3D Gravity Analysis in the Spatial Domain: Model Simulation by Multiple Polygonal Cross-Sections Coupled with Exponential Density Contrast

Abstract

An automatic 3D modeling technique is developed in the spatial domain to analyze the gravity anomalies produced by a concealed density interface with mass density contrast differing exponentially with depth. The sedimentary column above the interface is described with a stack of multiple vertical polygonal sections of unit thickness each. For such a case, the depth ordinates of the vertices of the cross-sections become the unknown parameters to be estimated from gravity data. Forward solution of the model space is realized in the spatial domain by a technique that combines both analytic and numeric approaches. Initial depths to the interface are calculated based on the Bouguer slab approximation and subsequently improved, iteratively, based on the ratio of the product of the observed gravity anomaly and existing depth parameter to the corresponding model gravity response. The iterative process continues until one of the predefined termination criteria is accomplished. Unlike the existing methods, the advantage of the proposed method is that the observed gravity anomalies need not necessarily be sampled/available at regular spatial grid intervals. The applicability of the proposed model is exemplified with a set of noisy gravity anomalies attributable to a synthetic structure before being applied to a real world gravity data. In the case of the synthetic example, the method has yielded a structure that was compatible with the assumed structure even in the presence of random noise. Application of the proposed method to the gravity data set from the Los Angeles Basin, California, using a prescribed exponential density function has yielded a model that concurs reasonably well with the published models.