Numerical Simulations


Numerical simulation of Earth EM responses using computers is of great importance in effective survey design and in the translation of observed data to reliable estimates of subsurface structure. Survey design and fundamental response understanding is achieved through the process of forward modeling, where the response at the receivers due to a user-specified resistivity structure is predicted numerically. Forward modeling techniques are complicated by the very non-linear relation between the response and the physical property (resistivity), and by the discontinuous nature of the electric field across resistivity contacts. Direct structural estimates from the data are accomplished through inversion, which typically must be iterative due also to the non-linear character of the physics. The diffusive nature of EM geophysics requires application of solution constraints, to avoid model artifacts not required by the data.

Inversion of geoelectrical profile data at EGI makes use of finite element forward modules developed at Utah over many years. The forward modules have been used in many publications where principle features of data sets have been reproduced in trial-and-error fitting. Current directions in two-dimensional (2-D) inversion emphasize automatic, iterative fitting of observations while constraining the solution to remain as close as possible to a-priori structural constraints (after Tarantola). For the 2-D problem, it is practical to generate parameter step estimates in the non-linear iterative procedure using the Gauss-Newton step.

Our main area of research is in definition of solution constraints and their implementation within the parameter covariance matrix of the non-linear step equation. Instead of using the popular but brute-force damping of solution slope or curvature, we instead exploit natural parameter correlations in diffusive EM such as conductivity-layer thickness to produce smooth, conservative solutions. Computer resource demands and solution conditioning are improved by allowing resistivity parameters (pixels) to grow both laterally and with depth in the Earth, in order to equalize their influence on the surface response through the concept of EM scaling.

An example image from our 2-D inversion approach applied to MT derives from a (confidential) data set in north-central Nevada acquired using a spread of ~60 contiguous bipoles of 100 m length each. The data frequency range spanned 10,000 Hz to 0.1 Hz and both apparent resistivity and impedance phase of the cross-strike (transverse magnetic) mode were inverted. The known geology includes an intrusive complex to the right, and hydrothermal alteration and remobilized graphite to the left, both apparently verified in the inversion image. Run time was approximately 4 hours on a 500 MHz Pentium-III. Data provided by Quantec Geoscience, Inc.
Numerical simulation of three-dimensional (3-D) structures has been advanced at EGI for many years. The two fundamental approaches taken are the integral equations (IE) and finite difference (FD) techniques. Integral equations is very efficient for generic model studies using simple structures. Structural discretization requirements can be relaxed in all three dimensions with distance from the model survey area, thereby greatly reducing computational needs and allowing simulation of moderate field data sets. Our derivation allows for a completely general layered earth host to the inhomogeneity, arbitrary electric sources at the surface, and three components of magnetic sources and receivers at the surface, in the air, or within boreholes. More recently, we have been developing capability for 3-D modeling of more complex structures using finite differences, in cooperation with Y. Sasaki of Kyushu University. The secondary electric field formulation is advantageous in that it is relatively immune to ill-conditioning and can incorporate the diverse source capability already represented by the integral equations platform. We have been working with Maxwell Technologies Systems Division to incorporate this algorithm in reservoir simulations considering temporal changes in resistivity with production.
 
Last Updated: 4/13/12