阅读说明：本技术 球面波ps反射系数计算方法及系统 (Spherical wave PS reflection coefficient calculation method and system ) 是由 李京南 马灵伟 胡华锋 于 2019-09-16 设计创作，主要内容包括：公开了一种球面波PS反射系数计算方法及系统。该方法可以包括：针对两层弹性介质模型,计算平面波PS反射系数；根据平面波PS反射系数,计算球面反射SV波的位函数；根据球面反射SV波的位函数,计算球面反射SV波沿垂直射线方向的位移；根据沿垂直射线方向的位移,计算球面波PS反射系数。本发明通过计算球面波PS反射系数,结果可用于分析球面反射波场特征,增强对地震波场传播规律的认识,为利用球面PS波进行地震反演奠定理论基础,也可用于指导地震勘探的处理解释过程。(A method and a system for calculating the PS reflection coefficient of spherical wave are disclosed. The method can comprise the following steps: calculating a plane wave PS reflection coefficient aiming at the two-layer elastic medium model; calculating a bit function of the spherical reflection SV wave according to the PS reflection coefficient of the plane wave; calculating the displacement of the spherical reflection SV wave along the direction of a vertical ray according to the bit function of the spherical reflection SV wave; and calculating the PS reflection coefficient of the spherical wave according to the displacement along the direction of the vertical ray. The method can be used for analyzing the characteristics of the spherical reflection wave field and enhancing the knowledge of the seismic wave field propagation rule by calculating the PS reflection coefficient of the spherical wave, lays a theoretical foundation for seismic inversion by using the PS wave of the spherical wave, and can also be used for guiding the processing and explaining process of seismic exploration.)

1. A method for calculating a PS (packet switched) reflection coefficient of a spherical wave is characterized by comprising the following steps:

calculating a plane wave PS reflection coefficient aiming at the two-layer elastic medium model;

calculating a bit function of the spherical reflection SV wave according to the PS reflection coefficient of the plane wave;

calculating the displacement of the spherical reflection SV wave along the direction of a vertical ray according to the bit function of the spherical reflection SV wave;

and calculating the PS reflection coefficient of the spherical wave according to the displacement along the direction of the vertical ray.

2. The spherical wave PS reflection coefficient calculation method according to claim 1, wherein the plane wave PS reflection coefficient is calculated by formula (1):

wherein R is_psIs the plane wave PS reflection coefficient, alpha₁And alpha₂Longitudinal wave velocity, beta, of the upper and lower media, respectively₁And beta₂Respectively the transverse wave speeds of the upper medium and the lower medium, a, b, c, D, E, F, G, H and D are intermediate parameters, D＝EF+GHp²p is a ray parameter, p is sin θ₁/α₁，θ₁And theta₂The incident angle and the transmission angle of the plane P wave,andthe reflection angle and the transmission angle of the plane SV wave.

3. The spherical wave PS reflection coefficient calculation method according to claim 1, wherein the bit function of the spherical reflected SV wave is calculated by equation (2):

where ψ is a bit function of a spherically reflected SV wave, A is a constant depending on the source intensity, i is a complex unit, ω is an angular frequency, t is time, J₀Is a zero order Bessel function, ξ₁Is the vertical slowness, xi, of the longitudinal wave of the upper medium₁＝(1/α₁ ²-p²)^1/2，η₁Is the vertical slowness, eta, of transverse waves of the upper medium₁＝(1/β₁ ²-p²)^1/2R is the offset, and h and z are the vertical distances of the source and receiver points, respectively, to the reflecting interface.

4. The spherical wave PS reflection coefficient calculation method according to claim 1, wherein the displacement of the spherical reflected SV wave in the vertical ray direction is calculated by formula (3):

wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J₁Is a first order Bessel function, s_rIs displacement of spherical reflection SV wave along r direction, s_zDisplacement of the spherical reflected SV wave in the z direction.

5. The spherical wave PS reflection coefficient calculation method according to claim 1, wherein the spherical wave PS reflection coefficient is calculated by equation (4):

wherein the content of the first and second substances,is the spherical wave PS reflection coefficient.

6. A system for calculating PS reflection coefficient of spherical waves, the system comprising:

a memory storing computer-executable instructions;

a processor executing computer executable instructions in the memory to perform the steps of:

calculating a plane wave PS reflection coefficient aiming at the two-layer elastic medium model;

calculating a bit function of the spherical reflection SV wave according to the PS reflection coefficient of the plane wave;

calculating the displacement of the spherical reflection SV wave along the direction of a vertical ray according to the bit function of the spherical reflection SV wave;

and calculating the PS reflection coefficient of the spherical wave according to the displacement along the direction of the vertical ray.

7. The spherical wave PS reflection coefficient calculation system of claim 6, wherein the plane wave PS reflection coefficient is calculated by equation (1):

wherein R is_psIs the plane wave PS reflection coefficient, alpha₁And alpha₂Longitudinal wave velocity, beta, of the upper and lower media, respectively₁And beta₂Respectively the transverse wave speeds of the upper medium and the lower medium, a, b, c, D, E, F, G, H and D are intermediate parameters, D＝EF+GHp²p is a ray parameter, p is sin θ₁/α₁，θ₁And theta₂The incident angle and the transmission angle of the plane P wave,andthe reflection angle and the transmission angle of the plane SV wave.

8. The spherical wave PS reflection coefficient calculation system according to claim 6, wherein the bit function of the spherical reflected SV wave is calculated by equation (2):

where ψ is a bit function of a spherically reflected SV wave, A is a constant depending on the source intensity, i is a complex unit, ω is an angular frequency, t is time, J₀Is a zero order Bessel function, ξ₁Is the vertical slowness, xi, of the longitudinal wave of the upper medium₁＝(1/α₁ ²-p²)^1/2，η₁Is the vertical slowness, eta, of transverse waves of the upper medium₁＝(1/β₁ ²-p²)^1/2R is the offset, and h and z are the vertical distances of the source and receiver points, respectively, to the reflecting interface.

9. The spherical wave PS reflection coefficient calculation system according to claim 6, wherein the displacement of the spherical reflected SV wave in the vertical ray direction is calculated by formula (3):

wherein s is the displacement of the spherical reflection SV wave along the direction of the vertical ray_rIs displacement of spherical reflection SV wave along r direction, s_zDisplacement of the spherical reflected SV wave in the z direction.

10. The spherical wave PS reflection coefficient calculation system according to claim 6, wherein the spherical wave PS reflection coefficient is calculated by equation (4):

wherein the content of the first and second substances,is the spherical wave PS reflection coefficient.

Technical Field

The invention relates to the technical field of seismic exploration, in particular to a method and a system for calculating a PS (polystyrene) reflection coefficient of a spherical wave.

Background

The theoretical basis of many current seismic processing and inversion methods is the Zoeppritz equation which is derived based on the plane wave theory, but the actual field seismic acquisition uses a point seismic source, and spherical waves are excited instead of plane waves. The method technology based on the plane wave hypothesis cannot fully utilize information contained in the seismic data, such as frequency-dependent characteristics of reflection coefficients and transmission coefficients, and even utilizes the information incorrectly, and the problem is particularly prominent in shallow or low-frequency seismic data. In order to further develop a more accurate seismic exploration method technology, the propagation characteristics and the propagation rules of spherical waves in a medium are researched and analyzed based on the point seismic source spherical wave theory, and the method has very important theoretical value and practical significance. At present, a great deal of research on the reflection coefficient of spherical waves of an acoustic medium and the reflection coefficient of spherical waves PP of an elastic medium exists, but the research on the reflection coefficient of PS of spherical waves of the elastic medium is rare, converted waves (namely S waves or transverse waves) also play an important role in seismic exploration, and the combined utilization of the transverse waves and the transverse waves for seismic exploration is an important research direction. Therefore, it is necessary to develop a method and a system for calculating the PS reflection coefficient of spherical waves.

The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.

Disclosure of Invention

The invention provides a method and a system for calculating a spherical wave PS reflection coefficient, which can be used for analyzing the characteristics of a spherical reflection wave field and enhancing the knowledge of the seismic wave field propagation rule by calculating the spherical wave PS reflection coefficient, laying a theoretical foundation for seismic inversion by using the spherical wave PS, and guiding the processing and interpretation process of seismic exploration.

According to one aspect of the invention, a method for calculating a PS reflection coefficient of a spherical wave is provided. The method may include: calculating a plane wave PS reflection coefficient aiming at the two-layer elastic medium model; calculating a bit function of the spherical reflection SV wave according to the PS reflection coefficient of the plane wave; calculating the displacement of the spherical reflection SV wave along the direction of a vertical ray according to the bit function of the spherical reflection SV wave; and calculating the PS reflection coefficient of the spherical wave according to the displacement along the direction of the vertical ray.

Preferably, the plane wave PS reflection coefficient is calculated by equation (1):

wherein R is_psIs the plane wave PS reflection coefficient, alpha₁And alpha₂Longitudinal wave velocity, beta, of the upper and lower media, respectively₁And beta₂Respectively the transverse wave speeds of the upper medium and the lower medium, a, b, c, D, E, F, G, H and D are intermediate parameters, D＝EF+GHp²p is a ray parameter, p is sin θ₁/α₁，θ₁And theta₂The incident angle and the transmission angle of the plane P wave,andthe reflection angle and the transmission angle of the plane SV wave.

Preferably, the bit function of the spherically reflected SV wave is calculated by equation (2):

where ψ is a bit function of a spherically reflected SV wave, A is a constant depending on the source intensity, i is a complex unit, ω is an angular frequency, t is time, J₀Is a zero order Bessel function, ξ₁Is the vertical slowness, xi, of the longitudinal wave of the upper medium₁＝(1/α₁ ²-p²)^1/2，η₁Is the vertical slowness, eta, of transverse waves of the upper medium₁＝(1/β₁ ²-p²)^1/2R is the offset, and h and z are the vertical distances of the source and receiver points, respectively, to the reflecting interface.

Preferably, the displacement of the spherically reflected SV wave in the direction of the perpendicular ray is calculated by the formula (3):

wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J₁Is a first order Bessel function, s_rIs displacement of spherical reflection SV wave along r direction, s_zDisplacement of the spherical reflected SV wave in the z direction.

Preferably, the spherical wave PS reflection coefficient is calculated by equation (4):

wherein the content of the first and second substances,is the spherical wave PS reflection coefficient.

According to another aspect of the present invention, a system for calculating PS reflection coefficient of spherical wave is provided, the system comprising: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: calculating a plane wave PS reflection coefficient aiming at the two-layer elastic medium model; calculating a bit function of the spherical reflection SV wave according to the PS reflection coefficient of the plane wave; calculating the displacement of the spherical reflection SV wave along the direction of a vertical ray according to the bit function of the spherical reflection SV wave; and calculating the PS reflection coefficient of the spherical wave according to the displacement along the direction of the vertical ray.

Preferably, the plane wave PS reflection coefficient is calculated by equation (1):

wherein R is_psIs the plane wave PS reflection coefficient, alpha₁And alpha₂Longitudinal wave velocity, beta, of the upper and lower media, respectively₁And beta₂Respectively the transverse wave speeds of the upper medium and the lower medium, a, b, c, D, E, F, G, H and D are intermediate parameters, D＝EF+GHp²p is a ray parameter, p is sin θ₁/α₁，θ₁And theta₂The incident angle and the transmission angle of the plane P wave,andthe reflection angle and the transmission angle of the plane SV wave.

Preferably, the bit function of the spherically reflected SV wave is calculated by equation (2):

where ψ is a bit function of a spherically reflected SV wave, A is a constant depending on the source intensity, i is a complex unit, ω is an angular frequency, t is time, J₀Is a zero order Bessel function, ξ₁Is the vertical slowness, xi, of the longitudinal wave of the upper medium₁＝(1/α₁ ²-p²)^1/2，η₁Is the vertical slowness, eta, of transverse waves of the upper medium₁＝(1/β₁ ²-p²)^1/2R is the offset, and h and z are the vertical distances of the source and receiver points, respectively, to the reflecting interface.

Preferably, the displacement of the spherically reflected SV wave in the direction of the perpendicular ray is calculated by the formula (3):

wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J₁Is a first order Bessel function, s_rIs displacement of spherical reflection SV wave along r direction, s_zDisplacement of the spherical reflected SV wave in the z direction.

Preferably, the spherical wave PS reflection coefficient is calculated by equation (4):

wherein the content of the first and second substances,is the spherical wave PS reflection coefficient.

The method and apparatus of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.

Drawings

The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.

Fig. 1 shows a flowchart of the steps of a spherical wave PS reflection coefficient calculation method according to the present invention.

FIG. 2 shows a schematic representation of a two-layer elastic media model according to one embodiment of the present invention.

FIG. 3 shows a graph comparing the amplitude of a plane wave PS reflection coefficient versus a spherical wave PS reflection coefficient as a function of angle of incidence, according to one embodiment of the invention.

FIG. 4 shows a comparison of the phase versus incident angle for a plane wave PS reflection coefficient and a spherical wave PS reflection coefficient, according to one embodiment of the present invention.

Detailed Description

The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

Fig. 1 shows a flowchart of the steps of a spherical wave PS reflection coefficient calculation method according to the present invention.

In this embodiment, the spherical wave PS reflection coefficient calculation method according to the present invention may include: step 101, calculating a plane wave PS reflection coefficient aiming at a two-layer elastic medium model; 102, calculating a bit function of the spherical reflection SV wave according to the PS reflection coefficient of the plane wave; 103, calculating the displacement of the spherical reflection SV wave along the direction of a vertical ray according to the bit function of the spherical reflection SV wave; and 104, calculating the PS reflection coefficient of the spherical wave according to the displacement along the direction of the vertical ray.

In one example, the plane wave PS reflection coefficient is calculated by equation (1):

wherein R is_psIs the plane wave PS reflection coefficient, alpha₁And alpha₂Longitudinal wave velocity, beta, of the upper and lower media, respectively₁And beta₂Respectively the transverse wave speeds of the upper medium and the lower medium, a, b, c, D, E, F, G, H and D are intermediate parameters, D＝EF+GHp²p is a ray parameter, p is sin θ₁/α₁，θ₁And theta₂The incident angle and the transmission angle of the plane P wave,andthe reflection angle and the transmission angle of the plane SV wave.

In one example, the bit function of a spherical reflected SV wave is calculated by equation (2):

where ψ is a bit function of a spherically reflected SV wave, A is a constant depending on the source intensity, i is a complex unit, ω is an angular frequency, t is time, J₀Is a function of the zero order bessel function,ξ₁is the vertical slowness, xi, of the longitudinal wave of the upper medium₁＝(1/α₁ ²-p²)^1/2，η₁Is the vertical slowness, eta, of transverse waves of the upper medium₁＝(1/β₁ ²-p²)^1/2R is the offset, and h and z are the vertical distances of the source and receiver points, respectively, to the reflecting interface.

In one example, the displacement of the spherically reflected SV wave along the vertical ray direction is calculated by equation (3):

wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J₁Is a first order Bessel function, s_rIs displacement of spherical reflection SV wave along r direction, s_zDisplacement of the spherical reflected SV wave in the z direction.

In one example, the spherical wave PS reflection coefficient is calculated by equation (4):

wherein the content of the first and second substances,is the spherical wave PS reflection coefficient.

FIG. 2 shows a schematic representation of a two-layer elastic media model according to one embodiment of the present invention.

Specifically, the spherical wave PS reflection coefficient calculation method according to the present invention may include:

for the two-layer elastic medium model shown in FIG. 2, the densities of the upper and lower layers of medium are respectively ρ₁And ρ₂The division plane is located at z-0 (horizontal r axis), S is a seismic source, and a spherical P wave excited by the seismic source S is at an incident angle theta₁And the spherical reflection SV wave is received at a receiving point P. Is calculated by formula (1)The plane wave PS reflection coefficient is calculated, and the bit function of the spherical reflection SV wave at P is calculated by equation (2).

The displacement of the spherical reflection SV wave in the r direction is:

a displacement in the z direction of

According to the nature of the Bessel function:

the displacement of the spherical reflection SV wave along the r direction can be obtained as

A displacement in the z direction of

Further, according to the bit function of the spherical reflection SV wave, calculating the displacement of the spherical reflection SV wave along the direction of the vertical ray through a formula (3); from the displacement in the vertical ray direction, the spherical wave PS reflection coefficient is calculated by equation (4).

The method can be used for analyzing the characteristics of the spherical reflection wave field and enhancing the knowledge of the seismic wave field propagation rule by calculating the PS reflection coefficient of the spherical wave, thereby laying a theoretical foundation for seismic inversion by using the PS wave of the spherical wave and guiding the processing and explaining process of seismic exploration.

Application example

To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention and that any specific details thereof are not intended to limit the invention in any way.

The model parameter of the two-layer elastic medium is alpha₁＝2000m/s，β₁＝880m/s，ρ₁＝2.4g/cm³，α₂＝2933.33m/s，β₂＝1882.29m/s，ρ₂＝2.0g/cm³The longitudinal wave velocity of the upper layer medium is smaller than that of the lower layer but larger than that of the lower layer, so that only the first critical angle, about 43 degrees, exists at the moment, and the head wave is generated after the critical angle; the seismic source is 500m above the interface, namely h is 500m, and the receiving position is 500m above the interface, namely z is 500 m; the angle of incidence is 0-89 °, and f is 50 Hz. Substituting the above parameters into equation (4) can calculate the corresponding PS reflection coefficient of the spherical wave. In addition, the same parameters are adopted to calculate the corresponding plane wave PS reflection coefficient according to the formula (1), and the plane wave PS reflection coefficient can be compared with the spherical wave PS reflection coefficient.

FIG. 3 shows a graph comparing the amplitude of a plane wave PS reflection coefficient versus a spherical wave PS reflection coefficient as a function of angle of incidence, according to one embodiment of the invention. FIG. 4 shows a comparison of the phase versus incident angle for a plane wave PS reflection coefficient and a spherical wave PS reflection coefficient, according to one embodiment of the present invention. The solid line is the PS reflection coefficient of the spherical wave and the dotted line is the corresponding PS reflection coefficient of the plane wave. It can be seen that the amplitude and phase of the reflection coefficient for the spherical wave PS are significantly different from the plane wave PS reflection coefficient over a range near and after the critical angle (38-75 °). This means that when elastic parameter inversion is performed using large angle or long offset data, a conventional method based on Zoeppritz equation approximation based on plane wave PS reflection coefficients produces a large error, and therefore, high-precision inversion is performed based on spherical wave PS reflection coefficients.

In conclusion, by calculating the PS reflection coefficient of the spherical wave, the result can be used for analyzing the characteristics of the spherical reflection wave field, enhancing the knowledge of the seismic wave field propagation rule, laying a theoretical foundation for seismic inversion by using the spherical PS wave and guiding the processing and explaining process of seismic exploration.

It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.

According to an embodiment of the present invention, there is provided a spherical wave PS reflection coefficient calculation system, including: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: calculating a plane wave PS reflection coefficient aiming at the two-layer elastic medium model; calculating a bit function of the spherical reflection SV wave according to the PS reflection coefficient of the plane wave; calculating the displacement of the spherical reflection SV wave along the direction of a vertical ray according to the bit function of the spherical reflection SV wave; and calculating the PS reflection coefficient of the spherical wave according to the displacement along the direction of the vertical ray.

In one example, the plane wave PS reflection coefficient is calculated by equation (1):

wherein R is_psIs the plane wave PS reflection coefficient, alpha₁And alpha₂Longitudinal wave velocity, beta, of the upper and lower media, respectively₁And beta₂Respectively the transverse wave speeds of the upper medium and the lower medium, a, b, c, D, E, F, G, H and D are intermediate parameters, D＝EF+GHp²p is a ray parameter, p is sin θ₁/α₁，θ₁And theta₂The incident angle and the transmission angle of the plane P wave,andthe reflection angle and the transmission angle of the plane SV wave.

In one example, the bit function of a spherical reflected SV wave is calculated by equation (2):

where ψ is a bit function of a spherically reflected SV wave, A is a constant depending on the source intensity, i is a complex unit, ω is an angular frequency, t is time, J₀Is a zero order Bessel function, ξ₁Is the vertical slowness, xi, of the longitudinal wave of the upper medium₁＝(1/α₁ ²-p²)^1/2，η₁Is the vertical slowness, eta, of transverse waves of the upper medium₁＝(1/β₁ ²-p²)^1/2R is the offset, and h and z are the vertical distances of the source and receiver points, respectively, to the reflecting interface.

In one example, the displacement of the spherically reflected SV wave along the vertical ray direction is calculated by equation (3):

wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J₁Is a first order Bessel function, s_rIs displacement of spherical reflection SV wave along r direction, s_zDisplacement of the spherical reflected SV wave in the z direction.

In one example, the spherical wave PS reflection coefficient is calculated by equation (4):

wherein the content of the first and second substances,is the spherical wave PS reflection coefficient.

The system can be used for analyzing the characteristics of the spherical reflection wave field and enhancing the knowledge of the seismic wave field propagation rule by calculating the PS reflection coefficient of the spherical wave, thereby laying a theoretical foundation for seismic inversion by using the PS wave of the spherical wave and guiding the processing and explaining process of seismic exploration.

It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.

Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.