  Marine controlled-source electromagnetic (CSEM) method has proved its
potential in detecting highly resistive hydrocarbon bearing formations. A novel
frequency domain CSEM inversion approach using fictitious wave domain time
stepping modelling is presented. Using Lagrangian-based adjoint state method,
the inversion gradient with respect to resistivity can be computed by the
product between the forward and adjoint fields. Simulation of the adjoint field
using the same modelling engine is challenging as it requires time domain
adjoint source time functions while only a few discrete frequencies of the data
residual are available for the inversion. A regularized linear inverse problem
is formulated in order to estimate a long time series from very few frequency
samples. It can then be solved using linear optimization technique, yielding a
matrix-free implementation. Instead of computing adjoint source time function
one by one at each receiver location, a basis function implementation has been
developed such that the inverse problem can be solved only once and 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, making efficient 3D CSEM inversion feasible. Numerical
examples are employed to demonstrate the application of our method.
