Application of Cauchy-type integrals in developing effective methods for depth-to-basement inversion of gravity and gravity gradiometry data

Abstract

One of the most important applications of gravity surveys in regional geophysical studies is determining the depth to basement. Conventional methods of solving this problem are based on the spectrum and/or Euler deconvolution analysis of the gravity field and on parameterization of the earth's subsurface into prismatic cells. We have developed a new method of solving this problem based on 3D Cauchy-type integral representation of the potential fields. Traditionally, potential fields have been calculated using volume integrals over the domains occupied by anomalous masses subdivided into prismatic cells. This discretization can be computationally expensive, especially in a 3D case. The technique of Cauchy-type integrals made it possible to represent the gravity field and its gradients as surface integrals. In this approach, only the density contrast surface between sediment and basement needed to be discretized for the calculation of gravity field. This was especially significant in the modeling and inversion of gravity data for determining the depth to the basement. Another important result was developing a novel method of inversion of gravity data to recover the depth to basement, based on the 3D Cauchy-type integral representation. Our numerical studies determined that the new method is much faster than conventional volume discretization method to compute the gravity response. Our synthetic model studies also showed that the developed inversion algorithm based on Cauchy-type integral is capable of recovering the geometry and depth of the sedimentary basin effectively with a complex density profile in the vertical direction.

Three-Dimensional Inversion of Magnetotelluric Data for the Sediment–Basement Interface

“…We computer simulated the synthetic MT data at 441 MT stations located on a rectangular grid at 9 frequencies ranging from 0.01 to 100 Hz using the basin model that was produced by the gravity inversion [4]. A 5% random noise was added to the synthetic data as well.…”

“…Among the passive-source geophysical methods, potential field surveys have been widely used to estimate the depth to basement for decades (e.g., [3], [4], [6], and [7]). It is well known, however, that potential field data have relatively low resolution to the deep target.…”

“…This type of parameterization has been widely used for potential field inversion to recover the depth to basement (e.g. [3], [4], and [7]). These parameterization approaches, however, have not been widely used for MT inversion problems, especially in the 3-D case.…”

Redatuming controlled-source electromagnetic data using Stratton–Chu type integral transformations

“…However, in a real case, the receivers can be deployed on irregular grids only due to various reasons (availability of difficult-to-access areas, costs optimization, etc.). It is well known that, using the data observed on a regular grid has a significant advantage over analyzing the data on an irregular grid in order to produce a robust inversion result (e.g., Cai and Zhdanov, 2015). In this section, we consider that the data are collected on an irregular grid as shown in Fig.…”

A level-set method for imaging salt structures using gravity data

“…According to Krahenbuhl and Li (2006), existing methods for salt imaging using gravity data fall under two general categories: the first is interface inversion and the second is generalized density inversion. Assuming a simple profile for the salt body and a known density contrast, interfaceinversion methods look for the shape of the salt-sediment interface (Barbosa et al, 1999;Cheng et al, 2003;Krahenbuhl and Li, 2006;Silva Dias et al, 2011;Ennen and Hall, 2011;Barnes and Barraud, 2012;Cai and Zhdanov, 2015); additional geological information is usually incorporated into the inversion process. For example, in Cheng et al (2003) the interface inversion requires the knowledge of both the top of a salt body and a part of the base of the salt body so as to determine the complete base of the salt body.…”