Summary
Electromagnetic (EM) methods are used to characterize the electrical conductivity distribution of the earth. EM geophysical surveys are increasingly being simulated and inverted in 3D, due in part to computational advances. However, the availability of computational resources does not invalidate the use of lower dimensional formulations and methods, which can be useful depending on the geological complexity as well as the survey geometry. Due to their computational speed, simulations in 1D or 2D can also be used to quickly gain geologic insight. For example, this insight can be used in an EM inversion starting with a 1D inversion, then building higher dimensionality into the model progressively. As such, we require a set of tools that allow a geophysicists to easily explore various model dimensionalities, such as 1D, 2D, and 3D, in the EM inversion. In this study, we suggest a mapping methodology that transforms the inversion model to a physical property for use in the forward simulations. Using this general methodology, we apply an EM inversion to a suite of models in one, two, and three dimensions, and suggest the importance of choosing an appropriate model space based on the goal of the EM inversion.
Introduction
Electromagnetic (EM) fields and fluxes can be used to excite the earth, and in a geophysical survey, we measure and interpret the resulting signals. These signals are sensitive to the conductivity distribution of the earth. By numerically solving Maxwell’s equations, we can compute the forward response for a system with a known conductivity distribution. To conduct a forward simulation for a 3D conductivity distribution, we require the property to be discretized numerically, and we typically employ a voxel-based mesh to discretize the earth. Once we have a mechanism to simulate EM fields and fluxes, we can consider approaching the inverse problem. The aim of an EM inversion is to recover a model that is consistent with the measured EM data and prior knowledge of the geologic setting.
Three dimensional EM inversion techniques using gradient based optimization have been actively developed and applied for various survey types and geologic settings (Oldenburg et al. (2013); Gribenko and Zhdanov (2007); Chung et al. (2014)). A gradient based inversion approach requires defining an objective function that will be minimized in the optimization. Equally important, yet often overlooked, is the definition of the model over which we minimize. Our focus in this paper is the construction of this inversion model in a flexible framework.