Statistical chirplet-based 3d extraction method for complex superimposed dense channel reservoirs

Abstract

The application discloses a three-dimensional extraction method of complex superimposed dense channel reservoir based on statistical linear frequency modulation, and comprises the following steps: S1, inputting a seismic signal x(t) to be analyzed, wherein t is time; S2, constructing a linear chirp transform in a time-frequency-chirp rate (TFC) three-dimensional space, wherein omega is frequency, and beta is a chirp rate; S3, combining a matrix calculation method, and introducing a group of bases to represent an instantaneous attribute value of a single-component signal; S4, introducing a sliding real-value frequency filter H(omega) to realize local representation of an instantaneous attribute value of a multi-component cross signal; S5, according to an inner product formula, constructing a statistical linear frequency modulation filter estimation and a time-frequency coefficient used for extracting an original time-frequency spectrum instantaneous frequency and an instantaneous chirp rate curve in the TFC space, and obtaining a statistical linear frequency modulation three-dimensional extraction transform value T x (t, omega, beta); S6, performing modulus operation on T x (t, omega, beta), and obtaining a time-frequency spectrum of the statistical linear frequency modulation three-dimensional extraction transform, so that the purpose of effectively identifying a complex superimposed dense channel sandstone reservoir is achieved.

Description

TECHNICAL FIELD

[0001] The application relates to a signal processing method, in particular to a three-dimensional extraction method for a complex superimposed dense channel reservoir based on statistical linear frequency modulation. BACKGROUND

[0002] The tight sandstone gas reservoirs are rich in resources in China, and the complex superimposed dense channel reservoirs have huge reserves, are one of the most potential oil and gas reservoirs in China and even the whole world, but the reservoirs usually have the characteristics of vertical multi-stage superposition, complex horizontal change and internal densification, so that the exploration and development are difficult, and how to identify the reservoirs with high precision is an important task for realizing the increase of reserves and production in the continental basin.

[0003] For the identification of the tight sandstone reservoir, a time-frequency analysis method is a powerful tool for processing and interpreting multi-component non-stationary signals and is an important method for mining the instantaneous spectrum information of the seismic signals, and can be used for horizontal reservoir spatial distribution description and vertical thin reservoir description. Common time-frequency analysis methods include short-time Fourier transform, wavelet transform, S transform and the like. In order to improve the adaptability of the time-frequency representation method to signals, high-precision time-frequency post-processing methods are proposed one after another, but the performance of these methods mostly depends on the representation ability of the basic transform. Especially, the separation condition of the multi-component signals will seriously affect the performance of the time-frequency post-processing method. When processing multi-component intersecting signals, the synchronous squeezing algorithm and the synchronous extraction algorithm cannot obtain the accurate information of the above signals in the aliasing area; between the components in the time-frequency inseparable area, the signals will produce serious cross interference, reducing the readability of the squeezing and extraction methods. Therefore, the analysis of the complex superimposed dense channel reservoir is limited. SUMMARY

[0004] In view of the above problems in the prior art, the application provides a three-dimensional extraction method for a complex superimposed dense channel reservoir based on statistical linear frequency modulation, which can obtain a time-frequency representation result with more focused energy in a higher-dimensional space, so as to effectively identify the complex superimposed dense channel reservoir.

[0005] In order to achieve the above purpose, the technical scheme adopted by the application is as follows: a three-dimensional extraction method for a complex superimposed dense channel reservoir based on statistical linear frequency modulation, comprising the following steps:

[0006] S1, inputting a seismic signal x(t) to be analyzed, wherein t is time;

[0007] S2, constructing a linear chirp transform in a time-frequency-chirp rate (TFC) three-dimensional space Wherein ω is frequency, and β is chirp rate;

[0008] S3, introducing a group of bases in combination with the matrix calculation method wherein denotes the linear chirp transform value obtained by using the window function tg(t);

[0009] S4, introducing a sliding real-valued frequency filter H(ω) to realize the local representation of the multi-component cross signal instantaneous attribute value;

[0010] S5, constructing a statistical chirp filter estimate in the TFC space according to the inner product formula and for extracting the time-frequency coefficients at the instantaneous frequency and the instantaneous chirp rate curves of the original time-frequency spectrum, to obtain a statistical chirp three-dimensional extraction transform value T x (t,ω,β);

[0011] S6, taking the modulus of T x (t,ω,β) to obtain the time-frequency spectrum of the statistical chirp three-dimensional extraction transform, so as to realize the purpose of effectively identifying complex superimposed dense channel reservoirs.

[0012] As a preferred, the linear chirp transform in the step S2 has an explicit expression as follows:

[0013]

[0014] wherein μ is time, ω is frequency, and β is chirp rate, is the conjugate function of the Gaussian window function g(t), and j is the imaginary unit;

[0015] As a preferred, the step S3 combines the method of matrix calculation, and introduces a set of bases to represent the instantaneous attribute value of the single-component signal:

[0016]

[0017] wherein denotes the linear chirp transform value obtained by using the window function tg(t), denotes the partial derivative of the linear chirp transform with respect to t, denotes the k-order instantaneous attribute value of the signal amplitude and phase, wherein k=1, 2;

[0018] As a preferred, the step S4 introduces a sliding real-valued frequency filter H(ω) to realize the local representation of the multi-component cross signal instantaneous attribute value, and the specific expression is as follows:

[0019]

[0020] Wherein, sigma is a certain real number controlling the size of real value frequency filter, e is exponential function;

[0021] As preferred, the step S5 is according to inner product formula The following matrix relationship is constructed:

[0022]

[0023] A kind of statistical chirp filter estimation is constructed in TFC space And For extracting time-frequency coefficient at the curve of instantaneous frequency and instantaneous chirp rate of original time-frequency spectrum;

[0024] Wherein, And The specific expression of the following formula:

[0025]

[0026] Wherein,

[0027] The time-frequency spectrum after statistical chirp three-dimensional extraction transformation is as follows:

[0028]

[0029] Wherein delta (t) is unit impulse function, It represents the local instantaneous frequency estimator satisfying extraction condition in three-dimensional synchronous extraction chirp rate transform (TDSECT) time-frequency domain.

[0030] The idea of the application is:

[0031] Firstly, input the seismic signal x (t) to be analyzed, wherein t is time;

[0032] Secondly, construct linear chirp transform in time-frequency-chirp rate (TFC) three-dimensional space Wherein omega is frequency, beta is chirp rate;

[0033] Thirdly, introduce a group of bases to represent the instantaneous attribute values of single-component signal, namely instantaneous frequency and instantaneous chirp rate;

[0034] Fourthly, introduce sliding real value frequency filter H (omega) in TFC space to realize local representation of instantaneous attribute values of multi-component cross signal;

[0035] Fifth, according to the inner product formula, a kind of statistical chirplet filter related to instantaneous attribute is constructed, and the instantaneous attribute estimation formula of multi-component cross signal is derived, which is used to extract the time-frequency coefficient at the instantaneous frequency and instantaneous chirp rate curve of original time-frequency spectrum, to obtain the statistical chirplet three-dimensional extraction transform value T x (t,ω,β);

[0036] Sixth, the modulus of T x (t,ω,β) is taken to obtain the time-frequency spectrum of statistical chirplet three-dimensional extraction transform, so as to achieve the purpose of effectively identifying complex superimposed dense channel reservoir.

[0037] The working principle of the application is as follows: in view of the problem that multi-component cross signals will produce serious cross interference between components in time-frequency inseparable area, a three-dimensional extraction method for complex superimposed dense channel reservoir based on statistical chirplet is proposed. First, input the seismic signal x(t) to be analyzed, wherein t is time; then construct linear chirp transform in time-frequency-chirp rate (TFC) three-dimensional space wherein ω is frequency, and β is chirp rate; then, a group of bases are introduced to represent the instantaneous attribute value of single-component signal by combining the method of matrix calculation; and a sliding real-value frequency filter H(ω) is introduced to realize the local representation of the instantaneous attribute value of multi-component cross signal; finally, according to the inner product formula, a statistical chirplet filter is constructed in TFC space to estimate and for extracting the time-frequency coefficient at the instantaneous frequency and instantaneous chirp rate curve of original time-frequency spectrum, to obtain the statistical chirplet three-dimensional extraction transform value T x (t,ω,β); the modulus of T x (t,ω,β) is taken to obtain the time-frequency spectrum of statistical chirplet three-dimensional extraction transform, so as to achieve the purpose of effectively identifying complex superimposed dense channel reservoir. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1 is the flowchart of the application;

[0039] Figure 2 is the time-frequency spectrum diagram of the feature extraction after the multi-component cross signal is processed by the short-time Fourier transform and rearrangement method: (a) is the time-frequency spectrum after the short-time Fourier transform processing, (b) is the local enlarged view of the box in (a), (c) is the time-frequency spectrum after the rearrangement method processing, and (d) is the local enlarged view of the box in (c);

[0040] Figure 3 is the time-frequency spectrum diagram of the feature extraction after the multi-component cross chirp signal is processed by the method of the application: (a) is the time-frequency spectrum after the method of the application processing, and (b) is the local enlarged view of the box in (a);

[0041] Figure 4 For comparison of the method of the present application with the ideal representation, (a) is an ideal time-frequency-chirp rate representation (ITFCR) of theoretical signal 1 (x1) and theoretical signal 2 (x2) in TFC space; (b) is a representation of theoretical signal 1 (x1) and theoretical signal 2 (x2) in TFC space after processing by the method of the present application, in which TDSECT represents a three-dimensional synchronous extraction chirp rate transform. DETAILED DESCRIPTION

[0042] The present application will be further described below in conjunction with the accompanying drawings.

[0043] Example 1: see Figure 1 A three-dimensional extraction method for complex superimposed dense channel reservoirs based on statistical linear frequency modulation, comprising the following steps:

[0044] S1, inputting a seismic signal x(t) to be analyzed, where t is time;

[0045] S2, constructing a linear chirp transform in a time-frequency-chirp rate (TFC) three-dimensional space where ω is frequency and β is chirp rate;

[0046] S3, introducing a set of bases to represent the instantaneous attribute value of a single-component signal, where represents a linear chirp transform value obtained by using a window function tg(t);

[0047] S4, introducing a sliding real-valued frequency filter H(ω) to realize local representation of the instantaneous attribute value of a multi-component cross signal;

[0048] S5, constructing a statistical linear frequency modulation filter estimate and in the TFC space according to an inner product formula, for extracting time-frequency coefficients at the instantaneous frequency and instantaneous chirp rate curves of the original time-frequency spectrum, to obtain a statistical linear frequency modulation three-dimensional extraction transform value T x (t, ω, β);

[0049] S6, taking the modulus of T x (t, ω, β) to obtain a time-frequency spectrum of the statistical linear frequency modulation three-dimensional extraction transform, to achieve the purpose of effectively identifying complex superimposed dense channel reservoirs.

[0050] As a preferred, the explicit expression of the linear chirp transform in step S2 is:

[0051]

[0052] where μ is time, ω is frequency, β is chirp rate, is the conjugate function of the Gaussian window function g(t), and j is the imaginary unit;

[0053] As a preference, the step S3 combines the method of matrix calculation, and introduces a set of bases to represent the instantaneous attribute value of the single-component signal:

[0054]

[0055] where represents the linear chirp transform value obtained by using the window function tg(t), represents the partial derivative of the linear chirp transform with respect to t, represents the k-order instantaneous attribute value of the signal amplitude and phase, where k = 1, 2;

[0056] As a preference, the step S4 introduces a sliding real-valued frequency filter H(ω) to realize the local representation of the multi-component cross signal instantaneous attribute value, and the specific expression is as follows:

[0057]

[0058] where σ is a certain real number that controls the size of the real-valued frequency filter, and e is an exponential function;

[0059] As a preference, the step S5 is based on the inner product formula The following matrix relationship is constructed:

[0060]

[0061] In the TFC space, a statistical linear frequency modulation filter estimation and is used to extract the time-frequency coefficients at the instantaneous frequency and the instantaneous chirp rate curve of the original time-frequency spectrum;

[0062] where, and The specific expressions are as follows:

[0063]

[0064] where,

[0065] The seismic time-frequency spectrum after the statistical linear frequency modulation three-dimensional extraction transform is:

[0066]

[0067] where δ(t) is a unit impulse function, The local instantaneous frequency estimator in the three-dimensional synchronous extraction chirp rate transform (TDSECT) time-frequency domain satisfies an extraction condition.

[0068] Referring to Figures 1 to 4 We take a multi-component cross-chirp signal as an example, whose sampling frequency is 512 Hz and sampling time is 1 s. The comparison of the results of the three methods can be seen in Figure 2 The time-frequency diagrams of (a) and (c) show that the energy of the short-time Fourier transform time-frequency spectrum is relatively dispersed, and the rearrangement method can better gather the signal near the instantaneous frequency ridge line. However, the time-frequency results of (b) and (d) show that both methods cannot obtain high-precision time-frequency representation of the multi-component cross signal near the cross point (t = 0.72 s), and serious cross interference and information mixing phenomenon occurs. Figure 2 The local magnification of the time-frequency results of (b) and (d) shows that both methods cannot obtain high-precision time-frequency representation of the multi-component cross signal near the cross point (t = 0.72 s), and serious cross interference and information mixing phenomenon occurs. Figure 3 The signal representation processed by the method of the present application has similar time-frequency spectrum, which shows the effectiveness of the proposed method, and has a more clear depiction result at t = 0.72 s. Figure 4 The comparison of the results of the present application method and the ideal representation can show the accuracy of the present application method, and the error of the time-frequency coefficient estimated by the TDSECT is extremely small. The processing result also shows that the cross signal on the time-frequency plane actually does not intersect in a higher dimensional space.

[0069] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for 3D extraction of complex superimposed dense channel reservoirs based on statistical chirp, characterized in that, The method comprises the following steps: S1, inputting a seismic signal x(t) to be analyzed, wherein t is time; S2, constructing a linear chirp transform in a time-frequency-chirp rate three-dimensional space where ω is the frequency and β is the chirp rate. S3, introduce a set of bases by a method similar to matrix calculation to represent the instantaneous attribute value of the single-component signal, wherein represents a linear chirp transform value obtained by using a window function tg(t); S4, introducing a sliding real-valued frequency filter H(ω) to realize local representation of the multi-component cross signal instantaneous attribute value; S5. According to the inner product formula Constructing a statistical chirplet filter estimator in time-frequency-chirp rate three-dimensional space and For extracting the time-frequency coefficients at the instantaneous frequency and instantaneous chirp rate curves of the original time-frequency spectrum, a statistical chirplet three-dimensional extraction transform T is obtained x (t, ω, β); S6, to T x (t, ω, β) is taken, the time-frequency spectrum of the statistical linear frequency modulation three-dimensional extraction transform is obtained, and the purpose of effectively identifying complex superimposed dense channel reservoirs is achieved.

2. The method according to claim 1, wherein, The linear chirp transform in the step S2 The explicit expression is: where μ is time, ω is frequency, and β is the chirp rate, is the conjugate of the Gaussian window function g(t), and j is the imaginary unit.

3. The method according to claim 1, wherein, The step S3 introduces a set of bases by a method similar to matrix calculation to represent the instantaneous attribute values of the single-component signal: wherein denotes a linear chirp transform value obtained by using a window function tg(t), denotes a partial derivative with respect to t of the linear chirp transform, denotes a k-th order instantaneous attribute value of the signal amplitude and phase, where k = 1, 2.

4. The method according to claim 1, wherein, The step S4 introduces a sliding real-valued frequency filter H(ω) to realize local representation of the multi-component cross signal instantaneous attribute value, and the specific expression is as follows: Wherein, σ is a certain real number for controlling the size of the real-valued frequency filter, and e is an exponential function.

5. The method according to claim 1, wherein, The step S5 is according to the inner product formula The following matrix relationship is constructed: Constructing a statistical chirplet filter estimate in time-frequency-chirp rate 3-D space and for extracting time-frequency coefficients at the instantaneous frequency and instantaneous chirp rate curves of the original time-frequency spectrum; wherein and The specific expressions of the above are as follows: wherein Statistical linear frequency modulation three-dimensional extraction transformation is as follows: where δ(t) is a unit impulse function, represents a local instantaneous frequency estimation algorithm that satisfies the extraction condition on the three-dimensional synchronous extraction chirp transform time-frequency domain.

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