The diagonalator: inverse data space full waveform inversion

Abstract

SUMMARY Full waveform inversion with the classic least-squares cost functional suffers from spurious local minima caused by cycle skipping in the absence of low frequencies in the seismic data. We present an alternative cost functional that is less sensitive to cycle skipping. It has the property of an annihilator, just like the functional used for velocity analysis with extended images based on subsurface shifts. For 2-D models with a line acquisition, the proposed functional applies a singular-value decomposition on the observed data and uses the eigenvectors to build a data panel that should be diagonal in the correct velocity model but has significant off-diagonal entries in the wrong model. By penalizing off-diagonal entries or maximizing values close to the main diagonal, the correct model should be found. We therefore call it the diagonalator. A convexity test demonstrates the superiority of the proposed functional over the classic least-squares approach. We present initial synthetic data tests on a subset of a North Sea velocity model. The diagonalator performs better than leastsquares data fitting in terms of resolving deeper events with full-bandwidth data. It also converges to an acceptable velocity model in the absence of low frequencies, when least-squares minimization fails.