An application of the NSGA-II algorithm in Pareto joint inversion of 2D magnetic and gravity data

Katarzyna Miernik,Andrzej Leśniak,Elżbieta Węglińska,Tomasz Danek

doi:10.7494/geol.2021.47.2.59

Katarzyna Miernik, Andrzej Leśniak + Show 2 more

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https://doi.org/10.7494/geol.2021.47.2.59

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Abstract

Joint inversion is a widely used geophysical method that allows model parameters to be obtained from the observed data. Pareto inversion results are a set of solutions that include the Pareto front, which consists of non-dominated solutions. All solutions from the Pareto front are considered the most feasible models from which a particular one can be chosen as the final solution. In this paper, it is shown that models represented by points on the Pareto front do not reflect the shape of the real model. In this contribution, a collective approach is proposed to interpret the geometry of models retrieved in inversion. Instead of choosing single solutions from the Pareto front, all obtained solutions were combined in one “heat map”, which is a plot representing the frequency of points belonging to all returned objects from the solution set. The conducted experiment showed that this approach limits the problem of equivalence and is a promising way of representing the geometry of the model that was retrieved in the inversion process.

Highlights

The inversion problem is generally understood to recreate the parameters of a physical system or the causes of a phenomenon based on indirect measurements and observations
The Non-dominated sorting genetic algorithm II (NSGA-II) engine was applied in parallel using 63 populations of 16 individuals per population, with a limit of 1,000 generations
Its geometry can still play a role in assessing the correctness of the retrieving model and in choosing between several feasible models (Menke 1989)

Summary

Introduction

The inversion problem is generally understood to recreate the parameters of a physical system or the causes of a phenomenon based on indirect measurements and observations. Inversion is the reconstruction of the parameters of the M model on the basis of measurement data d. The relationship between the observations (measurement data) and the recovered parameters of the model is described by the formula d = G(M)T, where:. D – vector of measurement data with the dimension l, d = (d1, ..., dl)T,. M – vector of model parameters with dimension n, M = (m1, ..., mn)T,. G – operator of the relationship between model parameters and measurement data (Tarantola 1987). The optimization approach was used to solve the inverse problem

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