Accelerated 2D FWI using the symmetry on inner product spaces

Full Waveform Inversion (FWI) is a common technique used in the oil and gas industry due to its capabilities to estimate subsurface characteristics such as material’s density and sound velocity with high resolution. The 2D time domain FWI method involves the modeling of the forward wavefield of the source and the backpropagated field of the difference between the modeled and observed data. Therefore, due to its high computational cost in terms of RAM consumption and execution time, the High Performance Computing (HPC) field is very useful to deal with these problems. There are computational state-of-the-art solutions that allow to increase the execution time such as the parallel programming paradigm that involves the use of multicore processor systems. Furthermore, there are mathematical solutions leveraging on the properties of the algorithm used that make it possible to enhance performance of the method. We propose in this paper a new way to compute the FWI gradient, by taking advantage of an inner product property. Additionally, a computational strategy is combined with this proposal in the inversion scheme, thus improving FWI performance.