Abstract: Systems and methods for seismic imaging of a subterranean geological formation include receiving parameter data representing one or more parameters of a seismic survey, the seismic data specifying an incident angle and an azimuth angle for each trace of the seismic survey; determining a relationship between the incident angle and the azimuth angle for each trace and a location in a spiral coordinate system, and generating a weighting function for applying a weight value to each trace seismic data based on the incident angle and the azimuth angle associated with each trace; and determining a residual moveout value of the seismic data for each location in the spiral coordinate system by applying the weighting function to each; and generating a seismic image representing the residual moveout value of the seismic data for each location in the spiral coordinate system.

Abstract: Seismic data from seismic exploration surveys are mapped into a hypercube of bins or voxels in a four-dimensional space (X, Y, Offset, and Azimuth) according to Common Mid-Point (or CMP) between source and receivers. The mapped data from individual voxels or bins is then analyzed by multimodal statistics. Robust estimates of first break picks are obtained from the analysis. The first break picks are then used to as seed inputs for autopicking iteration, which proceeds to convergence. Estimates of confidence levels in the data are provided for re-picking to reduce computer processing time in successive autopicking iterations. Analysis is provided of different seismic attributes such as azimuthal velocity variations indicative of anisotropy, positioning errors of sources/receivers, geometry errors, and three dimensional distribution of inversion residuals. Analysis is also performed of standard deviation of the travel time data useful for estimating data errors in the inversion covariance matrix.

Abstract: Seismic data from seismic exploration surveys are mapped into a hypercube of bins or voxels in a four-dimensional space (X, Y, Offset, and Azimuth) according to Common Mid-Point (or CMP) between source and receivers. The mapped data from individual voxels or bins is then analyzed by multimodal statistics. Robust estimates of first break picks are obtained from the analysis. The first break picks are then used to as seed inputs for autopicking iteration, which proceeds to convergence. Estimates of confidence levels in the data are provided for re-picking to reduce computer processing time in successive autopicking iterations. Analysis is provided of different seismic attributes such as azimuthal velocity variations indicative of anisotropy, positioning errors of sources/receivers, geometry errors, and three dimensional distribution of inversion residuals. Analysis is also performed of standard deviation of the travel time data useful for estimating data errors in the inversion covariance matrix.

Abstract: A method for building a three dimensional (3D) model of a subsurface formation includes selecting, from a set of seismic shots, a plurality of first arrival signals representing the seismic shots. The method includes applying a quality control function to the plurality of first arrival signals to obtain a set of remaining first arrival signals. For each remaining first arrival signals, the method includes applying a velocity inversion function to obtain a depth velocity value at a common-midpoint (CMP) location in a shot gather including the seismic shot associated with that remaining first arrival signal, the CMP location representing a lateral variation of the shot gather including that seismic shot. The method includes, based on the depth velocity value for the seismic shot associated with each remaining first arrival signal, generating a velocity model representing the 3D model of the subsurface formation.

Abstract: A method of seismic exploration above a region of the subsurface containing structural or stratigraphic features conducive to the presence, migration, or accumulation of hydrocarbons comprises accessing at least a portion of a blended seismic source survey, separating the at least two interfering seismic source excitations using inversion separation, producing one or more source gathers based on the separating, and using the one or more source gathers to explore for hydrocarbons within said region of the subsurface. The blended source seismic survey contains at least two interfering seismic source excitations therein, and the seismic source excitations can be produced by seismic source types having different signatures or frequency characteristics.

Abstract: A method for use in vertical seismic profiling includes: independently and simultaneously shooting a plurality of seismic sources in a plurality of shooting areas to impart seismic signals into a water bottom: receiving reflections of the seismic signals from a subterranean formation beneath the water bottom at a plurality of seismic receivers; and recording the received reflections; wherein, one of the seismic sources and the seismic receivers are disposed in a wellbore in the water bottom.

Abstract: There is described embodiments relating to a method of determining a wave field in an anisotropic subsurface of the Earth. The method includes numerically solving a decoupled quasi-acoustic single wave mode wave equation based on spatially varied anisotropic parameters, to determine the wave field in the anisotropic subsurface.

Abstract: The invention disclosed is a system for providing an aggregated econometric database with selectable sources of economic data. The econometric database is accessible to a system application that graphically displays econometric data over selected periods, and allows display of external economic data in conjunction with internal company metrics. The system applications further provide for identifying the features of indicators, economic and business forecasting, and providing alerts based on the available econometric data.

Abstract: Methods of compensating for source signature effects in seismic data are described. One method includes a step of receiving seismic data recorded with a receiver; a step of receiving source data of the seismic waves generated by the moving source; a step of receiving position data of the source while generating the seismic waves; a step of determining a transform operator using the source data, the position data, and a selected domain-transform operator; a step of determining a seismic model by mathematically optimizing a relationship between the transform and the seismic data; and a step of compensating for the source signature effects in the seismic data using the seismic model. A method for generating an image of a subsurface of a geographical area using seismic data includes compensating the seismic data for source signature effects using a model which assumes a moving, non-impulsive source.

Abstract: A seismic streamer includes a sensor comprises an axially oriented body including a plurality of axially oriented channels arranged in opposing pairs; a plurality of hydrophones arranged in opposing pairs in the channels; a pair of orthogonally oriented acoustic particle motion sensors; and a tilt sensor adjacent or associated with the particle motion sensors. The streamer has a plurality of hydrophones, as previously described, aligned with a plurality of accelerometers which detect movement of the streamer in the horizontal and vertical directions, all coupled with a tilt sensor, so that the marine seismic system can detect whether a detected seismic signal is a reflection from a geologic structure beneath the streamer or a downward traveling reflection from the air/seawater interface.

Abstract: Streamer redundancy. At least some illustrative embodiments are methods including: in a streamer towed by a survey vessel, sensing a first interconnection of a daisy chain the first interconnection between a first networked unit and a second networked unit, wherein the first networked unit and the second networked unit comprise a portion of a plurality of networked units; and determining that a fault condition exists on the first interconnection in response to the sensing; disabling the first interconnection responsive to the fault condition; enabling a second interconnection responsive to the fault condition, wherein the second interconnection couples the first networked unit and a third networked unit of the plurality of networked units and wherein the second interconnection does not couple to the second networked unit; and reporting information indicative of the fault condition to the survey vessel via the second networked unit.

Abstract: Seismic data recorded by subsurface seismic sensors placed in a borehole, such as an oil or gas well, are transformed via a process of upward wavefield propagation to pseudo-receivers at the surface of the earth. The seismic data thus transformed can be processed as though the data had been recorded by the pseudo-receivers at the surface rather than in the borehole where the data were actually recorded. This method accurately accounts for seismic source statics, anisotropy, and all velocity effects between the real receivers in the borehole and the pseudo-receivers at the surface of the earth.

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 technique includes processing seismic data indicative of samples of at least one measured seismic signal in a processor-based machine to, in an iterative process, determine basis functions, which represent a constructed seismic signal. The technique includes in each iteration of the iterative process, selecting another basis function of the plurality of basis functions. The selecting includes based at least in part on the samples and a current version of the constructed seismic signal, determining a cost function; and interpreting the cost function based at least in part on a predicted energy distribution of the constructed seismic signal to select the basis function.

Abstract: This invention is for a method for transforming a seismic trace into a compressed domain. The seismic source wavelet is transformed into a zero degree phase wavelet and a shifted 90 degree phase wavelet, and the two wavelets span a 2-dimensional sub-space. A dictionary is created by collecting the wavelets in the sub-space. In practice this dictionary is usually combined with conventional existing wavelet dictionaries. The seismic trace is projected onto the dictionary (sub-space alone or combined) to find the best matching projection, with a residual determined after each projection, wherein the sum of the residuals determines the fidelity of the data compression.

Abstract: Adaptive filtering method to remove ground roll from seismic data. In an M channel adaptive filter, weights Wi are set using an adaptive algorithm based on seeking the minimum in the partial differential of cost function J. The cost function includes an expansion of the primary trace d into d=dg+?d (where: dg is ground roll contribution and ?d=dsig+dran, where dsig is the reflected signal component and dran is a random noise component) and a corresponding expansion of the reference x into x=xg+?x (where xg is ground roll contribution and ?x=xsig+xran; where xsig is a reflected signal component and xran is a random noise component). The delta components are included in the denominator of cost function J to provide an optimal solution of the filter coefficients biased by the reflection signal and random noise is removed.

Abstract: Various implementations directed to seismic data processing using joint tomography are provided. In one implementation, a method may include receiving seismic data corresponding to a region of interest. The method may also include generating one or more first gathers and one or more second gathers based on the seismic data. The method may further include determining a relative shift in depth between at least a first event in the one or more first gathers and at least a second event in the one or more second gathers. The method may additionally include performing a joint tomography based at least in part on the first event, the second event, and the determined relative shift.

Abstract: A method is performed at a FPGA coprocessor having memory that stores a plurality of blocks of compressed seismic traces. The method includes: receiving, from a host, a request for processing a predefined set of seismic traces, the request including block location and trace header information; accessing one or more of the blocks of compressed seismic traces from the memory in accordance with the block location information; decompressing each of the one or more accessed blocks into one or more seismic traces thereby forming a plurality of decompressed traces of seismic data; selecting all or a portion of the decompressed traces of seismic data in accordance with the trace header information; processing the selected decompressed traces of seismic data by applying one or more predefined operations to the seismic data; and returning the processed seismic data to the host.

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 method of processing seismic data including convolving at least first and second seismic data traces or respective portions of at least first and second seismic data traces to forma composite trace. The travel time of an event may then be determined in the composite trace. This provides an improved method compared to the prior art technique of picking the travel time of an event individually in each one of a number of seismic data traces and averaging the individual picked travel times.

Abstract: Method for estimating residual moveout in common image gathers (51) of seismic data for use in velocity tomography (57). The method iteratively (56) flattens (55) the common image gathers against a specified reference trace through the application of conjugate-gradient least-squares inversion (53). Different from other picking methods which need to identify and track strong amplitudes, the inventive method automatically inverts for the depth residual for every grid point in the image gather. There is no need to identify and track events.

Abstract: The invention relates to a method of processing seismic data, the said seismic data comprising a gather of seismic traces organized according to one or several acquisition parameters, comprising the steps of: a) defining an equation for an RMO curve as a combination of elementary functions of the acquisition parameter(s), b) determining an RMO curve from the equation of step (a) as a combination of orthogonal elementary functions c) for a given time or at a given depth, determining the coefficients of the combination that optimize the semblance of traces along the RMO curve.

Abstract: Method of determining the velocity V and anellipticity ? parameters for processing seismic traces in a common midpoint (CMP) gather comprising:—a preliminary step to define a plurality of nodes (dtn, ?o), for each node (dtn, ?o) defined in the preliminary step, the following steps:—for static NMO correction of traces in the CMP gather as a function of the values of the said parameters dtn and ?o at the node considered, and calculation of the semblance function associated with the said NMO correction for the node considered; and—for each picked time to, a step including determination of the maximum semblance node (dtn (to), ?o (to)),—and a final step to convert the dtn (to) and ?o (to) parameters, so as to obtain the velocity to) and anellepticity ? (to) laws.

Abstract: A technique includes receiving first seismic data acquired by one or more receivers in response to energy produced by one or more seismic sources interacting with a subsurface feature. The first seismic data is indicative of measured reflection coefficients for image points for the subsurface feature, the measured reflection coefficients are associated with incidence angles, and a range of the incidence angles varies with respect to an image point position. The technique includes processing the first seismic data in a machine to generate second data indicative of a normal incidence reflection coefficient for at least one of the image points not associated with a normal angle of incidence.

Abstract: Method of determining the velocity V and anellipticity ? parameters for processing seismic traces in a common midpoint (CMP) gather comprising:—a preliminary step to define a plurality of nodes (dtn, ?o), for each node (dtn, ?o) defined in the preliminary step, the following steps:—for static NMO correction of traces in the CMP gather as a function of the values of the said parameters dtn and ?o at the node considered, and calculation of the semblance function associated with the said NMO correction for the node considered; and—for each picked time to, a step including determination of the maximum semblance node (dtn (to), ?o (to)),—and a final step to convert the dtn (to) and ?o (to) parameters, so as to obtain the velocity to) and anellepticity ? (to) laws.

Abstract: Methods and apparatus to calculate a distance from a borehole to a boundary of an anisotropic subterranean rock layer are disclosed. A disclosed example method includes transmitting a first signal from a first transmitter at a first location in a borehole traversing a subterranean formation, receiving the first signal at a first receiver after a first time period at a second location in the borehole, receiving the first signal at a second receiver after a second time period at a third location in the borehole, and calculating a first distance from the first transmitter to a first portion of a boundary of a subterranean rock layer adjacent to the borehole by compensating for an anisotropy of the subterranean rock layer based on the first time period and the second time period.

Abstract: Method of determining the velocity V and anellipticity ? parameters for processing seismic traces in a common midpoint (CMP) gather comprising:—a preliminary step to define a plurality of nodes (dtn, ?o), for each node (dtn, ?o) defined in the preliminary step, the following steps:—for static NMO correction of traces in the CMP gather as a function of the values of the said parameters dtn and ?o at the node considered, and calculation of the semblance function associated with the said NMO correction for the node considered; and—for each picked time to, a step including determination of the maximum semblance node (dtn (to), ?o (to)),—and a final step to convert the dtn (to) and ?o (to) parameters, so as to obtain the velocity to) and anellipticity ? (to) laws.

Abstract: A computer-implemented method for pseudo acoustic quasi-P wave propagation which remain stable in anisotropic media with variable tilt and is not limited to weak anisotropic conditions. The method includes acquiring a seismic exploration volume for a subsurface region of interest, and determining a modeling geometry for the seismic exploration volume. The method further includes propagating at least one wavefield through the seismic exploration volume utilizing the modeling geometry and initial conditions and preventing the accumulation of energy along the axis of symmetry of the seismic exploration volume and ensuring positive stiffness coefficients in the stress-strain relations through the use of finite quasi-S wave velocities thereby producing a stable wavefield. The method includes utilizing the stable wavefield to generate subsurface images of the subsurface region of interest.

Abstract: The invention relates to a method of processing seismic data, the said seismic data comprising a gather of seismic traces organised according to one or several acquisition parameters, comprising the steps of: a) defining an equation for an RMO curve as a combination of elementary functions of the acquisition parameter(s), b) determining an RMO curve from the equation of step (a) as a combination of orthogonal elementary functions c) for a given time or at a given depth, determining the coefficients of the combination that optimise the semblance of traces along the RMO curve.

Abstract: The invention relates to a method of processing seismic data, the said seismic data comprising a gather of seismic traces organised according to one or several acquisition parameters, comprising the steps of: a) defining an equation for an RMO curve as a combination of elementary functions of the acquisition parameter(s), b) determining an RMO curve from the equation of step (a) as a combination of orthogonal elementary functions c) for a given time or at a given depth, determining the coefficients of the combination that optimise the semblance of traces along the RMO curve.

Abstract: Method for processing seismic data. In one implementation, the method includes converting a common midpoint (CMP) gather of seismograms into one or more interferogram common midpoint (ICMP) gathers, generating a semblance spectrum for each ICMP gather, stacking the semblance spectrum from each ICMP gather to generate a combined semblance spectrum and deriving a normal moveout (NMO) velocity profile from the combined semblance spectrum.

Abstract: Shallow drilling hazards (44), such as karsts, caves, voids and unconsolidated discontinuities, that can pose significant risks to exploration and development well drilling operations are detected employing seismic refraction data on which a series of attribute analyses are performed, the resulting data being further processed to provide a three-dimensional visualization. Refracted wave raypaths (40, 46, 48) are highly distorted by encountering a karst feature with the occurrence of backscattering absorption. The resultant energy recorded at the surface receivers (52) is significantly reduced as compared to refracted waves recorded by other receivers (50) where no karsting is present. Multiple refractors are subjected to a relatively simple and rapid processing using commercially available software to track these differences and to map them in the near surface to improve the siting of wells and to alert drilling engineers and crews to the possibility of encountering the hazard.

Abstract: A method of processing seismic data comprises processing data representative of the acceleration wavefield so as to obtain information about the earth's subsurface direct from the seismic data representative of the acceleration wavefield. In conventional techniques for processing seismic data representative of the acceleration wavefield the data are transformed to the velocity domain at an early stage in the processing. The invention enables the transform step to be eliminated, thereby simplifying the processing and eliminating the risk that the transform might degrade the data. Furthermore, the increased sensitivity at high frequencies of a typical acceleration sensor compensates for the low-pass filter effect of the earth.

Abstract: A method is disclosed for processing seismic data. The method includes prestack depth migrating seismic measurements to compute common angle domain image gathers with an initial depth model. Residual moveout analysis is performed in the common angle domain, moveout corrections are derived in terms of the residual radii of curvature at zero reflection angle. Corrections for larger reflection angles are obtained from separate analyses for the coefficients of suitable series expansions. The residual radii of curvature at zero reflection angle can be used to improve the signal to noise ratio of the migrated data and to assess or improve the velocity model used for the prestack depth migration.

Abstract: A method and apparatus for predicting interbed multiples is described herein. Trace geometries may be generated for one or more desired shot-side traces, one or more desired receiver-side traces, and one or more desired interbed multiple generator traces, for a first target trace. A first set of reflections at the interbed multiple generator layer may be extracted from one or more recorded traces closest to the desired interbed multiple generator traces. A second set of reflections below the interbed multiple generator layer may be extracted from one or more recorded traces closest to the desired shot-side traces. A third set of reflections below the interbed multiple generator layer may be extracted from one or more recorded traces closest to the desired receiver-side traces. The interbed multiples for the first target trace may be estimated based on the first set, the second set, and the third set.

Abstract: This is a method of separating simultaneous sources that uses an inversion-type approach. Each source will preferably activated at a random time with respect to the others. These random delays tend to make the interference between sources incoherent while the reflections create coherent events within a series of shots. The shot separation is performed via a numerical inversion process that utilizes the sweeps for each shot, the start times of each shot, and the coherence of reflection events between nearby shots. This method will allow seismic surveys to be acquired faster and cheaper.

Abstract: A method for estimating seismic velocities in vertically transversely isotropic media includes generating an initial estimate of vertical interval velocity and interval normal moveout velocity with respect to depth from seismic data. An initial estimate is generated of a first anisotropy parameter with respect to depth. The first anisotropy parameter is related to the interval normal moveout velocity and the interval vertical velocity. An initial estimate is generated with respect to depth of a second anisotropy parameter. The second anisotropy parameter is related to the first anisotropy parameter and an interval anelliptic parameter. A first tomographic inversion is performed with respect to the interval normal moveout velocity and the second anisotropy parameter at a constant value of the first anisotropy parameter until travel time differentials reach minimum values. Layer depths are adjusted with the initial estimate of vertical interval velocity.

Abstract: A method for generating an average gamma factor for recorded PS data and recorded PP data. The method includes mapping one or more arrival times of the recorded PS data onto one or more expected arrival times of the recorded PP data using an estimated average gamma factor, identifying one or more corresponding pairs of events in the recorded PS data and the recorded PP data using forward modeling, applying geophysical reasoning on the corresponding pairs of events and generating the average gamma factor.

Abstract: A method for estimating seismic velocities in vertically transversely isotropic media includes generating an initial estimate of vertical interval velocity and interval normal moveout velocity with respect to depth from seismic data. An initial estimate is generated of a first anisotropy parameter with respect to depth. The first anisotropy parameter is related to the interval normal moveout velocity and the interval vertical velocity. An initial estimate is generated with respect to depth of a second anisotropy parameter. The second anisotropy parameter is related to the first anisotropy parameter and an interval anelliptic parameter. A first tomographic inversion is performed with respect to the interval normal moveout velocity and the second anisotropy parameter at a constant value of the first anisotropy parameter until travel time differentials reach minimum values. Layer depths are adjusted with the initial estimate of vertical interval velocity.

Abstract: Diagonal gather trace interpolation systems and methods are disclosed. In some embodiments, the method includes obtaining seismic traces from a marine seismic survey performed using typically two seismic sources fired in a flip-flop pattern. The seismic traces are processed in common field file trace groups from each cable by performing trace interpolation in opposing diagonal directions. Among other things, diagonal trace interpolation may improve azimuthal regularization. In any event, the disclosed interpolation methods maintain spatial bandwidth increased spatial resolution with increased inline and crossline sampling components. Diagonal gather trace interpolation exploits reduced input trace separation to provide improved stability and detection of a greater range of formation dip angles. After interpolation and regularization, the seismic traces may be imaged and interpreted for improved seismic exploration and monitoring.

Abstract: A method and apparatus for predicting a plurality of surface multiples for a plurality of traces in a record of seismic data. In one embodiment, the method includes providing a plurality of target traces at a nominal offset and a nominal azimuth; selecting a plurality of pairs of input traces, wherein the midpoints of the input traces in each pair are separated by half the nominal offset and the azimuth of a line connecting the midpoints of the input traces in each pair is equal to the nominal azimuth; convolving the selected pairs of input traces to generate a plurality of convolutions; and applying a three dimensional operator to the convolutions.

Abstract: A method of processing seismic data including convolving at least first and second seismic data traces or respective portions of at least first and second seismic data traces to forma composite trace. The travel time of an event may then be determined in the composite trace. This provides an improved method compared to the prior art technique of picking the travel time of an event individually in each one of a number of seismic data traces and averaging the individual picked travel times.

Abstract: Method for processing seismic data. In one implementation, the method includes converting a common midpoint (CMP) gather of seismograms into one or more interferogram common midpoint (ICMP) gathers, generating a semblance spectrum for each ICMP gather, stacking the semblance spectrum from each ICMP gather to generate a combined semblance spectrum and deriving a normal moveout (NMO) velocity profile from the combined semblance spectrum.

Abstract: Coherent wave noise energy is removed from seismic data by modeling both the P-wave primary energy and the coherent wave noise energy. The P-wave primary energy is modeled first and then subtracted from the input data. The data with the P-wave primary energy removed is used as the input for coherent wave energy removal. The coherent wave energy is modeled and subtracted from the original input data, i.e. the data input into P-wave primary removal. This leaves a dataset with P-wave primary energy and noise energy not related to coherent waves. This method can be utilized to remove all types of coherent noise with a velocity difference to the desired P-wave primary energy or with a different type of moveout (change of time of arrival with source-receiver distance) such as, for example, linear moveout.

Abstract: A computer-implemented method of accounting for angle-dependent wavelet stretch in seismic data based on a novel relationship between wavelet stretch and the cosine of a reflection angle of an acoustic ray. Conventional seismic data having at least one wavelet, such as data generated from a reflection seismic survey, is accessed. The data is processed such that at least one wavelet is subject to angle-dependent wavelet stretch. A reflection angle for at least one wavelet is also determined. An operator is utilized to calculate a wavelet stretch factor for at least one wavelet based on the cosine of the corresponding reflection angle of the wavelet. The wavelet stretch factor is applied to the seismic data to account for angle-dependent wavelet stretch.

Abstract: A method is disclosed for depth migrating seismic data. The method includes pre-stack time migrating the seismic data to form a stacked, time migrated image. The stacked, time migrated image is demigrated, and post-stack depth migration is then performed on the demigrated image. In some embodiments, the pre-stack time migration and the demigration account for ray bending in vertically transversely isotropic media.

Abstract: System and method for performing anisotropy corrections of post-imaging seismic data for a subsurface formation. The method may receive seismic data, preferably pre-stack seismic data comprising a plurality of traces, e.g., collected from a plurality of source and receiver locations. The seismic data may be imaged/migrated to produce imaged seismic data, which is organized into an arrangement that preserves aspects of the relative seismic propagation angle in the subsurface. One or more anisotropic parameters and corresponding corrections may be determined by analyzing the organized imaged seismic data. The determined parameters or corrections may be used to correct at least a subset of the imaged seismic data, thereby producing corrected seismic data which is useable in analyzing the formation. The corrected data may then optionally be stacked to produce a collection of corrected stacked traces, and/or analyzed as desired. The pre-stack data and/or the corrected seismic data may optionally be displayed.

Abstract: A technique for calculating traveltime of a seismic wave in three dimensional tilted transversely isotropic (3D TI) media includes determining a wave vector, defining a unit vector, calculating an angle of the wave vector from an axis and performing a slowness determination, wherein a unit vector for a symmetry axis is defined as: (cos ? sin ?, sin ? sin ?, cos ?); where ? represents the azimuth of the symmetry axis measured from the x direction; and, ? represents the dip angle of the symmetry axis measured from the z direction. The technique may be practiced as a computer implemented set of instructions, and may be incorporated into measurement equipment.

Abstract: The present invention provides a method and apparatus for arriving at true relative amplitude destretched seismic traces from stretched seismic traces. The method compensates for offset varying reflection interference effects due to normal moveout. Stretch factors ? and also input spectra are determined for NMOR stretched seismic traces. Estimates are then made of stretched wavelet spectra from the input spectra. A destretched wavelet spectra is then obtained. Shaping correction factors are determined by taking the ratio of the destretched wavelet spectra to the stretched wavelet spectra and are applied to the input spectra of the stretched traces to arrive at a destretched trace spectra. True relative amplitude scaling factors are computed by taking the ratio of a true relative amplitude property of the destretched wavelet spectra to a corresponding true relative amplitude property of the stretched wavelet spectra.

Abstract: A method is disclosed for amplitude preserving Kirchhoff time migration. The method includes calculating estimates of the geometrical spreading terms using a constant velocity approximation. Takeoff and emergence angles are accurately calculated based on a model of velocity which varies with respect to travel time. An image can be calculated at at least one travel time using the estimated weights and calculated takeoff and emergence angles.