aspects of the Walsh transform, an attempt has been made to apply it to some gravity data.A procedure has been developed for automated interpretation of gravity anomalies due to simple geometrical causative sources, viz., a sphere, a horizontal cylinder, and a 2-D vertical prism of large depth extent. The technique has been applied to data from the published literature to evaluate its applicability, and the results are in good agreement with the more conventional ones.

B. N. P. Agarwal

Papers

The application of Walsh transforms to interpret gravity anomalies due to some simple geometrically shaped causative sources: A feasibility study