阅读说明：本技术 基于速度梯度的崎岖海底界面的光滑处理方法 (Smooth processing method of rugged seabed interface based on velocity gradient ) 是由 韩复兴 衣馨 孙章庆 王雪秋 刘明忱 于 2020-06-08 设计创作，主要内容包括：本发明涉及一种基于速度梯度的崎岖海底界面的光滑处理方法,先由给定的速度模型引入时间因子,将对崎岖海底界面的光滑处理表示为偏微分方程；由速度模型的能量函数,构建基于速度梯度的偏微分方程；再求解能量函数的极小化,得到基于原始速度模型梯度表示的扩散函数的偏微分方程；最后由原始速度模型,确定扩散函数的具体表达式,使它在速度模型梯度值较大的地方具有较慢的扩散速度,在速度模型梯度值较小的地方具有较快的扩散速度。本发明将根据速度梯度得到的偏微分方程模型光滑公式进行离散化以及结合边界扩散函数及迭代次数,即可对原始给定的速度模型崎岖海底界面进行光滑处理,应用处理后的速度模型再进行偏移成像处理获得较好的成像效果。(The invention relates to a smooth processing method of a rugged seabed interface based on a velocity gradient, which comprises the steps of firstly introducing a time factor by a given velocity model, and expressing the smooth processing of the rugged seabed interface as a partial differential equation; constructing a partial differential equation based on a velocity gradient according to an energy function of the velocity model; solving the minimization of the energy function to obtain a partial differential equation of the diffusion function based on the gradient expression of the original velocity model; and finally, determining a specific expression of the diffusion function by the original speed model, so that the diffusion function has a slower diffusion speed at a place with a larger gradient value of the speed model and has a faster diffusion speed at a place with a smaller gradient value of the speed model. The invention discretizes the smooth formula of the partial differential equation model obtained according to the velocity gradient, combines the boundary diffusion function and the iteration times, can smooth the rugged seabed interface of the originally given velocity model, and obtains better imaging effect by applying the processed velocity model and then carrying out offset imaging processing.)

1. A method for smoothing a rugged seabed interface based on velocity gradient is characterized by comprising the following steps:

A. given a velocity model v (x, z) required by offset imaging, a partial differential equation is constructed according to the velocity model, a time factor t is introduced, and smoothing of the velocity model is expressed as:where F denotes a given specific algorithm, the original model velocity v, depending on the velocity and its spatial first and second derivatives₀As an initial condition, the solution v (x, z, t) of the partial differential equation gives a velocity model value when the iteration is performed for t times;

B. minimizing the energy function E (v) according to the energy function E (v) of the velocity model to construct a partial differential equation based on the velocity gradient;

C. solving the minimization of an energy function E (v) by adopting a variation method and a steepest descent method to obtain a partial differential equation of a diffusion coefficient based on the gradient representation of an original velocity model;

D. determining a specific expression of a diffusion coefficient according to the original speed model, so that the diffusion speed of the diffusion coefficient is low on a seabed rugged interface, the diffusion speed of the diffusion coefficient is high on a non-seabed rugged interface, and the spatial structure of the original speed model is not damaged while the speed model is smooth;

E. discretizing the formula obtained in the step C, selecting the boundary diffusion function and the iteration times given in the step D, smoothing the originally given rugged seabed speed model interface, and then applying the smoothed speed model to perform offset imaging.

2. A method for smoothing a rugged subsea interface based on velocity gradient according to claim 1, characterized by: step C, the partial differential equation is as follows:wherein the content of the first and second substances,is a divergence operator, and is a function of the divergence,is a gradient operator, which is a linear operator,is the value of the gradient of the velocity model,for the diffusion coefficient expression, g (0) ═ 1 is satisfied,

Technical Field

The invention belongs to the technical field of marine seismic exploration, particularly relates to a deep water data migration imaging processing method for marine seismic exploration, and particularly relates to a smooth processing method for a rugged seabed interface based on a velocity gradient.

Background

In the deep water seismic data processing, one frequently encountered problem is the migration imaging problem of deep water rugged seabed. The transverse speed of seismic waves propagating in the stratum is changed violently due to the rugged seabed, the ray path of the seismic waves is very complicated, and the energy of a wave field is correspondingly scattered on the rugged seabed, so that the homophase axis of reflected waves is seriously distorted, and the structure form of the seabed underlying stratum in the time migration profile is seriously distorted. Meanwhile, due to the existence of a rugged seabed, a conventional seismic wave time distance curve is not a hyperbola any more, so that the superposed amplitude and the travel time of a common reflection point (CMP) based on the hyperbola dynamic time difference hypothesis are distorted, the CMP superposed section is not a zero offset section any more, and the reflected wave cannot be well returned due to the post-superposition time offset, so that the structural form is seriously distorted, and a plurality of error zones are brought to the explanation of seismic data.

Aiming at the problem of seismic wave propagation caused by existence of the rugged seabed, Berryhil in 1979 firstly proposes a concept of wave equation reference surface continuation for solving the imaging problem of the rugged seabed. The algorithm extends the wave field from sea level to a new reference surface which can be transversely changed and has definite geological significance, replaces the sea water velocity with the velocity of the seabed stratum, and extends the wave field to the sea velocity model plane. The method eliminates the distortion influence of partial rugged seabed on seismic data in the numerical model test of the post-stack seismic data, but has not enough results to present the effectiveness of the datum plane continuation method for the processing of the actual rugged seabed seismic data. Later, many scholars considered that neither conventional time migration nor post-stack depth migration could solve the problem of seismic imaging in rough sea areas, pre-stack depth migration was an effective method for solving the problem of imaging in rough sea, and pre-stack depth migration was dependent on a given velocity model to a large extent. In 2010, the research of Yangkai et al shows that the existence of rugged seabed stratum has great influence on the reflection coverage times, reflection energy and incidence angle range of the underlying stratum, which results in obvious changes of the dynamic characteristics of waves, and indicates that the seismic exploration in a complicated rugged seabed area must select proper arrangement length and coverage times to obtain a good migration profile. In 2011, wanyong et al have shown that by using seismic wave illumination analysis techniques and numerical simulations, acquisition schemes and offset apertures required for imaging can be provided for better imaging results.

In summary, the above methods cannot solve the problems that the ray path of seismic waves is seriously deflected during propagation due to the drastic change of the lateral velocity in the seismic wave propagation process caused by the existence of a deep sea rugged seabed, the structure form of the underlying stratum in the time migration profile is seriously distorted, the imaging effect is poor or no imaging is performed, and a good migration imaging profile cannot be obtained.

Disclosure of Invention

The invention aims to provide a smooth processing method of a rugged seabed interface based on a speed gradient, which overcomes the defects of low offset imaging quality, no imaging of the stratum at the bottom of the rugged seabed or imaging blurring caused by the influence of the rugged seabed of a deep sea on wave field energy propagation. According to the method, the interface smoothing processing based on partial differential equation is combined with Gaussian beam prestack migration technology, and the interface of the rugged seabed is subjected to specific smoothing processing according to the velocity gradient, so that the penetrability of ray energy is enhanced, and imaging of the rugged seabed underburden is realized.

The purpose of the invention is realized by the following technical scheme:

a method for smoothing a rugged seabed interface based on velocity gradient comprises the following steps:

A. given a velocity model v (x, z) required for offset imaging, a partial differential equation is constructed according to the velocity model, and a time factor t is introduced, the smoothing of the velocity model can be expressed as:f denotes a given specific algorithm, usually dependent onThe first and second derivatives in velocity and its space. Velocity v of the original model₀For the initial condition, the solution v (x, z, t) of the partial differential equation gives the velocity model value at t iterations.

B. According to the energy function E (v) of the velocity model, since the mode (the square sum of the derivatives) of the velocity gradient is larger in the region (the rugged seabed fluctuating interface) where the transverse and longitudinal changes of the velocity model are severe, the energy function E (v) is minimized for achieving the purpose of smoothing the velocity model interface, so as to construct the partial differential equation based on the velocity gradient.

C. And solving the minimization problem of the energy function E (v) by adopting a variation method and a steepest descent method to obtain a partial differential equation of the diffusion coefficient represented by the original velocity model gradient.

D. According to the original speed model, a specific expression of the diffusion coefficient is determined, so that the diffusion coefficient has a slower diffusion speed at a place (seabed rugged interface) with a larger gradient value of the speed model and has a faster diffusion speed at a place (non-seabed rugged interface) with a smaller gradient value of the speed model, and the purpose of smoothing the speed model and simultaneously not damaging the spatial structure of the original speed model is achieved.

E. And D, discretizing the formula obtained in the step C, selecting the boundary diffusion function and the iteration times given in the step D, smoothing the originally given rugged seabed speed model interface, and then applying the smoothed speed model to perform offset imaging to obtain a better imaging effect.

Further, in step C, the partial differential equation is:wherein the content of the first and second substances,is the divergence operator and is the sum of the divergence operators,is a gradient operator, which is a linear operator,is the value of the gradient of the velocity model,for the diffusion coefficient expression, g (0) ═ 1 is satisfied,

compared with the prior art, the invention has the beneficial effects that:

compared with the conventional offset imaging for processing the speed model, the method has the advantages that the system and the space structure of the original speed model can be changed to different degrees by the smooth processing of different levels in the conventional model smooth processing, so that the ray path, the distribution of the time field and the amplitude in energy transmission are deviated to different degrees, and the offset imaging result is influenced finally; according to the method, a partial differential equation constructed based on the velocity gradient is adopted to smooth the rugged seabed interface of the model, and the partial differential equation has local feature retention performance, so that the rugged seabed interface with a larger gradient can be smoothly processed while the original velocity model space structure is retained through the iterative processing of the partial differential equation, and the penetrability of wave field propagation energy is enhanced; the processing method can realize accurate calculation of the wave field and improve the offset imaging quality under the condition of keeping the space structure of the original velocity model unchanged as much as possible.

Drawings

FIG. 1 is a schematic diagram of a discrete format of partial differential equations;

FIG. 2 is a raw rugged seafloor velocity model;

FIG. 3 is an offset profile obtained without smoothing;

fig. 4 shows the offset profile after smoothing.

Detailed Description

The invention is further illustrated by the following examples:

the invention relates to a smooth processing method of a rugged seabed interface based on a velocity gradient, which comprises the following steps:

A. given offset imagingA required velocity model v (x, z), a partial differential equation is constructed according to the velocity model, a time factor t is introduced, and the smooth processing of the velocity model interface is expressed as:the solution v (x, z, t) of the partial differential equation is the velocity model value obtained when the result is iterated t times.

B. According to the energy function E (v) of a given speed model, since the mode (the square sum of the derivatives) of the speed gradient is larger in the region (the rugged seabed fluctuating interface) where the transverse and longitudinal changes of the speed model are severe, the energy function E (v) is minimized for achieving the purpose of smoothing the speed model, so as to construct a partial differential equation based on the speed gradient.

C. Solving the minimization problem of the energy function E (v) by adopting a variation method and a steepest descent method to obtain a partial differential equation of the diffusion coefficient based on the gradient representation of the original velocity model:is the divergence operator and is the sum of the divergence operators,is a gradient operator, which is a linear operator,is the value of the gradient of the velocity model,for the diffusion coefficient expression, g (0) ═ 1 is satisfied,

D. according to the original speed model, a specific expression of the diffusion coefficient is determined, so that the specific expression has a slower diffusion speed at a place with a larger gradient value of the speed model (a seabed rugged interface) and a faster diffusion speed at a place with a smaller gradient value of the speed model (a non-seabed rugged interface), and the g(s) is taken to satisfy the form: g(s) ═ exp (- (s/k)²) G(s) are also called sidesThe bounds stops the smoothing function, which can be used to keep the edges of the image.

E. And D, discretizing the formula obtained in the step C, wherein a discretization schematic diagram is shown in figure 1. Selecting the distribution function given in step DAnd iteration times, namely, smoothing the originally given rugged seabed speed model interface, and then applying the smoothed speed model to perform offset imaging to obtain a better imaging effect. According to the schematic diagram of the discrete format of fig. 1, the discrete format is as follows:

wherein N, S, E, W are four directions of north, south, east and west respectively, and τ is time step lengthThe formula differential notation of where:

in order to better explain the effects of the above embodiments, a specific example is given below.