Western Atlas International, Inc.

Baker Hughes Corporation

Zeljko Jericevic

Otto N Fanini

William Henry Dragoset, Jr

Gary Arthur Sitton

Pravin Gupta

Berthold F Kriegshauser

Antonio Fabris

Antonio Fabirs

A method for correcting data measured by a well logging instrument for effects of cable yo-yo. The data are first preprocessed to reduce magnitude of spatial frequency components in the data occurring within a bandwidth of axial acceleration of the logging instrument which corresponds to the cable. Then eigenvalues of a matrix are shifted, over depth intervals where the smallest absolute value one of the eigenvalues changes sign, by an amount such that the smallest absolute value eigenvalue does not change sign. The matrix forms part of a system of linear equations by which the measurements made by the instrument are converted to values of a property of interest of earth formations. Artifacts which may remain in the data after the step of preprocessing are substantially removed by the eigenvalue shifting. In one embodiment, the step of preprocessing includes low pass filtering using a cutoff at the axial resolution limit of a sensor on the instrument. In another embodiment, preprocessing includes phase shifting the response of one sensor to another sensor on the instrument within the spatial frequency bandwidth of the cable yo-yo. Still another embodiment of preprocessing include phase synthesis of the response of one sensor to that of another sensor within the spatial frequency bandwidth of the cable yo-yo.

Method for correcting well log data for effects of changes in instrument velocity (cable yo-yo)

A method for correcting data measured by a well logging instrument for effects of cable yo-yo. The data are first preprocessed to reduce magnitude of spatial frequency components in the data occurring within a bandwidth of axial acceleration of the logging instrument which corresponds to the cable. Then eigenvalue, of a matrix are shifted, over depth intervals where the smallest absolute value one of the eigenvalues changes sign, by an amount such that the smallest absolute value eigenvalue does not change sign. The matrix forms part of a system of linear equations by which the measurements made by the instrument are converted to values of a property of interest of earth formations. Artifacts which may remain in the data after the step of preprocessing are substantially removed by the eigenvalue shifting. In one embodiment, the step of preprocessing includes low pass filtering using a cutoff at the axial resolution limit of a sensor on the instrument. In another embodiment, preprocessing includes phase shifting the response of one sensor to another sensor on the instrument within the spatial frequency bandwidth of the cable yo-yo. Still another embodiment of preprocessing include phase synthesis of the response of one sensor to that of another sensor within the spatial frequency bandwidth of the cable yo-yo.

Method for correcting well log data for effects of changes in instrument

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.

Efficient inversion of near singular geophysical signals

A method for estimating axial positions of formation layer boundaries from transverse electromagnetic induction signals. A first derivative is calculated with respect to depth of the induction signals. A second derivative of the signals is calculated. The second derivative is muted. Layer boundaries are selected at axial positions where the muted second derivative is non zero, and the first derivative changes sign. The selected boundaries are thickness filtered to eliminate boundaries which have the same axial spacing as the spacing between an induction transmitter and receiver used to measure the induction signals, and to eliminate boundaries having a spacing less than an axial resolution of the induction signals. In a preferred embodiment, the process is repeated using transverse induction measurements made at another alternating current frequency. Layer boundaries selected in both frequencies are determined to be the layer boundaries. An alternative embodiment includes Fourier transforming the induction signals into the spatial frequency domain, low pass filtering the Fourier transformed signals at a band limit about equal to the axial resolution of the induction signals, calculating a central first derivative of the filtered, Fourier transformed signals, calculating an inverse Fourier transform of the central first derivative, determining roots of the inverse Fourier transform, and testing localized properties of the inverse Fourier transform within a selected number of data sample points of the selected roots, thereby providing indications of formation layer boundaries at axial positions most likely to be true ones of the formation layer boundaries.

Method for determining the axial position of formation layer boundaries

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

Energy minimization in surface multiple attenuation

A physical signal is represented by a linear system. The linear system is transformed from the time and space domain to the frequency domain, generating a transformed system. The least significant portions in the transformed system are determined. The least significant portions are deleted from the transformed system, generating a smaller pruned system. The pruned system is solved in the frequency domain, generating a solution. The solution is inverse transformed from the frequency domain to the time and space domain, generating an approximation to the physical signal.

Approximate solution of dense linear systems

A method for determining the 2-dimensional distribution of horizontal and vertical electrical conductivities of earth formations surrounding a wellbore using measurements made by a transverse electromagnetic induction well logging instrument. A model is generated of the axial distribution of the horizontal and vertical conductivities, from induction signals acquired by the instrument using two-frequency alternating current. The model is generated by calculating an initial estimate of the conductivity distribution and axially inverting the estimate with respect to the measurements made using the two-frequency alternating current. Shoulder correction is applied to measurements made by the instrument using single-frequency alternating current. An estimate of the radial distribution of the conductivities is generated from the shoulder corrected induction signals acquired using the single-frequency alternating current. A 2-dimensional model is made of the conductivity distribution from the model of axial distribution and from the estimate of radial distribution. The two-frequency induction signals are corrected for near wellbore effects using two-frequency whole space responses calculated using the 2-dimensional model. The corrected two-frequency signals are then axially inverted to generate a 2-dimensional model. Using the corrected two-frequency signals in place of the acquired signals, all the previous steps are repeated until differences between the corrected two-frequency induction signals from successive repetitions (iterations) of the steps fall below a predetermined threshold. The two-dimensional model extant when process is halted becomes the final two-dimensional model.

Method for inversion processing of transverse electromagnetic induction

A method of compressing digital signals for transmission and/or storage. The method includes lossy compressing the digital signal to generate a lossy compressed signal. The compressed signal is decompressed locally to generate a local lossy decompressed signal. An error signal is calculated as the difference between the original digital signal and the local lossy decompressed signal. The power in the original digital signal and in the error signal is determined. A minimum resolution for quantizing the error signal is determined from a ratio of the power of the original signal with respect to power of the error signal. The error signals is lossy compressed by quantizing to at least the minimum resolution. Both the compressed digital signal and the compressed error signal are transmitted and/or stored. The lossy compressed error signal and the lossy compressed signal are recovered from storage or transmission. The lossy compressed signal and the lossy compressed error signal are decompressed, and the decompressed lossy compressed original signal and the decompressed lossy compressed error signal are summed to generate the recovered original digital signal.

Method for compression of high resolution seismic data

A marine seismic signal is transformed from time domain into frequency domain and represented by matrix D. The marine data signal is truncated in time, transformed into the frequency domain and represented by matrix D.sub.T. Eigenvalue decomposition D.sub.T =S.multidot..LAMBDA..multidot.S.sup.-1 of matrix D.sub.T is computed. Matrix product D.multidot.S is computed and saved in memory. Matrix inverse S.sup.-1 is computed and saved in memory. An initial estimate of the source wavelet w is made. Source wavelet w is computed by iterating the steps of computing diagonal matrix [I-w.sup.-1 .LAMBDA.], computing matrix inverse [I-w.sup.-1 .LAMBDA.].sup.-1, retrieving matrix product D.multidot.S and matrix inverse S.sup.-1 from memory, and minimizing the total energy in matrix product [D.multidot.S] [I-w.sup.-1 .LAMBDA.].sup.-1 S.sup.-1. Primary matrix P representing the wavefield free of surface multiples is computed by inserting computed value for w into the expression [D.multidot.S] [I-w.sup.-1 .LAMBDA.].sup.-1 S.sup.-1. Primary matrix P is inverse transformed from frequency domain into time domain.

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Houston, TX, United States of America

Zeljko Jericevic