The prerequisites for successful XWITM convergence are:
- apriori starting velocity
- bandpass filtered shot gathers
- accurate source wavelet estimate
The apriori velocity model should have a water profile and water bottom contrast inserted into it so it can accurately predict the direct arrival and water bottom events.
Using a filtered spike source propagated through the velocity model these events are modelled and the simulated traces are compared to the equivalently filtered field traces. A matching filter operation between the two sets of traces is performed and the derived filter is convolved with the filtered spike to obtain a reliable estimate of the field low-frequency source. The chart above illustrates the Jansz field application.
At this point, the velocity optimisation feedback loop can commence. For the longest length-scale initial updates the lowest usable frequency in the data is sought, which for streamer acquisition is usually no lower than 4Hz.
The steepest-descent "gradient", which is the model update direction for locally minimising the cost function, can be computed for both AWITM and FWI cost functions so it can be demonstrated that the AWITM gradient gives the correctly directed update for distant initial models needing macromodel updates.
The velocity model computation is run cycling through the shots in blocks of iterations at sequentially increasing frequencies incorporating progressively shorter length-scale resolution into the model. On a propagation mesh of 25m, the frequency range can be increased up to a limit 24Hz based on the required minimum number of grid points per wavelength stability condition.
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