Domain decomposition for high-frequency elastic full waveform inversion method and system

A computing system for imaging a formation of a subsurface, the computing system comprising:

• plural compute nodes, each compute node comprising,
• an interface configured to receive input data d related to the subsurface;
• and
• plural graphics processor units, GPUs connected to the interface, and configured to,
• discretizing a domain of the input data d along three different axes, selecting a first axis having a largest number of grid points, and splitting the domain along the selected first axis into plural subdomains corresponding to plural graphics processor units (GPUs);
• generate synthetic data u related to the subsurface, by applying an implicit finite-difference approach to a reflectivity model r, wherein applying the implicit finite-difference approach comprises:
• performing, in each GPU for a corresponding subdomain of the plural domains, first order partial derivatives along second and third axes without coordinating with other GPUs,
• performing first order partial derivatives along the first axis except for overlapping areas between adjacent subdomains, and, for the overlapping areas, exchanging data with the other GPUs prior to performing the first order partial derivatives along the first axis;
• update a velocity model V based on the input data d and the synthetic data u;
• and
• generate an image of the formation in the subsurface based on the updated velocity model, wherein the image is used to locate natural resources.

A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by one or more graphics processor units, implement a method for imaging a formation in a subsurface, the medium comprising instructions for:

• receiving input data d related to the subsurface;
• discretizing a domain of the input data d along three different axes, selecting a first axis having a largest number of grid points, and splitting the domain along the selected first axis into plural subdomains corresponding to plural graphics processor units (GPUs):
• generating synthetic data u related to the subsurface, by applying an implicit finite-difference approach to a reflectivity model r on the plural GPUs, wherein applying the implicit finite-difference approach comprises:
• performing, in each GPU for a corresponding subdomain of the plural domains, first order partial derivatives along second and third axes without coordinating with other GPUS,
• performing first order partial derivatives along the first axis except for overlapping areas between adjacent subdomains, and,
• for the overlapping areas, exchanging data with the other GPUs prior to performing the first order partial derivatives along the first axis;
• updating a velocity model V based on the input data d and the synthetic data u;
• and
• generating an image of the formation in the subsurface based on the updated velocity model, wherein the image is used to locate natural resources.