Joint Inversion Through A Level Set Formulation

Abstract

Geophysical data processing is a highly quantitative field that involves modelling, inversion and visualization. In most cases a geophysical experiment is conducted to collect data that are sensitive to a particular physical property of the earth. The data is processed and inverted to generate an earth model of the physical property in question. To better understand the structure of the earth, different experiments are conducted using a variety of imaging modalities. For example, from seismic, gravity and electromagnetic experiments we may obtain information about the earth's elastic, density and conductivity characteristics. Usually the data of each experiment are inverted separately to generate an ensemble of earth models. However, since the inversion process of each geophysical modality is typically carried out independently, most inversion algorithms do not utilize the information obtained through other modalities. In this research we propose to jointly invert the data obtained by two physical experiments since the information contained in each model can be used to correct the other model. In many of the cases the two models share the important structures, therefore, edges occur in the same locations. In order to exploit this information, we propose using a level set formulation of the problems. Assuming that both models take two known discrete values, we can then use a single level set function for both models together. This can be later extended to multi-level set functions and with unknown values. By using this formulation we are able to improve inversion results of both problems.