Normalized W transformation-based gas-bearing reservoir identification method

Abstract

The invention discloses a gas-bearing reservoir identification method based on normalized W transformation, and belongs to the field of seismic signal processing, and the normalized W transformation is obtained by multiplying a standard deviation function normalized along a time-varying dominant frequency on the basis of W transformation, so that the problems of energy splitting artifacts of the W transformation at the dominant frequency position and offset of peak frequency to two ends are effectively avoided; compared with W transformation and parameterized W transformation, under the action of a normalized standard deviation function, normalized W transformation provides more accurate spectrum representation with time positioning for non-stationary seismic signals, spectrum energy can be more effectively focused near a time-varying dominant frequency, and the time-frequency resolution is high. The peak amplitude and the average amplitude corresponding to each moment are calculated by using the time-frequency spectrum of the normalized W transformation, and then the peak amplitude and the average amplitude are subtracted to obtain the abnormal amplitude, so that the gas-bearing reservoir can be identified and delineated more finely.

Description

Technical Field

[0001] The invention belongs to the field of seismic signal processing, and in particular relates to a normalized W-transform gas reservoir identification method. Background Art

[0002] Spectral decomposition is an important technology for seismic data processing and interpretation. It maps one-dimensional seismic records to two-dimensional time-frequency domains, including short-time Fourier transform, wavelet transform, S transform, generalized S transform, etc., which effectively reveals geological anomalies hidden in non-stationary seismic data and is widely used in sedimentary cycle division, reservoir characterization, hydrocarbon detection, etc. In 2021, Wang proposed a time-frequency analysis method called W transform, which uses the time-varying main frequency to modify the standard deviation trend that varies with frequency in the S transform, thereby improving the energy focusing of the low-frequency band. In this way, the spectral energy of the W transform can be well focused near the main frequency of the waveform, rather than moving to higher frequencies like the S transform. However, for broadband seismic signals, due to the non-differentiable frequency of its standard deviation, the W transform has singularity near the main frequency, which is mainly manifested as energy splitting and the peak frequency shifts to both sides. An effective strategy is to parameterize the standard deviation so that it has frequency differentiability at the main frequency position, such as generalized W transform, three-parameter W transform, two-parameter W transform, etc.

[0003] Although these parameterized W transforms effectively avoid the energy splitting of the W transform at the main frequency, there is a large difference between the spectrum at the wavelet center moment and the Fourier transform spectrum, and this difference is largely related to the preset standard deviation function. Here, these parameterized W transforms are collectively referred to as W transforms, because their W transforms provide a less accurate spectrum distribution for non-stationary seismic signals, which directly affects the delineation of gas-bearing reservoirs and their hydrocarbon detection, thereby increasing the difficulty of predicting gas-bearing reservoirs. Therefore, it is urgent to design a method that can effectively correct the W transform spectrum, provide a more appropriate and accurate seismic spectrum decomposition result for non-stationary seismic signals, and thus perform fine gas-bearing reservoir identification. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a gas-bearing reservoir identification method using a normalized W transform. The present invention creates a normalized W transform by multiplying the W transform by a standard deviation function normalized along the time-varying main frequency, thereby avoiding the W transform from providing a less accurate time-varying spectrum representation for a non-stationary seismic signal. In addition, the abnormal amplitude can be obtained by using the time-frequency spectrum of the normalized W to more precisely identify and delineate the gas-bearing reservoir.

[0005] In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical solutions to achieve it:

[0006] The invention proposes a gas-bearing reservoir identification method based on normalized W transformation, which comprises the following steps:

[0007] S1. Calculate the seismic signal to be analyzed Time-varying main frequency ,in For time;

[0008] S2. Preset standard deviation function ,in represents the frequency, and then the W transform of the seismic signal is calculated ;

[0009] S3, using the standard deviation function in step S2 to normalize the W transform along the time-varying main frequency, to obtain the normalized W transform ;

[0010] S4, according to the normalized W transformation in step S3, the peak amplitude and the average amplitude of the amplitude spectrum corresponding to each moment are calculated, the abnormal amplitude is obtained by subtracting the peak amplitude and the average amplitude, and then the gas-bearing reservoir is identified and delineated according to the abnormal amplitude;

[0011] The time-varying main frequency in step S1 The specific calculation process includes the following steps:

[0012] S11: Calculate the Hilbert transform

[0013] Hilbert transform of the analyzed seismic signal is represented as

[0014]

[0015] in, represents the integral in the sense of Cauchy principal value, represents the time-integrated variable;

[0016] S12: Calculate instantaneous frequency

[0017] The instantaneous frequency of the seismic signal being analyzed It can be solved by the Hilbert transform of the seismic signal and is expressed as

[0018]

[0019] in, represents the instantaneous amplitude of the signal, and Respectively and The derivative of

[0020] S13: Calculate time-varying main frequency

[0021] Using a low pass filter De-weighting smoothing instantaneous frequency Get time-varying main frequency , which is expressed as

[0022]

[0023] in, is the time-integrated variable, It is a scale factor for adjusting the accuracy of the time-varying main frequency. Compared with the instantaneous frequency solved by Hilbert transform, the calculated time-varying main frequency can effectively eliminate the strong oscillation of the instantaneous frequency and has stronger stability.

[0024] Preferably, the specific calculation process of step S2 includes the following steps:

[0025] S21: Preset standard deviation function

[0026] Alternative standard deviation functions There are the following forms:

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] in, , , , , , , , is the preset constant, represents the Huber loss function, defined as:

[0034]

[0035] These standard deviation functions In time-varying frequency has a larger value everywhere, and when Towards The value of the standard deviation function is decreasing during the deviation;

[0036] S22: Calculate W transformation result

[0037] According to the preset standard deviation function, the W transform of the analyzed seismic signal for:

[0038]

[0039] in, represents the imaginary unit. The calculated W transform improves the energy focusing of the seismic signal in the low frequency band by setting a specific standard deviation function;

[0040] As a preference, the normalization W transformation in step S3 is represented as:

[0041]

[0042] Under the action of the normalized standard deviation function, the normalized W transform effectively avoids the energy splitting artifact of the W transform at the time-varying main frequency position and better focuses the spectral energy of the W transform near the time-varying main frequency.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The present invention multiplies the W transform by a standard deviation function normalized along the time-varying main frequency, which is called a normalized W transform. This effectively avoids the energy splitting artifacts at the main frequency position of the W transform and the problem of the peak frequency shifting to both ends. Compared with the W transform and the parameterized W transform, the normalized W transform proposed in the present invention, under the action of the normalized standard deviation function, not only provides a more accurate spectrum representation with time positioning for non-stationary seismic signals, but also can more effectively focus the spectrum energy near the time-varying main frequency and has a higher time-frequency resolution. The present invention uses the proposed normalized W transform to obtain the time-frequency spectrum of the seismic signal, calculates the peak amplitude and average amplitude corresponding to each moment, and then subtracts the two to obtain the abnormal amplitude, which can more accurately identify and delineate gas-bearing reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the present invention;

[0046] Figure 2 (a) Seismic profile and (b) time-varying main frequency of seismic data of a gas field;

[0047] Figure 3 The anomalous amplitude bodies obtained by (a) S transform, (b) W transform, (c) three-parameter W transform and (d) normalized W transform, respectively. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the accompanying drawings:

[0049] See also Figure 1, a gas-bearing reservoir identification method based on normalized W transformation, comprising the following steps:

[0050] S1. Calculate the seismic signal to be analyzed Time-varying main frequency ,in For time;

[0051] It should be noted that the calculated time-varying main frequency It can be obtained by Hilbert transform and low-pass filter weighting, which will be used as input in W transform and normalized W transform. The specific calculation process includes the following steps:

[0052] S11: Calculate the Hilbert transform

[0053] Hilbert transform of the analyzed seismic signal is represented as

[0054]

[0055] in, represents the integral in the sense of Cauchy principal value, represents the time-integrated variable;

[0056] S12: Calculate instantaneous frequency

[0057] The instantaneous frequency of the seismic signal being analyzed It can be solved by the Hilbert transform in step S11 and is expressed as

[0058]

[0059] in, represents the instantaneous amplitude of the signal, and Respectively and The derivative of

[0060] S13: Calculate time-varying main frequency

[0061] Compared with the instantaneous frequency solved by Hilbert transform, the calculated time-varying main frequency can effectively eliminate the strong oscillation of the instantaneous frequency. De-weighting smoothing instantaneous frequency To obtain, it is expressed as

[0062]

[0063] in, is the time-integrated variable, is a scale factor that adjusts the accuracy of the time-varying main frequency;

[0064] S2. Preset standard deviation function ,in represents the frequency, and then the W transform of the seismic signal is calculated , the specific calculation process includes the following two steps:

[0065] S21: Preset standard deviation function

[0066] It should be noted that the preset standard deviation function is calculated by the time-varying main frequency To set, its characteristic is that the time-varying main frequency has a larger value, and when Towards The value of the standard deviation function is constantly decreasing during the deviation. A suitable standard deviation function can be selected according to the actual application, and this embodiment does not make any specific restrictions.

[0067] Optionally, a standard deviation function is preset There are the following forms:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] in, , , , , , , , is the preset constant, represents the Huber loss function, defined as:

[0075] ;

[0076] S22: Calculate W transformation result

[0077] W transforms through the standard deviation function set above , which can effectively improve the energy focusing of seismic signals in the low frequency band. Different W transform results of seismic signals can be obtained according to different preset standard deviation functions. is represented as:

[0078]

[0079] in, represents an imaginary unit;

[0080] S3, using the standard deviation function in step S21 to normalize the W transform along the time-varying main frequency, to obtain a normalized W transform , is expressed as:

[0081]

[0082]

[0083] It should be noted that, under the action of the normalized standard deviation function, the normalized W transform effectively avoids the energy splitting artifact of the W transform at the time-varying main frequency position, and better focuses the spectral energy of the W transform near the time-varying main frequency, thereby improving the time-frequency resolution of the seismic signal;

[0084] S4. According to the normalized W transformation in step S3, the peak amplitude and the average amplitude of the amplitude spectrum corresponding to each moment are calculated, and the abnormal amplitude is obtained by subtracting the peak amplitude and the average amplitude. Then, the gas-bearing reservoir is identified and delineated according to the abnormal amplitude.

[0085] The material basis of the present invention is the seismic data body, and the channel-by-channel processing method is adopted.

[0086] Let's take an actual earthquake data as an example. Figure 2 (a) shows the seismic profile of a gas field. The horizontal axis represents the channel number, which is dimensionless. The vertical axis represents the time depth, which is in seconds (s). The color scale represents the amplitude, which is dimensionless. The curve at the 1 second position represents a horizontal formation line. The intersection of the horizontal formation line with well A and well B indicates the location of the reservoir, which is located in the ellipse. Well A represents a high-yield gas-bearing well, while well B is a dry well.

[0087] Figure 2 (b) shows the time-varying main frequency of the seismic data. The color scale represents the frequency in Hertz. It is the time-varying main frequency obtained by calculating the seismic data channel by channel using the method in step S1. This will be used as input in the W transform, three-parameter W transform and normalized W transform.

[0088] Figure 3The abnormal amplitude bodies obtained by (a) S transformation, (b) W transformation, (c) three-parameter W transformation and (d) normalized W transformation respectively, the color scale represents the amplitude, dimensionless. By comparing the abnormal amplitudes at the reservoir positions of the two wells, these methods can effectively characterize the strong abnormal amplitudes caused by the gas-bearing reservoir. Compared with the S transformation, W transformation and three-parameter W transformation, the normalized W transformation proposed in the present invention shows a higher-resolution abnormal amplitude body for the seismic data, the spectral energy is well concentrated, and the distribution characteristics of the gas-bearing reservoir are more clearly highlighted. In short, the present invention helps to provide a high-resolution seismic spectrum decomposition result for gas-bearing reservoir identification, and effectively delineates the location of the gas-bearing reservoir.

[0089] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A gas-bearing reservoir identification method based on normalized W transformation, characterized in that: The following steps are involved: S1. Calculate the seismic signal to be analyzed Time-varying main frequency ,in For time; S2. Preset standard deviation function ,in represents the frequency, and then the W transform of the seismic signal is calculated ; S3, using the standard deviation function in step S2 to normalize the W transform along the time-varying main frequency, to obtain the normalized W transform ; S4, according to the normalized W transformation in step S3, the peak amplitude and the average amplitude of the amplitude spectrum corresponding to each moment are calculated, the abnormal amplitude is obtained by subtracting the peak amplitude and the average amplitude, and then the gas-bearing reservoir is identified and delineated according to the abnormal amplitude; The time-varying main frequency in step S1 The specific calculation process includes the following steps: S11: Calculate the Hilbert transform Hilbert transform of the analyzed seismic signal is represented as ； in, represents the integral in the sense of Cauchy principal value, represents the time-integrated variable; S12: Calculate instantaneous frequency The instantaneous frequency of the seismic signal analyzed is represented as ； in, represents the instantaneous amplitude of the signal, and Respectively and The derivative of S13: Calculate time-varying main frequency Using a low pass filter De-weighting smoothing instantaneous frequency Get time-varying main frequency , which is expressed as ； in, is the time-integrated variable, is a scaling factor that adjusts the accuracy of the time-varying main frequency.

2. The gas-bearing reservoir identification method based on normalized W transformation according to claim 1, characterized in that: The specific calculation process of step S2 includes the following steps: S21: Preset standard deviation function Alternative standard deviation functions There are the following forms: ； ； ； ； ； ； in, , , , , , , , is the preset constant, represents the Huber loss function, defined as: ； S22: Calculate W transformation result W transform of the analyzed seismic signal for: ； in, Represents an imaginary unit.

3. The gas-bearing reservoir identification method based on normalized W transformation according to claim 1, characterized in that: Normalized W transformation in step S3 is represented as: 。

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