Abstract: A capacitive micromachined ultrasonic transducer having a wide reception band is provided. The capacitive micromachined ultrasonic transducer includes an element including a first sub-element and a second sub-element each including a cell. The cell includes a vibrating membrane that includes one of two electrodes formed with a spacing therebetween and that is vibratably supported. The capacitive micromachined ultrasonic transducer further includes a first detection circuit, a second detection circuit, and a combining circuit that combines a signal from the first detection circuit and a signal from the second detection circuit. The first sub-element is electrically connected to the first detection circuit, and the second sub-element is electrically connected to the second detection circuit. The first detection circuit and the second detection circuit have different cut-off frequencies.

Abstract: A marine node for recording seismic waves underwater. The node includes a spherical body made of a material that has a density similar to a density of the water so that the body is buoyant neutral; a first sensor located in the body and configured to record three dimensional movements of the node; a second sensor located in the body and configured to record pressure waves propagating through the water; and one or more cables connected to the first and second sensors and configured to exit the body to be connected to an external device. The body is coupled to the water.

Abstract: The present disclosure includes a method for suppressing 4D noise. The method includes calculating a first similarity map based on the similarity of one of one or more first 3D images and a second 3D image. The first and second 3D images are derived from first and second surveys, respectively. The method also includes calculating a second similarity map based on the similarity of one of the one or more first 3D images and a third 3D image, which is derived from the second survey. The method also includes calculating a third similarity map based on the similarity of first and second 4D images, which are based on differences between the 3D images. The method also includes generating a composite 4D image based at least on the first, second, and third similarity maps. The present disclosure may also include associated systems and apparatus.

Abstract: Systems and methods of detecting marine seismic survey parameters are provided. A data processing system can obtain seismic data from seismic data acquisition units disposed on a seabed responsive to an acoustic signal propagated from an acoustic source through a water column. The data processing system can determine from the seismic data, a direct arrival time for the acoustic signal at each of the plurality of seismic data acquisition units, and can obtain an estimated depth value of each of the plurality of seismic data acquisition units and an estimated water column transit velocity of the acoustic signal. The data processing system can apply a depth model and a water column transit velocity model to the estimated depth value and to the estimated water column transit velocity determine an updated depth value and an updated water column transit velocity for each of the plurality of seismic data acquisition units.

Abstract: Noise is removed from a data set by performing an integral transform operation that converts instances of noise into identifiable artifacts in the transformed data set. A model of the artifacts is constructed by creating a full-domain or partial-domain noise model and performing the same integral transform operation on the noise model. The resulting transformation of the noise model is adaptively subtracted from the transformed data set to remove the noise. The adaptive subtraction may employ a least-square error filter.

Abstract: A method for inferring incident count rates of electromagnetic energy at a detector is provided. In one embodiment, the method includes transmitting electromagnetic radiation through a fluid and receiving a portion of the electromagnetic radiation at a detector. The method also includes measuring the energy spectrum of the portion of the electromagnetic radiation received by the detector and using the measured energy spectrum and a physical model of detector response to electromagnetic radiation to infer incident count rates for discrete energy levels of the portion of the electromagnetic radiation received by the detector. Additional systems, devices, and methods are also disclosed.

Abstract: Systems and methods for detecting in motion railcar seismic data generated by defective railcar axles of a train traveling on a track. The method uses two or more seismic sensors on the side of the track to capture seismic noise generated by railcar wheels. A wheel that exceeds a preset seismic noise threshold in amplitude, will trigger a wheel tracking algorithm that calculates seismic phase shift data related to the actively tracked wheel noise level, to determine the precise location, in real time, of the faulty wheel carriage while moving. Knowing the precise location of the tracked wheel allows the system to isolate the railcar and capture the railcar and wheel carriage identification information. Subsequently, a railcar log is made on a computer database with the railcar identification information and made available to control centers via ground or satellite links.

Abstract: This disclosure is directed to systems and methods for stacking seismic data. The methods receive seismic data collected from a survey of a subterranean formation. A gather of seismic data may have flattened reflection events obtained as a result of normal moveout (“NMO”) corrections or pre-stack migration. Alternatively, the gather may be an unmigrated gather with non-horizontal reflection events. A smoothed-amplitude gather is generated from the gather. Traces of the gather are stacked to generate a trace with significantly reduced noise using corresponding smoothed amplitudes of the smoothed-amplitude gather as weights.

Abstract: Systems, media, and methods for processing seismic data are disclosed. For example, in one embodiment, the method may include receiving a plurality of partial image partitions of a migrated seismic image, and stacking the plurality of partial image partitions such that a first image is generated. The method may also include aligning the plurality of partial image partitions based at least partially on the first image. Aligning may include adjusting at least one of the plurality of partial image partitions and generating a displacement field. The method may also include, based at least in part on the displacement field, stacking the plurality of aligned partial image partitions to generate a second image. The method may further include based at least in part on the second image, realigning the plurality of aligned partial image partitions.

Abstract: A computer implemented method is provided for processing data representing a data entity having sub entities. The method includes analyzing queries to the data entity for deriving information about sets of the sub entities frequently queried together, and grouping the sub entities to a number of banks, each bank having a maximum width, based on the information about sets of sub entities frequently queried together, in order to reduce an average number of banks to be accessed for data retrieval.

Abstract: A system and method are provided for determining a broadband high definition reflectivity based image for a geographical area of interest (GAI). The system and method generate a conventional reflectivity image based on acquired seismic data for the GAI, generate a high frequency (HF) velocity model of the GAI based on the acquired seismic data, convert the HF velocity model into a low frequency (LF) reflectivity image, and adaptively merge the LF reflectivity image with the conventional reflectivity image to form the broadband HD reflectivity image of the GAI.

Abstract: Techniques are described for determining particle displacement or particle velocity data from particle acceleration measurements. In an embodiment, an apparatus comprises an interface configured to received particle acceleration data, one or more processors, and one or more storage media. The one or more storage media store instructions for determining one or more of particle velocity data or particle displacement data, based upon the particle acceleration data, by processing the particle acceleration data using a filter that at least approximates a Wiener filter and that uses one or more damping factors selected to provide stability in the presence of noise in the particle acceleration data.

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

Abstract: Method of performing a 3-D seismic survey using a plurality of vibroseis sources, and an array of seismic sensors arranged within a survey area. Each vibroseis source emits a distinctive acoustic signal and each seismic sensor of the array is in a continuous state of readiness to detect reflected acoustic signals. The method includes assigning vibroseis points (VPs) to each vibroseis source, moving each vibroseis source to assigned VPs where the vibroseis source emits an acoustic signal, recording the emission time of the acoustic signal by each vibroseis source at its assigned VPs together with the geographic position of the assigned VPs, continuously listening for reflected acoustic signals using the seismic sensors and recording a time domain record of the reflected acoustic signals received by each seismic sensor. Reflected acoustic signals associated with emission of an acoustic signal by a vibroseis source at an assigned VP are then determined.

Abstract: A method to perform a marine seismic survey includes obtaining marine seismic data corresponding to a subterranean formation under a water surface. The marine seismic data is generated from an underwater seismic sensor that is subject to an interference effect. The method further includes generating, by a computer processor and using a deconvolution operation, corrected marine seismic data based at least in part on the marine seismic data to compensate for the interference effect, and generating, by the computer processor, a marine seismic survey result based at least in part on the corrected marine seismic data.

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

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

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

Abstract: Disclosed are methods and apparatus for adaptive source electromagnetic (EM) surveying. In accordance with one embodiment, a source waveform signal is generated, and an outgoing EM signal which is based on the source waveform signal is transmitted using an antenna. A responsive electromagnetic signal is detected using at least one electromagnetic sensor, and a receiver waveform signal based on the responsive electromagnetic signal is obtained. A feedback control signal which depends on at least one input signal is determined. Based on the feedback control signal, the source waveform signal is adapted. Other embodiments, aspects, and features are also disclosed.

Abstract: Methods and apparatus to optimize parameters in a downhole environment are described. An example downhole tool includes a transmitter to transmit a signal into a subterranean formation and one or more receivers to receive at least a portion of the acoustic signal. The downhole tool also includes a processor configured to determine slownesses of different acoustic modes at a frequency of the signal received. Each of the slownesses is associated with a first parameter and a second parameter. The different acoustic modes have substantially different sensitivities to at least one of the first parameter or the second parameter. The processor to invert the determined slownesses of the different acoustic modes to determine an optimized value of the first parameter and an optimized value of the second parameter.

Abstract: Methods and systems utilizing seismic sensors configured or designed for use in seismic signal detection are provided so as to reduce the occurrence of spurious responses of the sensors. A method of seismic surveying using a seismic sensor may include the steps of deploying the seismic sensor at a location for seismic signal detection and acquiring seismic signals. The seismic signals may include high frequency response signals containing spurious response signals at an identifiable bandwith. The method may further include applying spurious response cancellation based on the bandwidth location of the spurious response signals and generating modified seismic waveforms having extended frequency bandwidth.

Abstract: Method for redatuming seismic data to any arbitrary location in the subsurface in a way that is consistent with the internal scattering in the subsurface. Direct arrival times are estimated from every point to every point on the edges of a virtual box in the subsurface (102). Green's functions are estimated by iterative optimization (103), using the direct arrival times as initial guesses (102), to minimize error in the source field reconstruction, which consists of the multidimensional auto-correlation of the Green's functions. The estimated Green's functions are the used to determine simulated internal multiple reflections (104). The measured data may be corrected by subtracting the simulated internal multiple reflections, or the Green's function may be used to do local imaging or local velocity model building, particularly advantageous in full wavefield inversion (104).

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

Abstract: Systems and methods according to these exemplary embodiments provide for attenuating noise which interferes with recordings of a seismic source. A method includes: generating a reference trace for a noise source; generating a primary trace for the seismic source; generating a first estimated convolutional operator between the reference trace and the primary trace; convolving the operator with the reference trace for a time frame to generate an estimated noise for the time frame; and subtracting the estimated noise from the primary trace to generate an output signal.

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 seismic vibrator receives a pilot signal having a predetermined waveform. The pilot signal causes vibrational actuation of at least one moveable element of the seismic vibrator. A continuous seismic signal having content in a first frequency bandwidth of multiple frequencies is generated by the seismic vibrator.

Abstract: A method for processing seismic data. The method may include receiving seismic data due to a plurality of seismic sources and applying a first operator to the seismic data in an ith domain to generate a first estimate of seismic data due to an ith seismic source. The ith domain may correspond to the ith seismic source of the plurality of seismic sources. The method may then include applying a second operator to the first estimate of seismic data due to the ith seismic source in one or more domains other than the ith domain to generate residual seismic data due to one or more seismic sources other than the ith seismic source. After applying the a second operator to the first estimate of seismic data due to the ith seismic source, the method may determine a second estimate of seismic data due to the ith seismic source based on the first estimate and the residual seismic data due to the seismic sources other than the ith seismic source. The method may then repeat some of the steps described above (i.e.

Abstract: Improved methods of processing seismic data which comprise amplitude data assembled in the offset-time domain in which primary reflection signals and noise overlap are provided for. The methods include the step of enhancing the separation between primary reflection signals and coherent noise by transforming the assembled data from the offset-time domain to the time-slowness domain. More specifically, the assembled amplitude data are transformed from the offset-time domain to the time-slowness domain using a Radon transformation according to an index j of the slowness set and a sampling variable ?p; wherein j = p max - p min + 1 ? ? µ ? ? sec ? / ? m ? ? ? p , ?p is from about 0.5 to about 4.0 ?sec/m, pmax is a predetermined maximum slowness, and pmin is a predetermined minimum slowness. Alternately, an offset weighting factor xn is applied to the assembled amplitude data, wherein 0<n<1, and the amplitude data are transformed with a Radon transformation.

Abstract: A method to attenuate unwanted signals in seismic data using seismic interferometry techniques. In one implementation, seismograms may be converted into seismic interferograms. In the seismic interferogram domain, unwanted signals may be attenuated by various techniques, such as muting, filtering and the like. The modified seismic interferograms may then be converted back into seismograms with the unwanted signals having been attenuated.

Abstract: An estimated frequency-wavenumber spectrum is generated by applying a first Anti-leakage Fourier transform method to aliased frequency components in temporal-transformed seismic data and applying a second Anti-leakage Fourier transform method to unaliased frequency components in the temporal-transformed seismic data. The second Anti-leakage Fourier transform method applies an absolute frequency-wavenumber spectrum extrapolated from unaliased frequencies to aliased frequencies to weight frequency-wavenumber components of the aliased frequencies. An inverse temporal and spatial Fourier transform is applied to the estimated frequency-wavenumber spectrum, generating trace interpolation of the seismic data.

Abstract: Improved methods of processing seismic data which comprise amplitude data assembled in the offset-time domain in which primary reflection signals and noise overlap are provided for. The methods include the step of enhancing the separation between primary reflection signals and coherent noise by transforming the assembled data from the offset-time domain to the time-slowness domain. More specifically, the assembled amplitude data are transformed from the offset-time domain to the time-slowness domain using a Radon transformation according to an index j of the slowness set and a sampling variable ?p; wherein j = p max - p min + 1 ? ? ? ? ? sec ? / ? m ? ? ? p , ?p is from about 0.5 to about 4.0 ?sec/m, pmax is a predetermined maximum slowness, and pmin is a predetermined minimum slowness. Alternately, an offset weighting factor xn is applied to the assembled amplitude data, wherein 0<n<1, and the amplitude data are transformed with a Radon transformation.

Abstract: Methods of processing seismic data to remove unwanted noise from meaningful reflection signals are provided for. Assembled seismic data are transformed from the offset-time domain to the time-slowness domain using a Radon transformation. Preferably, an offset weighting factor xn is applied to the amplitude data, wherein 0<n<1, and the Radon transformation is applied within defined slowness limits pmin and pmax that will preserve coherent noise, and according to an index j of the slowness set and a sampling variable ?p; wherein j = p max - p min + 1 ? ? µ ? ? sec ? / ? m ? ? ? p , ?p is from about 0.5 to about 4.0 ?sec/m. The coherent noise content of the transformed data is then enhanced, and the primary reflection signal content diminished by filtering at least a subset of the transformed data.

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: A method and apparatus for pre-inversion noise attenuation of seismic data. The method can generally comprise: (a) acquiring seismic data including receiver data corresponding to vibratory signals simultaneously generated by the multiple sources and detected by at least one of the receivers at a location remote from the sources and source data corresponding to the vibratory signals detected at a location in proximity to the sources; (b) attenuating noise present within at least a portion of the receiver data to generate corrected receiver data; and (c) inverting the corrected receiver data with the source data to separate the vibratory signals.

Abstract: Data processing means are described for calculating an estimated time of arrival of a seismic or microseismic P or S wave at a sensor station, based on a P to S wave velocity ratio, a calculated estimated time of origin of the event and, where the estimated arrival time of a P wave is to be calculated, a picked arrival time of the S wave at the sensor station or, where the estimated arrival time of a S wave is to be calculated, a picked arrival time of the P wave at the sensor station.

Abstract: A method and apparatus for seismic trace matching to well logs.

Abstract: An apparatus and method for processing a record of seismic traces. The method includes receiving the record of seismic traces in a time-offset domain, transforming the record of seismic traces to a tau-p domain, applying a zero offset inverse Q algorithm to the record of seismic traces in the tau-p domain, and transforming the record of seismic traces back to the time-offset domain.

Abstract: The invention relates to processing seismic data that contains both a desired signal and swell noise. The method is applicable to seismic data is in the frequency-space domain method and comprises determining a signal-only prediction filter from the seismic data at a first frequency at which swell noise is not present, and applying the prediction filter to seismic data at a second frequency at which swell noise is present. This attenuates swell noise in the seismic data at the second frequency. In one embodiment, the prediction filter for a frequency fL, the lowest frequency at which swell noise is present, is determined from seismic data at frequency fH+1, where fH is the highest frequency at which swell noise is present. The prediction filter for a frequency fL+1 is determined from seismic data at frequency fH+2, and so on, so that the prediction filter for frequency fH+1 is determined from seismic data at frequency f2H?L+1.

Abstract: Providing a set of seismic sources in a focusing array to enable concentrating seismic energy in a selected target point (k) in an underground formation, by performing a standard seismic survey of the underground formation using a set of impulsive seismic sources and a set of downhole seismic receivers j, and recording the signals uij(t), selecting a position k to be the target point; obtaining from the signals uij(t) the one-way travel times &tgr;ik from a number of sources i to the target point at the location k; and calculating ti=t0−&tgr;ik to obtain the activating times ti at which the impulsive seismic sources i have to be activated, in order to get a focusing array of the seismic sources i of which the seismic waves arrive at the target point k in phase at time t0.

Abstract: An inverse filtering method, comprising: generating a first filtered signal based on an input signal; and combining the first filtered signal with the input signal for obtaining a residual signal. The generating comprises: generating a second filtered signal, the generating being stable and causal; amplifying a of the second filtered signals with a prediction coefficient; obtaining the first filtered signal based on the a second filtered signal storing a first signal related to the input signal in a buffer; and retrieving from the buffer a delayed signal. Further a synthesis filtering method, an inverse filter device and a synthesis filter device are provided.

Abstract: A method of seismic imaging a subsurface formation using an array of seismic sources and an array of seismic receivers located subsurface, wherein there is a complex transmission medium between the two sets by creating a virtual source at a selected receiver within the array, time-reversing a portion of the signal related to the selected source and receiver and convolving the time-reversed portion of the signal with the signal at adjoining receivers within the array and repeating the process for signals attributable to various surface sources to create a seismic image of a target formation.

Abstract: A seismic prospection method in which a compression seismic wave is emitted into the subsoil and sensors are used to collect seismic data having at least a shear component, and in which the data corresponding to said shear component is processed to deduce information about the geology of the subsoil, the method being characterized in that an estimate of the ratio: ∫ Z 0 Z ⁢ v p ·   ⁢ ⅆ l / ∫ Z 0 Z ⁢ v s ·   ⁢ ⅆ l is determined where vp and vs are values for real loca

Abstract: This invention relates to using elastically nonlinear seismic imaging methods, to identify the bypassed hydrocarbons and the movement of the reservoir fluids in the reservoir due to injection and production processes. Time-lapse seismic recording is used to monitor the changes in the hysteretic nonlinear behavior of the pore fluids in the reservoir rocks. Since the nonlinear hysteretic behavior of the saturated reservoir rock generates harmonics of the primary seismic signal that propagates through it, the measurement of these harmonics is used to determine the changes in the reservoir fluids due to hydrocarbon production over time.

Abstract: The invention relates to a vibroseis analysis method in which frequency-sweep signals (10) are emitted into a subsurface, the signals reflected on the substrata of such a subsurface (10, 20) are logged and the logged signals are processed, a method in which the harmonics (20) of the fundamental signal (10) initially emitted are eliminated from the logged signals, by applying the steps consisting in: a) providing a time/frequency plot, showing the respective contributions of the fundamental (10) and of the harmonics (20) in the logged signal, b) providing a time/frequency plot also showing these contributions of the fundamental (10) and of the harmonics (20) in the logged signal, this plot having been stretched in the direction of the frequency axis such that the fundamental (10) of this plot is over the location of a harmonic (20) chosen from the plot; c) adapting the power amplitude of this stretched plot to make this amplitude correspond to that of the said chosen harmonic (20) of the plot; d) subtracti

Abstract: A method of comparing multiple seismic survey data sets of a reservoir, is provided, wherein a first seismic survey data set is taken at a first time and a second seismic survey data set is taken at a second time, to detect changes in the reservoir between the first time and the second time. Generally, the method comprises design of a crossequalization function for the second data set based on a comparison of unchanging portions of the two data sets. Also provided is a processing method for preparing each survey according to similar processing steps with information taken from each survey.

Abstract: A system and method of processing seismic signals wherein seismic data resulting from a reflected seismic wave is received at a multi-component receiver. A mask trace is generated as a function of the seismic data received at the multi-component receiver, and a single type of seismic signals from the seismic data received at the multi-component receiver is identified and extracted utilizing the mask trace. Generating the mask trace further includes multiplying the seismic data received at two of the components of the multi-component receiver to produce a first result. A positive/negative sign of the first result is identified to produce a first binary result. The first binary result is divided by a scaling factor to produce the mask trace.

Abstract: An apparatus and method for removing the distortion in marine seismic data resulting from the motion of the ship. The ship trails one or more seismic sources and receivers and moves forward at a known velocity. The seismic sources emit seismic waves that travel through the water and reflect off interfaces between rock formations below the ocean floor. The motion of the sources and receivers introduces distortion in the recorded seismic data that can be modeled using Doppler theory. The data preferably is corrected for source motion independently from the correction for receiver motion. The seismic data is first corrected for receiver motion and then for source motion. The technique for correcting for source motion includes correlating the receiver-corrected data with a reference sweep signal, performing an F-K transform, performing an inverse F-K transform on a selected subset of the F-K transformed data, and computing appropriate correction filters for the data resulting from the inverse F-K transform.

Abstract: The present invention relates to a time-lapse or 4-D seismic data processing method in which cross-correlation of trace information in a series of time-lapse seismic images is used to distinguish one source of noise from another source of noise. After a source of noise has been identified, an appropriate filter is constructed to provide a correction to the noise produced by this particular source of noise. The data from one of the time-lapse seismic images is then applied to the filter to produce a corrected image. Differences between the corrected image and an uncorrected image are then used to determine time-lapse changes in the underlying geological structure. By being able to provide filters specifically tailored to correct each of the different types of noise present in a series of time-lapse seismic images, an accurate image of the time-lapse changes in the underlying geological structure is attained.

Abstract: A method for inverting a seismic signal, wherein an input seismic signal is represented as an input vector i(t) of length m+n-1, an output seismic signal is represented as an output vector o(t) of length m, and a finite impulse response filter is represented as a solution vector u(t) of length n, satisfying a convolutional equation i(t)Xu(t)=o(t). An m.times.n Toeplitz matrix T(t,.tau.) corresponding to i(t) is calculated, satisfying a matrix equation T(t,.tau.).multidot.u(t)=o(t). Both sides of the matrix equation are transformed to the frequency domain, to generate a transformed equation. Both sides of the transformed equation are spectrally pruned, to generate a pruned equation. The pruned equation is then solved.

Abstract: A method is described for providing improved seismic data to a driller to indicate position and spatial extent of a drilling target which may be up to several hundreds of feet ahead of a drill bit. In one embodiment, the method includes the steps of: survey design and data modeling, and definition of a drilling target point and a drilling interruption point; drilling down to a depth at which drilling will be interrupted; interruption of drilling; look-ahead borehole seismic survey (VSP); continuation of drilling; data processing and interpretation; coordinate update for optimum target intersection; and steering of drilling by borehole seismic data interpretation.