Method, device, medium and equipment for suppressing random noise of three-component seismic data based on quaternion wavelet transform

Abstract

The application relates to a three-component seismic data random noise suppression method, device, medium and equipment based on a quaternion wavelet transform, which comprises the following steps: representing X, Y and Z three-component seismic data as a quaternion signal in the form of a quaternion array in a time-space domain; implementing quaternion wavelet transform on the quaternion array; using the quaternion wavelet transform to perform multi-layer decomposition on the quaternion signal in the form of the quaternion array, so as to obtain corresponding quaternion wavelet coefficients of each layer; calculating a threshold value by using a new threshold value estimation expression, and performing threshold value operation on the quaternion wavelet coefficients of each layer by using a semi-soft threshold value function, wherein the wavelet coefficients greater than the threshold value are reserved, and the wavelet coefficients less than the threshold value are set to zero; performing quaternion wavelet inverse transform on the threshold value processed quaternion wavelet coefficients, reconstructing a denoised quaternion signal, taking out X, Y and Z components from three virtual parts of the denoised quaternion signal, and completing vector denoising.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of seismology or seismic exploration technology, in particular to a three-component seismic data random noise suppression method, device, medium and equipment based on quaternion wavelet transform. BACKGROUND

[0002] In reflection seismic exploration, noise suppression and signal-to-noise ratio improvement are one of the important tasks of seismic data processing. Seismic data with high signal-to-noise ratio is crucial for subsequent processing (such as migration imaging, inversion interpretation). As the most common type of noise, random noise is mainly caused by environmental disturbance, instrument noise and human operation, etc. Its frequency band is wide and approximately satisfies Gaussian distribution, and is widely distributed in the entire seismic record. Based on the significant differences between random noise and effective signal in statistical characteristics, predictability, sparsity and low rank, the effective separation of noise and signal can be realized by corresponding methods.

[0003] With the shift of oil and gas exploration targets from conventional oil and gas reservoirs to unconventional oil and gas reservoirs such as subtle and tight reservoirs, the difficulty of exploration is increasing, and the traditional single-component longitudinal wave exploration has been difficult to meet the demand of fine description of complex reservoirs. Multi-wave and multi-component seismic exploration technology can effectively reduce the multi-solution of reservoir prediction and improve the accuracy of fluid identification and prediction by receiving full wave field information, so it has attracted widespread attention in the oil industry and is being applied more and more. Multi-component seismic data acquisition usually uses longitudinal wave source excitation to produce wave field containing P-P wave and P-S wave components, and is received by multi-component geophone. Land exploration mainly uses three-component geophone (horizontal X, Y components and vertical Z component), while offshore exploration uses four-component geophone (X, Y, Z components and pressure component P). However, the signal-to-noise ratio of multi-component data is generally low, especially for horizontal components (X, Y), so improving the signal-to-noise ratio of multi-component data is a key link in processing. Since the traditional single-component denoising method cannot effectively utilize the physical coupling relationship between components, it is difficult to meet the dual requirements of signal-to-noise ratio improvement and vector wave field structure protection. Therefore, multi-component data should be jointly denoised as a whole to fully exploit the correlation information between components, improve the signal-to-noise ratio, and protect the polarization characteristics of the vector wave field, providing a high-quality data basis for subsequent processing and interpretation.

[0004] However, the traditional denoising method cannot solve the problem of vector joint denoising of multi-component seismic data, and the existing vector denoising method is mostly a serial combination of scalar sparse transform, without using a real vector integral transform. SUMMARY

[0005] In view of the above problems, the purpose of the present application is to provide a three-component seismic data random noise suppression method, device, medium and equipment based on quaternion wavelet transform, which can realize joint random noise suppression processing of three-component data.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] The random noise suppression method for three-component seismic data based on quaternion wavelet transform described in this invention includes the following steps:

[0008] In the time-space domain (tx domain), the seismic data of the X, Y, and Z components are represented as quaternion signals in the form of quaternion arrays;

[0009] A quaternion wavelet transform is applied to the quaternion array, and the quaternion signal in the form of the quaternion array is decomposed into multiple layers using the quaternion wavelet transform to obtain the quaternion wavelet coefficients corresponding to each layer.

[0010] The threshold is calculated using a new threshold estimation expression. A semi-soft thresholding function is used to perform thresholding operations on the quaternion wavelet coefficients of each layer. Wavelet coefficients greater than the threshold are retained, and wavelet coefficients less than the threshold are set to zero.

[0011] Perform inverse quaternion wavelet transform on the thresholded quaternion wavelet coefficients to reconstruct the denoised quaternion signal. Extract the X, Y, and Z components from the three imaginary parts of the denoised quaternion signal to complete vector denoising.

[0012] The method for suppressing random noise in three-component seismic data, preferably, involves representing the seismic data of the X, Y, and Z components as quaternion signals in the form of quaternion arrays in the time-space domain (tx domain). The specific steps are as follows:

[0013] Select a set of 3C-2D seismic data containing random noise. X (t,x),D Y (t,x) and D Z (t,x);

[0014] Using quaternions, the noisy 3C-2D data D X (t,x), D Y (t,x) and D Z (t,x) can be combined into a quaternion array: D Q (t,x)=D X (t,x)i+D Y (t,x)j+D Z (t,x)k;

[0015] D Q (t,x) can be represented as D Q (t,x)=S Q (t,x)+N Q (t,x);

[0016] where S Q (t,x) = S X (t,x)i + S Y (t,x)j + S Z (t,x)k represents the quaternion effective signal; N Q (t,x) = N X (t,x)i + N Y (t,x)j + N Z (t,x)k represents the quaternion noise.

[0017] The three-component seismic data random noise suppression method preferably performs a quaternion wavelet transform on the quaternion D Q (t,x), and the specific steps are as follows:

[0018] In the quaternion wavelet domain, the wavelet energy of the effective signal and the noise has a difference in distribution characteristics, and the least square inversion problem method is used to recover the effective signal S Q from the noisy signal D Q by using the difference, and the least square inversion problem can be expressed as:

[0019]

[0020] where D Q is the noisy data; is a quaternion discrete orthogonal wavelet inverse transform; W Q is a quaternion wavelet coefficient; λ>0 is a regularization factor; represents the wavelet coefficient of the to-be-solved denoising result; p is a p-order norm, when p=0, the optimal solution can be obtained by performing a hard threshold operation on the wavelet coefficient W Q of the noisy data D Q , and the threshold is λ; when p=1, the optimal solution is obtained by performing a soft threshold operation on the wavelet coefficient W Q of D Q , and the threshold is λ 2 / 2.

[0021] The three-component seismic data random noise suppression method preferably has a new threshold estimation, and the specific steps are as follows:

[0022] When the random noise in the three-component noisy data satisfies the Gaussian distribution and the mutual independence assumption, the probability density function f(r) and the probability distribution function F(r) corresponding to the amplitude value of the noise can be simplified as expressions only with the amplitude r as a variable, as shown in formulas (2) and (3) respectively,

[0023]

[0024]

[0025] wherein, sigma is a noise standard deviation; u is an integral variable; r is a noise amplitude value;

[0026] When the probability value of the noise is 50%, the ratio of the noise amplitude value r and the noise standard deviation sigma is 1.5382, therefore, the noise standard deviation sigma is estimated by using formula (4):

[0027]

[0028] wherein, median() represents a median function; |D1| represents the noisy data D Q the modulus of the first layer wavelet decomposition coefficient sequence of (t,x);

[0029] The new threshold value lambda is calculated by using the empirical threshold value calculation formula (5):

[0030]

[0031] wherein, N represents the signal length; alpha>0 represents an adjustment factor; sigma is a noise standard deviation.

[0032] The three-component seismic data random noise suppression method, preferably, the semi-soft threshold function is expressed as formula (6):

[0033]

[0034] wherein, m>0 is an adjustment factor; W is a wavelet transform coefficient; lambda is a new threshold value; when m approaches 0, the threshold function approaches a hard threshold function, when m approaches infinity, the threshold function approaches a soft threshold function.

[0035] The three-component seismic data random noise suppression method, preferably, the denoising result is:

[0036] The application further provides a three-component seismic data random noise suppression device based on quaternion wavelet transform, comprising:

[0037] A first processing unit is used for representing X, Y and Z three-component seismic data as quaternion signals in the form of quaternion arrays in a time-space domain;

[0038] A second processing unit is used for implementing quaternion wavelet transform on the quaternion arrays, and using the quaternion wavelet transform to perform multi-layer decomposition on the quaternion signals in the form of quaternion arrays, so as to obtain corresponding quaternion wavelet coefficients of each layer;

[0039] The third processing unit is configured to calculate the threshold value by using the new threshold value estimation expression, and perform threshold operation on the quaternion wavelet coefficients of each layer by using a semi-soft threshold function, wherein the wavelet coefficients greater than the threshold value are reserved, and the wavelet coefficients less than the threshold value are set to zero.

[0040] The fourth processing unit is configured to perform quaternion wavelet inverse transformation on the threshold-processed quaternion wavelet coefficients, reconstruct the denoised quaternion signal, and take out the X component, the Y component and the Z component from three imaginary parts of the denoised quaternion signal, so as to complete vector denoising.

[0041] The application further provides a computer storage medium, which stores a computer program, and the computer program is executed by a processor to implement the method steps.

[0042] The application further provides a computer device, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the method steps when executing the computer program.

[0043] The application has the following advantages due to the above technical solutions.

[0044] (1) The application uses quaternion to jointly represent three-component seismic data in the time domain, and proposes a three-component seismic data vector denoising technology based on quaternion wavelet transform.

[0045] (2) The application uses a tower algorithm to realize multi-scale decomposition and reconstruction of the quaternion wavelet transform.

[0046] (3) The threshold value estimation expression used in the traditional wavelet threshold denoising method is developed for single-component data and is not suitable for joint denoising of three-component data. BRIEF DESCRIPTION OF DRAWINGS

[0047] Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The detailed description is made with reference to the accompanying drawings. The drawings are for purposes of illustration only and are not intended to be limiting. The same reference numbers in different drawings identify the same components. In the drawings:

[0048] Figure 1 are the X, Y and Z three-component original noise-free data and the data profile with random noise synthesized in the embodiment of the present application, wherein Figure 1 (a)-1(c) represent the X, Y and Z components of the original noise-free data, Figure 1 (d)-1(f) represent the X, Y and Z components of the data with random noise;

[0049] Figure 2 are the denoising results of the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method of the embodiment of the present application, wherein Figure 2 (a)-2(c) are respectively the denoising results of the X component by the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method; Figure 2 (d)-2(f) are respectively the denoising results of the Y component by the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method; Figure 2 (g)-2(i) are respectively the denoising results of the Z component by the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method;

[0050] Figure 3 are the random noise removed by the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method of the embodiment of the present application, wherein Figure 3 (a)-3(c) are respectively the random noise removed by the X component by the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method; Figure 3 (d)-3(f) are respectively the random noise removed by the Y component by the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method; Figure 3 (g)-3(i) are respectively the random noise removed by the Z component by the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method;

[0051] Figure 4 are the single-channel signals after denoising by the scalar wavelet transform, the series combination wavelet transform and the quaternion wavelet transform threshold method of the embodiment of the present application compared with the original noise-free single-channel signals, wherein Figure 4 (a) is the comparison of the denoising result of the X component by the scalar wavelet transform threshold method with the original noise-free single-channel signal; Figure 4 (b) is the comparison of the denoising result of the Y component by the series combination wavelet transform threshold method with the original noise-free single-channel signal;Figure 4 (c) is the comparison of the thresholding result of the quaternion wavelet transform of Z component with the original single channel signal without noise;

[0052] Figure 5 is the comparison of the vectorgram of the denoising results of X, Y and Z components with the original signal without noise; wherein, Figure 5 (a) is the comparison of the vectorgram of the denoising result of scalar wavelet transform with the original signal without noise; Figure 5 (b) is the comparison of the vectorgram of the denoising result of series wavelet transform with the original signal without noise; Figure 5 (c) is the comparison of the vectorgram of the denoising result of the quaternion wavelet transform of the present application with the original signal without noise;

[0053] Figure 6 is the original data of actual OBS data in a certain area, wherein, Figure 6 (a), Figure 6 (b) and Figure 6 (c) represent the X, Y and Z components of the actual OBS data, respectively.

[0054] Figure 7 is the denoising result of the actual OBS data by using the scalar wavelet transform, series combination wavelet transform and the quaternion wavelet transform of the present application, wherein, Figure 7 (a), Figure 7 (b) and Figure 7 (c) represent the denoising result of the X component by using the scalar wavelet transform, series combination wavelet transform and the thresholding method of the quaternion wavelet transform of the present application, respectively; Figure 7 (d), Figure 7 (e) and Figure 7 (f) represent the denoising result of the Y component by using the scalar wavelet transform, series combination wavelet transform and the thresholding method of the quaternion wavelet transform of the present application, respectively; Figure 7 (g), Figure 7 (h) and Figure 1 (i) represent the denoising result of the Z component by using the scalar wavelet transform, series combination wavelet transform and the thresholding method of the quaternion wavelet transform of the present application, respectively. DETAILED DESCRIPTION

[0055] Exemplary embodiments of the present application will be described herein below with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it is understood that the present application can be embodied in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the application to those skilled in the art.

[0056] The application provides a three-component seismic data random noise suppression method based on quaternion wavelet transform, first, a multi-scale decomposition and reconstruction of the quaternion wavelet transform is realized by using a tower algorithm, second, a threshold estimation method under the three-component condition is derived, and a vector threshold denoising method is proposed based on the same; compared with the traditional wavelet scalar threshold denoising method, the application can effectively improve the signal-to-noise ratio of the denoising result, and better protect the weak signal and the vector polarization characteristics of the multi-component data.

[0057] The three-component seismic data random noise suppression method based on the quaternion wavelet transform provided by the application comprises the following steps:

[0058] S1, representing X, Y and Z three-component seismic data as a quaternion signal in the form of a quaternion array in a time-space domain (t-x domain);

[0059] S2, performing a quaternion wavelet transform on the quaternion array, using the quaternion wavelet transform to perform multi-layer decomposition on the quaternion signal in the form of the quaternion array, and obtaining corresponding quaternion wavelet coefficients of each layer;

[0060] S3, calculating a threshold value by using a new threshold value estimation expression, and performing a threshold operation on the quaternion wavelet coefficients of each layer by using a semi-soft threshold function, wherein the wavelet coefficients greater than the threshold value are retained, and the wavelet coefficients less than the threshold value are set to zero;

[0061] S4, performing a quaternion wavelet inverse transform on the threshold-processed quaternion wavelet coefficients, reconstructing a denoised quaternion signal, taking out X, Y and Z components from three imaginary parts of the denoised quaternion signal, and completing vector denoising.

[0062] In the above embodiment, preferably, the X, Y and Z three-component seismic data is represented as a quaternion signal in the form of a quaternion array in a time-space domain (t-x domain), and the specific steps are as follows:

[0063] A group of 3C-2D seismic data D X (t,x), D Y (t,x) and D Z (t,x) are selected;

[0064] The 3C-2D noisy data D X (t,x), D Y (t,x) and D Z (t,x) are combined into a quaternion array D Q (t,x) = D X (t,x)i + D Y (t,x)j + D Z (t,x)k by using a quaternion tool;

[0065] D Q (t,x) can be expressed as D Q (t,x) = S Q (t,x) + N Q (t,x) ;

[0066] where S Q (t,x) = S X (t,x)i + S Y (t,x)j + S Z (t,x)k represents the quaternion effective signal; N Q (t,x) = N X (t,x)i + N Y (t,x)j + N Z (t,x)k represents the quaternion noise.

[0067] In the above embodiment, preferably, the quaternion wavelet transform is performed on the quaternion array D Q (t,x), and the specific steps are as follows:

[0068] In the quaternion wavelet domain, there is a difference in the distribution characteristics of the wavelet energy of the effective signal and the noise, and the effective signal S Q is recovered from the noisy signal D Q by using the difference by means of the least square inversion problem, and the least square inversion problem can be expressed as:

[0069]

[0070] where D Q is the noisy data; the quaternion discrete orthogonal wavelet inverse transform; W Q is the quaternion wavelet coefficient; λ>0 is a regularization factor; represents the wavelet coefficient of the denoising result to be solved; p is a p-order norm, when p=0, the optimal solution is obtained by performing the hard threshold operation on the wavelet coefficient W Q of the noisy data D Q , and the threshold is λ; when p=1, the optimal solution is obtained by performing the soft threshold operation on the wavelet coefficient W Q of D Q , and the threshold is λ 2 / 2.

[0071] In the above embodiment, preferably, the new threshold estimation, and the specific steps are as follows:

[0072] When the random noise in the three-component noisy data satisfies the Gaussian distribution and the non-correlation assumption, the probability density function f(r) and the probability distribution function F(r) corresponding to the amplitude value of the noise can be simplified as the expression with only the amplitude value r as the variable, as shown in formulas (2) and (3) respectively,

[0073]

[0074] wherein σ is the noise standard deviation; u is the integral variable; and r is the noise amplitude value;

[0075] When the probability value of the noise is 50%, the ratio of the noise amplitude value r and the noise standard deviation σ is 1.5382, and therefore, the noise standard deviation σ is estimated by using formula (4):

[0076]

[0077] wherein median() represents the median function; |D1| represents the modulus of the first layer wavelet decomposition coefficient sequence of the noisy data D Q (t,x);

[0078] The new threshold value λ expression is calculated by using the empirical threshold value calculation formula (5):

[0079]

[0080] wherein N represents the signal length, α>0 represents the adjustment factor; and σ is the noise standard deviation.

[0081] In the above embodiment, preferably, the semi-soft threshold function has the expression as shown in formula (6):

[0082]

[0083] wherein m>0 is the adjustment factor; W is the wavelet transform coefficient; λ is the new threshold value; when m→0, the threshold function tends to the hard threshold function, and when m→∞, the threshold function tends to the soft threshold function.

[0084] In the above embodiment, preferably, the quaternion wavelet coefficient after the threshold operation is subjected to the quaternion wavelet inverse transform, and the denoising result is obtained as: Embodiment 1:

[0085] The application is applied to the denoising of the synthesized 3C-2D model data, and the effect is compared with the scalar wavelet transform method and the series combination wavelet transform threshold denoising method. As shown in Figure 1 , the original three-component noise-free data is as shown in Figure 1(a) -1(c) shows, in the three components of data, respectively, to add Gaussian random noise, such as Figure 2 (d) -1(f) shows, wherein the horizontal X component and Y component data SNR is 1.0 dB, the vertical Z component SNR is 2.0 dB.

[0086] The scalar wavelet transform method, series combination wavelet transform method and quaternion wavelet transform method are used respectively to denoise the data containing noise, and the denoising results are shown in Figure 2 Figure 2 (a) -2(c) is the denoising result of X component; Figure 2 (d) -2(f) is the denoising result of Y component; Figure 3 (g) -2(i) is the denoising result of Z component. By comparison, it can be seen that the effective wave isophase of the scalar wavelet method denoising result is poor in smoothness and continuity, and there is obvious noise residue near the isophase edge, as indicated by the black arrow; the series combination wavelet transform method denoising effect is improved, but the continuity and smoothness of the effective wave isophase are still insufficient; and the denoising effect of the quaternion wavelet transform method is the most ideal, the effective wave isophase is naturally continuous, and the smoothness is also better. In addition, in the area shown by the black rectangular frame, the weak reflection axis in the denoising result of the scalar wavelet transform method is almost suppressed as noise, while the weak reflection axis is also well preserved in the series combination wavelet transform method and the quaternion wavelet transform method.

[0087] Figure 4 The random noise filtered by the three methods, by comparison, it can be seen that there is obvious effective reflection wave energy residue in the noise filtered by the scalar wavelet transform method, which causes greater damage to the energy of the isophase, as indicated by the black rectangular frame and the black arrow; the effective wave residual energy in the noise filtered by the series combination wavelet transform method is weak; the effective wave residual energy in the noise filtered by the quaternion wavelet transform method is the weakest, and the energy damage of the reflection wave isophase is the smallest. The signal-to-noise ratio is used to quantitatively analyze the denoising performance of the three methods, and the calculation formula of the signal-to-noise ratio is as follows,

[0088]

[0089] Wherein, D cl ean represents the original noise-free data; D d enoised represents the denoising result.

[0090] The SNR values of the denoising results of the three methods are shown in Table 1, and the three-component signal-to-noise ratio of the quaternion wavelet transform is improved by 1.65 dB than that of the scalar wavelet transform.

[0091] In addition, a single channel data is extracted for further comparison of denoising effect. Figure 4 ​(a)-4(c) respectively show the scalar wavelet transform, series combination wavelet transform method and quaternion wavelet transform denoising results and single channel comparison of original noise-free data X, Y and Z components. As shown in the black rectangular frame in the figure, the weak effective signal corresponding to the X component and the Y component is suppressed as noise by the scalar wavelet transform method; part of the noise energy is still left in the X and Y component denoising results obtained by the series combination wavelet transform; and the denoising result of the quaternion wavelet transform is better to protect the weak signal and match the original noise-free real data better. The waveform in the [730, 1110] ms time window in the middle green dashed box is drawn into a hodogram as shown in Figure 5 Figure 6 It can be seen that the vibration trajectory of the particle in the scalar wavelet transform denoising result deviates greatly from the vibration trajectory of the particle in the original noise-free signal, the series combination wavelet transform method is the second, and the denoising result of the quaternion wavelet transform method matches the original noise-free signal hodogram best. The experiment shows the superiority of the quaternion wavelet transform threshold denoising method in protecting the weak signal energy and maintaining the vector polarization structure characteristics of the seismic signal.

[0092] Table 1. SNR comparison of denoising results of three methods

[0093]

[0094] Example 2:

[0095] The application is applied to random noise suppression of 3C-2D OBS data in a work area. The data set is an OBS common receiver gather, containing X, Y and Z components, each component data containing 283 channels, channel spacing 20 m, each channel time sampling length 8 s, sampling rate 2 ms. The seismic data in the time window of [1.6, 1.9] s and channel number 235-283 is selected for denoising test. Figure 7 (a)-6(c) show the X, Y and Z components of the original data, from which it can be seen that there is a large amount of random noise in the data. Figure 7 The denoising results of the scalar wavelet transform, series combination wavelet transform and quaternion wavelet transform threshold method are shown. Figure 7 (a)-7(c) are respectively the X components denoised by the three methods, Figure 7 (d)-7(f) are respectively the Y components denoised by the three methods, ​ (g)-7(i) are respectively the Z components denoised by the three methods. By comparing the area shown in the black box, it can be seen that the quaternion wavelet transform threshold method has stronger random noise suppression capability, the reflection event structure in the denoising result is clear and continuous, there are fewer residual random noise energy points, and the profile is also cleaner.

[0096] ​The application further provides a device for suppressing random noise of three-component seismic data based on quaternion wavelet transform, which comprises:

[0097] a first processing unit for representing X, Y and Z three-component seismic data in a time-space domain as a quaternion signal in a form of a quaternion array;

[0098] a second processing unit for implementing quaternion wavelet transform on the quaternion array, using the quaternion wavelet transform to perform multi-layer decomposition on the quaternion signal in the form of the quaternion array, to obtain corresponding quaternion wavelet coefficients of each layer;

[0099] a third processing unit for calculating a threshold value using a new threshold value estimation expression, and performing threshold operation on the quaternion wavelet coefficients of each layer using a semi-soft threshold function, wherein the wavelet coefficients greater than the threshold value are reserved, and the wavelet coefficients less than the threshold value are set to zero;

[0100] a fourth processing unit for performing quaternion wavelet inverse transform on the threshold-processed quaternion wavelet coefficients, reconstructing a denoised quaternion signal, taking out X, Y and Z components from three imaginary parts of the denoised quaternion signal, and completing vector denoising.

[0101] The application further provides a computer storage medium, which stores a computer program, and the computer program is executed by a processor to realize the method steps of suppressing random noise of three-component seismic data based on quaternion wavelet transform.

[0102] The application further provides a computer device, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor realizes the method steps of suppressing random noise of three-component seismic data based on quaternion wavelet transform when executing the computer program.

[0103] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the application, and not to limit them; although the application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the application.

Claims

1. A method for suppressing random noise in three-component seismic data based on quaternion wavelet transform, characterized in that, The method comprises the following steps: representing three-component seismic data of X, Y and Z in a time-space domain (t-x domain) as a quaternion signal in the form of a quaternion array; applying a quaternion wavelet transform to the quaternion array, using the quaternion wavelet transform to perform multi-layer decomposition on the quaternion signal in the form of the quaternion array, and obtaining quaternion wavelet coefficients corresponding to each layer; calculating a threshold value using a new threshold value estimation expression, and performing threshold value operation on the quaternion wavelet coefficients of each layer using a semi-soft threshold value function, wherein wavelet coefficients greater than the threshold value are retained, and wavelet coefficients less than the threshold value are set to zero; performing a quaternion wavelet inverse transform on the threshold value processed quaternion wavelet coefficients, reconstructing a denoised quaternion signal, and obtaining X, Y and Z components from three imaginary part positions of the denoised quaternion signal to complete vector denoising. The method comprises the following steps: A set of 3C-2D seismic data with random noise is selected , and ; Using quaternions, 3C-2D seismic data containing random noise is processed. , and Combined into a quaternion array: ; is represented by ; wherein represents a quaternion valid signal; represents a quaternion noise; to a quaternion array Implementing the quaternion wavelet transform, the specific steps are: In the quaternion wavelet domain, there is a difference between the distribution characteristics of the wavelet energy of the effective signal and the noise. The effective signal is recovered from the noise signal by using the difference and a least square inversion problem method The least square inversion problem can be expressed as:​ (1) wherein, is the noisy data; is the quaternion discrete orthogonal wavelet transform; is the quaternion wavelet coefficient; is the regularization factor; denotes the wavelet coefficient of the denoising result to be solved; When , the optimal solution is obtained by implementing a hard threshold operation on the wavelet coefficient of the noisy data , and the threshold is denoted as ; when , the optimal solution is obtained by implementing a soft threshold operation on the wavelet coefficient of the noisy data , and the threshold is denoted as ; The new threshold value estimation comprises the following steps: When the random noise in the three-component noisy data satisfies the Gaussian distribution and the assumption of mutual independence, the probability density function corresponding to the amplitude value of the noise can be expressed as and the probability distribution function can be simplified as an expression with only the amplitude as a variable, as shown in Equations (2) and (3), respectively, ，(2) ，(3) wherein is the noise standard deviation; is the integral variable; r is the noise amplitude value; The ratio of the probability value of the noise to the noise amplitude value was 1.5382, and therefore, the noise standard deviation The new threshold value estimation comprises the following steps: was estimated using Equation (4) : .(4) wherein denotes the median function; denotes the modulus of the first level wavelet decomposition coefficient sequence of the noisy data denotes the modulus of the first level wavelet decomposition coefficient sequence of the noisy data The new threshold is calculated using the empirical threshold calculation formula (5) Expression: ,(5) wherein, N denotes signal length; denotes adjustment factor; The method comprises the following steps: is the noise standard deviation.

2. The method of claim 1, wherein, The semi-soft threshold function The expression is given by equation (6): （6） wherein, When the threshold function approaches the hard threshold function when the threshold function approaches the soft threshold function.

3. The method of claim 2, wherein, Denoising results are: .

4. A device for suppressing random noise of three-component seismic data based on quaternion wavelet transform, characterized in that, a first processing unit configured to represent three-component seismic data of X, Y and Z in a time-space domain (t-x domain) as a quaternion signal in the form of a quaternion array; a second processing unit configured to apply a quaternion wavelet transform to the quaternion array, use the quaternion wavelet transform to perform multi-layer decomposition on the quaternion signal in the form of the quaternion array, and obtain quaternion wavelet coefficients corresponding to each layer; a third processing unit configured to calculate a threshold value using a new threshold value estimation expression, and perform threshold value operation on the quaternion wavelet coefficients of each layer using a semi-soft threshold value function, wherein wavelet coefficients greater than the threshold value are retained, and wavelet coefficients less than the threshold value are set to zero; a fourth processing unit configured to perform a quaternion wavelet inverse transform on the threshold value processed quaternion wavelet coefficients, reconstruct a denoised quaternion signal, and obtain X, Y and Z components from three imaginary part positions of the denoised quaternion signal to complete vector denoising. The method comprises the following steps: The new threshold value estimation comprises the following steps: A set of 3C-2D seismic data containing random noise is selected , and ; Using quaternions, 3C-2D seismic data containing random noise is processed. , and Combined into a quaternion array: ; is represented by ; wherein denotes a quaternion valid signal; denotes a quaternion noise; to a quaternion array Implementing the quaternion wavelet transform, the specific steps are: In the quaternion wavelet domain, there is a difference between the distribution characteristics of the wavelet energy of the effective signal and the noise. The effective signal is recovered from the noise signal by using the difference and a least square inversion problem method The least square inversion problem can be expressed as:​ (1) in, This is noisy data; This is a quaternion discrete orthogonal wavelet transform; These are quaternion wavelet coefficients; As a regularization factor; Represents the wavelet coefficients of the denoising result to be obtained; when When, the optimal solution By analyzing noisy data wavelet coefficients The threshold is obtained by performing a hard thresholding operation, and is denoted as follows: ;when When, the optimal solution Yes wavelet coefficients The threshold is obtained by performing a soft thresholding operation, and is denoted as . ; The new threshold value estimation comprises the following steps: When the random noise in the three-component noisy data satisfies the Gaussian distribution and the assumption of mutual independence, the probability density function corresponding to the amplitude value of the noise can be simplified as an expression with only the amplitude and the probability distribution function as a variable, as shown in formulas (2) and (3) respectively , ，(2) ，(3) wherein is the noise standard deviation; is the integral variable; r is the noise amplitude value; At the probability value of the noise of 50%, the ratio of the noise amplitude value to the noise standard deviation The computer program is executed by the processor to implement the steps of the three-component seismic data random noise suppression method based on the quaternion wavelet transform according to any one of claims 1-3. is 1.5382, and therefore, the noise standard deviation is estimated using Equation (4): .(4) wherein denotes the median function; denotes the modulus of the first level wavelet decomposition coefficient sequence of the noisy data denotes the modulus of the first level wavelet decomposition coefficient sequence of the noisy data The new threshold is calculated using the empirical threshold calculation formula (5) Expression: ,(5) wherein, N denotes signal length; denotes adjustment factor; The processor executes the computer program to implement the steps of the three-component seismic data random noise suppression method based on the quaternion wavelet transform according to any one of claims 1-3. is the noise standard deviation.

5. A computer storage medium having stored thereon a computer program, characterized in that ​ 6. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, ​

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