Simultaneous full‐waveform inversion for source wavelet and earth model

Abstract

The theory of full‐waveform inversion developed by Tarantola (1988) included inversion for the source wavelet. Source‐wavelet inversion has been performed in the time domain by Zhou et al. (1997) and in the frequency domain by Pratt (1999). Minkoff and Symes (1997) performed simultaneous inversion for reflectivity and source based on primary reflections in a layered earth. Since we believe a synthetic study of the stability and accuracy of source inversion to be important to both seismic acquisition and inversion communities, we performed a simultaneous full‐waveform inversion for the source wavelet and model parameters (P‐wave velocity in this test). Our approach is distinguished from the previous research by taking into account all of the observed data including multiples and by its easy extension to a higher‐dimensional earth model. Our synthetic test shows very robust and accurate convergence of source‐wavelet inversion even with an inaccurate starting earth model. A good initial guess for the wavelet is not necessary for our inversion to work. In fact, we used an initial guess of zero for all of the results presented here. Due to inaccuracies in the earth model estimate, some artifacts could appear in the source inversion and would cause slower convergence. Our solution to this problem is to optimize the source wavelet with constraints on its spectrum and time duration.