Abstract: A method for determining migration before summation including recording seismic reflection traces, for constituting a collection of traces to be migrated before summation and without weight correction. The traces being classified according to a given criterion and using a velocity model. The method including determining, for each point of interest M in a domain (X, Z), at least one line of slope determined on the basis of a line of slope map, in determining the specular rays associated with one point M and for the line of slope, and in computing the time and amplitude characteristics of each of the specular rays for deducing therefrom the reflection factor in each point M.

Abstract: The present invention provides a method of migrating seismic records that retains the information in the seismic records and allows migration with significant reductions in computing cost. The present invention comprises phase encoding seismic records and combining the encoded seismic records before migration. Phase encoding can minimize the effect of unwanted cross terms while still allowing significant reductions in the cost to migrate a number of seismic records.

Abstract: Accurate and reliable traveltimes for a seismic exploration volume having a complex velocity structure are generated by selectively advancing a traveltime front at its minimum traveltime grid point, using an entropy-satisfying finite-difference approximation to the eikonal equation. A narrow band propagation zone is used to advance the finite difference stencil. Tentative traveltimes for the narrow band adjacent to the traveltime front are computed using the eikonal equation and arranged on a heap. The minimum traveltime (top of the heap) is selected as an accepted traveltime, saved in the output table, and removed from the heap. Tentative traveltimes for all non-accepted grid points neighboring the selected point are then computed/recomputed and put on the heap. The traveltime computation is fast, unconditionally stable, resolves any overturning propagation wavefronts, and ensures that the eikonal equation is globally solved for each point of the 3-D grid.

Abstract: An improved method for eliminating reflections from artificial model boundaries encountered in finite-difference acoustic wave propagation computations is based on applying two different boundary conditions at the artificial boundary. In this method one boundary condition generates reflections having the same polarity as the incident acoustic wave, and the other boundary condition generates reflections with opposite polarity. To apply the improved method simply compute both boundary conditions on a small narrow region adjacent the artificial boundary on a separate set of grids and average the two solutions.

Abstract: A method for the determination of migration velocities in seismic processing in which a blasting point S is associated with receivers (R.sub.1 to R.sub.n) which are separated by offsets such that in a given speed range, a first set of traces derived from the blasting point and registered on the receivers, and a second set of traces in constant and colinear offset to the first set are migrated. Two migrated images of the part of the site corresponding to the two sets of traces are obtained. The two images are correlated by means of a spatial two-dimensional correlation, the result thereof determining the deviation between the migration used and the investigated velocity. The result is particularly useful in the seismic prospection of a site.

Abstract: A marine seismic signal is transformed from time domain into frequency domain and represented by matrix D. The marine data signal is truncated in time, transformed into the frequency domain and represented by matrix D.sub.T Eigenvalue decomposition D.sub.T=S.LAMBDA.S.sup.-1 of matrix D.sub.T is computed. Matrix product D S is computed and saved in memory. Conjugate transpose [D S]* is computed and saved in memory. Matrix product [D S]*[D S] is computed and saved in memory. Matrix inverse S.sup.-1 is computed and saved in memory. Conjugate transpose (S.sup.-1)* is computed and saved in memory. Matrix product S.sup.-1 (S.sup.-1)* is computed and saved in memory. An initial estimate of the source wavelet w is made. Source wavelet w is optimized by iterating the steps of computing the diagonal matrix [I-w.sup.-1 .LAMBDA.], computing matrix inverse [I-w.sup.-1 .LAMBDA.].sup.-1, computing conjugate transpose [(I-w.sup.-1 .LAMBDA.).sup.-1 ]*, retrieving matrix products [D S]*[D S] and S.sup.-1 (S.sup.

Abstract: A novel fault framework method and apparatus automatically computes the relationships between intersecting fault surfaces. When faults are loaded into the novel fault framework apparatus, all intersecting fault pairs are determined and the fault fault intersection lines are computed and stored. The intersecting fault pairs are presented and available for automatic calculation of the major/minor and above/below fault pair relationships. The geometry of both intersecting fault surfaces are examined on either side of the fault fault intersection line. This, in combination with the relative size of the faults, is analyzed to compute the major/minor and above/below relationships based on geologic assumptions and knowledge of the origin of the fault surface data. When the relationships between intersecting faults is defined, the minor fault is appropriately truncated.

Abstract: A method for generating an unaliased 3-D DMO operator using two dimensional sampling theory to the spatial traverse of the operator as well as to the temporal axis. First a continuous DMO operator is generated along the line segment connecting a source and a receiver directed at an arbitrary azimuth relative to a biaxial output grid. The operator is discretized at spaced-apart sample points along the DMO aperture segment, the spacing being equal to or less than the output grid dimensions. A exponentially tapered sinc filter function is applied to the samples which are then interpolated onto the output grid.

Abstract: A method for representing in a space-time domain the trajectory of at one borehole by:a) producing a velocity-depth model (4) tied to the borehole (1), geologically representative of said area and including a representation of said trajectory (5) of said borehole;b) selecting at least one point (A) on or near said trajectory, said point (A) being defined by its space coordinates and by at least one dip-azimuth data pair; andc) at least modelling in a synthetic stack domain (9) the image (a) of the selected point (A), said image (a) being defined by space-time coordinates and by a dip-time vector and being obtained by zero offset ray tracing in the velocity-depth model (4).

Abstract: The object of the method according to the invention is to synthesize zero-offset seismic data from data acquired within the scope of three-dimensional (or possibly two-dimensional) multiple-offset seismic reflection prospecting operations in a subsurface environment. It mainly comprises selection of a distribution model of the velocities in the environment, seismic data prestack migration (stacking of the multiple-offset seismic events is achieved in the depth domain), and synthesis of zero-offset seismic data in the time domain by applying to the results obtained with this depth domain stacking a known modelling technique, for example that referred to as explosive reflector technique.

Abstract: A method of modelling at least travel time and apparent dip from seismic data that has been processed by at least one migration operator comprising the steps of taking the mid-point (N.sub.1) of a source (S)/receiver (R) system, applying ray tracing to the system relative to a given reflector, processing the parameters of the ray using a migration operator to obtain a first point of arrival (N'.sub.1) marked on the model, determining the offset (.DELTA.e1), and proceeding iteratively at each new point of arrival (N'.sub.i) until the offset (.DELTA.E) is less than or equal to the predetermined offset (.DELTA.e).

Abstract: A method for utilizing instantaneous phase and the derivatives of instantaneous phase as display and/or plot attributes for seismic reflection data processing and interpretation for two-dimensional and three-dimensional seismic data. The spatial frequency, dip magnitude and dip azimuth attributes of the seismic events are calculated using the rate of change of instantaneous phase with space, instantaneous frequency and velocity, and displayed or plotted to assist interpreters in identifying fault breaks and stratigraphic features in the earth's subsurface.

Abstract: An array of output image points is distributed over a velocity model of a subsurface region of interest. A fan of rays is shot from each of a plurality of acoustic source points along the surface, the angular separation between the rays being equal to .pi./n, where n is the number of rays. A family of traveltime wavefronts is erected at selected time intervals, .DELTA.t, along the ray trajectories. The resulting wavefront map is superimposed over the array of output image points. Sub-arrays of output image points will lie within discrete traveltime cells, the widths of which are defined by the separation between adjacent rays paths and the heights are defined by the wavefront separation distance. Ray segments, wavefront segments and output image points are identified by a velocity layer index. A velocity interface that may cut across a traveltime cell, divides the cell into two parts, each having a different layer index.

Abstract: A method of processing seismic signal data that uses a special Radon transform for dip moveout (DMO) including the steps of applying conventional pre-DMO steps to the traces, applying a special Radon DMO transform to the traces to obtain a post-DMO section in Radon domain, applying a conventional inverse Radon transform to obtain a post-DMO section in space-time domain with a time and space DMO shift on the traces, and applying conventional post-DMO steps to the resultant traces.

Abstract: A method for minimizing non-uniform insonification of subsurface formations in the presence of steep dips when advancing a swath of elongated parallel seismic streamer cables along a line of survey. A first acoustic source is stationed at the leading end of the swath and a second source is stationed at the trailing end of the swath. The sources are activated in alternate cycles at preselected timed intervals to provide down-dip and up-dip seismic data sets. The data sets are processed and merged to eliminate objectionable shadow zones.

Abstract: A method of migrating seismic data using offset checkshot survey measurements. The offset checkshot survey measurements involve raypaths similar to the migration raypaths for the seismic data, and are used to determine direct arrival traveltimes to receivers in a borehole. Embodiments of the invention provide for direct use of the traveltimes in migration, or indirect use of the traveltimes in migration via construction of a migration velocity model. The velocity model embodiments further provide for either traveltime error correction via use of interpolated error functions or construction of migration error tables. The invention can be employed for time, depth or Kirchhoff migration, in either two or three dimension, and in either prestack or poststack applications.

Abstract: A method for determining the reliability of time processed seismic reflection data near a significant velocity differential overhang includes displaying the seismic reflection data as a seismic section showing impedance differential interfaces. The position of an edge of the velocity differential overhang is located and acoustic velocity values are interpreted. A set of curves representing boundaries of reliability for predetermined dip values is determined. The set of curves representing boundaries of reliability may be displayed. The display of the set of curves representing boundaries of reliability may be overlaid on the seismic section representing the seismic reflection data. The dip angle for an interface of interest is approximated. The interface of interest is compared with the curve representing boundaries of reliability for the dip angle for the interface of interest to determine the extent of reliability of the data used to map the end of the interface under the overhang.

Abstract: Disclosed is a method for efficiently and accurately determining subsurface velocities for use in migration of seismic data. The method calls for restricting the number of traces considered to those lying upon that portion of the Kirchhoff summation curve wherein the integrand for Kirchhoff migration is smooth. In the preferred embodiment, only a random sample of traces within this aperture are used in the calculations. Improvements in efficiency on the order of a factor of 1000 can be realized with the preferred embodiment.

Abstract: A method for efficiently and accurately migrating seismic data recorded from an area of interest is disclosed. The method utilizes determining displacement values for every output sample in an area of interest, preferably by generating a displacement section from a velocity section and depth model. The displacement values are then used to select a migration aperture for the migration algorithm.

Abstract: A method for improving seismic sections includes generating seismic signals at source stations, recording seismic traces at receiver stations and gathering the seismic traces as a first gather at a common point as a function of the offsets between the source stations and the receiver stations. A common point (MMOCMP) is selected, a half-offset between source and receiver stations is redefined as a function of the distance between the selected common point MMOCMP and the RAWCMP, and the seismic traces are sorted as a function of the redefined half-offset, constituting a second gather of traces. The method permits one to obtain true located subsurface information at any desired point for velocity analysis.

Abstract: A method for three dimensional migration of a two dimensional grid of seismic data. The method involves computation of three dimensional time-dip functions at the intersections of lines in the grid. Inverse raytracing is used to correctly position the reflection events in the three dimensional volume encompassed by the grid. Migration of the seismic data is performed onto image surfaces defined from the correctly positioned reflection events.

Abstract: A method and device for obtaining a zero-offset seismic section from a stack seismic section produced from stack traces recorded along a given line of survey, is disclosed.

Abstract: A method of producing a velocity volume for a seismic survey volume, based on two-way time seismic data and process velocity data, is disclosed. Two-way time seismic data is loaded into a computer for a plurality of seismic shot lines in the survey region, as are process velocities for common depth points (CDPs) in the survey region. The process velocities correspond to velocities used to perform normal move-out, dip move-out, migration and other imaging processes. The computer can display the two-way time information in cross-section or map views, and can display the velocity functions as a function of two-way time. The human analyst enters interpreted velocities, based on actual data or on visualization of the horizons, into the cross-sectional view of the seismic shot line, and then edits the input velocity data to produce a velocity function, for each CDP of interest, that matches the interpreted values.

Abstract: Disclosed is a technique for processing seismic data to enable the data to be migrated without stacking. Seismic data provided in common midpoint gathers are converted to a domain defined in terms of the travel time and the first power of velocity of reflected waves, and migration is performed in this domain. The migrated seismic data is converted back to the offset domain, wherein velocity analyses may be performed prior to stacking of the data.

Abstract: An overturned wave is identified in initial seismic data and revised seismic data gathering parameters are calculated (e.g., a range of locations for a seismic source and detectors laterally displaced from the source). The gathered seismic data is used to image the interface by using an imaging algorithm capable of migrating downgoing and upcoming reflections.

Abstract: This invention provides a method for examining the geometry of the disposition of a plurality of sources and receivers over an area to be surveyed with a view to optimizing the array to avoid data shadow zones and to optimize the resulting seismic image. The method depends upon studying the statistical distribution of dip polarity in dip bins along selected CMP azimuths.

Abstract: A hybrid velocity model is used to image the subsalt reflector. A method for imaging subsalt reflectors includes receiving seismic data and depth migrating the raw data. Generated seismic P-waves are assigned a first P-wave velocity for travel outside a salt wedge. Prior to entering the salt wedge, the wave is treated as a compressional wave. Upon entering the salt wedge, the P-wave is treated as a converted S-wave and a corresponding S-wave velocity is assigned to the converted wave. When the converted S-wave exits the salt wedge, it is again converted, this time back to a P-wave. As this wave travels through the subsalt layer to a reflector interface, it is assigned a P-wave velocity. Thus, a velocity model which includes both P-wave and S-wave velocities is used to image reflectors below salt wedges.

Abstract: A three dimensional residual modeling operator is applied to seismic times that have been preprocessed by application of NMO and velocity independent DMO. The residual operator compensates for vertical velocity variation and anisotropy and its use precludes the need for ray tracing.

Abstract: A process for depth migration of seismic wave information that has been derived from geological media that causes rapid lateral velocity variations in seismic waves. The process includes the step of decomposing wavefields recorded at the earth's surface using Gaussian beams as basic functions. Then, according to the process, the set of Gaussian beams is extrapolated downward into the earth to obtain the subsurface wavefield. Finally, the wavefield is processed to provide depth-migrated images of subsurface reflectors.

Abstract: In areas where the velocity gradient is strong or exhibits a significant positive curvature, the usual phase shift f-k migration methods cannot properly image overtuned dips due to diving waves. In this disclosure, an Airy operator is substituted for the classical phase shift operator.

Abstract: A method is disclosed for a two-step residual migration of dipping seismic events. A first migration pass is done using a fully-vertically-variable but laterally-invariable migration velocity that is selected from a first-stage mmigration velocity function. The first-stage velocity function approaches, but is less than, the velocity minima as determined by scanning the true velocity field in an area of interest. The second migration pass is performed with the aid of a dip-dependent residual migration velocity. The residual migration velocity is defined as the square root of the difference between the true migration velocity and a second migration velocity appropriate to the migrated time following the first migration pass.

Abstract: The invention relates to a method for locating correct near vertical boundary or fault positions in a velocity model using common reflection point (CRP) gathers. Conventional migration velocity analysis examines the migrated image for hints to correct the velocity model. Vertical boundaries such as faults or salt flanks must be accurately determined to produce reliable images of deeper reflectors. Previous methods have placed faults by trial and error, since a depth image of a nearly vertical boundary is difficult to produce. The present method examines the sensitivity of CRP gathers to abrupt lateral changes across a nearly vertical fault to determine the location and the dip of a nearly vertical fault from a series of CRP gathers.

Abstract: A method for migrating seismic data for formations that are located in geological media that cause seismic waves to be refracted so substantially that the waves turn upward. The method includes the steps of tabulating a first phase shift function as a function of the wave vector and the angular frequency of seismic waves in the geological media, tabulating a second phase shift function, storing the tabulated values of the first and second phase shift functions, calculating a third phase shift function based upon the first and second phase shift functions; and migrating recorded seismic data using the first, second and third phase shift functions.

Abstract: Velocity spectra are computed from unmigrated CMP gathers after correction for dip moveout. The velocity spectra are then migrated to their true spatial position. The migrated velocity spectra are then used to calculate a migrated dip section.

Abstract: A method for improving velocity models so that constant-offset migrations estimate consistent positions for reflectors includes tomographic estimation of seismic transmission velocities from constant-offset depth migrations. A method of converting inconsistencies in reflector positioning from constant-offset migrations into equivalent errors in modeled travel times is introduced, so that conventional methods of traveltime tomography can improve the velocity model. An improved velocity model allows a more accurate migrated image of the subsurface. The estimated velocity model can also detect anomalous regions of geologic significance, such as low velocity gas accumulations and irregular near surface weathering. In an alternate embodiment the procedure can be iterative and allow alternating improvements in the positions of reflectors and in the velocity model.

Abstract: A method and apparatus for deriving a three-dimensional seismic image from an irregular grid of two-dimensional seismic data is provided. The two-dimensional seismic data incldue a plurality of shot lines. For each of the shot lines, a two-dimensional migration is performed therealong (22) to create a plurality of migrated shot lines. For each of a plurality of three-dimensional image points, the following substeps are performed. A migrated trace (X) is selected from each of the migrated shot lines that is closest to the image point (I). A further migration (30) is performed on each selected migrated trace (28) with respect to the image point (I). A three-dimensional migrated image (30) comprising the image points is thereby obtained. The invention allows the use of historical, irregular two-dimensional grids of seismic data to be efficiently used for the three-dimensional imaging of subsurface features.

Abstract: A method for performing velocity analysis while eliminating the effects on weak signals caused by strong signals includes migrating each event of the pre-stack trace to a single location instead of all possible locations. This correct location is determined by ray-tracing through a velocity model. The input trace is divided into many windows, and each window is migrated to a place determined by ray-tracing the center of the window through the model. If the velocity model is accurate, each event will be migrated to the proper location yielding an accurate depth section with no migration artifacts. As a by-product, if the model is not accurate, the post-migrated parts (PMP's) provide a clean velocity analysis.

Abstract: A method for determining the location of steeply dipping subsurfaces includes acquiring seismic reflection data, identifying select data which has characteristics indicating that the acoustic pulses which it represents have been reflected from a substantially horizontal interface and a steeply dipping interface, analyzing the select data to locate the steeply dipping interface and displaying the analyzed data.

Abstract: The present invention provides a three dimensional before stack depth migration of two dimensional or three dimensional seismic data. Ray tracing is used to move before stack trace segments to their approximate three dimensional position. The trace segments are scaled to depth, binned, stacked and compared to the model. The model can then be changed to match the depth trace segments which will be stacked better, moved closer to their correct three dimensional position and will compare better to the model.

Abstract: A model-based iterative method of depth-processing seismic data. An estimate of a geologic horizon is entered into a three-dimensional seismic model and synthetic shot records are determined from the model. Reflection tracks are estimated from the modeling results. The actual seismic traces are sorted into bins according to common reflection points determined from the reflection tracks and are stacked. The sorted and stacked data are used to estimate the difference between the seismic travel time and the model travel time, and the model is changed in order to match the seismic data. The process is repeated until the margin of error is acceptable. Lower horizons of interest are modeled in the same way until all the horizons of interest in a geological area are determined.

Abstract: A method for removing boundary-generated artifacts in synthetic and actual seismic data. After seismic data processing, undesirable boundary-generated artifacts appear in the final seismic section. To remove this unwanted noise from the section, zeros are added to the lower boundary of the seismic section. This essentially pushes the sources of the noise downward in time in the section. After padding with zeros, the seismic data is collapsed to their point sources of origin using the Stolt migration/diffraction algorithm. Once the data are collapsed, the size of the seismic section is reduced to its original size. Following the resizing of the section, the inverse of the earlier applied Stolt algorithm is applied to return the seismic data to its original form, minus the boundary-generated artifacts.

Abstract: A method is described for enhancing seismic data and, more particularly, for attenuating multiple reflection events in seismic data. Seismic data are sorted into common endpoint gathers, and selected multiple reflection events are corrected for time delays associated with the reflection of the seismic energy from common reflecting interfaces and aligned. The aligned multiple reflection events are attenuated and the resulting enhanced seismic data can then be inverse time-delay corrected for subsequent processing, including repetitions of the aligning and attenuation steps to suppress additional multiple reflection events in the seismic data.

Abstract: Seismic energy is generated at a multiplicity of source offsets from a borehole and offset VSP data is collected by an acoustic detector at a multiplicity of geophone depths for each source offset. The recorded data is sorted into Zero Source-Receiver (ZSR), common reflection point bins. Data from each offset VSP, ZSR common reflection point gather are dynamically moveout corrected with data adaptive parameters including reduced direct arrival times, dip, borehole deviation and stacking velocities. The moveout corrected VSP data are then stacked.

Abstract: A method for migrating seismic data in the frequency-wave number domain is provided for migrating the seismic data having large vertical and lateral velocity variations in a fast, efficient and accurate manner. A root-mean-square (RMS) velocity function is derived from a set of seismic data samples comprising a body of seismic data. A best fit migration velocity is determined from the seismic data so as to provide a best migration. The seismic data may then be partitioned into a series of discreet frames and stretched according to a predetermined algorithm. Each partition is migrated in series by a portion of the RMS Velocity function until the data are fully migrated. After migration, the migrated seismic data are inversely stretched vertically followed by an inverse lateral stretch to remove any distortion instilled in the data by the initial data stretching.

Abstract: Method of analyzing the structure of a medium by means of waves reflected by inner interfaces, comprises: (a) generating multiple coverage data represented by traces corresponding to a plurality of source-receiver pairs distributed according to an asymetric polynomial distribution with respect to a predetermined central point with optimal parameters which provide that all reflected events of such traces correspond to the same common reflecting point on a reflecting interface; (b) correcting the recorded traces according to an optimal time delay correction which converts all reflected events to the same phase and which depends on the local parameters of wave propagation velocity Vo at the reference level, and of radius of curvature r.sub.o of the wavefront emitted by a fictitious source located at the common reflecting point and coming to the central point at an angle of entry .beta.

Abstract: A method for carrying out dip moveout correction on seismic data which provides true-amplitude seismic images is provided. A calibration process is used to design a set of filters that correct the seismic amplitudes during dip moveout correction so as to provide true-amplitude imaging. These filtrs can be designed and applied in any known implementation of dip-moveout, in three or two dimensions.

Abstract: An endfire seismic array comprises one or more marine seismic cables having a plurality of acoustic-to-electrical hydrophone receivers spaced therealong, each being operatively connected in combination so that as a unit an endfire receiving beam pattern with respect to any frequency across the seismic band is formed by causing the signals from the individual hydrophone receivers to be additive for that frequency. A plurality of cables results in a more narrow beam than a single cable. A geologic or lithologic formation that is a dip change from the norm may be detected either as an extra strong increase or decrease in signal, depending on the mode of use.

Abstract: The present invention provides methods for processing converted wave seismic data which includes, fractional point gathering of the data in a manner consistent with a selected velocity model, dynamic correction of the data using parameters measured from the data to account for the asymmetric travel path of the converted wave rays and stacking the dynamically corrected data. Methods are also provided for updating the velocity model.

Abstract: Depositional reconstruction for petroleum location is a new exploration-development technique for delineating hydrocarbon accumulations and prospect development. The technique uses existing information and establishes a relationship between present day subsurface structure and stratigraphic prehistoric reservoir development for determination and projection of relative reservoir development, definition and grading of combination structural-stratigraphic type traps, determination of permeability barriers, migration paths, accumulation areas, prospect grading, pressure cells and prediction of fluid movement. Depositional reconstruction results in a summary map which outlines productive areas, shows potential extensions, graded prospects, relative reservoir developments, and the other stratigraphic conditions which control the successful economic exploitation of a potential horizon.

Abstract: Disclosed are a well logging process and a well logging system using dipmeter and other logs to find subsurface faults and unconformities and automatically produce therefrom, and with user interaction, a subsurface map of the structural and depositional environment and stratigraphic characteristics of subsurface formations particularly important in the search for and exploitation of subsurface resources such as hydrocarbons.