Deconvolution-Based Objective Functions for Full Waveform Inversion in the Laplace Domain

Objective functions are critical for successful seismic fullwaveform inversions (FWIs). Deconvolution-based objective functions yielded promising results in time- and frequency-domain inversions. In this study, we developed two deconvolution-based objective functions for Laplace-domain inversions. These objective functions are based on convolutional filters that transform one of the observed or modeled data into another. The objective functions are derived by forcing the convolutional filter to be a zero-lag delta function by updating the model parameters. We could obtain a relatively simple objective function in the Laplace domain since the convolution in the time domain is equivalent to the multiplication function in the Laplace domain and the Laplace transform of the delta function is unity. We compared the new deconvolution-based objective functions and the conventional logarithmic objective function using synthetic and Gulf of Mexico field data and obtained similar inversion results. We showed that the logarithmic objective function conventionally used in Laplace-domain FWIs can be understood in the framework of deconvolution-based objective functions, which explains the similar inversion results.