A curvelet domain high-pass filtering diffraction separation method

Abstract

The present invention relates to a curvelet domain high-pass filtering diffraction separation method. The method comprises obtaining seismic common-offset data for identifying hot dry rock faults; applying a curvelet transform to the seismic common-offset data to obtain multi-scale curvelet domain data, thereby obtaining a curvelet coefficient matrix containing reflection and diffraction top information; performing a two-dimensional fast Fourier transform on the coefficient matrix to obtain its spectrum; extracting the high-frequency portion of the spectrum using a frequency domain bandpass filter to separate the reflection and diffraction curvelet coefficients; and performing an inverse curvelet transform on the separated coefficients to obtain separated common-offset diffraction wave data. The method can solve the energy loss problem of diffraction wave separation imaging, thereby improving the fault resolution of hot dry rock seismic data, and has important application value in geothermal resource exploration and construction site selection.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic exploration, and in particular to a curvelet domain high-pass filtering diffraction separation method. Background Art

[0002] In the exploration and development of clean hot dry rock resources, hydraulic fracturing in areas with well-developed underground faults can reduce the cost of developing hot dry rock geothermal resources and achieve better thermal conductivity than fracturing in non-faulted areas. Therefore, fault identification in hot dry rock seismic data is particularly important. Underground faults and other unique geological structures often form discontinuities in the strata. When seismic waves propagate downward through these discontinuities, the wave energy re-radiates from the discontinuity, acting like a new earthquake source. This new source generates a new disturbance that propagates in the elastic space. This disturbance is called diffraction in seismic exploration, and this phenomenon is called diffraction. The diffraction of seismic waves at faults can effectively characterize the location and morphology of faults and other unique geological structures. Therefore, diffraction waves obtained from seismic exploration are extremely valuable in identifying faults in hot dry rock.

[0003] Diffraction waves are weak signals, often submerged in the background of reflected waves. Therefore, separating and imaging them is challenging, and methodological approaches are primarily categorized into data-domain and imaging-domain methods. Data-domain methods, which are the first to be studied, involve separating diffraction waves through methods such as signal transformation before seismic data migration. Most methods exploit the geometric differences between reflected and diffracted waves in the data domain, suppressing smooth, continuous reflected waves to separate hyperbolic diffraction waves with large curvature and poor continuity. Imaging-domain methods require a migration velocity model and utilize the differences in kinematic and dynamic characteristics of reflected and diffracted waves in the imaging domain to separate diffraction waves. Patent application CN111929729A protects an imaging diffraction separation method that separates the stable image point positions of reflected waves through Gaussian model fitting. However, the plane wave destruction filter method, the most commonly used in industry, removes energy from the reflected wave while also significantly losing energy from the diffracted wave, hindering diffraction imaging. Summary of the Invention

[0004] In view of the problems existing in the prior art, the present invention discloses a curvelet domain high-pass filtering diffraction separation method, comprising the following steps:

[0005] Step 1: Obtain seismic common offset data for identification of hot dry rock faults;

[0006] Step 2: applying Curvelet transform to the seismic common offset data to obtain Curvelet domain data with multiple scales and angle parameters, and obtaining a Curvelet coefficient matrix including reflection and diffraction tops;

[0007] Step 3: Perform a two-dimensional Fourier transform on the curvelet coefficient matrix to obtain the frequency distribution of the coefficient matrix;

[0008] Step 4: Based on the frequency distribution of the coefficient matrix and the high-frequency properties of the diffraction wave coefficients, a high-frequency bandpass filter is used to filter the low-frequency reflections, thereby separating the curvelet coefficients of reflection and diffraction in the frequency domain.

[0009] Step 5: Perform inverse Fourier transform on the separated curvelet coefficients in the frequency domain to obtain the diffraction curvelet coefficients, and then perform inverse curvelet transform to obtain the diffraction wave response of the hot dry rock fault in the seismic data.

[0010] As a preferred solution of the present invention, the curvelet transformation in step 2 is:

[0011]

[0012] Where f∈L 2 (R 2 ) is the seismic data containing both reflection waves and diffraction waves, c(j,l,k) is the curvelet coefficient after curvelet transformation, is the mother function of the curvelet after stretching, rotation and translation, and its form is as follows:

[0013]

[0014] Among them, j is the stretching scale parameter of Curvelet transform, l is the rotation angle parameter, and k is the translation parameter. Represents the translation variable at scale j and angle l, R θ is a rotation about angle θ:

[0015]

[0016] As a preferred solution of the present invention, the two-dimensional Fourier transform of the curvelet coefficient matrix in step 3 is specifically:

[0017]

[0018] in, is the x×y curvelet coefficient matrix, Φ(u,v) is the frequency distribution of the curvelet coefficient matrix, x and y are the length and width of the spatial variables, u and v are the frequency and wave number of the frequency domain variables, and t is time.

[0019] As a preferred solution of the present invention, the high-frequency bandpass filter in step 4 is specifically:

[0020]

[0021] Φ diffraction (u,v)=Φ(u,v)H(u,v)

[0022] Among them, H(u,v) is the high-pass filter operator, is the distance from the frequency coordinate to the center of the spectrum, D0 is the low-frequency range where the reflection curvelet coefficient is located; the spectrum of the curvelet coefficient matrix is ​​multiplied by the high-pass filter operator to obtain the diffraction frequency Φ diffraction .

[0023] As a preferred solution of the present invention, the inverse Fourier transform and inverse curvelet transform in step 5 are specifically:

[0024]

[0025]

[0026] in, is the curvelet generating function The Fourier transform original function, where W and V are the scale window function and the angle window function respectively. r and θ are the radius and rotation angle after the spatial variable x is transformed into frequency domain polar coordinates.

[0027] The beneficial effects of the present invention are as follows: the present invention adopts curvelet transform to solve the problem of multi-angle energy preservation of diffraction waves, so as to improve the energy of diffraction waves in the diffraction extraction process of hot dry rock seismic data, thereby accurately identifying discontinuous geological phenomena such as faults in hot dry rock, improving the resolution of hot dry rock seismic data for fault identification, and thus achieving the purpose of accurately locating small-scale heterogeneous geological bodies in underground space. The present invention can be widely used in hot dry rock resource exploration and fracturing site selection. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic block diagram of the working process of the present invention;

[0029] Figure 2 The common offset domain seismic data of the present invention;

[0030] Figure 3 It is the separated diffraction wave field of the present invention. DETAILED DESCRIPTION

[0031] Example 1

[0032] like Figure 1 As shown, a curvelet domain high-pass filtering diffraction separation method includes the following steps:

[0033] Step 1: Obtain seismic common offset data for dry hot rock fault identification, such as Figure 2 ;

[0034] Step 2: Apply Curvelet transform to the seismic common offset data to obtain Curvelet domain data with multiple scales and angle parameters, and obtain Curvelet coefficient matrix including reflection and diffraction tops; wherein Curvelet transform is:

[0035]

[0036] Where f∈L 2 (R 2 ) is the seismic data containing both reflection waves and diffraction waves, c(j,l,k) is the curvelet coefficient after curvelet transformation, is the mother function of the curvelet after stretching, rotation and translation, and its form is as follows:

[0037]

[0038] Among them, j is the stretching scale parameter of Curvelet transform, l is the rotation angle parameter, k is the translation parameter, R θ is a rotation about angle θ:

[0039]

[0040] Step 3: Perform a two-dimensional Fourier transform on the curvelet coefficient matrix to obtain the frequency distribution of the coefficient matrix, specifically:

[0041]

[0042] in, is the x×y curvelet coefficient matrix, Φ(u,v) is the frequency distribution of the curvelet coefficient matrix, x and y are the length and width of the spatial variables, u and v are the frequency and wave number of the frequency domain variables, and t is time;

[0043] Step 4: According to the frequency distribution of the coefficient matrix, the low-frequency reflection is filtered using a high-frequency bandpass filter based on the high-frequency properties of the diffraction wave coefficient, and the curvelet coefficients of reflection and diffraction are separated in the frequency domain. The high-frequency bandpass filter is specifically:

[0044]

[0045] Φ diffraction (u,v)=Φ(u,v)H(u,v)

[0046] Among them, H(u,v) is the high-pass filter operator, is the distance from the frequency coordinate to the center of the spectrum, D0 is the low-frequency range where the reflection curvelet coefficient is located; the spectrum of the curvelet coefficient matrix is ​​multiplied by the high-pass filter operator to obtain the diffraction frequency Φ diffraction ;

[0047] Step 5: Perform inverse Fourier transform on the separated curvelet coefficients in the frequency domain to obtain the diffraction curvelet coefficients. Then, through inverse curvelet transform, the diffraction wave response of the hot dry rock fault in the seismic data is obtained, as shown in Figure 5. Figure 3 , the inverse Fourier transform and inverse curvelet transform are specifically:

[0048]

[0049]

[0050] in, is the curvelet generating function The Fourier transform original function, where W and V are the scale window function and the angle window function respectively. r and θ are the radius and rotation angle after the spatial variable x is transformed into frequency domain polar coordinates.

[0051] If the functions implemented in this embodiment are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0052] Any portion not described in detail herein is prior art.

[0053] Although the specific embodiments of the present invention have been described in detail above, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by ordinary technicians in this field, various changes can be made without departing from the purpose of the present invention. Modifications or deformations that do not involve creative work are still within the scope of protection of the present invention.

Claims

1. A curvelet domain high-pass filtering diffraction separation method, characterized in that: The steps are as follows: Step 1: Obtain seismic common offset data for identification of hot dry rock faults; Step 2: applying Curvelet transform to the seismic common offset data to obtain Curvelet domain data with multiple scales and angle parameters, and obtaining a Curvelet coefficient matrix including reflection and diffraction tops; Step 3: Perform a two-dimensional Fourier transform on the curvelet coefficient matrix to obtain the frequency distribution of the coefficient matrix; Step 4: Based on the frequency distribution of the coefficient matrix and the high-frequency properties of the diffraction wave coefficients, a high-frequency bandpass filter is used to filter the low-frequency reflections, thereby separating the curvelet coefficients of reflection and diffraction in the frequency domain. Step 5: Perform inverse Fourier transform on the separated curvelet coefficients in the frequency domain to obtain the diffraction curvelet coefficients, and then perform inverse curvelet transform to obtain the diffraction wave response of the hot dry rock fault in the seismic data.

2. The curvelet domain high-pass filtering diffraction separation method according to claim 1, characterized in that: The curvelet transformation in step 2 is: Where f∈L 2 (R 2 ) is the seismic data containing both reflection waves and diffraction waves, c(j,l,k) is the curvelet coefficient after curvelet transformation, is the mother function of the curvelet after stretching, rotation and translation, and its form is as follows: Among them, j is the stretching scale parameter of Curvelet transform, l is the rotation angle parameter, k is the translation parameter, R θ is a rotation about angle θ:

3. The curvelet domain high-pass filtering diffraction separation method according to claim 1, characterized in that: The two-dimensional Fourier transform of the curvelet coefficient matrix in step 3 is specifically: in, is the x×y curvelet coefficient matrix, Φ(u,v) is the frequency distribution of the curvelet coefficient matrix, x and y are the length and width of the spatial variables, u and v are the frequency and wave number of the frequency domain variables, and t is time.

4. The curvelet domain high-pass filtering diffraction separation method according to claim 1, characterized in that: The high-frequency bandpass filter in step 4 is specifically: Φ diffraction (u,v)=Φ(u,v)H(u,v) Among them, H(u,v) is the high-pass filter operator, is the distance from the frequency coordinate to the center of the spectrum, D0 is the low-frequency range where the reflection curvelet coefficient is located; the spectrum of the curvelet coefficient matrix is ​​multiplied by the high-pass filter operator to obtain the diffraction frequency Φ diffraction .

5. The curvelet domain high-pass filtering diffraction separation method according to claim 1, characterized in that: The inverse Fourier transform and inverse curvelet transform described in step 5 are specifically as follows: in, is the curvelet generating function The Fourier transform original function, where W and V are the scale window function and the angle window function respectively. r and θ are the radius and rotation angle after the spatial variable x is transformed into frequency domain polar coordinates.

Images