A method for partial differential equation inversion, the method including receiving measured data do; selecting an objective function having first and second measures N.sub.1 and N.sub.2, wherein the objective function depends on three independent variables V, u, and f, V being a perturbation of a wave equation operator L from a background operator L.sub.0, u being a wavefield that satisfies the wave equation operator L, and f being a source function that describes the source of the waves; optimizing with a processor the objective function by finding a minimum or a maximum using the inversion; calculating with the processor solutions V*, u*, and f* of the three independent variables V, u, and f; and generating with the processor an image of an object based on the solutions V*, u*, and f*.

A method of generating a four dimensional seismic signal based on multiple sets of seismic data representing a subterranean formation. The method can include generating a tomographic velocity model based on a first set of raw seismic data and determining at least one Green's function based on the tomographic velocity model. The method can include generating a first image of a target region based on the first set of raw seismic data and the at least one Green's function. The method can include generating a second image of the target region based on a second set of raw seismic data and the at least one Green's function. The first and the second images can be compared, and a four-dimensional seismic signal can be determined based on the comparison.

The invention relates to a computer-implemented method for generating an image of a subsurface of an area of interest from seismic data. The method comprises providing seismic wavefields, providing a zero-offset seismic wavefield dataset, determining a seismic velocity parameter model w(x) comprising an initial model w.sub.0(x), a low frequency perturbation term δm.sub.b(x) and a high frequency perturbation term δm.sub.r(x), determining an optimal seismic velocity parameter model w.sub.opt(x) by computing a plurality of iterations, each iteration comprising calculating and optimizing a cost function, said cost function being dependent on the zero-offset seismic wavefield and on the low frequency perturbation term δm.sub.b(x) as a parameter in the optimization of the cost function, the high frequency perturbation term δm.sub.r(x) being related to the velocity parameter model w(x) to keep the provided zero-offset seismic wavefield data invariant with respect to the low frequency perturbation term δm.sub.b(x).

An exemplary embodiment of the present invention provides an anisotropic medium for full transmission of obliquely incident elastic waves considering a longitudinal wave and a shear wave by using an anisotropic medium designed to fully transmit elastic waves in a desired mode when elastic waves are obliquely incident to a boundary of different media. The anisotropic medium for fully transmitting an obliquely incident elastic wave according to an exemplary embodiment of the present invention includes: an incident medium to which an incident elastic wave including a longitudinal wave and a shear wave, and being obliquely incident with a predetermined incidence angle, is incident and reflected; a transmission medium to which a transmitting elastic wave including a longitudinal wave and a shear wave is transmitted; and an anisotropic medium, installed between the incident medium and the transmission medium, for blocking reflection of a predetermined reflecting elastic wave as a predetermined full transmission condition is satisfied, and fully transmitting a transmitting elastic wave in a predetermined type of full transmission, wherein the full transmission condition includes a phase matching condition based on a wavenumber relationship of an eigenmode in the anisotropic medium, and a polarization matching condition based on a relationship between a polarization vector and an amplitude of the eigenmode.

Systems, methods, and apparatuses directed to determining a long wavelength velocity model using acquired seismic data lacking low-frequency data is disclosed. Determination of the long wavelength velocity model may include generating a time-delayed signal from the acquired seismic data to produce low-frequency information and reducing a residual energy between the time-delayed signal from the acquired seismic data and a time-delayed signal of modeled data using an objective function to produce an optimized initial velocity model using full waveform inversion. Moreover, a full waveform inversion on the optimized initial velocity model using acquired data can be used to produce a velocity model more accurately representing subterranean formations.

A system and method are disclosed for predicting, and optionally removing surface multiples from acquired seismic data that lacks surface consistency, such as seismic data acquired using an Ocean Bottom Cable (OBC) or Ocean Bottom Node (OBN) system where the sources are located at or near the water's surface and the receivers are located at or near the ocean's floor. By processing the acquired seismic data using seismic interferometry, source side and/or receiver side operators can be generated which satisfy the surface consistency requirement of techniques such as Surface Related Multiple Elimination (SRME) so that SRME or the like can be used to predict the surface multiples.

A method of generating diffraction images based on wave equations includes generating a source wavefield and a receiver wavefield. Based on the source wavefield, a first source wavefield propagating in a first direction and a second source wavefield propagating in a second direction are generated. Based on the receiver wavefield, a first receiver wavefield propagating in the first direction and a second receiver wavefield propagating in the second direction are generated. A first seismic image is generated based on the first source wavefield and the first receiver wavefield. A second seismic image is generated based on the second source wavefield and the second receiver wavefield. A final seismic image is generated based on the first seismic image and the second seismic image.

Active source surface wave prospecting method which is applicable to technical field of geological prospecting, comprising: collecting, by detector at preset station, surface wave data transmitted from seismic source; calculating to obtain dispersion energy graph on basis of vector wave-number transformational algorithm and according to surface wave data; extracting dispersion curve from dispersion energy graph, dispersion comprising base-order surface wave dispersion curve and high-order surface wave dispersion curve; establishing initial stratigraphic model according to base-order surface wave dispersion curve and high-order surface wave dispersion curve, performing, according to initial stratigraphic model, joint inversion on base-order surface wave dispersion curve and high-order surface wave dispersion curve to obtain inverting data of stratigraphic texture. Accuracy of surface wave prospecting result is effectively improved. Further provided are surface wave exploration device and terminal device.

The invention relates to a computer-implemented method for generating an image of a subsurface of an area of interest from seismic data. The method comprises providing seismic wavefields, providing a zero-offset seismic wavefield dataset, determining a seismic velocity parameter model w(x) comprising an initial model w.sub.0(x), a low frequency perturbation term δm.sub.b (x) and a high frequency perturbation term δm.sub.r(x), determining an optimal seismic velocity parameter model w.sub.opt(x) by computing a plurality of iterations, each iteration comprising calculating and optimizing a cost function, said cost function being dependent on the zero-offset seismic wavefield and on the low frequency perturbation term δm.sub.b(x) as a parameter in the optimization of the cost function, the high frequency perturbation term δm.sub.r(x) being related to the velocity parameter model w(x) to keep the provided zero-offset seismic wavefield data invariant with respect to the low frequency perturbation term δm.sub.b(x).

A system for seismic imaging of a subterranean geological formation, the system includes a receiver configured to obtain seismic data comprising a data volume representing a post-stacked image. The system includes a filtering module configured to: apply frequency-wavenumber (F-K) filter to the data volume extract a negative-dip structure image and apply the frequency-wavenumber (F-K) filter to the data volume extract a positive-dip structure image. The system includes a diffraction rendering module configured to: multiply the positive-dip structure image with the negative-dip structure image and generate a diffraction-enhanced seismic image representing a geological formation of the data volume.