CN111538083A - A Smoothing Method for Rugged Seabed Interface Based on Velocity Gradient - Google Patents

Abstract

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.

Description

A Smoothing Method for Rugged Seabed Interface Based on Velocity Gradient

technical field

The invention belongs to the technical field of marine seismic exploration, in particular to a method for data migration and imaging of deep water data in marine seismic exploration, and in particular to a method for smoothing a rough seabed interface based on velocity gradients.

Background technique

In deep-water seismic data processing, one of the frequently encountered problems is the migration imaging problem of deep-water rugged seafloor. Due to the rough seabed, the lateral velocity of seismic wave propagation in the formation changes drastically, the ray path of seismic wave propagation becomes very complicated, and the wave field energy is diffusely scattered on the rugged seabed, resulting in serious distortion of the reflected wave event axis, resulting in time offset. The structural shape of the underlying strata in the profile is severely distorted. At the same time, due to the existence of the rugged seabed, the conventional seismic wave time-distance curve is no longer a hyperbola, which will distort the stacking amplitude and travel time of the common reflection point (CMP) based on the hyperbolic dynamic time difference assumption, and the CMP stacking profile is no longer a For the zero-offset profile, the post-stack time migration cannot make the reflected waves homing well, resulting in serious distortion of the structural shape, which brings many misunderstandings to the interpretation of seismic data.

In view of the above-mentioned problems of seismic wave propagation caused by the rugged seabed, Berryhil first proposed the concept of wave equation datum extension in 1979 to solve the problem of rugged seabed imaging. The algorithm extends the wave field from the sea level downward to a new horizontally variable base level with clear geological significance, replaces the sea water velocity with the velocity of the seabed formation, and then extends the wave field upward to the sea velocity model plane. . This method eliminates the distortion effect of some rugged seabeds on seismic data in the numerical model verification of post-stack seismic data, but for the processing of actual rugged seabed seismic data, so far there is not enough results to show the effectiveness of the above-mentioned base-level extension method. Later, many scholars believed that neither conventional time migration nor post-stack depth migration could solve the seismic imaging problem in rugged seabed areas. depends on the given velocity model. In 2010, research by Yang Kai et al. showed that the existence of rugged seabed strata has a great influence on the number of reflection coverage, reflected energy and incident angle range of the underlying strata, resulting in significant changes in the dynamic characteristics of waves, pointing out that in complex Seismic exploration in rugged seabed areas must select appropriate arrangement length and coverage times to obtain better migration profiles. In 2011, Wang Yong et al. showed that by using seismic wave illumination analysis technology and numerical simulation, an acquisition scheme and an offset aperture required for imaging can be provided for obtaining better imaging results.

To sum up, none of the above methods can solve the drastic change in lateral velocity during seismic wave propagation caused by the existence of the deep-sea rugged seabed, resulting in serious deflection of the ray path during the propagation of seismic waves, resulting in serious distortion of the underlying strata in the time-migrated profile, and imaging. Due to the problem of poor effect or no imaging, it is impossible to obtain a better offset imaging section.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a method for smoothing the rough seabed interface based on velocity gradient, so as to overcome the influence of the deep sea rough seabed on the wave field energy propagation and cause the migration imaging quality to be low, the stratum at the bottom of the rugged seabed to be unimaged, or the imaging to be blurred. Shortcomings. The invention combines the interface smoothing processing based on partial differential equations with the Gaussian beam pre-stack migration technology, and performs specific smoothing processing on the interface of the rugged seabed according to the velocity gradient, thereby enhancing the penetration of ray energy and realizing the rugged seabed subsurface. Layer imaging.

The purpose of this invention is to realize through the following technical solutions:

A method for smoothing rough seabed interface based on velocity gradient, comprising the following steps:

F表示给定的特定算法，通常依赖于速度及其空间上一、二阶导数。原始模型速度v₀为初始条件，偏微分方程的解v(x,z,t)即给出了迭代t次时的速度模型值。A. Given the velocity model v(x,z) required for migration imaging, build a partial differential equation based on this velocity model, and introduce a time factor t, then the smoothing of the velocity model can be expressed as:

F represents a given specific algorithm, usually depending on the speed and its first and second derivatives in space. The original model velocity v ₀ is the initial condition, and 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 in the region where the lateral and longitudinal changes of the velocity model are relatively severe (the rough seabed undulating interface), the modulus of the velocity gradient (the sum of the squares of the derivatives) is larger. Therefore, to achieve The purpose of the smooth interface of the velocity model is to minimize the energy function E(v), so as to construct the partial differential equation based on the velocity gradient.

C. Use the variational method and the steepest descent method to solve the minimization problem of the energy function E(v), and obtain the partial differential equation of the diffusion coefficient based on the gradient of the original velocity model.

D. According to the original velocity model, determine the specific expression of the diffusion coefficient, so that it has a slower diffusion velocity in the place where the gradient value of the velocity model is large (the rough seabed interface), and in the place where the gradient value of the velocity model is small (non-seabed) The rough interface) has a faster diffusion rate, and its purpose is to smooth the velocity model without destroying the spatial structure of the original velocity model.

E. By discretizing the formula obtained in step C and selecting the boundary diffusion function and the number of iterations given in step D, the originally given rough seabed velocity model interface can be smoothed, and then the smoothed velocity model can be applied A better imaging effect can be obtained by performing offset imaging.

其中，

·是散度算子，

是梯度算子，

是速度模型的梯度值，

为扩散系数表达式，满足g(0)＝1，

Further, in step C, the partial differential equation is:

in,

is the divergence operator,

is the gradient operator,

is the gradient value of the velocity model,

is the expression of diffusion coefficient, satisfying g(0)=1,

Compared with the prior art, the beneficial effects of the present invention are:

Compared with the velocity model processing in the conventional migration imaging, the smoothing processing of different levels in the conventional model smoothing processing will bring different degrees of changes to the system and spatial structure of the original velocity model, and furthermore, the ray path, the ray path, the spatial structure of the original velocity model will be changed in different degrees. The distribution and amplitude of the time field bring different degrees of deviation, which ultimately affect the results of migration imaging; the present invention uses the partial differential equation constructed based on the velocity gradient to smooth the rough seabed interface of the model, because the partial differential equation has local feature retention performance Therefore, through the iterative processing of partial differential equations, the rough seabed interface with large gradient can be smoothed while maintaining the spatial structure of the original velocity model, thereby enhancing the penetration of wave field propagation energy; the processing method of the present invention can keep the Accurate calculation of wave field and improvement of migration imaging quality can be achieved without changing the spatial structure of the original velocity model.

Description of drawings

Figure 1 is a schematic diagram of the discrete format of partial differential equations;

Fig. 2 The original rough seabed velocity model;

Fig. 3 Offset profile obtained without smoothing;

Figure 4. Offset profile after smoothing.

Detailed ways

Below in conjunction with embodiment, the present invention is further described:

The smooth processing method of the rough seabed interface based on the velocity gradient of the present invention comprises the following steps:

偏微分方程的解v(x,z,t)即为结果迭代t次时所获得的速度模型值。A. Given the velocity model v(x,z) required for migration imaging, build a partial differential equation based on this velocity model, introduce a time factor t, and express the smoothing of the velocity model interface 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 the given velocity model, since in the region where the lateral and longitudinal changes of the velocity model are more severe (the rough seabed undulation interface), the modulus of the velocity gradient (the sum of the squares of the derivatives) is larger, therefore, To achieve the smoothness of the velocity model, the energy function E(v) must be minimized to construct a partial differential equation based on the velocity gradient.

·是散度算子，

是梯度算子，

是速度模型的梯度值，

为扩散系数表达式，满足g(0)＝1，

C. Use the variational method and the steepest descent method to solve the minimization problem of the energy function E(v), and obtain the partial differential equation of the diffusion coefficient represented by the gradient of the original velocity model:

is the divergence operator,

is the gradient operator,

is the gradient value of the velocity model,

is the expression of diffusion coefficient, satisfying g(0)=1,

D. According to the original velocity model, determine the specific expression of the diffusion coefficient, so that it has a slower diffusion velocity in the place where the gradient value of the velocity model is large (the rough seabed interface), and in the place where the gradient value of the velocity model is small (non-seabed Rugged interface) has a faster diffusion speed, take g(s) to satisfy the form: g(s)=exp(-(s/k) ² ), g(s) is also known as the boundary stop smoothing function, which can be used to Keep the edges of the image.

和及迭代次数，就可以对原始给定的崎岖海底速度模型界面进行光滑处理，然后应用光滑处理后的速度模型再进行偏移成像就可以获得较好的成像效果。根据图1的离散格式示意图，离散格式如下：E. The formula obtained in step C is discretized, and the schematic diagram of the discretization is shown in Figure 1. Choose the distribution function given in step D

and the number of iterations, the original rough seabed velocity model interface can be smoothed, and then the smoothed velocity model can be used to perform migration imaging to obtain better imaging results. According to the schematic diagram of the discrete format in Figure 1, the discrete format is as follows:

表示的式差分符号，其中：Among them, N, S, E, and W are the four directions of north, south, east, and west, respectively, and τ is the time step, where the

expressed in differential notation, where:

In order to better illustrate the effect of the above specific implementation manner, a specific example is given below.

Example

Given a rough seabed velocity model, as shown in Figure 2: the model size is 2400×2000, the grid size is 2.0m×2.0m, the numerical simulation records a total of 11 shots, each shot has a total of 480 receptions, the track spacing is 10m, and the sampling interval is 2ms . Next, we analyze the migration imaging profiles obtained before and after smoothing the rough seabed interface of the original velocity model by applying Gaussian beam pre-stack migration imaging.

By comparing the results obtained by the original velocity model migration imaging in Fig. 3 with the results obtained by the migration imaging after smoothing the undulating interface in Fig. 4, it can be seen that the rough seafloor interface results are smoothed by partial differential equations. The quality of the migration profile is improved to a great extent. The quality of the migration profile obtained by the smoothed velocity model in Fig. 4 is clearer, and the unimaging area of the rough subsurface stratum in Fig. 4 is also better. imaging effect. To sum up, the method of the present invention can achieve better imaging effect of the strata at the bottom of the rugged seabed.

Claims (2)

1. a smooth processing method based on the rough seabed interface of velocity gradient, is characterized in that, comprises the following steps: A. Given the velocity model v(x, z) required for migration imaging, construct a partial differential equation according to the velocity model, introduce a time factor t, and the smoothing of the velocity model is expressed as:

Among them, F represents a given specific algorithm, which depends on the velocity and its first and second derivatives in space. The original model velocity v ₀ is the initial condition, and the solution v(x, z, t) of the partial differential equation gives the iterative Velocity model value at t times; B. According to the energy function E(v) of the velocity model, minimize the energy function E(v) to construct a partial differential equation based on the velocity gradient; C. Use the variational method and the steepest descent method to solve the minimization of the energy function E(v), and obtain the partial differential equation of the diffusion coefficient represented by the gradient of the original velocity model; D. According to the original velocity model, determine the specific expression of the diffusion coefficient, so that the diffusion speed is slow in the rough seabed interface, and the diffusion speed is fast in the non-subsea rough interface, which is smooth to the velocity model and does not destroy the spatial structure of the original velocity model; E. Discretize the formula obtained in step C, select the boundary diffusion function and the number of iterations given in step D, smooth the interface of the originally given rough seabed velocity model, and then apply the smoothed velocity model to bias the Move imaging. 2. a kind of smooth processing method based on the rough seabed interface of velocity gradient according to claim 1, is characterized in that: step C, described partial differential equation is:

in,

is the divergence operator,

is the gradient operator,

is the gradient value of the velocity model,

is the expression of diffusion coefficient, satisfying g(0)=1,

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