Abstract: Estimation of velocity models inclusive of receiving seismic data inclusive of data that corresponds to a seismic image, adding a velocity perturbation to a current velocity model that represents a portion of the subsurface responsible for a distortion in the seismic image to generate a perturbed velocity model, generating an image via seismic migration of the seismic data and the perturbed velocity model, generating and assigning a measure of quality to the image, determining whether the measure of quality assigned to the image is an optimal measure of quality at a particular location of the current velocity model, and updating the current velocity model to generate a revised velocity model utilizing the measure of quality assigned to the image when the measure of quality assigned to the image is determined to be the optimal measure of quality at the particular location of the current velocity model.

Abstract: A method for seismic exploration uses visco-acoustic FWI to model velocity and quality factor Q for an explored subsurface formation. The method employs frequency-dependent velocity to reduce cross-talk between Q and velocity and may be used for both isotropic and anisotropic media.

Abstract: A computer-implemented method and computing system apparatus programmed to perform operations of the computer-implemented method for obtaining a subsurface stack image, subsurface angle gathers, and a subsurface velocity model over an entire survey region having high velocity contrast geo-bodies. Particularly, user inputs, input velocity models, and surface-seismic data are obtained by fixed source and receiver pairs and then used by the computer program product embedded within the computing system apparatus to minimize the number of iterations, required to obtain a final velocity model, a final stack image, and final angle gathers wherein their flatness deviation is equal to, or less than, a user-defined flatness value. Therefore, the attributes developed by said computer-implemented method and system can help solve the imaging problem of sub high velocity contrast geo-bodies like subsalt, or salt overhung deep mini basins.

Abstract: According to one embodiment, a structure evaluation system of the embodiments includes a plurality of sensors, an arrival time determiner, a reliability calculator, and a map generator. The plurality of sensors detect elastic waves. The arrival time determiner determines arrival times of the elastic waves using elastic waves detected by the plurality of respective sensors. The reliability calculator calculates reliabilities related to measurement waveforms of the elastic waves on the basis of the arrival times. The map generator generates a first map on the basis of the calculated reliabilities or the reliabilities and a distance.

Abstract: A reflection full waveform inversion method updates separately a density model and a velocity model of a surveyed subsurface formation. The method includes generating a model-based dataset corresponding to the seismic dataset using a velocity model and a density model to calculate an objective function measuring the difference between the seismic dataset and the model-based dataset. A high-wavenumber component of the objective function's gradient is used to update the density model of the surveyed subsurface formation. The model-based dataset is then regenerated using the velocity model and the updated density model, to calculate an updated objective function. The velocity model of the surveyed subsurface formation is then updated using a low-wavenumber component of the updated objective function's gradient. A structural image of the subsurface formation is generated using the updated velocity model.

Abstract: A zero-offset wavefield synthesis workflow to calculate a synthesized zero-offset wavefield output without the commitment to an rms velocity field output to circumvent velocity uncertainty. Said zero-offset wavefield synthesis workflow comprises calculating a migration cube output. Rendering a demigration cube output from said migration cube output with a demigration cube calculation. Rendering said synthesized zero-offset wavefield output from said demigration cube output with a zero-offset wavefield synthesis procedure.

Abstract: A seismic modeling system is provided which may include a seismic model data storage device, and a processor cooperating with the seismic model data storage device to identify an obstruction within a seismic model spatial domain data set having a lateral boundary, and define a suspect area including spatial domain data within the lateral boundary and directly below the obstruction. The processor may further inpaint the suspect area in the seismic model spatial domain data set based upon an exemplar inpainting algorithm.

Abstract: In a general implementation, systems, apparatus, and methods for AVO of imaging condition in ERTM include the described system provides for an efficient and accurate vector wavefield decomposition with a corresponding modified dot-product imaging condition of ERTM by employing a modified AVO algorithm. In some implementations, the phases of source wavelet and multicomponent records are modified using a 1/?2 filter and the amplitudes of the extrapolated wavefields are scaled using ?2 and ?2, where ?, ? and ? are the angular frequency, local P- and S-wave velocities, respectively. The results yield correct phases, amplitudes, and physical units for separated P- and S-mode wavefields. Divergence and curl operators may then be applied to the phase-corrected and amplitude-scaled elastic wavefields to extract vector P- and S-wavefields. With the separated vector wavefields, a modified dot-product imaging condition can be employed to produce PP and PS reflectivity images.

Abstract: According to one embodiment, there is provided a method of correcting recorded seismic data where each receiver clock is potentially inaccurate. Since the seismic wave field is not random, and contains coherent events that are recorded by all receivers in a local area, it is possible to estimate the differences in the time reference by comparing the recordings of different receivers in a local area. With no external time reference, time signal, or pilot trace, an entire seismic data itself can be used to determine how each receiver's clock is drifting from true time.

Abstract: A method and system are described for creating a subsurface model. In this method, discontinuous functions are interpolated in a subsurface model. The method extrapolates specified values over discontinuous manifolds by embedding the manifold in a higher-dimensional space that amplifies distances across discontinuities and thus eliminates special consideration to prevent extrapolation across discontinuities. The resulting subsurface model may be used in reservoir simulations and hydrocarbon operations.

Abstract: Techniques are disclosed relating to reducing noise in marine seismic survey data. A shot-by-shot depth migration of recorded marine seismic survey data that includes multiples wavefields indicative of surface reflections may be performed. Post-migration data generated by the migration may include angle information derived from the multiples wavefields. Attributes of the marine seismic survey data may be corrected using the angle information in order to identify a potential sub-surface structure.

Abstract: Computer systems and methods are provided for seismic wavefield processing, including time domain reconstructed full wavefield inversion (TDRFWI) of seismic survey data. Suitable methods include forward propagating a source signal based on a model of a subsurface region, generating a residual based on the forward-propagated wavefield in comparison to field data, back propagating the residual to generate a reconstructed source perturbation, and adding the reconstructed source perturbation to the source signal to generate a reconstructed source wavefield. The reconstructed source perturbation can be forward propagated to generate a reconstructed wavefield perturbation, and added to the reconstructed wavefield perturbation to reconstruct the wavefield. The propagations can be performed in the time domain, and the model can be updated based on the reconstructed wavefield and reconstructed source perturbation to generate high fidelity subsurface images.

Abstract: The method processes, for each of a plurality of shots at respective source locations, seismic traces recorded at a plurality of receiver locations. Common-mid-point-modulated data are also computed by multiplying the seismic data in each seismic trace by a horizontal mid-point. A depth migration process is applied to the seismic data to obtain a first set of migrated data, and to the mid-point-modulated data to obtain a second set of migrated data. For each shot, aperture values are estimated and associated with respective subsurface positions. A migrated value for a depth and an aperture in a surface aperture common image gather at a horizontal position is a migrated value of the first set of migrated data for a shot such that the estimated aperture value associated with that subsurface position is the aperture.

Abstract: A modified direct search Neighborhood Algorithm (NA), similar to genetic or evolutionary algorithms, is used for automatic calibration of Stratigraphic Forward Models (SFM) to data constraints. The modified NA comprises explicit escape clauses from local minima and admissible solutions, thereby preventing a natural tendency of conventional NAs to converge and oversample a single minimum. The density of models in parameter space is used to define local minima. Admissible solutions are defined by considering error thresholds taking into account that SFM may be imperfect and that calibration constraints may be uncertain. The modified NA algorithm obtains a plurality of geological scenarios that agree with the data, and which can be used for further analysis and prediction.

Abstract: In some embodiments, a seismic processing method comprises assembling a specularity gather by determining a specularity value at each of a plurality of subsurface locations, and summing trace amplitudes into a plurality of bins, each bin characterized by a range of specularity values. The specularity value at a subsurface location is computed according to an angle between a normal to a local reflector and a direction of a total (source+receiver) traveltime gradient. For example, the specularity may be proportional to (e.g. equal to) a magnitude of the cosine of the angle. A diffraction image may be generated by summing specularity gather data over specularity, with specular event amplitudes attenuated relative to diffractive event amplitudes.

Abstract: A method for generating seismic attribute gathers, the method including: computing, with a computer, seismic images with a field dataset; generating, with a computer, synthetic data corresponding to the seismic images; computing, with a computer, an attribute volume by applying an expectation method to the synthetic data; mapping, with a computer, the attribute volume to the seismic images; and generating, with a computer, seismic attribute gathers by stacking the seismic images mapped to the attribute volume.

Abstract: Systems and methods are provided for de-noising seismic data recorded by seismic receivers. A first portion of the seismic data having a first signal-to-noise ratio (SNR) to is processed to generate a de-noising operator or function. The de-noising operator is applied to a second portion of seismic data having a second SNR to remove noise from the second portion of the seismic data, where the first SNR is greater than the second SNR.

Abstract: Embodiments of the invention provide a method for classifying seismic attributes, including generating data points by cross plotting seismic attributes from a first data volume and a second data volume, encompassing at least one of the generated data points within a polygon, generating a reference line, determining an interpolation direction relative to the reference line, and assigning an attribute value to the at least one generated data point encompassed within the polygon wherein the assigned attribute value is interpolated based on the combination of its position to the reference line along the interpolation direction and the shape of the polygon.

Abstract: Systems and methods for identifying matching properties between a group of bodies representing a geological structure and a table of properties by performing property matching on the group of bodies to convert each body to a respective compartment represented by a triangulated mesh of the bounding body.

Abstract: Embodiments of a system are provided for forming enhanced seismic array traces using virtual seismic sensors in addition to the real seismic sensors to form a virtual seismic array. The system receives the signal responses from the real sensors, processes the signal responses from the sensors to define virtual signals using a narrowband decomposition of the complex envelope of the sensor signal responses, calculates second- and fourth-order statistics to derive steering vectors for the array of real sensors, and forms a virtual seismic array in response thereto. Machines, computer program product, and computer-implemented methods are provided for forming enhanced seismic array traces by receiving the array responses from sensors, processing the signals to define virtual sensor signals and a virtual seismic array, and forming an array response for the virtual seismic array to form a seismic trace of enhanced resolution.

Abstract: According to one embodiment, subsurface ray directions in beam migration or subsurface wave propagation directions in reverse time migrations are used to obtain additional Specular Filter (SF) and Dip Oriented Partial Imaging (DOPI) images. SF migration applies a specular imaging condition during migration with a pre-specified subsurface dip field. It boosts the S/N ratio in both images and gathers, by effectively removing migration noise. DOPI images are produced by decomposing a standard migration image according to subsurface dip inclination or/and dip azimuth groups, providing various views of the subsurface image. Both SF and DOPI migration images can supply valuable additional information compared to a standard migration image, and they can be efficiently generated during migration.

Abstract: This disclosure presents computational systems and methods for obtaining high-resolution, three-dimensional seismic images of a region of a subterranean formation using separated up-going and down-going wavefields that include primary and multiple reflections obtained by processing dual-sensor towed streamer seismic data. The inclusion of multiple reflections reduces acquisition footprints in migration of the seismic data. The computational systems and methods produce high-resolution images in a region of a subterranean formation that lies below a body of water. The methods and systems employ a digitally encoded wavefields constructed from a discrete sampling of a two-dimensional slice of a three-dimensional wavefield and stored in one or more tangible, physical data-storage devices.

Abstract: Computing device and method for calculating time-shifts associated with travel-times of seismic waves emitted by a source and recorded by plural seismic detectors after reflection from a subsurface structure. The method includes receiving seismic data (d) that includes plural traces related to a subsurface, wherein the seismic data (d) is in a time-space domain; transforming with a processor the seismic data (d) from the time-space domain to a radon domain; picking linear events from the seismic data in the radon domain; calculating the time-shifts associated with the picked linear events; correcting the seismic data (d) based on the time-shifts to obtain new seismic data (d?); and computing an image of the subsurface based on the new seismic data (d?). The time-shifts are calculated per trace and per event.

Abstract: Computing systems and methods to producing a reverse time migration model dip-guided image using processed vertical seismic profile data are provided. In one embodiment, vertical seismic profile data for a subsurface geological formation is obtained. One or more dip estimates corresponding to the subsurface geological formation are also obtained. One or more model dip-guided reverse time migration imaging conditions are determined and applied to the obtained vertical seismic profile data to produce the processed vertical seismic profile data.

Abstract: To perform inversion to produce a model of a structure, a filtering operator based at least on an angle between a propagating direction of a source wavefield and a propagating direction of a back-propagated receiver wavefield is computed. The filtering operator is used in performing the inversion to produce the model of the structure.

Abstract: A method of conducting a seismic survey of an area including a region of high seismic velocity regimes in a shallow overburden. According to the method, a zone is identified in which the boundary of the high seismic velocity region has a substantially constant critical angle and a course is plotted through the identified zone. A zone based directional seismic source is applied sequentially, with a directivity angle equal to or close to the measured critical angle. The response is detected using receivers.

Abstract: A method for analyzing seismic data by generating a post-migration common image gather in a dip angle domain from measured seismic data; detecting concave features related to reflection events in the common image gather and apexes; filtering out part of the concave features in the common image gather in a vicinity of the detected apexes; applying a hybrid Radon transform to the filtered common image gather to separate residues of the concave features from other image features related to diffraction events; and applying an inverse hybrid Radon transform to an image containing the separated features related to diffraction events to obtain a transformed common image gather in the dip angle domain.

Abstract: A disclosed example method includes providing, in a borehole, a transmitter (Tx) and receivers (Rxs) spaced linearly from Tx at known distances, measuring linear propagation times (LPts) for a signal to propagate from Tx to each of Rxs, determining an inline velocity (VINL) based on LPts, measuring reflection times (Rts) for a signal to propagate from Tx to each of the Rxs via a boundary, for each of Rts, providing a time-distance anisotropic velocity (TDAV) relationship depending on an effective signal velocity (ESV) in an anisotropic formation adjacent the boundary as a function of reflection angle for the reflection time signal to the boundary, VINL and orthogonal velocity, performing semblance processing to combine the TDAV relationships with VINL for a best-fit calculation of the ESVs for the different reflection angles of the reflection time signals, and calculating a distance for the corresponding receiver to the boundary on the calculation.

Abstract: Seismic data representing the propagation of seismic energy through a geologic volume of interest is processed. The seismic energy propagates through the geologic volume of interest from one or more source locations at or near the geologic volume of interest to one or more detector locations at or near the geologic volume of interest. In processing the seismic data, the seismic energy is modeled as beams (e.g., Gaussian beams). The processing performed (i) corrects for misalignment of the one or more source locations and/or the one or more detector locations with a regular, predetermined mesh, and (ii) steers the seismic data based on the modeled beams.

Abstract: Methods of and apparatus to image one or more subsurface formation features are disclosed. An example method includes generating acoustic waves with a transmitter and receiving the acoustic waves and acoustic data contained therein at one or more receivers. The example method also includes extracting one or more S-S, P-S or S-P reflected waveform data from the acoustic data, estimating a dip of the one or more subsurface formation features, migrating the one or more S-S, P-S or S-P reflected waveform data with the estimated dip and mapping the migrated one or more S-S, P-S or S-P reflected waveform data. In addition, the example method includes identifying one or more permeable subsurface formation features using the mapped migrated one or more S-S, P-S or S-P reflected waveform data.

Abstract: According to one embodiment, subsurface ray directions in beam migration or subsurface wave propagation directions in reverse time migrations are used to obtain additional Specular Filter (SF) and Dip Oriented Partial Imaging (DOPI) images. SF migration applies a specular imaging condition during migration with a pre-specified subsurface dip field. It boosts the S/N ratio in both images and gathers, by effectively removing migration noise. DOPI images are produced by decomposing a standard migration image according to subsurface dip inclination or/and dip azimuth groups, providing various views of the subsurface image. Both SF and DOPI migration images can supply valuable additional information compared to a standard migration image, and they can be efficiently generated during migration.

Abstract: A method can include receiving a request for a dip value for a location within a sub-surface volume; responsive to the request, locating complimentary dip values for locations within the sub-surface volume where the location for the requested dip value lies within bounds defined by the locations for the complimentary dips values; and interpolating a value for the requested dip value based on the complimentary dip values. Various other apparatuses, systems, methods, etc., are also disclosed.

Abstract: A technique includes processing first data indicative of a first image of a subsurface region of interest on a machine to generate second data indicative of a second image. The first image is derived from measurements of seismic waves, which propagate in a plurality of directions, and the second image is generated by partitioning the first image based on the directions. The technique includes processing the second data to determine a dip decomposition for each of the directions; and based on the dip decompositions and the directions, generating an angle domain common image gather.

Abstract: The process of obtaining seismic data includes deploying a seismic energy source and seismic receivers, actuating the source, and detecting seismic energy resulting therefrom at the receivers. The process further includes digitally sampling seismic energy detected at the receivers indexed with respect to time to form a plurality of traces and sorting the traces to form a plurality of shot gathers. In addition, the process includes applying a depth migration technique to the shot gathers to generate two images according to the cross-correlation imaging condition (I0) and the gradient-based imaging condition (I1) for each shot gather. A reflection angle (?) or a general domain parameter (?) is computed at each subsurface position and the images are mapped according to the corresponding reflection angle or the general domain parameter to form common image gathers. Amplitude correction is applied to common image gathers and the images and common image gathers are stored on non-transitory computer-readable media.

Abstract: Refracted energy travel time can help to derive anisotropic parameters in a target layer. These anisotropic parameters allow us to both explore for new reservoirs and to understand stress and fracturing in existing reservoirs. This information can be used to i) detect oil reservoirs, ii) spot naturally fractured, hence high production zones, iii) detect dominant natural stress directions, iv) better place horizontal wells to optimize production, v) monitoring man made fractures or induced directional stress changes. The method is demonstrated using synthetic and real data.

Abstract: A system and method for subsurface characterization including depth and structural uncertainty estimation is disclosed. In one embodiment, the method may include determining a detectability threshold for moveout in a seismic data gather based on the seismic data and computing a depth uncertainty function, wherein the depth uncertainty function represents an error estimate that is used to analyze an interpretation of the seismic data. In another embodiment, the method may include receiving a depth uncertainty volume and at least one interpreted horizon from seismic data, extracting a depth uncertainty cage for each of the interpreted horizons based on the depth uncertainty volume, and simulating multiple realizations for each of the interpreted horizons, constrained by the depth uncertainty cage. The multiple realizations may be used for analyzing changes to geometrical or structural properties of the at least one interpreted horizon.

Abstract: A method for displaying exploration and production (E&P) data set during an E&P tool session of a field having a subterranean formation. The method includes generating, by an E&P tool executing on a computer processor during the E&P tool session, an E&P data set based on a subterranean formation field data set, displaying, to a user controlling the E&P tool session, the E&P data set as a multi-dimensional canvas, generating, by the computer processor and in response to a user input identifying a point in the multi-dimensional canvas, a strike&dip tool tip, and further displaying the strike&dip tool tip superimposing the multi-dimensional canvas, wherein the strike&dip tool tip is tagged to the point in the multi-dimensional canvas.

Abstract: The present disclosure relates to determining the attenuation of an electromagnetic signal passing through a conductive material. An antenna is provided and placed in relatively close proximity to the conductive material. An alternating current is passed through the antenna and the impedance of the antenna is measured. The attenuation is determined using the measured impedance. A single frequency measurement may be made, or multiple measurements using different frequencies may be made. Grouped parameters based on properties of the material and the frequency of the current are used to relate the coil impedance to the attenuation. A current frequency for which the ratio of the antenna's resistive part of the impedance to the angular frequency of the current is substantially insensitive to at least one of the parameters is preferred.

Abstract: There is a method of seismic data processing that includes receiving seismic data that includes a set of seismic traces, each trace including a signal recorded by a sensor after having been propagated in a subsurface area; migrating the seismic data according to a first velocity model; picking from the time-migrated seismic data one or more events corresponding to one or more subsurface reflectors so as to obtain a set of facets locally approximating the event; kinematic demigrating the picked set of facets so as to obtain simplified seismic data that includes the set of facets and a set of attributes associated with the set of facets; migrating the set of facets based on a second velocity model; and updating the initial velocity model based on an alignment of migrated points within the set of facets.

Abstract: Computing systems and methods to producing a reverse time migration model dip-guided image using processed vertical seismic profile data are provided. In one embodiment, vertical seismic profile data for a subsurface geological formation is obtained. One or more dip estimates corresponding to the subsurface geological formation are also obtained. One or more model dip-guided reverse time migration imaging conditions are determined and applied to the obtained vertical seismic profile data to produce the processed vertical seismic profile data.

Abstract: A best fitting trace in seismic data is determined for a desired trace to be reconstructed. A dip-based correction is calculated per trace and per sample for differences in azimuth, common midpoint coordinates, and offset between the best fitting trace and the desired trace. The dip-based correction is applied to the best fitting trace to reconstruct the desired trace for 3D surface-related multiple prediction.

Abstract: An iterative dip-steering median filter is provided for random noise attenuation in seismic data where conflicting dips are indicated in the data. A number of dominant dips inside a processing window or sample of the data are identified by a Fourier-radial transform in the frequency-wavenumber domain. A median filter is then applied along the dominant dip to remove noise, and the remaining signal after filtering is retained for further median filter iterations. Iterations are repeated to apply the median filter along the most dominant dip in the remaining data. The processing continues in subsequent iterations until all selected dips have been processed. The remaining signal of each iteration is then summed for final output.

Abstract: The invention is a method for extrapolating missing near-offset seismic data (101) so that the data may be used, for example, in SRME or another multiple-reflection elimination method. The invention uses the reciprocity principle (102) to relate two seismic states (acoustic or elastic) that can occur in a time-invariant, bounded domain in space. One of these states represents the physical experiment for the acquisition of the actual seismic data where near-offset traces are missing, and the other state represents a synthetic experiment with no missing near offset traces, computer-generated on a much simpler earth model. The reciprocity relationship used to relate these two states is iteratively inverted for the missing near-offset traces (103), preferably using only part of the synthetic data (102) so as to reduce inversion artifacts. The reference model acts as a constraint on the near-offset extrapolation.

Abstract: A method can include, within a neighborhood, selecting a sample seismic trace and neighboring seismic traces, individually time shifting each of the neighboring seismic traces with respect to the sample seismic trace to determine a set of individual time shift values that correspond to individual maximum cross correlation values for each of the neighboring seismic traces with respect to the sample seismic trace, determining series of inline direction and crossline direction first derivative values for the set of time shift values, determining an inline average dip value and a crossline average dip value based on the series of first derivative values, and storing to a memory storage device, coordinates for the sample seismic trace, the inline average dip value, and the crossline average dip value. Various other apparatuses, systems, methods, etc., are also disclosed.

Abstract: Device and method for estimating an event-related main anisotropy axis for a volume in a subsurface. The method includes selecting a velocity migration model for the given volume of the subsurface; receiving seismic data for the given volume; migrating the seismic data based on the velocity migration model; picking locally coherent events from the migrated data; and performing a tomographic process based on invariants to calculate the event-related main anisotropy axis.

Abstract: A computer implemented method for retrieving seismic data from a seismic section provided in a bitmap format. The method includes reconstructing a two dimensional matrix of seismic interpolated data in which a value at a given pixel in the matrix is proportional to local density of wiggles in the seismic section with an added value of a previously calculated pixel. The method may be implemented in either of computer hardware configured to perform said method and computer software embodied in a non-transitory, tangible, computer-readable storage medium. Also disclosed are corresponding computer program product and data processing system.

Abstract: Computer instructions, computing device and method for processing seismic data under-sampled in an angle domain, the seismic data corresponding to a reverse time migration, three-dimensional, angle domain common image gather (ADCIG). The method includes receiving the seismic data; calculating, based on the seismic data, shot and receiver wave-fields with an RTM wave propagation engine; applying a wave-fields decomposition algorithm to obtain a propagation direction for the shot and receiver wave-fields; forming the ADCIG by applying an image condition to the shot and receiver wave-fields; determining that specular energies of the ADCIG are under-sampled around a reflection angle; during the step of forming the ADCIG, extrapolating the specular energies to a neighborhood of the reflection angle; and generating an image of a subsurface that is being surveyed based on the extrapolated specular energies.

Abstract: Dips are calculated for a series of sets of adjacent multiple contribution traces, from seismic data representative of subsurface formations, in the vicinity of a boundary of an aperture of a multiple contribution gather, the seismic data acquired by deploying a plurality of seismic sensors proximate an area of the earth's subsurface to be evaluated, the seismic sensors generating at least one of an electrical and optical signal in response to seismic energy. The boundary of the aperture of the multiple contribution gather is recursively extended, based on the calculated dips. Multiple contribution traces in the multiple contribution gather with the extended aperture boundary are stacked to generate predicted multiple traces. The predicted multiple traces are subtracted from the seismic data to generate surface-related multiple attenuated data useful for imaging the subsurface formations.

Abstract: Beamed data can be obtained from shot gather data, and debeamed data can be obtained from beamed data. Shot gather data for a geophysical volume of interest in a first domain and/or beamed data in a third domain may be received. The first domain has a component relating to seismic wave propagation time and a spatial component relating to lateral spacing. The third domain has a component relating to local plane wave arrival time at a beam center surface location and a component relating to plane wave arrival directions. Data may be transformed between the first domain and a second domain. The second domain has a frequency component and a spatial component corresponding to the spatial component of the first domain. A forward or reverse transform may be applied to transform shot gather data in the first domain to/from beamed data in the third domain.

Abstract: Seismic survey data is converted into a subsurface data volume that users can view to understand and analyze the subsurface structures in the survey region. At least some of the disclosed systems and methods employ three-dimensional reverse time migration using wave equations adapted for use in formations having tilted transverse isotropy. Relative to existing methods, the disclosed systems and methods rely on fewer approximations and suffer fewer limitations on the circumstances in which they can be employed. Moreover, because the disclosed wave equations are derived from Hooke's law (and consequently they operate on fields that are directly tied to physical quantities), they demonstrate an increased stability relative to existing methods. Survey data analysts employing the disclosed systems and methods should obtain better images of the subsurface and be better able to identify reservoirs and deposits for commercial exploitation.