Naser Meqbel

ModEM: A modular system for inversion of electromagnetic geophysical data

Abstract We describe implementation of a modular system of computer codes for inversion of electromagnetic geophysical data, referred to as ModEM. The system is constructed with a fine level of modular granularity, with basic components of the inversion – forward modeling, sensitivity computations, inversion search algorithms, model parametrization and regularization, data functionals – interchangeable, reusable and readily extensible. Modular sensitivity computations and generic interfaces to parallelized inversion algorithms provide a ready framework for rapid implementation of new applications or inversion algorithms. We illustrate the code׳s versatility and capabilities for code reuse through implementation of 3D magnetotelluric (MT) and controlled-source EM (CSEM) inversions, using essentially the same components.

Joint 3D inversion of multiple electromagnetic datasets

Electromagnetic methods are routinely applied to image the subsurface from shallow to regional structures. Individual electromagnetic methods differ in their sensitivities towards resistive and conductive structures and in their exploration depths. If a good balance between different electromagnetic data can be be found, joint 3D inversion of multiple electromagnetic datasets can result in significantly better resolution of subsurface structures than the individual inversions.We present a weighting algorithm to combine magnetotelluric, controlled source electromagnetic, and geoelectric data. Magnetotelluric data are generally more sensitive to regional conductive structures, whereas controlled source electromagnetic and geoelectric data are better suited to recover more shallow and resistive structures. Our new scheme is based on weighting individual components of the total data gradient after each model update. Norms of individual data residuals are used to assess how much of the total data gradient must be assigned to each method to achieve a balanced contribution of all datasets for the joint inverse model. Synthetic inversion tests demonstrate advantages of joint inversion in general and also the influence of the weighting. In our tests, the controlled source electromagnetic data gradients are larger than those of the magnetotelluric and geoelectric datasets. Consequently, direct joint inversion of controlled source electromagnetic, magnetotelluric, and geoelectric data results in models that are mostly dominated by structures required by the controlled source electromagnetic data. Applying the new adaptive weighting scheme results in an inversion model that fits the data better and resembles more the original model. We used the modular system electromagnetic as a framework to implement the new joint inversion and briefly describe the new modules for forward modelling and their interfaces to the modular system electromagnetic package.

Three-Dimensional Multi-Scale and Multi-Method Inversion to Determine the Electrical Conductivity Distribution of the Subsurface (Multi-EM)

Combining different electromagnetic (EM) methods in joint inversion approaches can enhance the overall resolution power. Every method is associated with a particular sensitivity pattern. By assembling complementary patterns, subsurface imaging becomes more complete and reliable. We describe different paths to obtain multi-EM inversions. First, a joint inversion approach using finite difference forward operators is outlined that formulates the problem of minimizing the objective function using different weights for each individual method. Then we address a sequential approach using finite element methods on unstructured grids to cycle through the different EM methods iteratively. Both methods are based on a traditional parametrization using piecewise constant model parameters which may be inefficient when describing the usually rather coarse models. Therefore, we investigate wavelet-based model representations as an alternative.

Non-linear Smoothness-constrained Model Error and Resolution Estimates

A comparison of error and resolution properties of 2-D models of electrical resistivity from single and joint inversions of direct-current resistivity (DCR) and radiomagnetotelluric (RMT) data is presented. Linearized model resolution and error estimates are computed from the Jacobian and its smoothness-constrained generalized inverse. As a novelty, linearized model errors are compared to most-squares error estimates to better account for non-linearity. For a synthetic example, linearized analyses yield model errors up to 30 to 40 per cent for data errors of two per cent and resolving kernels spread over several cells in the vicinity of the investigated cell. Most importantly, linearized errors are in good agreement with most-squares errors and, hence, linearized model errors can be representative. DCR data can constrain both resistive and conductive structures whereas RMT data provide superior constraints for conductive structures. For structures within the depth ranges of exploration of both methods, error and resolution of joint inverse models are equal to or better than those of single inversions. For structures outside the depth range of exploration of one method, error and resolution of joint inverse models are close to those of the best single inversion given appropriate data weighting.