Frequency domain adaptive waveform inversion
Matthew Eaid, Scott Keating, Kristopher A. Innanen
Full waveform inversion (FWI) attempts to find a high-resolution model of subsur- face parameters, carrying a high likelihood of having produced the observed seismic data. While classic FWI is generally quite successful, the high degree of nonlinearity involved in seismic inverse problems, coupled with the oscillatory nature of seismic data can invoke a phenomenon known as cycle skipping, leading to locally minimized objective functions. Generally, when cycle skipping occurs the updated model is a worse representation of the true subsurface than the starting model was.
Extended waveform inversion is a relatively new idea that is an umbrella for a suite of inversion techniques that extend the model space, usually by some nonphysical parameter, and then drive that parameter to an ideal quantity, matching the predicted to the observed data. They combat the cycle skipping problem by adding a degree of freedom to the model space and forming objective functions that do not rely on sample-by-sample differences. The flavour of extended waveform inversion we present is known as adaptive waveform inversion (AWI) which extends the model space in convolutional Wiener filter coefficients and attempts to drive them towards a zero-lag delta spike. Originally derived in the time domain, we present a frequency domain alternative and discuss special considerations for frequency domain implementation. We then show one example where AWI is more robust then FWI and discuss the challenges going forward.