CN112505751A - Spherical wave PS reflection coefficient calculation method and system - Google Patents

Spherical wave PS reflection coefficient calculation method and system Download PDF

Info

Publication number
CN112505751A
CN112505751A CN201910871993.2A CN201910871993A CN112505751A CN 112505751 A CN112505751 A CN 112505751A CN 201910871993 A CN201910871993 A CN 201910871993A CN 112505751 A CN112505751 A CN 112505751A
Authority
CN
China
Prior art keywords
wave
spherical
reflection coefficient
reflection
calculating
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201910871993.2A
Other languages
Chinese (zh)
Other versions
CN112505751B (en
Inventor
李京南
马灵伟
胡华锋
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
China Petroleum and Chemical Corp
Sinopec Geophysical Research Institute
Original Assignee
China Petroleum and Chemical Corp
Sinopec Geophysical Research Institute
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by China Petroleum and Chemical Corp, Sinopec Geophysical Research Institute filed Critical China Petroleum and Chemical Corp
Priority to CN201910871993.2A priority Critical patent/CN112505751B/en
Publication of CN112505751A publication Critical patent/CN112505751A/en
Application granted granted Critical
Publication of CN112505751B publication Critical patent/CN112505751B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/282—Application of seismic models, synthetic seismograms
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
    • G01V1/30—Analysis
    • G01V1/307—Analysis for determining seismic attributes, e.g. amplitude, instantaneous phase or frequency, reflection strength or polarity

Abstract

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.

Description

Spherical wave PS reflection coefficient calculation method and system
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):
Figure BDA0002203111090000021
wherein R ispsIs 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,
Figure BDA0002203111090000022
Figure BDA0002203111090000023
Figure BDA0002203111090000024
Figure BDA0002203111090000025
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,
Figure BDA0002203111090000026
and
Figure BDA0002203111090000027
the 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):
Figure BDA0002203111090000028
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):
Figure BDA0002203111090000031
wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J1Is a first order Bessel function, srIs displacement of spherical reflection SV wave along r direction, szDisplacement of the spherical reflected SV wave in the z direction.
Preferably, the spherical wave PS reflection coefficient is calculated by equation (4):
Figure BDA0002203111090000032
wherein the content of the first and second substances,
Figure BDA0002203111090000033
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):
Figure BDA0002203111090000034
wherein R ispsIs 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,
Figure BDA0002203111090000041
Figure BDA0002203111090000042
Figure BDA0002203111090000043
Figure BDA0002203111090000044
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,
Figure BDA0002203111090000045
and
Figure BDA0002203111090000046
the 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):
Figure BDA0002203111090000047
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):
Figure BDA0002203111090000048
wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J1Is a first order Bessel function, srIs displacement of spherical reflection SV wave along r direction, szDisplacement of the spherical reflected SV wave in the z direction.
Preferably, the spherical wave PS reflection coefficient is calculated by equation (4):
Figure BDA0002203111090000051
wherein the content of the first and second substances,
Figure BDA0002203111090000052
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):
Figure BDA0002203111090000061
wherein R ispsIs 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,
Figure BDA0002203111090000062
Figure BDA0002203111090000063
Figure BDA0002203111090000064
Figure BDA0002203111090000065
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,
Figure BDA0002203111090000066
and
Figure BDA0002203111090000067
the 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):
Figure BDA0002203111090000068
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):
Figure BDA0002203111090000071
wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J1Is a first order Bessel function, srIs displacement of spherical reflection SV wave along r direction, szDisplacement of the spherical reflected SV wave in the z direction.
In one example, the spherical wave PS reflection coefficient is calculated by equation (4):
Figure BDA0002203111090000072
wherein the content of the first and second substances,
Figure BDA0002203111090000073
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:
Figure BDA0002203111090000081
a displacement in the z direction of
Figure BDA0002203111090000082
According to the nature of the Bessel function:
Figure BDA0002203111090000083
the displacement of the spherical reflection SV wave along the r direction can be obtained as
Figure BDA0002203111090000084
A displacement in the z direction of
Figure BDA0002203111090000085
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):
Figure BDA0002203111090000101
wherein R ispsIs 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,
Figure BDA0002203111090000102
Figure BDA0002203111090000103
Figure BDA0002203111090000104
Figure BDA0002203111090000105
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,
Figure BDA0002203111090000106
and
Figure BDA0002203111090000107
the 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):
Figure BDA0002203111090000108
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):
Figure BDA0002203111090000111
wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J1Is a first order Bessel function, srIs displacement of spherical reflection SV wave along r direction, szDisplacement of the spherical reflected SV wave in the z direction.
In one example, the spherical wave PS reflection coefficient is calculated by equation (4):
Figure BDA0002203111090000112
wherein the content of the first and second substances,
Figure BDA0002203111090000113
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.

Claims (10)

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):
Figure FDA0002203111080000011
wherein R ispsIs 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,
Figure FDA0002203111080000012
Figure FDA0002203111080000013
Figure FDA0002203111080000014
Figure FDA0002203111080000015
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,
Figure FDA0002203111080000016
and
Figure FDA0002203111080000017
the 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):
Figure FDA0002203111080000018
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):
Figure FDA0002203111080000021
wherein s is the displacement of the spherical reflection SV wave along the vertical ray direction, and J1Is a first order Bessel function, srIs displacement of spherical reflection SV wave along r direction, szDisplacement 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):
Figure FDA0002203111080000022
wherein the content of the first and second substances,
Figure FDA0002203111080000023
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):
Figure FDA0002203111080000031
wherein R ispsIs 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,
Figure FDA0002203111080000032
Figure FDA0002203111080000033
Figure FDA0002203111080000034
Figure FDA0002203111080000035
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,
Figure FDA0002203111080000036
and
Figure FDA0002203111080000037
the 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):
Figure FDA0002203111080000038
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):
Figure FDA0002203111080000041
wherein s is the displacement of the spherical reflection SV wave along the direction of the vertical rayrIs displacement of spherical reflection SV wave along r direction, szDisplacement 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):
Figure FDA0002203111080000042
wherein the content of the first and second substances,
Figure FDA0002203111080000043
is the spherical wave PS reflection coefficient.
CN201910871993.2A 2019-09-16 2019-09-16 Spherical wave PS reflection coefficient calculation method and system Active CN112505751B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910871993.2A CN112505751B (en) 2019-09-16 2019-09-16 Spherical wave PS reflection coefficient calculation method and system

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910871993.2A CN112505751B (en) 2019-09-16 2019-09-16 Spherical wave PS reflection coefficient calculation method and system

Publications (2)

Publication Number Publication Date
CN112505751A true CN112505751A (en) 2021-03-16
CN112505751B CN112505751B (en) 2023-03-21

Family

ID=74924073

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910871993.2A Active CN112505751B (en) 2019-09-16 2019-09-16 Spherical wave PS reflection coefficient calculation method and system

Country Status (1)

Country Link
CN (1) CN112505751B (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113820748A (en) * 2021-08-23 2021-12-21 西安理工大学 Method for acquiring ground gliding wave time course when seismic SV wave is totally reflected
CN116148925A (en) * 2023-04-18 2023-05-23 山东省科学院海洋仪器仪表研究所 VTI medium spherical longitudinal wave reflection coefficient analysis method
CN117665917A (en) * 2024-02-01 2024-03-08 山东省科学院海洋仪器仪表研究所 Analysis method for spherical wave reflection coefficient of submarine fluid-VTI solid interface

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4363113A (en) * 1975-02-10 1982-12-07 Seiscom Delta, Inc. Seismic exploration with simulated plane waves
US5610875A (en) * 1995-09-29 1997-03-11 Western Atlas International, Inc. 3-D converted shear wave rotation with layer stripping
CN103149586A (en) * 2013-02-04 2013-06-12 西安交通大学 Tilted layered viscoelasticity dielectric medium wave field forward modelling method
CN104570072A (en) * 2013-10-16 2015-04-29 中国石油化工股份有限公司 Method for modeling reflection coefficient of spherical PP wave in viscoelastic medium
US20160146961A1 (en) * 2014-11-25 2016-05-26 Cgg Services Sa Method for elastic model perturbation estimation from reverse time migration
CN107478325A (en) * 2017-09-07 2017-12-15 安徽大学 A kind of free field restoring method of unstable state flat sound source
CN107861153A (en) * 2017-10-25 2018-03-30 中国地质大学（北京） The fast solution method of thin layer PP wave reflection coefficients

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4363113A (en) * 1975-02-10 1982-12-07 Seiscom Delta, Inc. Seismic exploration with simulated plane waves
US5610875A (en) * 1995-09-29 1997-03-11 Western Atlas International, Inc. 3-D converted shear wave rotation with layer stripping
CN103149586A (en) * 2013-02-04 2013-06-12 西安交通大学 Tilted layered viscoelasticity dielectric medium wave field forward modelling method
CN104570072A (en) * 2013-10-16 2015-04-29 中国石油化工股份有限公司 Method for modeling reflection coefficient of spherical PP wave in viscoelastic medium
US20160146961A1 (en) * 2014-11-25 2016-05-26 Cgg Services Sa Method for elastic model perturbation estimation from reverse time migration
CN107478325A (en) * 2017-09-07 2017-12-15 安徽大学 A kind of free field restoring method of unstable state flat sound source
CN107861153A (en) * 2017-10-25 2018-03-30 中国地质大学（北京） The fast solution method of thin layer PP wave reflection coefficients

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
ARNIM B. HAASE ET AL.: "Spherical Wave AVO Modeling of Converted Waves in Isotropic Media", 《SEG INT"L EXPOSITION AND 74TH ANNUAL MEETING》 *
ARNIM B. HAASE ET AL.: "Spherical-wave AVO modeling in elastic and anelastic media", 《CREWES RESEARCH REPORT》 *
JINGNAN LI ET AL.: "A novel expression of the spherical-wave reflection coefficient at a plane interface", 《GEOPHYSICAL JOURNAL INTERNATIONAL》 *
MILANA AYZENBERG ET AL.: "Effective reflection coefficients for curved interfaces in transversely isotropic media", 《GEOPHYSICS》 *
徐仲达等: "平面波反射系数与AVO技术", 《石油物探》 *
李京南等: "球面波ＰＰ反射系数的频变特征研究", 《地球物理学报》 *
李胜军等: "球面波的反射Ｐ波ＡＶＯ分析", 《地球物理学报》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113820748A (en) * 2021-08-23 2021-12-21 西安理工大学 Method for acquiring ground gliding wave time course when seismic SV wave is totally reflected
CN113820748B (en) * 2021-08-23 2024-03-26 西安理工大学 Ground sliding wave time course acquisition method when seismic SV wave is subjected to total reflection
CN116148925A (en) * 2023-04-18 2023-05-23 山东省科学院海洋仪器仪表研究所 VTI medium spherical longitudinal wave reflection coefficient analysis method
CN117665917A (en) * 2024-02-01 2024-03-08 山东省科学院海洋仪器仪表研究所 Analysis method for spherical wave reflection coefficient of submarine fluid-VTI solid interface
CN117665917B (en) * 2024-02-01 2024-04-30 山东省科学院海洋仪器仪表研究所 Analysis method for spherical wave reflection coefficient of submarine fluid-VTI solid interface

Also Published As

Publication number Publication date
CN112505751B (en) 2023-03-21

Similar Documents

Publication Publication Date Title
CN112505751B (en) Spherical wave PS reflection coefficient calculation method and system
CN109737956B (en) SINS/USBL phase difference tight combination navigation positioning method based on double transponders
Pailhas et al. Analysis and classification of broadband echoes using bio-inspired dolphin pulses
CN103620442A (en) Estimating position and orientation of an underwater vehicle relative to underwater structures
CN112254797A (en) Method, system and medium for improving prediction precision of ocean sound field
KR102097641B1 (en) Method for estimating direction of incidence of sound source using spherical microphone arrays
CN102508247B (en) Method for rapidly measuring parameters of three-dimensional oblique sea bottom based on ray acoustics
CN116148925B (en) VTI medium spherical longitudinal wave reflection coefficient analysis method
CN107132575A (en) The method that fracture azimuth is predicted based on shear wave polarographic analysis
Stovas et al. Wave characteristics in elliptical orthorhombic media
Zhang et al. A calibration method of ultra-short baseline installation error with large misalignment based on variational Bayesian unscented Kalman filter
JP6718098B2 (en) Position estimation apparatus and method
Sun et al. Generalized Radon transform approach to target motion parameter estimation using a stationary underwater vector hydrophone
WO2008076615A2 (en) Computing an absorption parameter for a mode-converted seismic wave
JP2003318842A (en) Device and method for estimating and calculating reception electric field intensity, and program and recording medium
CN111435174B (en) Method and device for compensating amplitude of seismic data in strong reflection area
Drira et al. Image source detection for geoacoustic inversion by the Teager-Kaiser energy operator
US20150153466A1 (en) Source Start Time Determination
GODIN A 2-D description of sound propagation in a horizontally-inhomogeneous ocean
Makarov On measurement of acoustic pulse arrival angles using a vertical array
CN112649845A (en) Spherical wave reflection coefficient calculation method and system
KR102262400B1 (en) Apparatus and method for estimating directional angles of underwater acoustic sources
Sun et al. An adaptive model for the location of low-frequency sound sources in shallow sea environments
CN112649857A (en) Fluid factor direct inversion method and system based on pre-stack seismic data
CN109655899A (en) VSP seismic data instantaneous angular composes calculation method and system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant