2D Modelling with Linearized Integral Equations

Abstract

A reduced COPROD2 data set with response estimates at twenty sites for four periods (85 s to 683 s) is interpreted, using an iterative modelling scheme on the basis of linearized integral equations. Input data are the anomalous fields, here Eax and Baz for E-polarisation, which are derived from the supplied impedances Zxy and the magnetic transfer functions Tzy. Prior to 2D modelling a normal 1D reference model is introduced (here a 3-layer model) and an anomalous domain defined (here from zero to 40 km depth and 200 km in width). It is subdivided into M subdomains of constant anomalous conductivity. The linearisation of the nonlinear data functional is performed by approximating the internal field Ex within the anomalous domain. An iterative process is started with the normal field Enx of the 1D reference model as internal field, gradually improving this first approximation. The evolving linear problem is solved by the least-squares method, adapting the data kernel with each iteration step better to the model which arises from the application of this kernel to the data. No Frechet derivatives of the data functional are involved and no starting model is required. A first set of models is derived from MT data alone, a second set from combined MT/GDS data, increasing the number of subdomains from M = 1 to M = 64. It is found that with M = 8 (i.e. with 20 × 50 km2 subdomains) the resolution power of the data is exhausted. The resulting models have an almost uniform top layer and a deep-seated central region of reduced resistivity of 10 Ωm at 20 to 40 km depth. Further modelling studies show that a deep origin of the observed anomalies is indeed more likely than a shallow origin and that the modelling results do not depend significantly on the used periods. The mean residual (if only MT data are used) is greater than the data error and the individual residuals are not randomly distributed; both indicate that the data have not been exploited to their fullest possible extent. Forward modelling shows that the models are not in good agreement with B-polarisation impedances. © 1993, Society of Geomagnetism and Earth, Planetary and Space Sciences. All rights reserved.