Abstract: The amplitude spectrum is generated within a selected time window of a seismic time scale recording. The rate of change, Q, of the natural logarithm of the signal amplitude is measured with respect to frequency. A Q-derived static time shift is computed and applied to the selected seismic time scale trace to correct the raw seismic times for dispersion-induced time distortion. Amplitude-correction and phase-correction filters are applied to the static-corrected trace to provide a new time scale trace corrected for velocity dispersion which is processed to provide a physical model of the subsurface of the earth.

Abstract: A method is disclosed to identify existence of near-surface drilling hazards in the vicinity of a sea floor location comprising the steps of: obtaining 3D seismic data for the seafloor in the vicinity of the sea floor location; preparing high resolution 3D vertical profiles from the 3D seismic data; preparing an artificially-illuminated rendered surface based on the 3D seismic data; and identifying existence of near-surface hazards in the vicinity of the sea floor location by visual analysis of the rendered surface with reference to the high resolution 3D vertical profiles. Deep tow and geohazard surveys, which are expensive and time consuming are not required in the practice of the present invention. 3D seismic surveys that are used in the practice of the present invention have often been prepared for other purposes.

Abstract: A method of determining the acoustic propagation velocity of an earth formation penetrated by a wellbore by processing signals from an array acoustic wellbore logging tool. The tool includes a transmitter and a plurality of receivers axially spaced apart from the transmitter. The method includes the steps of combining signals generated by ones of the receivers in response to acoustic energy propagated through the wellbore from the transmitter, to generate a synthesized signal corresponding to another one of the receivers. The step of combining includes time shifting signals from the ones of the receivers by an amount corresponding to a predetermined velocity for each propagation mode and the axial distance between the ones of receivers and the other receiver. The synthesized signal is compared to the signal generated at the other receiver in response to the acoustic energy to determine a degree of correspondence between the synthesized signal and the received signal.

Abstract: A multivariate stochastic simulation application that involves the mapping of a primary variable from a combination for sparse primary data and more densely sampled secondary data. The method is applicable when the relationship between the simulated primary variable and one or more secondary variables is non-linear. The method employs a Bayesian updating rule to build a local posterior distribution for the primary variable at each simulated location. The posterior distribution is the product of a Gaussian kernel function obtained by simple kriging of the primary variable and a secondary probability function obtained directly from a scatter diagram between primary and secondary variables.

Abstract: Apparatus and method are disclosed for use with a horizon picking method for 3D seismic data. Variables such as picking method, whether simple or iterative, score required of an iterative method and .DELTA.T between target wavelets and seed wavelet are input into the computer. During the picking process, parameters as to the number of successful picks and the number of failed picks because of the method of picking and because of failed picks due to the score not being achieved in the iterative method and because of failed picks due to the difference in time between the target wavelet and the seed wavelet being greater than the .DELTA.T variable are recorded. Parameters as to successful picking percentage of all target traces attempted to be picked and failure percentages are displayed simultaneously with the picked horizon and the input picking parameters.

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: A method for spectral noise abatement from seismic data. The data are decomposed into organizational components from which a noise component can be resolved by well-known iterative methods. A statistic is calculated by comparing the measured spectral content of the data with a model spectrum. The seismic data are scaled in proportion to the ratio between the model spectrum and the measured spectrum, following which the processed signal traces are displayed as representative of a cross section of the earth.

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: The relative amplitudes of seismic reflection data contains very useful information about the subsurface earth formations. Surface and subsurface-consistent amplitude processing identifies and corrects for the variability introduced by instrumentation and surface distortions. Dynamic amplitude decomposition, the subject of this disclosure, identifies and compensates for reflection amplitude fading due to subsurface transmission absorption media.

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 method for adaptively creating a filter for removing coherent environmental noise from a multitrace digitized seismic recording requires the presence, on the recording, of a limited sample of pure noise that is uncontaminated by desired signal. The pure noise sample is used to discover the location of the noise source and from that discovery, to extrapolate and reconstruct the characteristics of the noise envelope as it would appear on the seismic recording. The reconstructed noise envelope is used as a noise reference for input to a conventional iterative adaptive noise cancellation filter loop. For stability, the loop gain is minimized by temporally and spatially averaging the filter coefficients for each sample interval.

Abstract: A method for associating each descendent picked point with a parent seed point is disclosed which is used in a computerized method of automatically picking horizons from a three dimensional volume of seismic data traces. Such association of each and point to each of its descendent picked points is recorded in computer memory. The method further includes displaying a path from a descendent picked point back to a starting seed point which led to its selection as a picked point.

Abstract: A discretized lithologic model of the subsurface is defined by a regular array of pixels. Each pixel corresponds to one of a finite number of possible lithoclasses such as sand, shale or dolomite. The lithoclasses are unknown except at a small number of sparsely distributed control pixels associated with borehole locations. Associated with each pixel there is a multivariate record of seismic attributes that may be statistically correlatable with the local lithology. A Monte Carlo method is used to simulate the lithoclass spatial distribution by combining the lithologic data at control pixels with the seismic-attribute data records. Using Indicator Kriging, a prior probability distribution of the lithoclasses is calculated for each pixel from the lithology values at neighboring pixels. The likelihood of each lithoclass is also calculated in each pixel from the corresponding conditional probability distribution of seismic attributes.

Abstract: A method for displaying seismic attributes in an open three-dimensional format is provided. The conventional two-dimensional variable-amplitude traces that represent the magnitude of a selected seismic attribute as a function of time are converted to three-dimensional format. The three-dimensional converted traces are hung beneath a model of their corresponding data-gathering stations to provide a forest of seismic traces in a wire-frame environment. The open configuration of the seismic traces permits the interpreter to see a perspective view of the structure of the subsurface of the earth from any desired viewing angle.

Abstract: Seismic data is combined with well log data to generate a two-dimensional geopressure prediction display; this permits deviated and horizontal well planning plus lithology detection. Shale fraction analysis, compaction trend, and seismic velocity may be automatically or interactively generated on a computer work station with graphics displays to avoid anomalous results. Corrections to velocity predictions by check shots or VSP, and translation of trend curves for laterally offset areas increases accuracy of the geopressure predictions. Multiple wells' logs in a basin permits analysis fluid migrations.

Abstract: The method sequentially determines dips and corresponding estimated dip components of traces in a panel of data. The method can be applied to any data which can be represented as a function of two coordinates. In particular, the method can be applied to seismic data traces. The method in one embodiment sums data on traces along a preselected range of trial dips on a panel of data. The energy of the summed data with their corresponding trial dip are then displayed. The dip which has the peak of maximum energy on the display is then selected as a valid dip. An estimated dip component of the selected dip is then determined and subtracted from the traces along the selected dip. The process is then repeated, sequentially, determining a dip and an estimated dip component from the panel of data until the desired number of dips and estimated dip components are determined or the residual energy of the remaining data on the traces are below a preselected value.

Abstract: A method of processing seismic data wherein seismic data signals having a first part which shows a slow variation in offset and a second part which shows a slow variation in midpoint, is modelled using a model which allows the two parts to be separated. The individual parts may be reconstructed from the model. One of the parts corresponds to offset dependent noise and can be effectively removed from the seismic data.

Abstract: The present invention provides a method for rapidly and efficiently generating traveltime tables from complex velocity models for application in depth migration. Initially, a velocity model is received which may include a plurality of velocities with various subsurface reflectors or boundaries. The model is plotted with the boundaries defining closed area cells within the model, with the cells having given velocity structures. The outside of each cell, or the cell wall, is made up of a series of segments. In the first basic step, traveltimes are computed from a preselected source location to each sample point on each segment. In this step, the order of processing all the cells is important. Therefore, the present method proceeds from those cells that are closest to the source location first to those cells that are further away in an expanding wave front from the source location.

Abstract: A method of geophysical exploration is described for transforming qualitative descriptors of seismic data into a quantifiable decision-making tool to estimate the formation properties as well as economic potential of a selected formation in the earth's subsurface. Qualitative descriptors of the waveform of seismic events contained in a first set of seismic signals are obtained and correlated with formation properties to obtain a series of one or more histograms. Qualitative descriptors of seismic events contained in a second set of seismic data can be obtained and transformed into estimates of formation properties as well as estimates of the economic potential of a selected formation for producing hydrocarbons employing such histograms.

Abstract: A method and apparatus of rapidly generating horizon maps from a three dimensional volume of seismic traces is disclosed. During batch processing of the digital data representing trace wavelets, "1"'s are "0"'s are determined for each seismic trace of the volume. A bit volume is produced of which a "1" at a depth of a trace indicates that a horizon exists at that depth and at other depths of "1"'s of adjacent traces which are within a predetermined depth. In a real time mode, an explorationist selects a seed point thereby identifying a "1" on a particular trace at a particular depth. An automatic scanning procedure finds all other "1"'s at depths of adjacent traces. Each found "1" of adjacent traces is redesignated a seed point and the process is continued until no more "1"'s can be found. A horizon map is created from the depths of each found "1".

Abstract: The present invention provides method of interpolating spatially aliased seismic data. This method produces high resolution interpolated data based on a locally planar model of reflection events using a two dimensional power diversity slant stack process that transforms the data from the t-x-y domain to t-xslope-yslope domain. The present invention further provides an improved technique for the 3D interpolation of aliased events and is applicable to the interpolation of 2D seismic data.

Abstract: A method of translating a drawn or imagined model into a numerical format. Working from a paper sketch or interpreted seismic display, the geological horizons and faults are digitized in any order. If the horizon is unbroken, it is digitized continuously as one piece, if it is broken by faulting, it is digitized as a series of elements. Digitizing ceases if the horizon terminates within the model. During preconditioning the boundaries of the model are added as another element. A search is performed and if intersecting elements are found, the shortest limb is deleted. A second search locates elements which do not terminate at an intersection. If the element is from a horizon, it is projected until it intersects another element, if an unconnected fault element, the element is deleted back to its first intersection point. The first phase of cell construction identifies segments which connect only to themselves and produces single segment cells.

Abstract: A method for generating a three dimensional velocity model from a grid of two dimensional lines is presented. Each of the two dimensional lines is common offset depth migrated and the migrated common offset sections are sorted into common image point (CIP) gathers. The proposed method examines all the common image point gathers from all the two dimensional lines and extracts out of plane three dimensional information. An initial three dimensional model is constructed from the two dimensional depth sections by mapping the depth images of several reflectors from each two dimensional line. Ray tracing through this initial three dimensional model, the out of plane three dimensional information is used to compute a set of corrections to the boundaries in the three dimensional model. The three dimensional model boundaries are then iterated until all mismatches are minimized.

Abstract: A technique is disclosed for determining properties of an anisotropic elastic medium, such as earth formations. Acoustic waves are established in the medium. At several spaced locations in the medium, there are measured at least two orthogonal components of acoustic waves which have propagated through the medium. For positions corresponding to a plurality of adjacent ones of the spaced locations, there are computed model composite waves which would result from the superposition of a plurality of model acoustic waves, each having selected model parameters. The model acoustic waves include a plurality of model acoustic shear waves and the model parameters include model velocities and model polarizations for each of the model acoustic shear waves. An error value is determined, the error value depending on the differences, at each of the plurality of adjacent ones of the locations, between measured wave components and the model composite wave. The model parameters are then modified.

Abstract: A method for using mode converted P- or S- wave data to delineate the surface of an anomalous geologic structure such as a salt dome is disclosed. Seismic wavefields are propagated from near the surface, through the earth, and through the anomalous geologic unit, so that a wavefield encounters the geologic unit at a non-normal incidence angle to generate a converted S- wave. Incidence angles of the direct arrival and converted waves are then determined. The intersection point of each converted S- wave raypath with each direct arrival raypath is determined, to provide a length of the raypaths. Travel times along the raypaths are determined, and a point on the interface of the anomalous geologic unit with the surrounding earth is determined by comparing raypath travel time differences with the recorded arrival time differences.

Abstract: Methods are provided which utilize a sonic tool for quantitatively determining parameters of a velocity profile of an altered zone in a rock formation traversed by a borehole. Synthetic amplitude information for the formation is generated by a computer model, by providing the computer with a proposed velocity profile for the formation, including values for parameters such as the radius of the altered zone and the acoustic velocities in the altered zone. The synthetic amplitude information is then compared with amplitude information (e.g. peak or total energy) of a compressional headwave as measured by the array sonic tool. If the comparison provides differences exceeding predetermined thresholds, the values for the parameters of the model are adjusted according to a least squares fit procedure until suitable values are found. The suitable values are then taken as the parameter values.

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 of deterministically computer generating a model of a response voltage waveform of a seismic receiver employed in a seismic, particularly marine, data gathering system, the model incorporating factors that have been identified as significant contributions to amplitude, such as directivity, divergence, attenuation, interbed multiples, and transmissivity. The model is generated from the mathematical manipulation of well log data and data gathering system characteristics into a seismic range equation, namely: ##EQU1## where E.sub.r (f)=received energy densityE(f)=radiated energy densityD(.theta..sub.s, .phi..sub.s, f)=source directivity along .theta..sub.s, .phi..sub.s direction at the sourceA.sub.c (.theta..sub.H, .phi..sub.H, f)=Capture area along .theta..sub.H, .phi..sub.H direction at the hydrophone arrayR.sub.T =target reflection coefficientD.sub.

Abstract: In accordance with the invention, there is provided a system for determining the location of an acoustic impedance boundary within the earth. A seismic signal is generated at a first location and detected at a second location so that the signal travels from the source to the acoustic impedance boundary and from the acoustic impedance boundary to the sensor. In a first embodiment, the travel time from source to receiver and the direction, in three dimensions, of the arrival path of the signal at the sensor are determined. Utilizing the determined direction of travel to the sensor and known information regarding the velocity profile of the earth strata between the source and the acoustic impedance boundary and between the receiver and the acoustic impedance boundary, a calculated travel path from the source to receiver is determined over which the calculated travel time substantially equals the measured travel time.

Abstract: A method of rapidly generating horizon maps from a three dimensional volume of seismic traces is disclosed. During batch processing of the digital data representing trace wavelets, "1"'s or "0"'s are determined for each seismic trace of the volume. A "1" at a depth of a trace indicates that a horizon exists at that depth and at other depths of "1"'s of adjacent traces which are within a predetermined depth. In a real time mode, an explorationist selects a seed point thereby identifying a "1" on a particular trace at a particular depth. An automatic scanning procedure finds all other "1"'s at depths of adjacent traces. Each found "1" of adjacent traces is redesignated a seed point and the process is continued until no more "1"'s can be found. A horizon map is created from the depths of each found "1". A record is maintained of parent and child bits whereby seed bits are designated as parent bits and each found bit is designated a child bit.

Abstract: A method of deconcolving the non-ideal frequency response from acoustic vibrations transmitted along a structure such as a drill string is disclosed. The deconvolution retains the values of the transmission time between the signal source and the receiver, in the form of an exponential phase term, and is multiplied by the amplitude frequency response of the structure. The input data time series, after transformation into the frequency domain, is then divided by the deconvolution operator. The deconvolution method may be used in a noise reduction method where both axial and torsional vibrations are generated from the same location, where one of the time series is shifted by the amount of the time delay, so that the vibrations generated from the same location coincide, providing reinforcement of the desired signal.

Abstract: A method for enhancing seismic data is described for attenuating undesired coherent noise in both stacked seismic signals as well as in unstacked ordered gathers of seismic signals. In particular, coherent noise, as represented by reflection events, is identified to be attenuated, and a datum line is constructed in the seismic data. Each seismic signal can then be nonhyperbolically time-shifted so as to align the identified reflection event with the datum line. The seismic data can then be filtered with a dip filter having a dip angle corresponding to that of the datum line to attenuate the aligned reflection event.

Abstract: A method of assigning seismic traces obtained by means of one or more seismic sources (1) and receivers (2) wherein, a plane containing each source (1) and receivers (2) is divided into a regular array of regions (12-18), for example a rectangular array referred to cartesian coordinates (X-Y). The regions cover at least a middle portion of a line (11) joining each source (1) to each receiver (2). Diagonals (19-25) intersect the line (11) at respective intersection points and offspring traces are allocated to these points.

Abstract: A method of predicting pore pressures at a proposed drilling location using Interval Transit Times derived from seismic data and Interval Transit Times from a calibrated normal geopressure trend. Seismic Interval Transit Times derived pore pressures and actual pore pressures derived from logs in a drilled well at an offset location are used to correlate graphically or analytically the seismic Interval Transit Times to normal geopressure interval transit times from a proposed drilling location to be used in the prediction of pore pressures at the proposed location.

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: Methods of geophysical exploration are provided for estimating the burial conditions of sedimentary material in a selected basin. The burial conditions can include measures of porosity, lithology, pore fluid pressure, effective pressure, and density. In particular, a reference velocity profile is developed for a model of the sedimentary material comprising the basin and is compared to a velocity profile obtained from seismic data to obtain estimates of the burial conditions of the sedimentary material.

Abstract: A seismic ray-tracing model performs economic exploration of subsurface structures, which 1) allows amplitude, frequency, mode, and other "synthetic filtering" of the model's calculations and 2) allows model interpolations, approximations, and other "synthetic sensitivity" terminations of ray-tracing calculations. The model output can be directly matched to the filtration and sensitivity of actual seismic data. The model structure is capable of the extensive calculations similar to current extensive forward models, but ray-tracing calculations are accomplished in discrete pairs (allowing interpolation between divergent ray pairs and partially simulating detector sensitivity) and ray-tracing calculations are terminated if an amplitude under a threshold level signal strength is encountered. The amplitude threshold level can be set to match filtering used on actual seismic data. This sensitivity and filter matching achieves maximum reliability while still avoiding unnecessary calculations, e.g.

Abstract: Weathering corrections are determined from first arrival times of refraction stacked traces of common end point gathers. The refraction stacked traces are generated by selecting traces having receiver source offsets greater than the crossover distance and stacking such traces over at least an interval comprising first arrival times. Optionally, a predictor function is used to select first arrivals and the first arrivals are selected from a refraction stacked trace section.

Abstract: A method of enhancing geophysical data comprising processing the geophysical data into ordered gathers of seismic signals, transforming the seismic signals of each ordered gather into synthetic traces having reflection event amplitudes of only one polarity, combining the synthetic traces of each ordered gather, and restoring the positive and negative polarities to the reflection events in the combined synthetic traces.

Abstract: A method for rapidly and efficiently generating traveltime tables for application in depth migration initially includes receiving a velocity model which may include a plurality of velocities in multiple layers between various subsurface reflectors. The model is plotted on a two dimensional grid with the subsurface reflectors identified. A traveltime to the first reflector is determined. Traveltimes from the sources on each layer boundary to all grid points above the next reflector are determined. For the initial iteration, the layer boundary is the surface and the source is the actual source used in shooting the line. For layers below the surface there will be more than one source or secondary source. The actual determination of traveltimes for these lower layers may be done by comparing the traveltimes to all points on the first reflector. The minimum traveltime is selected as the true traveltime to the first reflector. Next, all points where the reflector intersects the grid are found.

Abstract: A method for calculation of raypaths and wavepaths from traveltime tables for the tomographic estimation of transmission velocities includes picking the earliest traveltime of waves transmitted between different source and receivers locations. A velocity model that describes transmission velocities in a region of interest is obtained. Traveltime from each source position to each point in the region of interest and traveltimes from each receiver loaction to each point in the region of interest are extrapolated. The extrapolated traveltimes from the source and receiver to each point in the region of interest are added together to quantify the path of a wave between one source and one receiver. All points in the region of interest whose total traveltimes are less than half a wavelength greater than the minimum traveltime are found. A representative raypath that passes through the center of the estimated wavepath region for each source and receiver location are saved.

Abstract: A method for tracking seismic events such as boundaries of formation layers of earth formations is disclosed. Especially adapted for tracking such events in a two-dimensional slice of 3-D seismic volume data, the method begins by designating a starting data point on the seismic event. The method tracks such event through the grid of data by sequentially establishing areas or "tiles" of data about the starting point. The tiles are defined by data points of the grid. Each of the data points is then tested to see if it meets an acceptance criterion for the seismic event. Such data points of the tile are stored as identifying the seismic event only if certain of the data points of the tile pass the acceptance citerion. Next, each of the data points of a previously accepted tile are used as a starting data point about which a new tile is defined. The process is repeated until no more tiles are available for testing.

Abstract: A method for quantitatively determining an accurate subsurface velocity prior to data migration includes steps whereby the accuracy of the velocity can be defined by measuring the deviation in depth as a function of offset in the common reflection point (CRP) gather. A point on reflector is selected and the CRP gather is formed. If the image is not flat, the velocity is adjusted until it is flat. The velocity is decreased and the far offset end of the image will be imaged to shallower depth than the near offset end. The velocity is increased and the image will tilt down at the far offset end. An error is defined which is the theoretical accuracy limit for the determination of velocity using the CRP method. A factor is defined that indicates the reliability of the image for a reflector.

Abstract: The growth of a hydraulic fracture increases the period of free oscillations in the well connected to the fracture. Simultaneously, the decay rate of free oscillations decreases. The properties of forced oscillations in a well also change during fracture growth. All of these effects result from the changing impedance of the hydraulic fracture that intersects the well. Hydraulic fracture impedance can be defined in terms of the hydraulic resistance and the hydraulic capacitance of a fracture. Fracture impedance can be determined directly by measuring the ratio of down hole pressure and flow oscillations or indirectly from well head impedance measurements using impedance transfer functions. Well head pressure measurements can also be used to evaluate fracture impedance by comparing them to pressure oscillations computed with hydraulic models that include fractures with different impedances.

Abstract: The present invention relates generally to methods of enhancing seismic data and, more particularly, to methods of attenuating noise in seismic signals. The seismic data are sorted into gathers of seismic signals, and selected coherent events in each gather of seismic signals are aligned. The gathers of seismic signals are then processed so as to transform the balance of the coherent events in each gather of seismic signals into incoherent events. A two-dimensional filter is then applied to the transformed signals to attenuate incoherent events.

Abstract: An improved method for modeling the velocity of seismic energy in subterranean rock layers is described. The velocity is assumed to vary such that the gradient of the velocity, that is, the direction of maximum change in the velocity, is at all times perpendicular to the interfaces between the rock layers. Improved methods of generating a representation of a subterranean structure of the earth are also disclosed.

Abstract: A method of deterministically computer generating a model of a response voltage waveform of a seismic receiver employed in a seismic, particularly marine, data gathering system, the model incorporating factors that have been identified as significant contributions to amplitude, such as directivity, divergence, attenuation, interbed multiples, and transmissivity. The model is generated from the mathematical manipulation of well log data and data gathering system characteristics into a seismic range equation, namely: ##EQU1## where E.sub.r (f)=received energy densityE(f)=radiated energy densityD(l.theta..sub.s, .phi..sub.s,f)=source directivity along .theta..sub.s,.phi..sub.s direction at the sourceA.sub.c (.theta..sub.H,.phi..sub.H,f)=Capture area along .theta..sub.H,.phi..sub.H direction at the hydrophone arrayR.sub.T =target reflection coefficientD.sub.

Abstract: A method for providing an optimum model having at least two dimensions of a heterogeneous medium, representing the variations of at least one physical parameter, for example the acoustic impedance of underground formations, and satisfying as well as possible the data measured in situ, for example well-logging in wells in studying the sub-soil as well as other data relative to the medium studied, for example geological information and seismic surface recordings. The method includes the construction of a reference model and the definition of covariance operators which model the uncertainties not only in the medium studied but also in the recordings obtained from outside the medium, for example seismic sections. Comparison between the effective recordings and others which are formed on the basis of the constructed model, makes it possible to check the validity thereof.

Abstract: A system of monitoring the fluid contents of a petroleum reservoir, wherein a reservoir model is employed to predict the fluid flow in the reservoir, includes a check on the reservoir model by comparison of synthetic seismograms with the observed seismic data. If the synthetic output predicted by the model agrees with the observed seismic data, then it is assumed that the reservoir is being properly worked. If not then the reservoir model, in particular its reservoir description, is updated until it predicts the observed seismic response. The seismic survey may be periodically repeated during the productive life of the reservoir and the technique used to update the reservoir model so as to ensure that the revised reservoir description predicts the observed changes in the seismic data and hence reflects the current status of fluid saturations. Implementation of this invention results in more efficient reservoir management.