Rapid 3-D Magnetotelluric Inversion

By Gabor Hursán and Michael Zhdanov

Introduction

3-D electromagnetic inversion remains a challenging computational problem. Geophysical inverse problems are well known to be ill-posed (ambigous and unstable). Moreover, three-dimensional inversion, which normally involves thousands of data and unknown model parameters, is extremely resource consuming. In this project, we develop a rapid integral-based inversion scheme capable of handling massive data sets and large models.

Key elements of rapid 3-D inversion

Quasi-analytical approximation as a forward operator (Hursan and Zhdanov, 2001) in the initial stage of inversion and contraction integral equation based forward modeling at the final stage of inversion (Hursan and Zhdanov, 2002)

Simple Frechet matrix for anomalous field and magnetotelluric data (Zhdanov and Hursan, 2000; Hursan and Zhdanov, 2001)

Fast sensitivity matrix manipulations exploiting convolution properties of the Green's operator (Hursan, 2001)

Tikhonov regularization with an option of smooth and focusing stabilizers (Zhdanov, 2002)

Reweighted regularized conjugate gradient  method (Zhdanov and Hursan, 2001; Zhdanov, 2002)

Synthetic data inversion

In this synthetic model study we inverted an array magnetotelluric (MT) data set simulated above a tilted dyke structure. The sketch of the model with the redeiver locations and the discretization of the inverted area are shown in the Figure below.

Figure 1.

The inversion reveals well the basic structure of the anomalous body. The top of the anomaly, which is closer to the receivers, is resolved better than the bottom structure.

Figure 2. 3-D view of the true and inverted models.

Inversion of the Minamikayabe area data

The New Energy and Industrial Technology Development Organization (NEDO) has been conducted an area magnetotelluric survey in the Minamikayabe area, which is important due to its geothermal potential (Takasugi et al., 1992). The area is characterized by a resistive magmatic intrusion surrounded by fractured host rocks with relatively hich conductivity. 

The locations of the receivers with the discretization of the inverted area are shown below. The number of cells in the inverted area is 26 x 26 x 11 = 7436 cells.

Figure 3.

The results of the inversion show the location of the resistive inhomogeneity. The smooth and focusing stabilizers result in slightly different models, however, the main features are similar.

Figure 4. 3-D view of the inverted models obtained by the inversion of the Minamikayabe area data.

Inversion of the MT data collected for mineral exploration in Canada

INCO Exploration has conducted a 3-D magnetotelluric survey in Canada, where massive sulfide deposits associated with troctolite intrusions have been discovered. Data collected at 256 MT stations along six profiles were used for the inversion. The inverted area is subdivided into 56 x 50 x 12 = 33600 rectangular cells.

Figure 5.The location of MT profiles with the discretization of the inverted area for the inversion.

he main purpose of this inversion is to locate conductive zones, so the images below show the areas with conductivities higher than specific values.

Figure 6-7.Results of 3-D inversion of the Canadian MT data.

CPU time requirements of different inversions

Perhaps the most important advantage of this inversion scheme is its speed. Using a Sun Ultra Sparc 10 workstation with 256 Mbyte of memory we can perform massive inversions involving thousands of data and ten thousands of unknown model parameters within 15 minutes. This opens the possiblity of widespread use of the ideas behind this method.

References

Hursan, G., 2001, Storage reduction and fast matrix multiplication for integral-based geophysical problems: Proceedings of 2001 CEMI Annual Meeting.

Hursan, G., and M. S. Zhdanov, 2001, Rapid 3-D magnetotelluric inversion: Proceedings of 2001 CEMI Annual Meeting.

Hursan, G. and M. S. Zhdanov, 2002, Contraction integral equation method in 3-D electromagnetic modeling: Radio Science, 37, No. 6, 1089.

Takasugi S., Keisaku T., Noriaki K., and Shigeki, M., 1992, High spatial resolution of the resistivity structure revealed by a dense network MT measurement - a case study in the Minamikayabe area, Hokkaido, Japan: J. Geomag. Geoelectr., 44, 289-308.

Zhdanov, M. S., Fang, S., and G. Hursan, 2000, Electromagnetic inversion using quasi-linear approximation: Geophysics, 65, 1501-1513.

Zhdanov, M. S., and Hursan, G., 2000, 3-D electromagnetic inversion based on quasi-analytical approximation: Inverse Problems, 16, 1297-1322.

Zhdanov, M.S. 2002, Geophysical inverse theory and regularization problems: Elsevier, Amsterdam - New York - Tokyo, 628 pp.