Error propagation and model update analysis in three-dimensional CSEM inversion

Abstract

This study examines error propagation from data space to model space during three-dimensional inversion of controlled-source electromagnetic data using a Gauss-Newton based algorithm. An expression for model parameter correction is obtained using higher-order generalised singular value decomposition for various regularisation strategies. Inverse modelling is performed for different types of noise employing distinct regularisation schemes to investigate the impact of error. Data corrupted with random noise suggests that the random noise mainly propagates when regularisation parameters are small, owing to the high-frequency nature of random noise. Furthermore, the random noise predominantly causes artefacts in the shallower part of the inverted model. However, it has little impact on the estimation of major anomalies because the anomaly primarily depends on the smoothly varying parts of data. These observations are valid for both isotropic and anisotropic inversions. Resistive geological anomalies, like vertical dyke or vertical fractures, may pose a significant challenge for isotropic inversion in terms of convergence and data fit, even if the subsurface is isotropic. On the other hand, anisotropic inversion performs remarkably well in such cases, showing faster convergence and better data fit than isotropic inversion. Anisotropic inversion is indispensable in the case of an anisotropic host medium, as isotropic inversion produces significant artefacts and poorer data fit. Numerical experiments suggest that, in general, anisotropic inversion produces relatively better data fit and faster convergence, even in the case of isotropic subsurface. However, due to the varying degree of sensitivity of CSEM data on thin resistive bodies, caution is required in interpreting an anisotropy obtained using anisotropic inversion. An investigation of field data also supports the observations obtained using synthetic experiments.