3D fictitious wave domain CSEM inversion by adjoint source estimation

Abstract

Marine controlled-source electromagnetic (CSEM) method has proved its potential in detecting highly resistive hydrocarbon bearing formations. To image the subsurface resistivity, this paper presents the first application of a frequency domain CSEM inversion approach using fictitious wave domain timestepping modelling. Each inversion iteration requires the gradient of the misfit with respect to resistivity computed by the product between the forward and adjoint fields. Simulation of the adjoint field using fictitious time modelling is challenging as it requires the time domain adjoint source functions while only a few discrete frequencies of the data residual are available for the inversion. To overcome this issue, we formulate a regularized linear inverse problem to estimate a long time series from very few frequency samples. It can then be solved using linear optimization technique in matrix-free manner. Instead of computing adjoint source time function one by one at each receiver location, a basis function implementation has been designed, such that the linear inversion can be solved only once and then reused every time to construct all time-domain adjoint sources. The method allows computing all frequencies of the EM fields in one go without heavy memory and computational overhead. Numerical examples are employed to demonstrate the application of our method.