Abstract: A method for imaging a subsurface formation using at least two seismic sources and receivers comprises: a) creating a wave field in the formation, b) obtaining a set of responses for each receiver and performing wave field separation on them, c) obtaining a virtual source signal for at least a first receiver k by cross-correlating at least part of the response of a second receiver m with at least part of the response of the first receiver k and summing the cross-correlated responses from the sources, making receiver k a virtual source, d) for each virtual source, estimating an amplitude radiation pattern by performing a transform of the response data, e) deconvolving at least one virtual source signal with at least part of the estimated radiation pattern for that receiver to produce an amplitude-corrected virtual source signal, and f) using that signal to create an image of the subsurface formation.

Abstract: Systems, methods, and instructions encoded in a computer-readable medium can perform operations related to refining information on characteristics of natural fractures of a subterranean formation. Fracture pattern models are generated based on sampling an initial distribution of values for a fracture parameter. Each fracture pattern model may include, for example, a model of natural fractures in a subterranean formation. Each fracture pattern model is compared to microseismic event data for a subterranean region. A refined distribution for the fracture parameter is generated based on the comparison. Generating the refined distribution may include, for example, selecting values of the fracture parameter from fracture pattern models that correlate with the microseismic event data. In some implementations, an injection treatment may be simulated and/or designed based on the refined distribution.

Abstract: Systems and methods perform consistent dip estimation for seismic imaging. An example system applies global consistency constraints during iterative volume dip estimation of a seismic volume to improve upon conventional dip estimation methods. With each iteration, the system applies single and joint dip constraints, checking local dip estimates for reciprocity, causality, consistency, and vertical and lateral continuity. At discontinuities in the seismic volume, local divergences are marked with a quality attribute. Upon convergence of the volume dip estimation, the volume may be rendered in 3D, including the discontinuities. In performing volume dip estimation, the system can also provide automatic horizon interpretation and automatic fault detection.

Abstract: A beam tomography computer implemented method and system for generating improved seismic images and earth models without dependence on reflector structure is disclosed. Recorded seismic data is transformed into data beams which are compared to forward modeled beams using an earth model having a velocity model to compute raypaths and a seismic image to specify the reflectors. The tomographic updates to the earth model and velocity model are based on misalignments between the data beams and the same beams forward modeled from the velocity model and the seismic image. The updated earth model and seismic image better describe the true propagation of the beams through the earth.

Abstract: Seismic data acquired at or near a geologic volume of interest is processed. This may include forming an image of the geologic volume of interest from the seismic data. The seismic data may be processed by aggregating energy arrivals to reduce the number of imaging processes that must be performed to determine an image of the geologic volume of interest. This aggregation may be based on groupings of energy arrivals referred to herein as clusters.

Abstract: Passive seismic data is collected from measurements of seismic sensors in respective sensor assemblies, where the passive seismic data is based on measurements collected during periods when no active seismic source was activated. Attenuation of surface noise in the passive seismic data is performed using data from divergence sensors in at least some of the sensor assemblies. The passive seismic data with surface noise attenuated is output to allow for performing an operation related to a subterranean structure using the passive seismic data with the surface noise attenuated.

Abstract: A system, which may be and/or may include a computer system, and method for identifying a fault patch position from a seismic data volume. The system and method may include defining an initial active surface in the seismic data volume; identifying one or more active surfaces by minimizing the value of a function for energy; tracking back the active surfaces to find a set of control points; and producing the fault patch position formed by the set of control points.

Abstract: A fingerprint processing system may include a fingerprint database for storing fingerprint data having at least one void therein. At least one processor may cooperate with the fingerprint database for inpainting data into the at least one void in the fingerprint data based upon propagating fingerprint contour data from outside the at least one void into the at least one void.

Abstract: A method of hydrodynamics-based gridding (Hydro-Grids) for creating geologic models of subsurface volumes, such as reservoirs, is disclosed. Geologic data is obtained. Vertical grid surfaces are created. Lateral grid surfaces are created to correspond to surfaces of constant geologic time during the deposition of sediments in the subsurface volume. Geologic properties within each cell are represented as values within each cell created by the vertical and lateral surfaces. Reservoir performance is simulated using the represented geologic properties of the subsurface volume. A hydrocarbon reservoir is developed based on the simulated reservoir performance.

Abstract: A method for monitoring the movement of fluid through a subsurface formation of interest, comprising: a) providing a set of signals obtained by transmitting seismic waves through the formation of interest and receiving signals emanating from the multi-layered system in response to the seismic waves with one or more receivers located a distance from the seismic source(s), b) identifying one or more critically refracted waves among the signals so as to generate a first data set of refracted signals, c) repeating steps a) and b) after a period of time so as to generate a second data set of refracted signals, d) comparing the second data set to the first data set so as to generate a time-lapse data set, e) imaging the time-lapse data set using travel time tomography; and f) inferring information about the movement of fluid based on the image generated in step e).

Abstract: A method of measuring the compressibility, and/or the density, of small particles, and especially nano-particles, in suspension is described. The static method uses steady pressures and measures the d-c (static) compressibility of particles. The ultrasonic method utilizes an ultrasonic pulsed doppler system to measure the compressibility of particles at ultrasonic frequencies, which may differ from static values. These methods can also be used together to provide overlapping and complementary information about the particles. In addition, the ultrasonic pulsed doppler system also provides a way to measure particle density.

Abstract: A system, which may be and/or may include a computer system (1, 100), and method (3) for identifying a fault patch position from a seismic data volume (103). The system and method may include defining an initial active surface (310) in the seismic data volume (103); identifying (914) one or more active surfaces by minimizing the value of a function for energy; tracking back (916) the active surfaces to find a set of control points; and producing (918) the fault patch position formed by the set of control points.

Abstract: A method of calculating a seismic noise image for a formation comprises the steps of: a) obtaining data representing a multicomponent seismic signal from at least one receiver, in response to transmitting seismic waves into the formation; b) obtaining a velocity model of the earth formation; c) determining a plurality of wave field components; d) obtaining a set of second components; e) obtaining, for each subsurface point, at least two products, each product comprising the product of a selected wave field component and a different second component; and f) and generating a noise image by calculating at least one difference between different products for at least one image point.

Abstract: Embodiments use seismic processing methods that account for the spatial variability of surface wave velocities. Embodiments analyze surface wave properties by rapidly characterizing spatial variability of the surface waves in the seismic survey data (302). Filtering criteria are formed using the spatial variability of the surface waves (204). The filtering criteria can then be used to remove at least a portion of the surface waves from the seismic data (206, 319). The rapid characterization involves estimating a local group velocity of the surface waves by cross-correlation of the analytic signals (302).

Abstract: Method for removing air wave noise from shallow water controlled source electromagnetic survey data, using only the measured data and conductivity values for sea water (140) and air. The method is a calculation performed numerically on CSEM data and resulting in an estimate of those data that would have been acquired had the water layer extended infinitely upward from the seafloor. No properties of the sub-sea sediments are used. Synthetic electromagnetic field data are generated for (a) an all water model (141) and (b) an air-water model (146-147) of the survey region. These simulated results are then used to calculate (148-150) electromagnetic field values corresponding to a water-sediment model with water replacing the air half space, which represent measured data adjusted to remove air wave noise.

Abstract: A method of processing data obtained from seismic prospecting of an earth formation, comprises obtaining data representing a multicomponent seismic signal from a multicomponent seismic receiver at a receiver location in an earth formation, in response to transmitting seismic waves into the earth formation; performing a wave-equation migration of the multicomponent seismic signal to obtain a seismic image of the earth formation, wherein the polarization of the seismic wave at the receiver location is taken into account and wherein a seismic image value at a point in the earth formation is calculated from a sum of products of a source field component for a particular dimension and a complex conjugated back propagated wave field component for the same dimension, summed over a plurality of dimensions.

Abstract: Methods and systems for the detection and localization of microseismic events are proposed which operate in real-time. Hypocenters in three spatial dimensions are provided along with an estimate of the event origin time. Sensor positions may be distributed in 3D space, and are not confined to linear arrays in vertical wells. A location of the event is approximated and a grid search, based on the approximate location of the event, is used to derive a residual function over a finer sampling followed by a gradient search of the residual function to optimize the location of the event.

Abstract: Systems and methods in which data compression techniques are utilized to fill a predetermined channel capacity are shown. According to one configuration, event data points within test data are selected for communication via the data communication channel and a data decimator is utilized to identify other data points within the test data to fill or substantially fill the predetermined channel capacity. The foregoing data decimator may employ one or more variables for selecting data for communication, wherein one or more of the variables are preferably adjusted in decimator iterations to select an optimum or otherwise desirable subset of data for communication. Data decimators may additionally or alternatively implement a suitable “growth” function to select the particular data for communication and/or the amount of data communicated.

Abstract: A Laplace transform system comprising a processor, a measured time domain wavefield, a velocity model, and Laplace damping constants, wherein the processor is programmed to calculate a substantially about zero frequency component of a Fourier transform of a time domain damped wavefield, wherein the time domain damped wavefield is damped by the Laplace damping constants to obtain long wavelength velocity information for deeper subsurface regions.

Abstract: Coherency analysis, such as semblance scan or stacking amplitude, is used to locate diffractors. Once the diffractors are located, noise energy originating from the diffractors is minimized. Locations of each diffractor are determined by comparing the lateral coherency of the received amplitudes that each assumed diffractor position generates.

Abstract: An exemplary embodiment of the present invention provides a method for interpolating seismic data. The method includes collecting seismic data of two or more types over a field (401), determining an approximation to one of the types of the seismic data (402), and performing a wave-field transformation on the approximation to form a transformed approximation (405), wherein the transformed approximation corresponds to another of the collected types of seismic data. The method may also include setting the transformed approximation to match the measured seismic data of the corresponding types at matching locations (408), performing a wave-field transformation on the transformed approximation to form an output approximation (412), and using the output approximation to obtain a data representation of a geological layer (416).

Abstract: A multicomponent induction logging tool is used on a MWD bottomhole assembly. Multifrequency focusing that accounts for the finite, nonzero, conductivity of the mandrel is applied. Using separation of modes, the principal components and relative dip angles in an earth formation are determined. The results are used for reservoir navigation in an earth formation.

Abstract: The invention is a method, having applications for the development of reservoirs, for predicting the production of an underground reservoir, comprising generating and updating a parameterized geologic model from production data and seismic data and in particular 4D seismic data which may be used in development of oil reservoirs. According to the method, production data are simulated from the geologic model and a flow simulator, and a petro-elastic depth model is deduced therefrom. A depth/time conversion model is then defined, by means of which the petro-elastic model is converted into time. The model is adjusted by correcting the lag induced by the depth/time conversion and by recalibrating the model. The geologic model is optimized by comparing, through an objective function, the real measurements with the simulation responses (production responses and seismic attributes in time) by updating in particular the depth/time conversion model.

Abstract: A method and system for processing synchronous array seismic data includes acquiring synchronous passive seismic data from a plurality of sensors to obtain synchronized array measurements. A reverse-time data process is applied to the synchronized array measurements to obtain a plurality of dynamic particle parameters associated with subsurface locations. These dynamic particle parameters are stored in a form for display. Maximum values of the dynamic particle parameters may be interpreted as reservoir locations. The dynamic particle parameters may be particle displacement values, particle velocity values, particle acceleration values or particle pressure values. The sensors may be three-component sensors. Zero-phase frequency filtering of different ranges of interest may be applied. The data may be resampled to facilitate efficient data processing.

Abstract: A method and system for processing synchronous array seismic data includes acquiring synchronous passive seismic data from a plurality of sensors to obtain synchronized array measurements. A reverse-time data process is applied to the synchronized array measurements to obtain a plurality of dynamic particle parameters associated with subsurface locations. These dynamic particle parameters are stored in a form for display. Maximum values of the dynamic particle parameters may be interpreted as reservoir locations. The dynamic particle parameters may be particle displacement values, particle velocity values, particle acceleration values or particle pressure values. The sensors may be three-component sensors. Zero-phase frequency filtering of different ranges of interest may be applied. The data may be resampled to facilitate efficient data processing.

Abstract: A computer-implemented method is provided for searching and analyzing a seismic data volume acquired in a seismic survey to determine potential for hydrocarbon accumulations in an associated subsurface region. Surfaces describing the seismic data volume are obtained. The surfaces are enumerated. At least one enumerated surface is selected. The at least one selected surface is augmented when the selected surface does not substantially cover an area associated with the seismic data volume. The augmenting is performed until all selected surfaces substantially cover the area. The at least one selected surface is displayed, with geologic or geophysical data associated therewith, for visual inspection or interpretation, or saving digital representations thereof to computer memory or data storage.

Abstract: The present invention is a method of hydrodynamics-based gridding (Hydro-Grids) for creating geologic models of subsurface volumes, such as reservoirs. Vertical grid surfaces may be chosen in an unstructured fashion to provide lateral resolution where needed. Lateral grid surfaces are created to represent surfaces of constant geologic time based on simulation of the depositional processes that created the subsurface volume. The values of geologic properties are then specified within each cell created by the intersections of the vertical and lateral surfaces. The geologic data may include, for example, seismic data, outcrop studies, well log data, core data, numerical modeling data, and interpreted stratigraphic surfaces based on seismic data. The modeled geologic properties of the subsurface volume may include, for example, grain size distribution, connectivity, net-to-gross, porosity, permeability and pore pressure.

Abstract: A method and system of detecting and mapping a subsurface hydrocarbon reservoir includes determining ratio data for a plurality of orthogonal spectral components of naturally occurring low frequency background seismic data. The ratio data may be compared, plotted, contoured and displayed as a subsurface hydrocarbon reservoir map or a hydrocarbon potential map. The ratio data may represent a vertical spectral component of the seismic data over a horizontal spectral component of the seismic data. The subsurface hydrocarbon reservoir map may include contouring the ratio data over a geographical area associated with the seismic data.

Abstract: Method of imaging seismic data recorded using a set of seismic receivers positioned to receive seismic responses from a subsurface formation upon activating a seismic source. The seismic responses are direction-sensitive responses. A virtual signal received by receiver k from the virtual source at the position of receiver m is determined by processing involving cross correlating at least part of the responses of a receiver m with at least part of the responses of a seismic receiver k. Part of direction-sensitive responses or part of the virtual signal that contains a component of the wave field at receiver m traveling in a first direction and part of the direction-sensitive responses or part of the virtual signal that contains a component of the wave field at the receiver k traveling in a second direction may be removed.

Abstract: A method for generating a synthetic seismogram. In one implementation, a ray tracing may be performed on a subsurface. The ray tracing may generate a plurality of rays. A first seismic wavefront by may be reconstructed by triangulating a first plurality of control points that correspond to the plurality of rays. Each control point may represent an end point of a ray at the first seismic wavefront. The plurality of rays may be propagated to a second seismic wavefront. The second seismic wavefront may have a hole associated with at least one missing ray at the second seismic wavefront. A plurality of points on a circle may be defined that correspond to a second plurality of control points defining the hole. The second seismic wavefront may be reconstructed based on the plurality of points on the circle.

Abstract: A method of locating subsurface hydrocarbon reservoirs includes acquiring seismic data, dividing the seismic data into time windows, applying a data transform to the seismic data having a plurality of components to obtain a smoothed frequency spectrum, selecting one or more local maxima and minima, determining a frequency product as a function of the maxima and minima in a form for display. Lower and higher ratio thresholds may be selected to further discriminate frequency product selection for display. A display or map of frequency products over a survey area may indicate the presence of subsurface fluid reservoirs.

Abstract: A method and system of processing seismic data includes acquiring three-component seismic data and combining horizontal components of the three-component seismic data to obtain a merged horizontal component. Frequency spectra are determined for the acquired three-component seismic data. A ratio of a vertical component of the seismic data to the merged horizontal component is determined. A V/H integration-measure is obtained from the integration of the area bounded by a selected minimum-amplitude value and the amplitude values greater than the selected minimum-amplitude value and the V/H integration-measure is stored in a form for display.

Abstract: The present invention incorporates the use of model-driven and data-driven methodologies to attenuate multiples in seismic data utilizing a prediction model which includes multiply-reflected, surface-related seismic waves. The present invention includes beam techniques and convolving a predicted multiples beam with a segment of a modeled pegleg beam to obtain a convolved multiples beam. The convolved multiples beam can then he deconvolved to attenuate the multiples that are present in the original input beam.

Abstract: The invention relates to methods and computer-readable medium to implement computing the propagation velocity of seismic waves in the earth. The invention computes the true propagation velocity of seismic waves in the earth, which is a condition of obtaining an accurate image of subsurface geology that can be used to prospect for oil and gas deposits. In an embodiment, the method of computing the propagation velocity of seismic waves in earth, includes providing an estimate of the propagation velocity, generating a time shift gather using a depth migration at a plurality of locations of the earth, converting each of the time shift gathers to a semblance gather, transforming each semblance gather into a velocity gather whose energy peaks represent a root-mean-square average of the propagation velocity along the forward and backward path between earth's surface and a point of the subsurface geology, and converting the energy peaks to the propagation velocity.

Abstract: The instant invention is a method for numerically propagating waves or solving wave equations on a digital computer. This invention can be used to compute highly accurate solutions to the wave equation, in fact in some cases it computes the analytical solution, something previously considered impossible. The instant method can also propagate waves that are not described by differential equations, such as anisotropic scalar waves. The invention has the advantages that it is computationally efficient, accurate, and flexible. Of importance is the ability to propagate waves that simulate the P-wave arrivals in both isotropic and anisotropic media with a scalar as opposed to a vector equation.

Abstract: This patent deals with methods to extract and analyze seismic signals due to resonance phenomena in an enclosed oil, gas, or water reservoir, which are passively excited by seismic background noise, locating thereby the presence of the reservoir by doing qualitative and quantitative estimates via forward modeling. Measurements are first used in a qualitative analysis in eight steps. The influence of gas bubbles is important. A quantitative method in form of a numerical simulation using one of several specific physical concepts is used for further analysis. By using successive forward modeling, together with investigation and feedback and in conjunction with the Monte Carlo method, more details are gained. It is also possible to determine the fluid type. The uniqueness of the methods is first that it is purely passive; second it is directly sensitive to the oil or gas, because the resonance effect is only present for a fluid.

Abstract: A method of constructing an image representative of a heterogeneous medium by a procedure of joint inversion of seismic data represented on different time scales having an application for underground reservoir exploration. Sequential inversion of the seismic data is performed so as to determine a first model from the seismic data expressed in a first time scale, and a second model from the seismic data expressed in the second time scale. A scale factor t1(t0) allowing synthetic data described in a first time scale to be expressed in a second time scale is defined by a differential equation relating the traveltime variations of a seismic wave to the models resulting from the sequential inversion. Finally, joint inversion wherein a cost function using the scale factor is minimized is carried out so as to evaluate a difference between the synthetic data and the seismic data expressed in another time scale.

Abstract: According to a preferred aspect of the instant invention, there is provided herein a system and method for Interpolation of seismic data with a POCS (projection onto convex sets) algorithm that can produce high quality interpolation results, at a reduced computational cost. In particular, optimizing the threshold calculations, allowing for aliased data, allowing the algorithm to skip unneeded Fourier transforms, and parallelization makes the method more practical and robust. Robust interpolation of aliased data may be done by limiting the calculations of the beginning iterations to the lowest temporal and spatial frequencies included in the data, then gradually allowing higher temporal and spatial frequencies into the following iterations.

Abstract: A method for acquiring and analyzing time-series data using singularities is described. This method allows for the analysis of data over a wide spectrum of frequencies. Once the data is acquired in an oil field, singularities of the data are extracted; and the extracted singularities are utilized to interpret the formation properties related to the data.

Abstract: A computer-implemented method for processing data includes accepting a first collection of traces corresponding to signals received over time due to reflection of seismic waves from subsurface structures. A Radon transform is defined with respect to a set of wavefront parameters of the seismic waves. The transform defines a summation of amplitudes of the seismic waves over trajectories defined by the wavefront parameters. The Radon transform is applied to the first collection of traces, so as to convert the first collection into a multidimensional data array that is defined as a function of at least two of the wavefront parameters. The multidimensional data array is processed to produce a second collection of traces having an improved imaging quality with respect to the first collection. The second collection of traces is processed to generate a seismic image of the subsurface structures at the improved imaging quality.

Abstract: Method for building a subsalt velocity model. In one implementation, the method may include determining a velocity of a sedimentary area surrounding a salt body, determining an initial velocity of a subsalt sedimentary area disposed below the salt body by interpolating the velocity of the surrounding sedimentary area with one or more boundaries defining the salt body, and updating the initial velocity of the subsalt sedimentary area.

Abstract: A method of determining geological information related to a subsurface volume. In one embodiment, the method comprises obtaining a seismic information related to a subsurface volume; determining a horizon volume that automatically maps the seismic information into a flattened volume, wherein one axis of the flattened volume corresponds to chronostratigraphic time, and wherein horizons represented by the seismic information are automatically accounted for in the horizon volume, and are shifted by the horizon volume into the flattened volume to be substantially planar and substantially perpendicular to the axis of the flattened volume that corresponds to chronostratigraphic time; determining a derivative of the horizon volume with respect to chronostratigraphic time; and determining geological information related to the subsurface volume based on the derivative of the horizon volume with respect to chronostratigraphic time.

Abstract: A method of determining a horizon volume. In one embodiment, the horizon volume is determined from obtained seismic information, and maps the obtained seismic information onto a flattened volume such that in the flattened volume, horizons represented in the obtained seismic information are shifted to be substantially coplanar with a surface defined by the horizon volume as an estimate of a single chronostratigraphic time such that the parameters of the flattened volume include (i) a two-dimensional position in a surface plane, and (ii) a metric related to chronostratigraphic time.

Abstract: Correcting seismograms to compensate for absorption or dissipative effects that occur in the earth. In one implementation, a ratio of traveltime (t) to absorption parameter (Q) may be computed for each seismogram. The ratio may be referred to as R. Further, the ratio may be computed for a predetermined set of traveltimes. As a result, a system of linear equations may be generated, where each ratio is represented by a linear equation having a number of unknown components. The system of linear equations may then be solved for the unknown components. The solved components may then be recombined or added to generate an estimate of R. In one implementation, only a portion of the solved components may be added. The seismograms may then be corrected using the estimate of R. As such, the seismograms may be corrected for absorption effects in a surface consistent manner.

Abstract: Methods and systems for investigating subterranean formations are disclosed. A method for investigating subterranean formations includes obtaining formation property data for a volume of interest in the subterranean formation s; presenting the formation property data as a collection of objects in a three-dimensional volume that represents the volume of interest; filtering the collection of objects based on proximity to a reference point and a selected property associated with a subset of the collection of objects; and displaying objects that satisfy the proximity to the reference point and the selected property.

Abstract: A method and system of processing seismic data includes acquiring three-component seismic data and combining horizontal components of the three-component seismic data to obtain a merged horizontal component. Frequency spectra are determined for the acquired three-component seismic data. A ratio of a vertical component of the seismic data to the merged horizontal component is determined. A V/H integration-measure is obtained from the integration of the area bounded by a selected minimum-amplitude value and the amplitude values greater than the selected minimum-amplitude value and the V/H integration-measure is stored in a form for display.

Abstract: To generate an absorption parameter model, estimated values of an effective absorption parameter are received, where the estimated effective absorption parameter values represent absorption encountered by a seismic wave in a subterranean structure. Based on the estimated effective absorption parameter values, an absorption parameter model is generated that varies absorption parameter values along at least one dimension of the subterranean structure.

Abstract: Various methods are disclosed for identifying faults in a seismic data volume. In some method embodiments, the fault identification method comprises determining a planarity value for each of multiple positions of an analysis window in the data volume. The planarity value may be indicative of the planarity of discontinuities in the analysis window, and may be further filtered by limits on the verticality and centrality of the discontinuities. Thus a filter may be determined for suppressing relatively non-planar, relatively non-vertical, and relatively un-centered discontinuities from a discontinuity display, thereby enhancing a display of faults present in the seismic data volume.

Abstract: Systems and methods for enhancing the resolution of a seismic data image displayed on a face of a sampling probe. The enhanced image represents a maximum resolution of at least a portion of the seismic data image. The seismic data image is enhanced by extracting seismic data that are perpendicular to a reflection surface that is closest to a center of the sampling probe and positioning the extracted seismic data in a visible planar face of the sampling probe.

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.