CN111427080A - Method for extracting space-variant generalized wavelets of seismic data - Google Patents
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Abstract
The invention relates to a method for extracting seismic data space-variant generalized wavelet, which solves the problem that the seismic wavelet extracted by the prior art can not truly reflect the energy attenuation and phase distortion of seismic signals and the change characteristics of the seismic signal in space, and comprises the following steps: (1) estimating initial parameters of the space-variant wavelet according to the seismic data power spectrum; (2) determining global generalized wavelet reference frequency; (3) estimating a space-variant fractional order value of the generalized wavelet; (4) optimizing global generalized wavelet reference frequency; (5) optimizing the space-variant fractional order value of the generalized wavelet; (6) and constructing the space-variant seismic generalized wavelet. The method has the advantages that the extraction method is stable in operation, strong in noise resistance, concise in extracted seismic generalized wavelet form, and capable of truly reflecting space-variant characteristics such as absorption attenuation of seismic signals in the stratum medium propagation process.
Description
Technical Field
The invention relates to a method for extracting seismic data wavelets, in particular to a method for extracting seismic data space-variant generalized wavelets.
Background
The seismic wavelet should reflect the waveform distortion and other effects caused by the absorption and attenuation of the viscoelastic medium of the stratum during the propagation process of the seismic wave. The formation viscoelastic medium has a filtering effect on the seismic signals, the energy of the seismic signals is gradually absorbed and attenuated by the formation medium in the process of underground medium propagation, and the absorption and attenuation degrees of different frequency components of the signals are different. It is particularly important that the seismic signals have phase distortion while being attenuated, because the propagation velocities of different frequency components of the signals are different, i.e. dispersion or phase delay exists. Therefore, it is highly desirable to extract space-variant seismic wavelets from seismic data that truly reflect the above-described stratigraphic filtering effects.
The seismic wavelets extracted by the existing wavelet estimation method based on the zero phase and the constant phase cannot accurately represent the effects of waveform distortion and the like. And smoothing the power spectrum of the seismic data to obtain the power spectrum of the wavelet during zero-phase wavelet extraction, and setting the phase of the wavelet to be zero to obtain the symmetrical zero-phase wavelet on a time axis. However, the actual seismic signal is affected by dispersion and is never a zero-phase wavelet. An effective method for extracting constant phase wavelets is a kurtosis scanning method. In statistics, the kurtosis may measure how far the seismic sequence deviates from the Gaussian normal distribution, and thus the phase of the seismic wavelet may be determined based on the maximum kurtosis value. However, the ordinary phase wavelet still cannot truly reflect the absorption and dispersion effects of the seismic signals in the formation propagation process.
In the absence of well logs as a reflection coefficient model, the extraction of the mixed-phase wavelet requires the use of higher order statistical analysis methods. The high-order statistics of the seismic data can accurately reflect the phase information, so that the accuracy of seismic wavelet estimation can be improved by using the high-order statistics including third-order cumulant and fourth-order cumulant (Mixed-phase wavelet estimation by iterative linear estimation of high-order statistics,Journal of Geophysics andengineering, vol: 4/2007/inventor; CN 102096101A/2010; CN 103645500A/2013). However, because of the need to calculate the higher-order statistics and to perform numerical analysis operation on the higher-order statistics, the wavelet estimation method has huge calculation amount and poor stability, and the application of the method in the actual seismic data analysis is severely limited. Therefore, the invention provides a method for extracting the space-variant seismic wavelet from the actual seismic data, which truly reflects the change characteristics of the seismic signal in the viscoelastic space and has the anti-noise capability and stability in the operation process.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide the method for extracting the seismic data space-variant generalized wavelet, and the extracted seismic wavelet can truly reflect the energy attenuation and phase distortion of seismic signals and the change characteristics of the seismic signals in space.
The invention provides a method for extracting seismic data space-variant generalized wavelets, which is characterized by comprising the following steps: (1) estimating initial parameters of the space-variant wavelet according to the seismic data power spectrum; (2) determining global generalized wavelet reference frequency; (3) estimating a space-variant fractional order value of the generalized wavelet; (4) optimizing global generalized wavelet reference frequency; (5) optimizing the space-variant fractional order value of the generalized wavelet; (6) and constructing the space-variant seismic generalized wavelet.
The invention provides a method for extracting space-variant seismic wavelets from actual seismic data. The inventor first proposed the theory of "Generalized seismic wavelets" internationally in 2015 (Generalized seismic wavelets,Geophysical Journal International203/2015/inventor), the following Wang's generalized wavelet theory, which is characterized in that only two parameters are needed to define the asymmetric wavelet. Therefore, the present invention proposes herein to characterize the space-variant wavelet in the actual seismic data using the above generalized wavelet theory. The invention has the first beneficial effects of noise resistance and stability of the operation process. The second beneficial effect of the invention lies in the space-variant characteristic of the seismic wavelet, and the extracted wavelet can truly reflect the energy attenuation and phase distortion of the seismic signal and the change characteristic of the seismic signal in space.
As optimization, step (1) estimates the initial parameters of the space-variant wavelet according to the seismic data power spectrum, and the optimization is realized by three steps; firstly, selecting a time-space window at different positions of a seismic data body, and calculating a power spectrum of the seismic data; secondly, setting a frequency band representative wavelet power spectrum of the seismic data power spectrum, and calculating basic statistical characteristics of the power spectrum, including mean frequency and standard deviation; then, the corresponding generalized wavelet fractional order value and the reference frequency are determined according to the basic statistical characteristics of each window power spectrum.
As optimization, determining the reference frequency of the generalized seismic wavelet adapting to the global situation in the step (2); according to the physical meaning of the Wang's generalized wavelet reference frequency as the natural frequency of the seismic source, the generalized wavelet reference frequency of each window is subjected to median filtering to obtain a substituteReference frequency global to table (ƒ)0)。
As an optimization, in step (3), the fractional order value corresponding to each window is estimated according to the global reference frequency and the mean frequency and standard deviation of each window.
As an optimization, the generalized wavelet order value (u) The calculation method of (2):
the calculation method uses mean frequency synchronously (ƒ) m ) And standard deviation (ƒ) σ ) The possible calculation error in calculating the fractional order value is reduced.
As optimization, the global generalized wavelet reference frequency is optimized through seismic spectrum matching in the step (4), and matching coefficients are provided as follows:
mid-pair actual seismic spectrumW obs(ƒ) and seismic wavelet spectraW(ƒ) respectively carrying out normalization processing, wherein the result of dot product (-) is the cross correlation coefficient; in the formula adoptNThe average of the cross correlation coefficients characterizes the matching coefficient.
As optimization, the optimization formula of seismic spectrum matching in step (4) is as follows:
in the formulakDenoted is window number, ƒ0 refIs an initial estimated value of reference frequency as a model constraint of a parameter optimization problem, and a constraint coefficient is set to beμ(ii) a And the anti-noise capability of the optimization process is enhanced by adopting the reference frequency initial estimation value as a model constraint.
As optimization, the optimization of the fractional order value of the space-variant generalized wavelet is realized through the matching of the seismic frequency spectrum in the step (5), and the optimization formula is provided as follows:
in the formulauAs a function of space variation of fractional orderu(t,x) Longitudinally over timet(or depth)z) And varies with distance in the transverse directionxAnd the number of the first and second electrodes is changed,u refit is the initial estimate. In the above-mentioned optimization process of fractional order, the model is constrained by using the initial estimation, and the change form of the model in time and space is also constrained, and the coefficients of the three constraints are respectively set as (A)μ 1,μ 2,μ 3)。
As optimization, the step (6) is realized by two steps; firstly, calculating the generalized wavelet spectrum of each window; and then, carrying out inverse Fourier transform on the frequency spectrum in a numerical solution calculation mode to obtain the generalized wavelet of the time domain.
The method for extracting the seismic data space-variant generalized wavelet has the following advantages after the technical scheme is adopted: the extraction method is stable in operation and has very strong anti-noise capability, the extracted seismic generalized wavelet is concise in form, and the extracted wavelet can truly reflect space-variant characteristics such as absorption attenuation and the like of seismic signals in the process of stratum medium propagation.
Drawings
FIG. 1 is a block diagram of a flow chart of a seismic data space-variant generalized wavelet extraction method of the present invention; FIG. 2 is a waveform comparison diagram between the seismic generalized wavelets (dotted line) and the measured seismic wavelets (solid line) extracted at different depths by the seismic data space-variant generalized wavelet extraction method of the present invention; FIG. 3 is a seismic data section of an embodiment of the seismic data space-variant generalized wavelet extraction method of the present invention, where two space-time windows a and b are selected on the left side, and two space-time windows c and d are selected on the right side; FIG. 4 is a diagram of the spectrum of the actual seismic data and the waveform of the extracted generalized seismic wavelet according to the method for extracting space-variant generalized wavelet from seismic data of the present invention.
Detailed Description
The method for extracting the seismic data space-variant generalized wavelet comprises the following steps: (1) estimating initial parameters of the space-variant wavelet according to the seismic data power spectrum; (2) determining global generalized wavelet reference frequency; (3) estimating a space-variant fractional order value of the generalized wavelet; (4) optimizing global generalized wavelet reference frequency; (5) optimizing the space-variant fractional order value of the generalized wavelet; (6) and constructing the space-variant seismic generalized wavelet. The invention proposes to adopt Wang's Generalized wavelet theory to represent the space-variant wavelets extracted from the actual seismic data, because the theory is characterized in that the asymmetric Generalized seismic wavelets (Generalized differential wavelets) can be defined only by two parameters.Geophysical Journal InternationalVol 203/2015/inventors). The method has the first beneficial effect that the space-variant characteristic is adopted, and the extracted seismic wavelet can truly reflect the energy attenuation and phase distortion of the seismic signal and the change characteristics of the seismic signal in space. The invention has the second beneficial effects of noise resistance and stability in the operation process.
Estimating initial parameters of space-variant wavelets according to a seismic data power spectrum, and realizing the estimation by three steps; firstly, selecting a time-space window at different positions of a seismic data body, and calculating a power spectrum of the seismic data; secondly, setting a frequency band representative wavelet power spectrum of the seismic data power spectrum, and calculating basic statistical characteristics of the power spectrum, including mean frequency and standard deviation; then, the corresponding generalized wavelet fractional order value and the reference frequency are determined according to the basic statistical characteristics of each window power spectrum.
Determining the reference frequency of the generalized seismic wavelet adapting to the global situation in the step (2); according to the physical meaning of Wang's generalized wavelet reference frequency as the natural frequency of the seismic source, the generalized wavelet reference frequency of each window is subjected to median filtering to obtain the reference frequency capable of representing the global (ƒ)0)。
And (3) estimating the fractional order value corresponding to each window according to the global reference frequency and the mean frequency and the standard deviation of each window. Generalized wavelet order of score (u) The calculation method of (2):
the calculation method uses mean frequency synchronously (ƒ) m ) And standard deviation (ƒ) σ ) The possible calculation error in calculating the fractional order value is reduced.
In the step (4), the global generalized wavelet reference frequency is optimized through the matching of the seismic frequency spectrum, and the matching coefficients are provided as follows:
mid-pair actual seismic spectrumW 0bs(ƒ) and seismic wavelet spectraW(ƒ) respectively carrying out normalization processing, wherein the result of dot product (-) is the cross correlation coefficient; in the formula adoptNThe average of the cross correlation coefficients characterizes the matching coefficient. The optimization formula of the seismic frequency spectrum matching in the step (4) is as follows:
in the formulakDenoted is window number, ƒ0 refIs an initial estimated value of reference frequency as a model constraint of a parameter optimization problem, and a constraint coefficient is set to beμ(ii) a And the anti-noise capability of the optimization process is enhanced by adopting the reference frequency initial estimation value as a model constraint.
And (5) realizing optimization of the fractional order value of the space-variant generalized wavelet through matching of seismic frequency spectrums, and providing an optimization formula as follows:
in the formulauAs a function of space variation of fractional orderu(t,x) Longitudinally over timet(or depth)z) And varies with distance in the transverse directionxAnd the number of the first and second electrodes is changed,u refit is the initial estimate. Of the above fractional orderIn the optimization process, the model is constrained by using the initial estimation, and simultaneously, the change form of the model in time and space is also constrained, and the coefficients of the three constraints are respectively set as (μ 1,μ 2,μ 3)。
The step (6) is realized by two steps; firstly, calculating the generalized wavelet spectrum of each window; and then, carrying out inverse Fourier transform on the frequency spectrum in a numerical solution calculation mode to obtain the generalized wavelet of the time domain.
As shown in the drawings, in order to make the extraction method and advantages of the seismic data space-variant generalized wavelet more clear, the following detailed description is made on the embodiments of the present invention with reference to the drawings. The invention provides a method for extracting space-variant generalized seismic wavelets based on an actual seismic data power spectrum, and FIG. 1 is a basic flow chart of the method.
And S101, estimating initial parameters of the space-variant wavelet according to the seismic data power spectrum, and realizing the space-variant wavelet by three steps. Firstly, selecting time-space windows at different positions of a seismic data body, constructing a super-long sequence by seismic channels in each window, and calculating a power spectrum of the super-long sequence; secondly, selecting an initial frequency and a cut-off frequency, ensuring that the seismic data power spectrum in the initial frequency and the cut-off frequency can represent the power spectrum of the wavelet, and calculating the basic statistical characteristics of the cut-off frequency band power spectrum, including a mean frequency and a standard deviation; then, the generalized wavelet fractional order value and the reference frequency corresponding to each window are determined according to the basic statistical characteristics of the seismic power spectrum.
And step S102, determining the global generalized wavelet reference frequency. The invention indicates that the physical meaning of the Wang's generalized wavelet reference frequency is the natural frequency of a seismic source, the seismic sources in the same seismic data volume are consistent, and the natural frequencies of the seismic sources are also consistent. Median filtering the reference frequencies of the windows based on the physical significance to obtain a generalized wavelet reference frequency representing the global (ƒ)0)。
Step S103, estimating the space-variant fractional order of the generalized wavelet (u) The invention proposes the following calculation method:
mean frequency is used synchronously during the calculation (ƒ) m ) And standard deviation (ƒ) σ ) Fractional order values are calculated, rather than just one of the two, to reduce the potential error of fractional order calculation that may be caused by estimation errors of these basic statistical properties.
And step S104, realizing the optimization of the global generalized wavelet reference frequency through the matching of the seismic frequency spectrum. The invention provides the following matching coefficients:
spectrum of real seismic data in formulaW obs(ƒ) and seismic wavelet spectraW(ƒ) performing normalization processing, wherein the vector dot product (. cndot.) is the cross-correlation coefficient, and the formula adoptsNThe average of the cross correlation coefficients characterizes the matching coefficient. The invention provides a seismic frequency spectrum matching optimization method which comprises the following steps:
in the formulakIs the window number, initial estimate ƒ of the reference frequency0 refModel constraint as a parameter optimization problem, with constraint coefficients set toμThe aim is to enhance the noise immunity and stability of the parameter optimization process.
And step S105, optimizing the space-variant fractional order value of the generalized wavelet. The optimization of the fractional order value of the space-variant generalized wavelet is realized by matching the seismic frequency spectrum as follows:
in the formulauAs a function of space variation of fractional orderu(t,x) Longitudinally over timet(or depth)z) And varies with distance in the transverse directionxAnd the number of the first and second electrodes is changed,u refit is the initial estimate. In the above-mentioned optimization process of fractional order, the model is constrained by using the initial estimation, and the change form of the model in time and space is also constrained, and the coefficients of the three constraints are respectively set as (A)μ 1,μ 2,μ 3)。
And S106, constructing the seismic space-variant generalized wavelet, and realizing the seismic space-variant generalized wavelet by two steps. Firstly, calculating the generalized wavelet spectrum of each window; then, Fourier inverse transformation is carried out on the wavelet spectrum by adopting a numerical solving calculation mode to obtain the generalized wavelet in the time domain.
The invention also provides two embodiments to illustrate the beneficial effects of the invention. Example fig. 2 compares the waveforms of a generalized seismic wavelet (dashed line) extracted according to the method of the present invention with a measured seismic wavelet (solid line). Seismic wavelets with depth of formationzAnd the depth position of the measured earthquake is from 600 meters to 1700 meters. Global generalized seismic wavelet reference frequency extracted by the embodimentf 0At 32.4 hz, the fractional order values become progressively smaller with increasing depth. Therefore, as shown in fig. 2, the method has the beneficial effect that the extracted generalized seismic wavelet can truly reflect the space-variant characteristics of the seismic signal such as absorption attenuation and the like in the process of stratum medium propagation.
Embodiments fig. 3-4 demonstrate the effect of the method of the present invention in extracting space-variant generalized wavelets from actual seismic data. FIG. 3 shows an actual seismic data profile. In order to demonstrate the effect of the method, only the upper and lower windows a and b are selected from the left side of the seismic data section, and the upper and lower windows c and d are selected from the right side of the seismic data section. The time period of the seismic data profile is 3.3-5.0 seconds, and the noise resistance and the stability of the method can be checked by selecting the seismic data at such deep part.
FIG. 4 is a diagram of the frequency spectrum of the actual seismic data and the waveform of the corresponding generalized seismic wavelet in the seismic data space-variant generalized wavelet extraction method of the present invention. As shown in FIG. 4, the method for extracting the seismic data space-variant generalized wavelet has the advantage of simple seismic wavelet form, and the reference frequency of the generalized seismic wavelet is 19.5 Hz. For the two-column comparison chosen in example fig. 4, the fractional order values of the generalized wavelet vary less significantly laterally, but vary significantly in the longitudinal direction. Therefore, as shown in fig. 4, the space-variant generalized wavelet extraction method has the advantages of good stability, strong anti-noise capability, precise extraction of the space-variant characteristics of the generalized seismic wavelets and the like.
Claims (9)
1. A method for extracting seismic data space-variant generalized wavelets is characterized by comprising the following steps: (1) estimating initial parameters of the space-variant wavelet according to the seismic data power spectrum; (2) determining global generalized wavelet reference frequency; (3) estimating a space-variant fractional order value of the generalized wavelet; (4) optimizing global generalized wavelet reference frequency; (5) optimizing the space-variant fractional order value of the generalized wavelet; (6) and constructing the space-variant seismic generalized wavelet.
2. The method for extracting space-variant generalized wavelets of seismic data according to claim 1, wherein the step (1) of estimating initial parameters of the space-variant wavelets according to a seismic data power spectrum is implemented in three steps; firstly, selecting a time-space window at different positions of a seismic data body, and calculating a power spectrum of the seismic data; secondly, setting a frequency band representative wavelet power spectrum of the seismic data power spectrum, and calculating basic statistical characteristics of the power spectrum, including mean frequency and standard deviation; then, the corresponding generalized wavelet fractional order value and the reference frequency are determined according to the basic statistical characteristics of each window power spectrum.
3. The method for extracting space-variant generalized wavelets of seismic data according to claim 1, wherein the reference frequency of the generalized seismic wavelets adapted to the global is determined in step (2); according to the physical meaning of Wang's generalized wavelet reference frequency as the natural frequency of the seismic source, the generalized wavelet reference frequency of each window is subjected to median filtering to obtain the reference frequency capable of representing the global (ƒ)0)。
4. The method for extracting space-variant generalized wavelets of seismic data according to claim 1, wherein in step (3), the fractional order value corresponding to each window is estimated according to the global reference frequency and the mean frequency and standard deviation of each window.
6. The method for extracting space-variant generalized wavelets of seismic data according to claim 1, wherein the global generalized wavelet reference frequency is optimized by matching the seismic spectrum in step (4), and the matching coefficients are provided as follows:
mid-pair actual seismic spectrumW obs(ƒ) and seismic wavelet spectraW(ƒ) respectively carrying out normalization processing, wherein the result of dot product (-) is the cross correlation coefficient; in the formula adoptNThe average of the cross correlation coefficients characterizes the matching coefficient.
7. The method for extracting space-variant generalized wavelets of seismic data according to claim 6, wherein the optimization formula of seismic spectrum matching in step (4) is as follows:
in the formulakDenoted is window number, ƒ0 refIs an initial estimated value of reference frequency as a model constraint of a parameter optimization problem, and a constraint coefficient is set to beμ(ii) a And the anti-noise capability of the optimization process is enhanced by adopting the reference frequency initial estimation value as a model constraint.
8. The method for extracting space-variant generalized wavelets of seismic data according to claim 1, wherein the optimization of the fractional order of the space-variant generalized wavelets is realized through seismic spectrum matching in step (5), and the optimization formula is as follows:
in the formulauAs a function of space variation of fractional orderu(t,x) Longitudinally over timetOr depth ofzAnd varies with distance in the transverse directionxAnd the number of the first and second electrodes is changed,u refthen it is the initial estimate; in the above-mentioned optimization process of fractional order, the model is constrained by using the initial estimation, and the change form of the model in time and space is also constrained, and the coefficients of the three constraints are respectively set as (A)μ 1,μ 2,μ 3)。
9. The method for extracting space-variant generalized wavelets of seismic data according to claim 1, wherein the step (6) is implemented in two steps; firstly, calculating the generalized wavelet spectrum of each window; and then, carrying out inverse Fourier transform on the frequency spectrum in a numerical solution calculation mode to obtain the generalized wavelet of the time domain.
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