Synthesis of Alternative Equations of Subsurface Resistivity with Meta Heuristic PSO Technique for Layered Earth MT Data Inversion

Abstract

Geophysical data is inverted by various optimization techniques to determine subsurface layered parameter. The conventional equation of calculating apparent resistivity by Cagniard (1953) is common to determine optimum solution. In the present study, we are discussing the alternative equations of calculating apparent resistivity and particle swarm optimization (PSO) over synthetic (noise free and noisy) data to improve the results with respect to conventional equation. PSO has the ability of exploration that is it search the whole range of the search space for optimum solution. The study includes the Probability Distribution Function of the optimized results with 68.27% confidence interval.

Results have been compared with published inversion paper giving conclusion that proposed techniques has better outcomes than earlier.

.Introduction

We are discussing the inverse problem of 1D MT noise free and noisy (10% random noise) synthetic data analyzing the cumulative effect of various definitions of apparent resistivity on optimization technique. Calculating PDF of optimized result enhances model parameter shown in the table.

Purpose

The proposed technique is used earlier but in the present study we combine the properties of alternative definitions of apparent resistivity and PSO technique to improve the accuracy and results. The optimized results shown in the table are better than the earlier work done with the same technique

Method

PSO, a meta heuristic algorithm based on behavior of swarm move in same direction in search of food analogous to this behavior particles move toward global solution in the defined search range.

The apparent resistivity is calculated by alternative equations defined by Spies & Eggers (1986) and Shireesha & Harinarayana (2013) to define the cost function.

Results

The optimization results are shown in the table with true model taken by Shaw and Shalivahan (2007) for three layer and Xiong, J. et.al. (2018) for four layer given below along with the mean model of PDF of selected models.