Abstract: Methods and systems described herein are directed to determining properties of a subterranean formation using an acoustic wave-equation with a novel formulation in terms of a velocity model and a reflectivity model of the subterranean formation. The acoustic wave equation may be used with full-waveform inversion to simultaneously build velocity and reflectivity models of a subterranean formation. The velocity and reflectivity models may be employed for quantitative interpretation. The velocity and reflectivity models may be employed to determine impedance and density of the subterranean formation for prospectivity assessment. The acoustic wave equation may be also used with least-squares reverse time migration in the image or data domains, to build a reflectivity model of the subterranean formation with enhanced resolution and amplitude fidelity.

Abstract: Methods and systems described herein are directed to determining properties of a subterranean formation using an acoustic wave-equation with a novel formulation in terms of a velocity model and a reflectivity model of the subterranean formation. The acoustic wave equation may be used with full-waveform inversion to build high-resolution velocity and reflectivity models of a subterranean formation. The acoustic wave equation may be also used with least-squares reverse time migration in the image and space domains, to build a reflectivity model of the subterranean formation with enhanced resolution and amplitude fidelity. The velocity and reflectivity models of materials that form the subterranean formation reveal the structure and lithology of features of the subterranean formation and may reveal the presence of oil and natural gas reservoirs.

Abstract: This disclosure describes processes and systems for generating a high-resolution velocity model of a subterranean formation from recorded seismic data gathers obtained in a marine seismic survey of the subterranean formation. A velocity model is computed by iterative FWI using reflections, resolving the velocity field of deep subterranean targets without requiring ultralong offsets. The processes and systems use of an impedance sensitivity kernel to characterize reflections in a modeled wavefield, and then use the reflections to compute a velocity sensitivity kernel that is used to produce low-wavenumber updates to the velocity model. The iterative process is applied in a cascade such that position of reflectors and background velocity are simultaneously updated. Once the low-wavenumber components of the velocity model are updated, the velocity model is used as an input of conventional FWI to introduce missing velocity components (i.e., high-wavenumber) to increase the resolution of the velocity model.

Abstract: Inversion with exponentially encoded seismic data can include exponentially encoding acquired seismic data and associated synthetic seismic data, storing the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data, determining a one-dimensional (1D) Wasserstein distance between the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data, and generating an adjoint source based on the 1D Wasserstein distance. The example method also includes adapting a dynamic weight implementation of a sensitivity kernel to the adjoint source to build a gradient associated with the acquired seismic data and the associated synthetic seismic data, and iteratively inverting a waveform associated with the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data based on the gradient. An image of a subsurface location can be generated based on results of the iterative inversions.

Abstract: Methods and systems described herein are directed to determining properties of a subterranean formation using an acoustic wave-equation with a novel formulation in terms of a velocity model and a reflectivity model of the subterranean formation. The acoustic wave equation may be used with full-waveform inversion to build high-resolution velocity and reflectivity models of a subterranean formation. The acoustic wave equation may be also used with least-squares reverse time migration in the image and space domains, to build a reflectivity model of the subterranean formation with enhanced resolution and amplitude fidelity. The velocity and reflectivity models of materials that form the subterranean formation reveal the structure and lithology of features of the subterranean formation and may reveal the presence of oil and natural gas reservoirs.

Abstract: Inversion with exponentially encoded seismic data can include exponentially encoding acquired seismic data and associated synthetic seismic data, storing the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data, determining a one-dimensional (1D) Wasserstein distance between the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data, and generating an adjoint source based on the 1D Wasserstein distance. The example method also includes adapting a dynamic weight implementation of a sensitivity kernel to the adjoint source to build a gradient associated with the acquired seismic data and the associated synthetic seismic data, and iteratively inverting a waveform associated with the exponentially encoded acquired seismic data and the exponentially encoded associated synthetic seismic data based on the gradient. An image of a subsurface location can be generated based on results of the iterative inversions.

Abstract: The present disclosure is related to a velocity model update with a full waveform inversion gradient. At least one method can include updating a velocity model of a subsurface, which can include suppressing high wavenumber components of the velocity model provided by reflected energy with a decomposed full waveform inversion gradient. Low wavenumber components can be preserved in the velocity model.

Abstract: In one embodiment, a reverse time migration module is configured with a visco-acoustic wave equation for media with heterogeneous attenuation solved using a pseudo-analytical method. Seismic data is obtained for a zone of interest, and a model is created for the zone of interest. The model has spatial variability in velocity and quality factor. Pseudo-analytic Q-compensating reverse time migration (PA-Q-RTM) is performed using the reverse time migration module and the model for the zone of interest to obtain PA-Q-RTM seismic data. In another embodiment, a system for processing seismic data includes a reverse time migration module configured with a visco-acoustic wave equation that is solved from the pseudo-analytical method. The system operates to obtain seismic data for a zone of interest and perform PA-Q-RTM using a model for the zone of interest to obtain PA-Q-RTM seismic data for the zone of interest. Other embodiments and features are also disclosed.

Abstract: The present disclosure is related to a velocity model update with a full waveform inversion gradient. At least one method can include updating a velocity model of a subsurface, which can include suppressing high wavenumber components of the velocity model provided by reflected energy with a decomposed full waveform inversion gradient. Low wavenumber components can be preserved in the velocity model.

Abstract: In one embodiment, a reverse time migration module is configured with a visco-acoustic wave equation for media with heterogeneous attenuation solved using a pseudo-analytical method. Seismic data is obtained for a zone of interest, and a model is created for the zone of interest. The model has spatial variability in velocity and quality factor. Pseudo-analytic Q-compensating reverse time migration (PA-Q-RTM) is performed using the reverse time migration module and the model for the zone of interest to obtain PA-Q-RTM seismic data. In another embodiment, a system for processing seismic data includes a reverse time migration module configured with a visco-acoustic wave equation that is solved from the pseudo-analytical method. The system operates to obtain seismic data for a zone of interest and perform PA-Q-RTM using a model for the zone of interest to obtain PA-Q-RTM seismic data for the zone of interest. Other embodiments and features are also disclosed.