Full waveform inversion is a powerful technique for refining the velocity model used for migration after the best possible tomographic resolution is achieved. Because of its computational cost and nonlinearity, FWI has been the subject of many computational ideas.
Classical full waveform inversion (FWI) is usually implemented in the time or the frequency domain. The frequency-domain version (FD) has a formulation simple to understand in terms of matrices. One of its advantages is that it permits the use of a multigrid approach for bootstrapping from low to high frequencies. Its limitation, however, is that it becomes very expensive to calculate in 3 dimensions because a large system of equations must be solved at each frequency. On the other hand, the time-domain (TD) approach has better scalability for 3D seismic surveys. In the time domain, rather than solving one frequency at a time for many shots in one parallelized system of equations as in the FD, all frequencies are solved simultaneously for each shot, but with many shots simultaneously solved using coarse-grained parallelization. In addition, fine-grained parallelism with Graphics Processing Units (GPUs) can be used on each processing node to accelerate finite difference calculations. On the negative side, bootstrapping from low to high frequencies in TD requires one to use additional steps to achieve a waveform matching between data and the finite difference predictions. This is particularly important to achieve super-resolution FWI, which is to push the frequency content for FWI to what usually has been achieved through Least-Squares Migration.
The comments above refer to classical FWI. These days, however, we will hear about out-of-thebox computational directions. One that is gathering momentum really fast is the use of Recursive Neural Networks (RNN). This approach is significantly more expensive than traditional techniques but it presents interesting possibilities to experiment with, using different cost functions and constraints. Finally, a possible next step for FWI computations is the use of quantum computers (QC) to accelerate modelling. Although QC resources available today are not yet capable to perform these calculations, it is time to start thinking on how to implement Finite Difference modelling for wavefields using QC logic.
In this talk, we will discuss mostly the classical computation approaches in the time domain, some of the steps required for the multigrid implementation, and then venture briefly into the Machine Learning and Quantum Computing directions.
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