Building accurate initial models using gain functions for waveform inversion in the Laplace domain

We suggest an initial model building technique using time gain functions in the Laplace domain. Applying the gain expressed as a power of time is equivalent to taking the partial derivative of the Laplace-domain wavefield with respect to a damping constant. We construct an objective function, which minimizes the logarithmic differences between the gained field data and the partial derivative of the modeled data with respect to the damping constant. We calculate the modeled wavefield, the partial derivative wavefield, and the gradient direction in the Laplace domain using the analytic Green's function starting from a constant velocity model. This is an efficient method to generate an accurate initial model for a following Laplace-domain inversion. Numerical examples using two marine field datasets confirm that a starting model updated once from a scratch using the gradient direction calculated with the proposed method can be successfully used for a subsequent Laplace-domain inversion.