Quantities of Interest for Surface based Resistivity Geophysical Measurements

Abstract

The objective of traditional goal-oriented strategies is to construct an optimal mesh that minimizes the problem size needed to achieve a user prescribed tolerance error for a given quantity of interest (QoI). Typical geophysical resistivity measurement acquisition systems can easily record electromagnetic (EM) fields. However, depending upon the application, EM fields are sometimes loosely related to the quantity that is to be inverted (conductivity or resistivity), and therefore they become inadequate for inversion. In the present work, we study the impact of the selection of the QoI in our inverse problem. We focus on two different acquisition systems: marine controlled source electromagnetic (CSEM), and magnetotellurics (MT). For both applications, numerical results illustrate the benefits of employing adequate QoI. Specifically, the use as QoI of the impedance matrix on MT measurements provides significant computational savings, since one can replace the existing absorbing boundary conditions (BCs) by a homogeneous Dirichlet BC to truncate the computational domain, something that is not possible when considering EM fields as QoI.

Dimensionally adaptive hp-finite element simulation and inversion of 2D magnetotelluric measurements

“…After that, in [21] we designed an automatically adapted Perfectly Matched Layer (PML) [22,23] suitable for scenarios where the material properties change abruptly, as the case of air-ground interface in MT. In a subsequent conference paper [24], we noticed that MT quantities of interest (QoI), namely impedances, exhibit a superior convergence behavior than that offered by the EM fields themselves. In [23], we developed a secondary field formulation where the primary field was given by an exact one dimensional (1D) solution [25] (rather than the traditional solution over a homogeneous space) in order to reduce the computational cost of solving a direct problem without reducing the accuracy.…”