Embodiments of the present disclosure describe methods for efficient wavefield solutions, the methods including defining a wave equation as a linear portion and as a nonlinear portion; and solving the wave equation via an iterative process, the iterative process including, at each iteration, performing LU decomposition before solving the nonlinear portion, or obtaining best finite difference coefficients by solving an optimization equation.

A method and apparatus for identifying features of a subsurface region, including: obtaining an initial physical property model and survey data for the subsurface region; identifying a current model to be the initial physical property model; and executing one or more iterations of: generating synthetic data and forward wavefields with the current model and the survey data by forward modeling with forward wave equations representing isotropic wave-mode-independent attenuation; generating adjoint wavefields with the synthetic data and the survey data by adjoint modeling with adjoint wave equations representing isotropic wave-mode-independent attenuation; computing an objective function gradient with the forward wavefields and the adjoint wavefields by solving gradient equations with the corresponding wave equations representing isotropic wave-mode-independent attenuation; computing a search direction of the objective function; searching for a possible improved model along the search direction; and updating the current model to be the possible improved model.

The present disclosure describes methods and systems, including computer-implemented methods, computer program products, and computer systems, for generating a velocity model and a density model for a subsurface region of a hydrocarbon reservoir. One method includes: receiving, by a data processing apparatus, a set of seismic data of the hydrocarbon reservoir; setting, by the data processing apparatus, an initial velocity model and an initial density model; generating, by the data processing apparatus, wavefields of the hydrocarbon reservoir based on the set of seismic data; selecting, by the data processing apparatus, a spatial direction; generating, by the data processing apparatus, a velocity gradient and a reflectivity gradient of the selected spatial direction based on the wavefields; and updating, by the data processing apparatus, the velocity model and the density model using the velocity gradient and the reflectivity gradient of the selected spatial direction.

A method includes receiving seismic data for a geologic region of the Earth; building a velocity model of the geologic region of the Earth; selecting at least one mode of multiple and corresponding travel time data from a data storage where the travel time data correspond to at least one complex ray signature in the geologic region of the Earth and are based at least in part on the velocity model; performing migration on the seismic data using at least the selected travel time data to generate processed seismic data; and rendering an image of the geologic region of the Earth to a display where the image includes at least a multiple image.

A method may include obtaining seismic data regarding a geological region of interest. The method may further include obtaining a property model regarding the geological region of interest. The method may further include determining an adjoint migration operator based on the property model. The method may further include updating the property model using the seismic data and a conjugate gradient solver in a least-squares reverse time migration to produce a first updated property model. The conjugate gradient solver is based on the adjoint migration operator. The method may further include updating the first updated property model using a threshold shrinkage function to produce a second updated property model. The threshold shrinkage function comprises a sign function and a maximum function that are applied to the first updated property model. The method may further include generating a seismic image of the geological region of interest using the second updated property model.

A method is described for seismic imaging including generating extended image gathers by extended reverse time migration of a seismic dataset using an earth model; processing the extended image gathers to generate processed image gathers; performing extended modeling based on the processed image gathers to generate a modeled seismic dataset; enhancing the processed image gathers to generate an enhanced image; performing extended modeling based on the enhanced image gathers to generate a modeled enhanced dataset; differencing the modeled enhanced dataset and the modeled seismic dataset to determine a data residual; inverting the data residual to generate a model residual; updating the earth model based on the model residual to create an updated earth model; performing seismic imaging of the seismic dataset using the updated earth model to create an improved seismic image. The method may be executed by a computer system.

A system for seismic imaging of a subterranean geological formation uses a two-way imaging condition. A seismic signal is emitted into a subterranean formation and recorded at receiver(s). Source and receiver wavefields are decomposed into respective right-down/left-up and left-down/right-up propagating waves. The right-down/left-up and left-down/right-up direction can be defined along the direction emitted from the source or receiver to corresponding direction in two dimensional (2D) case. An imaging condition for generating both a positive-dip structure image and a negative-dip structure image is the inner product of the wavefields. Applying the sample-by-sample multiplication imaging condition to the opposite dip images, the diffraction energy is retained while the reflection energy is significantly attenuated. The diffraction image can be used to detect faults and fractures in subsurface regions.

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. The velocity and reflectivity models reveal the structure and lithology of features of the subterranean formation and may reveal the presence of oil and natural gas reservoirs.

Methods and apparatuses for processing seismic data acquired with multicomponent sensors build an accurate S-wave velocity model of a surveyed underground formation using a full waveform inversion (FWI) approach. PS synthetic data is generated using approximative acoustic equations in anisotropic media with a P-wave model, a current S-wave velocity model and a reflectivity model as inputs. The current S-wave velocity model is updated using FWI to minimize an amplitude-discrepancy-mitigating cost function that alleviates the amplitude mismatch between the PS observed data and the PS synthetic data due to the use of the approximative acoustic equations.

Methods for inversion of seismic data to infer subsurface physical property parameters, comprising constructing an inhomogeneous anisotropy model and/or inhomogeneous V.sub.S/V.sub.P or V.sub.P/V.sub.S model; and inverting the seismic data in a sequential or simultaneous approach to obtain at least one subsurface physical property parameter using an elastic inversion algorithm and the inhomogeneous anisotropy model and/or inhomogeneous V.sub.S/V.sub.P or V.sub.P/V.sub.S model. Constructing an inhomogeneous anisotropy model may comprise deriving geobodies from at least one of seismic facies analysis, regional geologic information, or seismically derived earth models; and adjusting at least one of ε, δ, γ, or parameters of the elastic stiffness tensor matrix in a homogeneous anisotropy model in areas corresponding to the geobodies. Constructing an inhomogeneous V.sub.S/V.sub.P or V.sub.P/V.sub.S model may comprise deriving geobodies and adjusting values in a homogeneous V.sub.S/V.sub.P or V.sub.P/V.sub.S model in areas corresponding to the geobodies.