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Novel Approach for 1D Resistivity Inversion Using the Systematically Determined Optimum Number of Layers

Ammar Alali, Frank Dale Morgan, Darrell Coles

Determining the correct number of layers as input for 1D resistivity inversion is important for constructing a model that represents the subsurface accurately. Current common methods to select the number of layers are performed in one of three ways: by trial-and-error and choosing the best model data-fit, by using the modified F-test, smooth over-parameterization, or through trans-dimensional model parameterization. Although these methods are creative approaches, they are computationally expensive, as well as time-consuming and painstaking in practice. In this article, we provide a method that solves the problem of choosing the correct number of layers represented by the apparent resistivity curve. The method follows the two-steps approach suggested by Simms and Morgan (1992) to systematically recover the optimum number of layers. The first step is to run a fixed-thickness inversion using a large number of layers in which the number of layers and layer thicknesses are fixed, and resistivity values are inversion parameters. We then cumulatively sum the outcome of the first inversion over depth (the resistivity model) to determine the optimum number of layers based on changes of the slope. The detected number of layers is used as an input parameter for the second step; which is running a variable-thickness inversion (layer thicknesses and resistivities are both inversion parameters) for the outcome, the final resistivity model. Each step uses the Ridge Trace damped least-square inversion. The two inversion steps are integrated to run sequentially. The method determines all inversion parameters based on the data in a self-consistent manner. This proposed method uses a robust ridge trace regression algorithm, which has proven to be stable, accurate, and at least a hundred times faster than current methods.