Perspectives on full-waveform inversion

Gary F. Margrave and Matthew Yedlin and Kristopher A. H. Innanen


We examine and compare the standard seismic inversion methodology, denoted SM, and full-waveform inversion, denoted FWI. We find many parallels but also interesting differences. Both methods produce a detailed impedance model (or impedance image) as the end product but differ in how this is created. SM first produces a reflectivity image (i.e. a migrated section) that is then converted to impedance, in a step called impedance inversion, by incorporating low-frequency information from an external source, typically well control. In a preparatory step, the reflectivity image is calibrated by comparing it to synthetic seismograms at well locations. We call this well validation and it serves to estimate the seismic wavelet whose removal matches the seismic reflectivity image to the well reflectivity. Alternatively, FWI creates an impedance image as the result of an iteration which gradually adds detail into an initial impedance model. The impedance update at each iteration comes from a type of migration of the data difference, which is the difference between the recorded data and synthetic data predicted by the impedance model as it exists at the iteration’s beginning. This migrated data difference is derived from theory as the gradient of the data misfit function, or sum-of-squares of the data difference. Essentially the impedance model is calibrated by comparing synthetic data to recorded data, and we call this data validation.

Both methods require low frequency information but FWI requires this in the data while SM incorporates wells. Both methods require knowledge of the source waveform, but SM achieves this by deconvolution and tying to wells which FWI commonly estimates this in the iteration. SM validates the model at wells and never attempts to predict synthetic data. FWI validates the model through data prediction and comparison to the raw data but does not incorporate well control. SM produces a migrated reflectivity image while FWI uses migration to estimate the gradient of the misfit function. However, we show that this gradient is actually a rather poor migration which lacks gain correction.

FWI is the method of the future but we suggest that a viable step forward is iterative modelling, migration, and inversion or IMMI. Such an approach can incorporate any migration method and can use both well validation and data validation.

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