Self-adaptive regular tensor constrained time-frequency domain pre-stack seismic inversion method

Abstract

The invention belongs to the field of conventional and unconventional oil and gas resource seismic exploration, and provides a time-frequency domain pre-stack seismic inversion method based on adaptive regular tensor constraint. According to the method, the difference of to-be-inverted parameters and non-stationary time-varying and frequency-varying characteristics of seismic data are fully considered, and a self-adaptive regular tensor related to a seismic data time-frequency spectrum is established; on the basis, a regular coefficient matrix containing seismic data non-stationary time-varying and frequency-varying information and an inversion objective function are constructed in a time-frequency domain by using a self-adaptive regular tensor. According to the method, the problem that the difference between the to-be-inverted parameters and the non-stationary characteristic of the seismic data are not fully considered in the conventional pre-stack inversion is solved, and a new method way is provided for improving the robustness and the accuracy of the pre-stack seismic inversion.

Description

Technical Field

[0001] This invention belongs to the field of seismic exploration of conventional and unconventional oil and gas resources. It provides a time-frequency domain pre-stack seismic inversion method with adaptive regular tensor constraints for subsurface lithology analysis, reservoir prediction, and fluid identification. Background Technology

[0002] Pre-stack inversion is a key method for obtaining elastic parameters such as P-wave and S-wave impedance and density of subsurface strata. Robust and accurate pre-stack seismic inversion is of great significance for lithological description, oil and gas reservoir prediction and fluid identification.

[0003] Existing pre-stack inversion methods typically operate in the time domain, achieving relatively stable inversion results by imposing regularization constraints such as low-frequency models and data domain regularization terms on the inversion objective function. However, these methods do not adequately consider the differences between the parameters to be inverted and the non-stationary time-varying and frequency-varying characteristics of seismic data when applying regularization constraints, resulting in insufficient stability and accuracy of pre-stack inversion. Time-frequency analysis can extract non-stationary information from seismic data. The time-spectrum of seismic data integrates the characteristics of the time and frequency domains, and the time-varying and frequency-varying characteristics of the seismic time-spectrum can be fully utilized to apply regularization constraints during inversion. This invention aims to provide an adaptive regularized tensor-constrained time-frequency domain pre-stack seismic inversion method to achieve more robust and accurate pre-stack seismic inversion. Summary of the Invention

[0004] The purpose of this invention is to provide an adaptive regularized tensor-constrained pre-stack seismic inversion method in the time-frequency domain. Its key feature is that it fully considers the non-stationary time-varying and frequency-varying characteristics of seismic data, constructing an adaptive regularized tensor related to the time-spectrum of the pre-stack seismic data. Based on this adaptive regularized tensor, a regularized coefficient matrix and an inversion objective function containing the non-stationary time-varying and frequency-varying information of the seismic data are constructed in the time-frequency domain. The method includes the following steps:

[0005] (1) Input pre-stack near-angle stacked seismic data Pre-stack mid-angle stacked seismic data Pre-stacked far-angle stacked seismic data , Represents the real number field. This represents the number of time sampling points;

[0006] (2) Input well logging data and stratigraphic data, and extract near-angle seismic wavelets through well-seismic calibration. Mid-angle seismic wavelet Long-angle seismic wavelet And establish a logarithmic initial model. ,in , , These are the initial models for longitudinal wave impedance, transverse wave impedance, and density, respectively.

[0007] (3)Use , and Calculate the average seismic data :

[0008]

[0009] (4) Calculation Time-frequency amplitude spectrum ,use Establish an adaptive canonical tensor that considers the differences in the parameters to be inverted and the non-stationary time-varying and frequency-varying characteristics of the seismic data. :

[0010]

[0011] in, To construct the time-frequency amplitude spectrum To adaptive regular tensor The mapping operator; the subscripts l, m, and n represent the parameter domain, frequency domain, and time domain, respectively, and the ranges of values ​​for l, m, and n are respectively... , , ;when When, it corresponds to the adaptive canonical tensor of the longitudinal wave impedance; when When, it corresponds to the adaptive canonical tensor of the transverse wave impedance; when At that time, it corresponds to the adaptive canonical tensor of density;

[0012] (5) Given a set of frequency vectors containing J frequencies sum and frequency vector Corresponding frequency sampling point vector j is the index number, and its value range is... ;

[0013] (6) The following time-frequency domain pre-stack seismic forward modeling equations are established:

[0014]

[0015] in, Frequency vector corresponding The time spectrum, Represents the field of complex numbers; It is a vector containing logarithmic longitudinal impedance, logarithmic transverse impedance, and density; The time-frequency domain pre-stack seismic inversion mapping matrix is ​​generated using seismic incident angle and frequency vector. and Construction of time-frequency domain functions;

[0016] (7) Establish the pre-stack seismic inversion objective equation that reflects the differences in the parameters to be inverted and the non-stationary time-varying and frequency-varying characteristics of the seismic data:

[0017]

[0018] in, Represents L2 norm operations. This indicates finding the minimum value;

[0019] It utilizes adaptive regularization tensors The constructed regular coefficient matrix is ​​defined as follows:

[0020]

[0021] in, , Represents diagonal matrix operations;

[0022] (8) The seismic P-wave impedance is calculated using the following formula. transverse wave impedance and density :

[0023]

[0024] in, This indicates the operation of natural exponents. Attached Figure Description

[0025] Figure 1 The data represents pre-stack seismic data in this embodiment of the invention. The horizontal axis represents angle in degrees (°), and the vertical axis represents time in seconds (s).

[0026] Figure 2 The adaptive regular tensor of this invention is shown in the figure, wherein: (a) the figure is shown in the figure. (a) The corresponding longitudinal wave impedance adaptive canonical tensor, with the horizontal axis representing frequency in Hertz (Hz) and the vertical axis representing time in seconds (s); (b) Figure is The corresponding transverse wave impedance adaptive canonical tensor, with the horizontal axis representing frequency in Hertz (Hz) and the vertical axis representing time in seconds (s); (c) Figure is The density adaptive regular tensor corresponding to time is shown on the horizontal axis as frequency in Hertz (Hz) and on the vertical axis as time in seconds (s).

[0027] Figure 3The following are the pre-stack inversion results of embodiments of the present invention, wherein: (a) Figure shows the longitudinal wave impedance inversion results, with the horizontal axis representing longitudinal wave impedance in meters per second multiplied by grams per cubic centimeter (m / s·g / cm³) and the vertical axis representing time in seconds (s); (b) Figure shows the transverse wave impedance inversion results, with the horizontal axis representing transverse wave impedance in meters per second multiplied by grams per cubic centimeter (m / s·g / cm³) and the vertical axis representing time in seconds (s); (c) Figure shows the density inversion results, with the horizontal axis representing density in grams per cubic centimeter (g / cm³) and the vertical axis representing time in seconds (s). Detailed Implementation

[0028] To make the technical solution of the present invention clearer and its advantages more apparent, the specific embodiments of the technical solution of the present invention will be clearly and completely described below with reference to the figures. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0029] (1) Input as follows Figure 1 The pre-stack near-angle stacked seismic data shown Pre-stack mid-angle stacked seismic data Pre-stacked far-angle stacked seismic data , Represents the real number field. This represents the number of time sampling points;

[0030] (2) Input well logging data and stratigraphic data, and extract near-angle seismic wavelets through well-seismic calibration. Mid-angle seismic wavelet Long-angle seismic wavelet and establish such Figure 3 The logarithmic initial model is shown by the gray dashed line. ,in , , These are the initial models for longitudinal wave impedance, transverse wave impedance, and density, respectively.

[0031] (3)Use , and Calculate the average seismic data :

[0032]

[0033] (4) Calculation Time-frequency amplitude spectrum ,use Establish an adaptive canonical tensor that considers the differences in the parameters to be inverted and the non-stationary time-varying and frequency-varying characteristics of the seismic data. :

[0034]

[0035] in, To construct the time-frequency amplitude spectrum To adaptive regular tensor The mapping operator; the subscripts l, m, and n represent the parameter domain, frequency domain, and time domain, respectively, and the ranges of values ​​for l, m, and n are respectively... , , ;when When, it corresponds to the adaptive canonical tensor of the longitudinal wave impedance; when When, it corresponds to the adaptive canonical tensor of the transverse wave impedance; when At that time, it corresponds to the adaptive canonical tensor of density;

[0036] (5) Given a set of Frequency vector of each frequency , , , , , The values ​​are 15, 25, 40, 60, and 80 Hz (Hertz), respectively, and the frequency vector is... Corresponding frequency sampling point vector j is the index number, and its value range is... ;

[0037] (6) The following time-frequency domain pre-stack seismic forward modeling equations are established:

[0038]

[0039] in, Frequency vector corresponding The time spectrum, Represents the field of complex numbers; It is a vector containing logarithmic longitudinal impedance, logarithmic transverse impedance, and density; The time-frequency domain pre-stack seismic inversion mapping matrix is ​​generated using seismic incident angle and frequency vector. and Construction of time-frequency domain functions;

[0040] (7) Establish the pre-stack seismic inversion objective equation that reflects the differences in the parameters to be inverted and the non-stationary time-varying and frequency-varying characteristics of the seismic data:

[0041]

[0042] in, Represents L2 norm operations. This indicates finding the minimum value;

[0043] It utilizes adaptive regularization tensors The constructed regular coefficient matrix is ​​defined as follows:

[0044]

[0045] in, , Represents diagonal matrix operations;

[0046] (8) The following formula is used to calculate the result. Figure 3 The seismic P-wave impedance is shown by the solid black line in the middle. transverse wave impedance and density :

[0047]

[0048] in, This indicates the operation of natural exponents.

[0049] from Figure 3 The pre-stack seismic inversion results of this invention show that the results obtained by the method of this invention are in good agreement with the well logging measurements, thus confirming the reliability of this invention.

[0050] The advantages and novelty of this invention are as follows: Taking full account of the non-stationary time-varying and frequency-varying characteristics of seismic data, an adaptive regular tensor related to the time spectrum of seismic data was established; Based on the adaptive regular tensor, a regular coefficient matrix and inversion objective equation containing non-stationary time-varying and frequency-varying information of seismic data are constructed in the time-frequency domain, providing a new method for improving the robustness and accuracy of pre-stack seismic inversion.

[0051] The above embodiments are only used to illustrate the present invention. The implementation steps of the method can be varied. Any equivalent transformations and improvements made on the basis of the technical solution of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. An adaptive canonical tensor-constrained pre-stack seismic inversion method in the time-frequency domain, comprising the following steps: (1) input pre-stack near angle stack seismic data (2) input pre-stack middle angle stack seismic data (3) input pre-stack far angle stack seismic data , denotes the real field, is the number of time samples; (2) input logging data and horizon data, extract near angle seismic wavelet by well-seismic calibration , middle angle seismic wavelet , far angle seismic wavelet , and establish logarithmic initial model , wherein , , respectively are initial models of longitudinal wave impedance, transverse wave impedance and density (3) using , and , compute average seismic data : ； (4) calculating time-frequency amplitude spectrum , using establishing an adaptive regularization tensor considering the difference of the parameters to be inverted and the non-stationary time-varying and frequency-varying characteristics of the seismic data : ； wherein, is the constructed time-frequency amplitude spectrum is the mapping operator from the adaptive regular tensor to the parameter domain; the value ranges of l, m, n are , , respectively; when , the adaptive regular tensor corresponds to the longitudinal wave impedance; when , the adaptive regular tensor corresponds to the transverse wave impedance; when , the adaptive regular tensor corresponds to the density. (5) Given a set of frequency vectors containing J frequencies and a frequency vector corresponding frequency sample point vector , j is an index number, and the value range is ; (6) The following time-frequency domain pre-stack seismic forward modeling equations are established: ； wherein, is a frequency vector corresponding to a time-frequency spectrum, denotes the complex domain; is a vector containing the log compressional impedance, the log shear impedance and the density; is a time-frequency domain prestack seismic inversion mapping matrix, constructed using a seismic angle of incidence, a frequency vector and a time-frequency domain function of (7) Establish the pre-stack seismic inversion objective equation that reflects the differences in the parameters to be inverted and the non-stationary time-varying and frequency-varying characteristics of the seismic data: ； wherein denotes the L2 norm operation, denotes the minimum value; is constructed using the adaptive regular tensor The regular coefficient matrix is defined as follows: ； wherein , denotes the diagonal matrix operation; (8) The seismic P-wave impedance is calculated using the following formula. transverse wave impedance and density : ； in, This indicates the operation of natural exponents.

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