阅读说明：本技术 一种基于稀疏变换学习的地震波阻抗反演方法 (Seismic wave impedance inversion method based on sparse transform learning ) 是由 陈雷平 李曙 贺达江 于 2019-11-19 设计创作，主要内容包括：本发明公开了一种基于稀疏变换学习的地震波阻抗反演方法,与传统解决方案相比,本发明解决了现有的基于稀疏性先验信息的地震波阻抗反演存在的稀疏表示性能差、稀疏性利用不充分、存在阶梯效应、对薄层和弱反射层的识别不利等问题,通过稀疏变换学习的方式构造一种可根据波阻抗自适应变化的稀疏变换,对波阻抗进行稀疏表示,并将稀疏表示结果应用于地震反演中。(The invention discloses a seismic wave impedance inversion method based on sparse transform learning, which solves the problems of poor sparse representation performance, insufficient sparse utilization, step effect, unfavorable identification of a thin layer and a weak reflection layer and the like of the existing seismic wave impedance inversion based on sparse prior information.)

1. A seismic wave impedance inversion method based on sparse transform learning is characterized by comprising the following steps:

inputting earthquake and well logging data and horizon interpretation information;

step two, constructing self-adaptive sparse transformation:

to be invertedThe wave impedance is m, the wave impedance m to be inverted is arranged into a column vector m according to columns_v：m_vVec (m); the function vec () is a vectorization function, i.e.: arranging data to be processed into a column vector according to columns;

let X_iRepresenting a slave wave impedance m_vAnd extracting an operator of the ith data segment, wherein the ith wave impedance data segment is expressed as:

b_i＝X_im_v.

d is sparse transformation and is used for sparsely representing wave impedance, and then the wave impedance data segment b_iExpressed as:

Db_i＝DX_im_v＝ε_i+e_i,

wherein epsilon_iIs b is_iSparse coding of e_iModeling error for a sparse transform domain;

let the whole wave impedance vector m_vDividing the wave impedance data into K wave impedance data segments which are mutually overlapped, and under the sparse transformation D, expressing the sparse regularization problem of the wave impedance as follows:

α are coefficients of sparse regular terms, the construction problem of the adaptive sparse transform based on sparse transform learning is written as:

i represents an identity matrix; wherein K is the number of mutually overlapped wave impedance data segments; d^HA conjugate transpose matrix representing D;

the sparse transformation D is obtained through learning training;

step three, establishing an objective function

Establishing the following objective function of the seismic wave impedance inversion problem:

wherein G is a forward operator for synthesizing seismic data from wave impedances; μ is the regularization factor of the sparse transform learning problem; s represents the original seismic data obtained by observation;

step four, solving the objective function

4.1) sparse coding, namely solving:

obtained with a hard threshold operation:

wherein the content of the first and second substances,

HT_γ(Γ) is a contracting function in hard threshold operations, defined by the formula:

gamma denotes a threshold value, and gamma denotes a variable of a function;

4.2) update for sparse transform: fix sparse coding epsilon first_iAnd then solving:

obtaining updated sparse transform D; fast solution using singular value decomposition: is provided with

D＝RL^H；

where L represents the left matrix after singular value decomposition, R^HThe conjugate transpose of the right matrix after singular value decomposition is represented; sigma represents a singular value matrix which is a diagonal matrix;

4.3) solving the wave impedance to obtain an inversion result: fixing the sparse code epsilon obtained in the first step and the second step_iAnd sparse transformation D, solving the following least square problem to obtain an inversion result

Step five, inverting the result

2. The seismic wave impedance inversion method based on sparse transform learning of claim 1, wherein in the second step, the step of obtaining the sparse transform D through learning training is as follows:

input wave impedance, solving

Technical Field

The invention relates to the field of seismic inversion, in particular to a seismic wave impedance inversion method based on sparse transform learning.

Background

Seismic inversion is a process of reversely deducing parameters of the earth medium by using seismic data, well logging data and the like obtained by observation. In modern geophysical exploration, seismic inversion is one of the core techniques. The quality of the seismic inversion results is influenced by a plurality of factors, wherein the prior information is one of the most important factors. In recent years, a trend in seismic inversion technology has been to more efficiently and reasonably utilize a priori information in the inversion.

Sparsity is important prior information which is widely researched and used by academia in recent years, and has important application in the fields of signal and image denoising, data reconstruction and the like. In the field of seismic exploration, sparsity is mainly used for seismic data denoising, reflection coefficient inversion/sparse deconvolution, reflection coefficient sparse constraint-based wave impedance inversion and the like. At present, no literature report is available for directly carrying out sparse representation on seismic wave impedance by using variable sparse transformation and carrying out wave impedance inversion by using sparsity.

Most of the existing seismic wave impedance inversion methods using sparsity as prior information utilize the sparsity of reflection coefficients. For example, Zhang et al, 2014 published in Journal of Applied geophils: seismicricbased on L1-norm mist function and total variation regularization is to first use the sparsity of the reflection coefficients (in L0, L1 or Lp (0)<p<1) Norm) to obtain a sparse reflection coefficient sequence, and then obtaining the wave impedance by utilizing the relation between the wave impedance and the reflection coefficient. The process is shown in figure 1. In the figure, the first step is to solve an objective function with a reflection coefficient r as a target by using a sparse optimization method, so as to obtain a sparse reflection coefficient sequence r. The second step is composed of sparse reflection coefficient sequence and wave impedance value m (t) at 0 moment₀) The wave impedance m (t) is obtained by using an integral formula.

Another class of wave impedance inversion methods that use sparse prior information is based on Total Variation (TV) regularization. The objective function of such a method can be expressed as:

in the formula, m is seismic wave impedance to be inverted, G is a positive operator, and S is observed seismic data. TV () represents the full variational function, OtherTerms refers to the other constraint terms in the objective function. The core idea of this type of method is that it is believed that good inversion results should have small total variation. For example, Li and Peng (2017) are published in Journal of geophilics and engineering: seismic acid immunization with multi-parameter regulation; gholoamine (2015) was published in Geophysics: nonlinear multichannel amplification by total-variation regulation; li et al (2018) published in Journal of geophilics and Engineering: the methods proposed by Fast multi-trace impedance inversion using differential total p-variation regularization in the frequency domain, etc. belong to this class. The essence of the fully variant regularization is to exploit the sparsity of the gradient of m.

In summary, the existing wave impedance inversion method using sparse prior information is based on sparsity of reflection coefficients under L0, L1 or Lp (0< p <1) norm or sparsity of wave impedance under full-variation norm. Although the expression and use of such sparseness are simple and easy to understand, there are problems that the expression of sparseness of wave impedance is too simple and the use of sparseness is insufficient.

Disclosure of Invention

The invention aims to disclose a seismic wave impedance inversion method based on sparse transform learning, which solves the problems of poor sparse representation performance, insufficient sparse utilization, step effect, unfavorable identification of a thin layer and a weak reflection layer and the like of the existing seismic wave impedance inversion based on sparse prior information.

In order to achieve the purpose, the technical scheme of the invention is as follows:

a seismic wave impedance inversion method based on sparse transform learning comprises the following steps:

inputting earthquake and well logging data and horizon interpretation information;

step two, constructing self-adaptive sparse transformation:

let the wave impedance m to be inverted be m, arrange the wave impedance m to be inverted into a column vector m according to columns_v：m_vVec (m); the function vec () is a vectorization function, i.e.: arranging data to be processed into a column vector according to columns;

let X_iRepresenting a slave wave impedance m_vAnd extracting an operator of the ith data segment, wherein the ith wave impedance data segment is expressed as:

b_i＝X_im_v.

d is sparse transformation and is used for sparsely representing wave impedance, and then the wave impedance data segment b_iExpressed as:

Db_i＝DX_im_v＝ε_i+e_i,

wherein epsilon_iIs b is_iSparse coding of e_iModeling error for a sparse transform domain;

let the whole wave impedance vector m_vDividing the wave impedance data into K wave impedance data segments which are mutually overlapped, and under the sparse transformation D, expressing the sparse regularization problem of the wave impedance as follows:

α are coefficients of sparse regular terms, the construction problem of the adaptive sparse transform based on sparse transform learning is written as:

i represents an identity matrix; wherein K is the number of mutually overlapped wave impedance data segments; d^HA conjugate transpose matrix representing D;

the sparse transformation D is obtained through learning training;

step three, establishing an objective function

Establishing the following objective function of the seismic wave impedance inversion problem:

wherein G is a forward operator for synthesizing seismic data from wave impedances; μ is the regularization factor of the sparse transform learning problem; s represents the original seismic data obtained by observation;

step four, solving the objective function

4.1) sparse coding, namely solving:

obtained with a hard threshold operation:

wherein the content of the first and second substances,representing the obtained sparse coding;

HT_γ(Γ) is a contracting function in hard threshold operations, defined by the formula:

gamma denotes a threshold value, and gamma denotes a variable of a function;

4.2) update for sparse transform: fix sparse coding epsilon first_iAnd then solving:

obtaining updated sparse transform D; fast solution using singular value decomposition: is provided with

The singular value of (a) is decomposed into: l sigma R^HAnd then the solving result of D is as follows:

D＝RL^H；

where L represents the left matrix after singular value decomposition, R^HThe conjugate transpose of the right matrix after singular value decomposition is represented; sigma represents a singular value matrix which is a diagonal matrix;

4.3) solving the wave impedance to obtain an inversion result: fixing the sparse code epsilon obtained in the first step and the second step_iAnd sparse transformation D, solving the following least square problem to obtain an inversion result

Step five, inverting the resultThe entire inversion process is completed by reverting to the original 2-dimensional profile or 3-dimensional data volume following the reverse process as in the vec () function.

In a further improvement, in the second step, the step of obtaining the sparse transform D through learning training is as follows:

input wave impedance, solvingThe optimized expression obtains D, and the process of obtaining D is called sparse transformation learning because D obtained by each iteration is related to the input wave impedance and is a sparse transformation matrix.

Description of the drawings:

FIG. 1 is a flow chart of a two-step inversion of wave impedance based on reflection coefficient sparsity;

FIG. 2 is a flow chart of the present invention;

FIG. 3 is a diagram of a true model of wave impedance;

FIG. 4 is a diagram of an initial model of wave impedance;

FIG. 5 is a graph of seismic data used for inversion;

FIG. 6 is a seismic wavelet plot;

FIG. 7 is a graph of the wave impedance inversion results of the present invention.

Detailed Description