Joint MT and CSEM data inversion using a multiplicative cost function approach

Abstract

We have developed an inversion algorithm for jointly inverting controlled-source electromagnetic (CSEM) data and magnetotelluric (MT) data. It is well known that CSEM and MT data provide complementary information about the subsurface resistivity distribution; hence, it is useful to derive earth resistivity models that simultaneously and consistently fit both data sets. Because we are dealing with a large-scale computational problem, one usually uses an iterative technique in which a predefined cost function is optimized. One of the issues of this simultaneous joint inversion approach is how to assign the relative weights on the CSEM and MT data in constructing the cost function. We propose a multiplicative cost function instead of the traditional additive one. This function does not require an a priori choice of the relative weights between these two data sets. It will adaptively put CSEM and MT data on equal footing in the inversion process. The inversion is accomplished with a regularized Gauss-Newton minimization scheme where the model parameters are forced to lie within their upper and lower bounds by a nonlinear transformation procedure. We use a line search scheme to enforce a reduction of the cost function at each iteration. We tested our joint inversion approach on synthetic and field data.

Monitoring geothermal reservoir developments with the Controlled-Source Electro-Magnetic method — A calibration study on the Reykjanes geothermal field

“…MT, resistivity logs) may be necessary (Scholl et al (2010)). In an attempt to increase the resolution of the resistivity image at depths greater than 2/3km, we have looked into the possibility of jointly inverting CSEM and MT over the area of interest (Abubakar et al (2011)). Since our MT dataset is of poor quality, we used the legacy MT dataset collected over the Reykjanes geothermal field instead (Karlsdóttir and Vilhjálmsson (2016)).…”

Bayesian joint inversion of controlled source electromagnetic and magnetotelluric data to image freshwater aquifer offshore New Jersey

“…Jointly inverting EM data sets with standard inverse methodsusing gradients to find a minimizer of an objective function-often yields significant, qualitative improvements in the inverted model parameters (e.g. Abubakar et al 2011). Because these methods do not provide true, non-linear estimates of model parameter uncertainty, however, this qualitative improvement is difficult to quantify.…”

Joint 3D inversion of multiple electromagnetic datasets

“…The cross-gradient formulation of Meju (2004, 2007) is implemented as an additional constraint in the formulation of a non-linear least squares inversion problem and aims at identifying structural features common in electrical resistivity and seismic velocity models. For joint inversion of marine MT and CSEM datasets, Abubakar et al (2011) formulated the objective function of the inverse problem as a multiplicative term. Moorkamp et al (2011) adopted the cross-gradient approach to a 3D joint inversion framework for seismic, MT, and gravity data.…”

“…Moorkamp et al (2011) adopted the cross-gradient approach to a 3D joint inversion framework for seismic, MT, and gravity data. For joint inversion of marine MT and CSEM datasets, Abubakar et al (2011) formulated the objective function of the inverse problem as a multiplicative term. These authors argued that, in a Gauss-Newton inversion scheme, the multiplicative formulation of the objective function will automatically put CSEM and MT data on equal basis in the inversion process without the need for any additional weighting between the datasets.…”