A hybrid finite-difference and integral-equation method for modeling and inversion of marine controlled-source electromagnetic data

Abstract

One of the major problems in the modeling and inversion of marine controlled-source electromagnetic (CSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward-modeling algorithms should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter/receiver positions. To this end, we have developed a novel 3D modeling and inversion approach, which combines the advantages of the finitedifference (FD) and integral-equation (IE) methods. In the framework of this approach, we have solved Maxwell's equations for anomalous electric fields using the FD approximation on a staggered grid. Once the unknown electric fields in the computation domain of the FD method are computed, the electric and magnetic fields at the receivers are calculated using the IE method with the corresponding Green's tensor for the background conductivity model. This approach makes it possible to compute the fields at the receivers accurately without the need of very fine FD discretization in the vicinity of the receivers and sources and without the need for numerical differentiation and interpolation. We have also developed an algorithm for 3D inversion based on the hybrid FD-IE method. In the case of the marine CSEM problem with multiple transmitters and receivers, the forward modeling and the Fréchet derivative calculations are very time consuming and require using large memory to store the intermediate results.To overcome those problems, we have applied the moving sensitivity domain approach to our inversion. A case study for the 3D inversion of towed streamer EM data collected by PGS over the Troll field in the North Sea demonstrated the effectiveness of the developed hybrid method.

Inversion for 3D Conductivity and Chargeability Models Using EM Data Acquired by the New Airborne TargetEM System in Ontario, Canada

“…The 3D modeling and sensitivity calculations are based on the hybrid finite difference (FD) and integral equation (IE) method [29,30]. This technique employs an anomalous field formulation where the total field is split into background and anomalous fields,…”

Deep learning electromagnetic inversion with convolutional neural networks

“…In the presented scheme, forward modelling is employed only for the generation of synthetic data used in NN training. For the spatial discretization of Equation (3), I use the 3-D finite-difference method based on staggered grids that is still commonly applied in geophysical problems (e.g., Kelbert et al, 2014;Jaysaval et al, 2014;Commer et al, 2015;Yoon et al, 2016). The details of the forward modelling algorithm are given in Appendix A.…”

Three-Dimensional Transient Electromagnetic Numerical Simulation Using FDFD Based on Octree Grids

“…For a loop source, we only need to assign values to the source vectors of J x and J y , as J z is always a zero vector. According to equation 5, we substitute equations (6) to (8) into equations (9) to (11); then, we can obtain equations (12) to (14), as shown at the bottom of the next page. According to Ax = b, the components in equations (12) to 14can be expressed as equations (15) to (17), as shown at the bottom of the next page.…”

“…Then, he analyzed the influence of grid spacing on the calculation error and deduced the corresponding error expression. Yoon [14] combined FDFD with the integral equation method for numerical simulation of marine controllable sources. First, the electric field component is calculated by the FDFD method, and then the magnetic field at the receiver is calculated accurately by the integral equation method to reduce the computational complexity.…”