Efficient calculation of the steepest descent direction for source-independent seismic waveform inversion: An amplitude approach

In seismic waveform inversion, if we have no information on source signature, we need to invert seismic data and source signature either simultaneously or successively. In order to avoid the iterative update of the source signature in waveform inversion based on classical, local optimization techniques, we propose two source-independent objective functions using amplitude spectra of Fourier-transformed wavefields. One is constructed by normalizing the amplitude spectra of observed data and modeled data with respect to the respective reference amplitudes. The other is achieved by cross-multiplying the amplitude spectra of observed data and modeled data with the respective reference amplitudes. In the computation of the steepest descent direction, we circumvent explicitly computing the Jacobian by employing a matrix formalism of the wave equation in the frequency domain. Through numerical examples for the Marmousi model, we demonstrate that our inversion algorithms can reproduce the subsurface velocity structure without estimating source signature.