The Diagonalator, an Alternative Cost Functional for Wave-equation Inversion

The classic least-squares cost functional for full waveform inversion suffers from local minima due to loop skipping in the absence of low frequencies in the seismic data. Velocity model building based on subsurface spatial or temporal shifts may break down in the presence of multiples in the data. Cost functionals that translate this idea to the data domain, with offset- or time-shifts, can handle multiples. An earlier data-domain formulation suffered from cross-talk between events. Here, we present a multishot extension that should be less sensitive to cross-talk. It has the property of an annihilator, similar to the functional used for velocity analysis with extended images based on subsurface shifs. However, since it operates in the data domain, it should be able to handle multiples. For 2-D models with line acquistion, the proposed functional applies a singular-value decomposition on the observed data and uses the eigenvectors to build data panel that should be diagonal in the correct velocity model, but has significant off-diagonal entries in the wrong model. By minimizing these offdiagonal entries or maximizing the main diagonal, the correct model should be found. We therefore named it the diagonalator. We present initial tests on a simple, horizontally layered velocity model.