Computation of analytical sensitivity matrix for the frequency-domain EM data: MATLAB code

Among many applications of the sensitivity matrix is its use for performing nonlinear least-squares inversion of geophysical data. The mainstream finite difference approach is approximate. Some previous works have discussed the accurate analytical computation approach for the sensitivity matrix of the 1D geophysical problems but the codes are not publicly accessible. Using the basic differentiation rules (product and quotient) and the logarithmic differentiation the MATLAB code for analytical computation of the 1D recursive transverse electric frequency-domain electromagnetic forward response is presented. Because only a single call to the sensitivity matrix subroutine is needed for analytical computation the computation time is a linear function of the number of parameters. However, the computation time for the sensitivity matrix computation via the approximate method is a quadratic function of the model parameters. Experimentation results show that the analytical method increasingly gain speed over its counterpart approximate method (for instance, the analytical route is a million times faster than approximate method when the number of parameters is a million) with no loss of accuracy.