CN109188512B - Irregular sector grid-based fluctuating tunnel space forward modeling system and method - Google Patents
Irregular sector grid-based fluctuating tunnel space forward modeling system and method Download PDFInfo
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Abstract
The invention discloses a fluctuating tunnel space forward modeling system and method based on irregular sector grid subdivision, belonging to the field of petroleum exploration, and the forward modeling method comprises the following steps: inputting a fluctuating tunnel space elevation function, geodetic coordinates of a seismic source and a detector, and longitudinal and transverse wave speeds and densities of a tunnel space model, carrying out irregular sector grid subdivision on the fluctuating tunnel space model, mapping the fluctuating tunnel space model to a rectangular grid subdivision model under a curved fan coordinate system, deriving an elastic wave first-order speed-stress equation of the curved fan coordinate system, carrying out wave field updating by using a full-staggered grid mechanism under the curved fan coordinate system, absorbing artificial boundary reflection under a three-direction absorption boundary condition under the curved fan coordinate system, converting the wave field snapshot into a Cartesian coordinate system, and outputting shot records and wave field snapshots of the fluctuating tunnel space model. The invention can more accurately simulate the seismic wave field propagation in some special geological environments, such as tunnels, well logging and drilling spaces.
Description
Technical Field
The invention belongs to the field of petroleum exploration, and particularly relates to a fluctuating tunnel space forward modeling system and method based on irregular sector grid subdivision
Background
Petroleum is an important strategic resource for guaranteeing national safety, and with the rapid increase of the external dependence of the supply and demand of petroleum in China year by year, the strengthening of the seismic exploration theoretical research is urgently needed to improve the oil and gas reserves and the yield in China. The underground structure of the main oil and gas exploration area in China is complex, the lithological difference of reservoirs is large, great challenges are brought to seismic exploration, and the main difficulties are shown as follows: the seismic wave propagation rule is complex, the effective seismic information is weak, and high-precision seismic imaging is difficult. Aiming at the complexity of geological structures of exploration areas in China, researches on seismic wave propagation rules and high-precision imaging theories of complex media need to be systematically developed.
With the deep development of oil and gas exploration, the more complex the geological structure is, and great challenges are brought to seismic exploration. Aiming at the complexity of geological structures of exploration areas in China, the research on dielectric seismic wave propagation rules and high-precision imaging theories and methods needs to be systematically carried out, so that more important geophysical basis is better provided for recognition, description, excavation and the like of oil and gas reservoirs.
In special geological environments such as tunnels, well logging, drilling and the like, the traditional rectangular coordinate elastic wave equation based on rectangular grids cannot accurately simulate a seismic wave field.
Disclosure of Invention
Aiming at the technical problems in the prior art, the invention provides a forward simulation system of the fluctuating tunnel space based on irregular sector mesh subdivision and a simulation method based on the forward simulation system.
The technical solution adopted by the invention is as follows:
a fluctuating tunnel space forward modeling system based on irregular sector grid subdivision comprises an input module, a grid generation module, a coordinate transformation module, a wave field continuation module, an absorption boundary module, a coordinate inverse transformation module and an output module which are sequentially connected;
the input module is configured to input a fluctuating tunnel space elevation function, geodetic coordinates of a seismic source and a detector, and a longitudinal and transverse wave speed and density model of a tunnel space model;
the grid generation module is configured for irregular sector grid subdivision of the space model of the fluctuating tunnel;
a coordinate transformation module configured for mapping the undulating tunnel spatial model to a model of a rectangular mesh subdivision under a curved fan coordinate system;
the wave field continuation module is configured to derive a first-order velocity-stress equation of elastic waves in a curved fan coordinate system, and wave field updating is carried out by utilizing a full-staggered grid mechanism under the curved fan coordinate system;
an absorption boundary module configured to absorb the artificial boundary reflection under a three-direction absorption boundary condition under a curved fan coordinate system;
an inverse coordinate transform module configured for transforming the wave field snapshot into a cartesian coordinate system;
and the output module is used for outputting the shot record and the wave field snapshot of the fluctuation tunnel space model.
A fluctuating tunnel space forward modeling method based on irregular sector mesh generation adopts the fluctuating tunnel space forward modeling system based on the irregular sector mesh generation, and comprises the following steps:
step 1: inputting a fluctuating tunnel space elevation function, geodetic coordinates of a seismic source and a detector, and longitudinal and transverse wave speeds and density models of a tunnel space model through an input module;
step 2: irregular sector mesh subdivision is carried out on the space model of the fluctuating tunnel through a mesh generation module;
and step 3: mapping the space model of the fluctuating tunnel to a model of rectangular grid subdivision under a curved fan coordinate system through a coordinate transformation module, and transforming through a coordinate transformation formula shown as follows:
wherein, theta represents an angle variable under a polar coordinate system, r represents a radius variable under the polar coordinate system,
and gamma respectively represents an angle variable and a radius variable under a curved fan coordinate system;and
are defined separately
Maximum radius under a sector coordinate system and a curved sector coordinate system;
and 4, step 4: deducing an elastic wave first-order velocity-stress equation of a curved fan coordinate system through a wave field continuation module, wherein the equation under the curved fan coordinate system can be expressed as follows:
wherein t is time; rho is density, and lambda and mu are Lame constants; v. ofθAnd vrThe velocity of the angular component and the radial component, respectively; tau isrr，τθθ，τrθIs an auxiliary stress field under a fan-shaped coordinate system; gamma ray0And r0Respectively representing the maximum radius under a fan-shaped coordinate system and a curved fan coordinate system; partial derivative of
And
can be obtained by the following formula:
and 5: wave field updating is carried out by utilizing a full-staggered grid mechanism under a curved fan coordinate system, and second-order precision O (delta t) is used at the second order2) Spatially using a high order precision O (Delta theta)2M,Δγ2M) Solving equation (2) in a finite difference format, where M represents spatial precision; let f denote any wave field value, then the time partial derivative and two-component spatial partial derivative of f can be written as:
wherein,
to representSpatial derivative of direction, DγRepresenting the spatial derivative in the gamma direction, at is the time step,
and Δ γ are eachGrid step length in direction and gamma direction, amRepresenting a finite difference operator, superscript n representing a time coordinate, and subscripts i, j representing a space coordinate;
in order to improve the stability of forward simulation under the curved fan coordinate system, a full-staggered grid mechanism under the curved fan coordinate system is used for carrying out numerical value dispersion;
the recurrence format of the wavefield update is:
wherein,
step 6: through the absorption boundary module, the artificial boundary reflection is absorbed under the three-direction absorption boundary condition under the curved fan coordinate system, and the curved fan coordinate system comprises three boundaries: an outer boundary, an inner boundary and an angle boundary;
for the outer boundary, adopting a complex frequency shift perfect matching layer in the radius direction under a curved fan coordinate system to carry out artificial boundary reflection pressing; for the inner boundary, at the relief of the tunnel space:
substituting equation (7) into equation (2) yields the undulation free surface boundary condition:
for angular boundaries there are two cases, the first case being a closed model (θ ∈ [0,2 π ]), then the boundary condition is satisfied:
the second case is the non-closed model (theta is equal to 0, theta)max],θmaxLess than 2 pi), pressing artificial boundary reflection by adopting a complex frequency shift perfect matching layer in the angle direction under a curved fan coordinate system;
and 7: transforming the wave field snapshot into a Cartesian coordinate system through a coordinate inverse transformation module;
and 8: and outputting the shot records and the wave field snapshots of the space model of the fluctuating tunnel through an output module.
Preferably, in step 4, the two-dimensional elastic velocity stress wave equation in the cartesian coordinate system is:
wherein v isxAnd vzVelocity, τ, of the horizontal and vertical components, respectivelyxx，τzz，τxzIs the stress field, t is the time; rho is density, and lambda and mu are Lame constants; in some special geological environments such as tunnel space, the forward modeling method under the traditional Cartesian coordinate system cannot accurately model seismic waves; to overcome this difficulty, equation (10) is first transformed into a sector coordinate system in which the elastic wave equation is:
wherein v isθAnd vrThe velocity of the angular component and the radial component, respectively; tau isrr，τθθ，τrθIs an auxiliary stress field under a fan-shaped coordinate system; applying the chain rule, equation (11) in the curved fan coordinate system can be expressed as:
wherein the partial derivative
And
can be obtained by the following formula:
the beneficial technical effects of the invention are as follows:
compared with the traditional forward modeling method, the method can more accurately model the seismic wave field propagation in certain special geological environments, such as tunnels, well logging and drilling spaces. In order to process a tunnel space containing irregular surface topography, the invention develops a transition coordinate system to improve the precision of a finite difference forward modeling method under a sector coordinate. In the method, a tunnel space containing irregular surface topography is divided into irregular fan-shaped grids, and then wave field calculation is carried out under curved fan coordinates, wherein an undulating surface is mapped to a plane; and solving a wave equation in the curved fan coordinate system by adopting a fully-staggered grid numerical discrete format under the curved fan coordinate system. In addition, the complex frequency shift perfect matching layer, the columnar free surface and the circumferential boundary condition under the curved fan coordinate system are used for absorbing unwanted artificial reflection around the curved fan coordinate.
The fluctuating tunnel space forward simulation method based on irregular sector grid subdivision provides an accurate forward simulation wave field for the tunnel space with severe fluctuating surface, is beneficial to analyzing the propagation rule of seismic waves in the exploration area, and provides more important geophysical basis for identifying oil and gas reservoirs under the fluctuating tunnel space, describing excavation and the like.
Drawings
FIG. 1 is a flow chart of a forward modeling method of undulating tunnel space based on irregular sector mesh subdivision according to the present invention;
FIG. 2 is a schematic diagram of a fully-interleaved grid under a curved fan coordinate system;
FIG. 3 shows a three-directional absorption boundary condition under a curved fan coordinate system;
FIG. 4 illustrates an irregular tunnel space model; wherein (a) a cartesian coordinate system; (b) a curved coordinate system; (c) a sector coordinate system; (d) a curved fan coordinate system;
FIG. 5 is a wave field snapshot under a curved fan coordinate system obtained by the method of the present invention; wherein (a), (c), (e) show angular directions; (b) (d), (f) show the radial direction; (a) and (b) is 500 ms; (c) (d) is 1000 ms; (e) (f) is 1500 ms;
FIG. 6 is a wave field snapshot in a Cartesian coordinate system obtained by the method of the present invention; wherein (a), (c), (e) show angular directions; (b) (d), (f) show the radial direction; (a) and (b) is 500 ms; (c) (d) is 1000 ms; (e) (f) is 1500 ms;
FIG. 7 is a shot record obtained using the method of the present invention; (a) is an angular direction; (b) is in the radial direction;
FIG. 8 is a wave field snapshot in a curved fan coordinate system obtained by a conventional method; wherein (a), (c), (e) show angular directions; (b) (d), (f) show the radial direction; (a) and (b) is 500 ms; (c) (d) is 1000 ms; (e) (f) is 1500 ms;
FIG. 9 is a wave field snapshot in a curved fan coordinate system obtained by a conventional method; wherein (a), (c), (e) show angular directions; (b) (d), (f) show the radial direction; (a) and (b) is 500 ms; (c) (d) is 1000 ms; (e) (f) is 1500 ms;
fig. 10 is a schematic structural diagram of a fluctuating tunnel space forward modeling system based on irregular sector mesh subdivision in the present invention.
Detailed Description
In special geological environments such as tunnels, well logging, drilling and the like, the traditional rectangular coordinate elastic wave equation based on rectangular grids cannot accurately simulate a seismic wave field. Based on the technical problems, the invention provides a system and a method for improving finite difference forward modeling under a sector coordinate through a transition coordinate system, so as to be suitable for special geological environments such as complex tunnels.
The invention relates to a fluctuating tunnel space forward modeling method based on irregular sector grid subdivision, which comprises the steps of firstly dividing a tunnel space containing irregular surface topography into irregular sector grids, and then calculating a wave field under a curved fan coordinate, wherein a fluctuating earth surface is mapped to a plane. And solving a wave equation in the curved fan coordinate system by adopting a fully-staggered grid numerical discrete format under the curved fan coordinate system. In addition, the complex frequency shift perfect matching layer, the columnar free surface and the circumferential boundary condition under the curved fan coordinate system are used for absorbing unwanted artificial reflection around the curved fan coordinate.
The invention provides an accurate forward simulation wave field for the tunnel space with severe undulating surface, analyzes the propagation rule of seismic waves in the exploration area, and better provides more important geophysical basis for the identification, description, excavation and the like of oil and gas reservoirs in the undulating tunnel space.
The present invention will be described in more detail with reference to the accompanying drawings and specific embodiments.
Example 1
A fluctuating tunnel space forward modeling system based on irregular sector grid subdivision is structurally shown in figure 10 and comprises an input module, a grid generation module, a coordinate transformation module, a wave field continuation module, an absorption boundary module, a coordinate inverse transformation module and an output module; the modules are connected in sequence;
the input module is configured to input a fluctuating tunnel space elevation function, geodetic coordinates of a seismic source and a detector, and longitudinal and transverse wave speeds and density models of a tunnel space model;
the grid generation module is configured for irregular sector grid subdivision of the space model of the fluctuating tunnel;
a coordinate transformation module configured for mapping the undulating tunnel spatial model to a model of a rectangular mesh subdivision under a curved fan coordinate system;
the wave field continuation module is configured to derive a first-order velocity-stress equation of elastic waves in a curved fan coordinate system, and wave field updating is carried out by utilizing a full-staggered grid mechanism under the curved fan coordinate system;
an absorption boundary module configured to absorb the artificial boundary reflection under a three-direction absorption boundary condition under a curved fan coordinate system;
an inverse coordinate transform module configured for transforming the wave field snapshot into a cartesian coordinate system;
and the output module is used for outputting the shot record and the wave field snapshot of the fluctuation tunnel space model.
Example 2:
on the basis of the above embodiment, the present invention further provides a forward modeling method for undulating tunnel space based on irregular sector mesh generation, the flow of which is shown in fig. 1, and the method specifically includes the following steps:
step 1: inputting a space elevation function of the fluctuating tunnel, geodetic coordinates of a seismic source and a detector, and a longitudinal and transverse wave speed and density model of the tunnel space model.
Step 2: and (4) performing irregular sector grid subdivision on the space model of the fluctuating tunnel.
And step 3: mapping the space model of the undulating tunnel to a rectangular mesh generation model under a curved fan coordinate system, and converting by a coordinate conversion formula as shown in the following:
wherein, theta represents an angle variable under a polar coordinate system, r represents a radius variable under the polar coordinate system,
and γ represents an angle variable and a radius variable in a curved fan coordinate system, respectively.And
and respectively defining the maximum radius under a fan-shaped coordinate system and a curved fan coordinate system.
And 4, step 4: deducing a first-order velocity-stress equation of the elastic wave in a curved fan coordinate system, wherein a two-dimensional elastic velocity stress fluctuation equation in a Cartesian coordinate system is
Wherein v isxAnd vzVelocity, τ, of the horizontal and vertical components, respectivelyxx，τzz，τxzIs the stress field, t is the time; ρ is the density and λ and μ are Lame constants. In some special geological environments such as tunnel space, the forward modeling method under the traditional Cartesian coordinate system cannot accurately model seismic waves. To overcome this difficulty, equation (2) is first transformed into a sector coordinate system in which the elastic wave equation is:
wherein v isθAnd vrThe velocity of the angular component and the radial component, respectively; tau isrr，τθθ，τrθIs an auxiliary stress field under a fan-shaped coordinate system. Applying the chain rule, equation (3) in the curved fan coordinate system can be expressed as:
wherein the partial derivative
And
can be obtained by the following formula:
and 5: the wave field is updated by using a full-staggered grid mechanism under a curved fan coordinate system, and the invention uses second-order precision O (delta t) on the second order2) Spatially using a high order precision O (Delta theta)2M,Δγ2M) Equation (4) is solved for the finite difference format of (a), where M represents spatial precision. Let f denote any wave field value, then the time partial derivative and two-component spatial partial derivative of f can be written as:
where at is the step of time in which,
and Δ γ are each
Grid step length in direction and gamma direction, amRepresenting a finite difference operator, the superscript n representing the time coordinate and the subscript i, j representing the space coordinate.
In order to improve the stability of forward simulation in the curved fan coordinate system, the invention uses a full-staggered grid mechanism in the curved fan coordinate system to carry out numerical value dispersion (figure 2).
The recurrence format of the wavefield update is:
wherein,
step 6: the artificial boundary reflection is absorbed under the condition of three-direction absorption boundary under the curved fan coordinate system, and the curved fan coordinate system comprises three boundaries: an outer boundary, an inner boundary and a corner boundary (fig. 3).
For the outer boundary, the invention adopts a complex frequency shift perfect matching layer in the radius direction under a curved fan coordinate system to carry out the suppression of artificial boundary reflection; for the inner boundary, at the relief of the tunnel space:
substituting equation (9) into equation (4) yields the undulation free surface boundary condition:
there are two cases for the corner boundary. The first case is a closed model (θ ∈ [0,2 π ]), then the boundary condition is satisfied:
the second case is the non-closed model (theta is equal to 0, theta)max],θmaxLess than 2 pi), and pressing artificial boundary reflection by adopting a complex frequency shift perfect matching layer in the angle direction under a curved fan coordinate system.
And 7: the wavefield snapshot is transformed into a cartesian coordinate system.
And 8: and outputting the shot records and the wave field snapshots of the space model of the fluctuating tunnel.
The fluctuating tunnel space forward modeling method based on irregular sector grid subdivision provides an accurate forward modeling wave field for the tunnel space with severe fluctuating surface, is beneficial to analyzing the propagation rule of seismic waves in the exploration area, and provides more important geophysical basis for identifying oil and gas reservoirs under the fluctuating tunnel space, describing excavation and the like.
Application experiments
The fluctuating tunnel space forward modeling method based on irregular sector grid subdivision is applied to irregular tunnel space model data, and obtains an ideal calculation effect.
Inputting a space elevation function of a fluctuating tunnel, geodetic coordinates of a seismic source and a detector, and longitudinal and transverse wave speeds and densities of a tunnel space model, wherein the longitudinal wave speed of the irregular tunnel space model is shown in figure 4(a), the longitudinal and transverse wave speeds meet Poisson's body, and the density model passes through rho of 0.31vp 0.25Obtaining; irregular sector mesh generation is carried out on the space model of the fluctuating tunnel, and the mesh generation is shown as a solid line in a figure 4 (a); mapping the space model of the undulating tunnel to a model of rectangular grid subdivision under a curved fan coordinate system, wherein fig. 4(b) and 4(c) are respectively models under the curved coordinate system and a fan-shaped coordinate system, and fig. 4(d) is a model under a final curved fan coordinate system; deducing a first-order velocity-stress equation of the elastic wave in a curved fan coordinate system; by curved fansA full-staggered grid mechanism (figure 1) under a coordinate system carries out wave field updating; absorbing artificial boundary reflection under a three-direction absorption boundary condition (figure 2) under a curved fan coordinate system; the obtained wave field snapshot in the curved fan coordinate system is shown in fig. 5, the wave field snapshot is transformed into the cartesian coordinate system, and the shot record (shown in fig. 7) and the wave field snapshot of the relief tunnel space model are output, as shown in fig. 6.
As can be seen from fig. 5, 6 and 7, the wave field propagation characteristics of seismic waves in the undulating tunnel space can be accurately simulated by the undulating tunnel space forward modeling method based on irregular sector mesh subdivision provided by the invention. The influence of severe fluctuation of the earth surface is eliminated, and direct waves, reflected waves, converted waves and surface waves can be well simulated. In comparison, the method provided by the invention also adopts a conventional curved grid forward modeling method to simulate the space model of the fluctuating tunnel. The resulting wavefield snapshots in the curved grid coordinate system and the cartesian coordinate system are shown in fig. 8 and 9. The conventional method generates abnormal noise as shown by the arrows in the drawing, compared to the method of the present invention. Therefore, the result proves that the forward modeling method can obtain a more accurate and practical forward modeling result.
Parts not described in the above modes can be realized by adopting or referring to the prior art.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (3)
1. A fluctuating tunnel space forward modeling system based on irregular sector mesh subdivision is characterized in that: the system comprises an input module, a grid generation module, a coordinate transformation module, a wave field continuation module, an absorption boundary module, a coordinate inverse transformation module and an output module which are sequentially connected;
the input module is configured to input a fluctuating tunnel space elevation function, geodetic coordinates of a seismic source and a detector, and a longitudinal and transverse wave speed and density model of a tunnel space model;
the grid generation module is configured for irregular sector grid subdivision of the space model of the fluctuating tunnel;
a coordinate transformation module configured to map the undulating tunnel space model to a model of rectangular mesh subdivision in a curved fan coordinate system, transformed by a coordinate transformation formula as shown below:
wherein, theta represents an angle variable under a polar coordinate system, r represents a radius variable under the polar coordinate system,
and gamma respectively represents an angle variable and a radius variable under a curved fan coordinate system;and
are defined separately
Maximum radius under a sector coordinate system and a curved sector coordinate system;
the wave field continuation module is configured to derive a first-order velocity-stress equation of elastic waves in a curved fan coordinate system, and wave field updating is carried out by utilizing a full-staggered grid mechanism under the curved fan coordinate system;
an absorption boundary module configured to absorb the artificial boundary reflection under a three-direction absorption boundary condition under a curved fan coordinate system;
an inverse coordinate transform module configured for transforming the wave field snapshot into a cartesian coordinate system;
and the output module is used for outputting the shot record and the wave field snapshot of the fluctuation tunnel space model.
2. An undulating tunnel space forward simulation method based on irregular sector mesh generation, which adopts the undulating tunnel space forward simulation system based on irregular sector mesh generation as claimed in claim 1, and is characterized by comprising the following steps:
step 1: inputting a fluctuating tunnel space elevation function, geodetic coordinates of a seismic source and a detector, and longitudinal and transverse wave speeds and density models of a tunnel space model through an input module;
step 2: irregular sector mesh subdivision is carried out on the space model of the fluctuating tunnel through a mesh generation module;
and step 3: mapping the space model of the fluctuating tunnel to a model of rectangular grid subdivision under a curved fan coordinate system through a coordinate transformation module, and transforming through a coordinate transformation formula shown as follows:
wherein, theta represents an angle variable under a polar coordinate system, r represents a radius variable under the polar coordinate system,
and gamma respectively represents an angle variable and a radius variable under a curved fan coordinate system;
and
are defined separately
Maximum radius under a sector coordinate system and a curved sector coordinate system;
and 4, step 4: deducing an elastic wave first-order velocity-stress equation of a curved fan coordinate system through a wave field continuation module, wherein the equation under the curved fan coordinate system can be expressed as follows:
wherein t is time; rho is density, and lambda and mu are Lame constants; v. ofθAnd vrThe velocity of the angular component and the radial component, respectively; tau isrr，τθθ，τrθIs an auxiliary stress field under a fan-shaped coordinate system; gamma ray0And r0Respectively representing the maximum radius under a fan-shaped coordinate system and a curved fan coordinate system; partial derivative of
And
can be obtained by the following formula:
step 5, performing wave field updating by using a full-staggered grid mechanism under a curved fan coordinate system, and using second-order precision O (△ t) on the second order2) Spatially using a high order precision O (△ theta)2M,△γ2M) Solving equation (2) in a finite difference format, where M represents spatial precision; let f denote any wave field value, then the time partial derivative and two-component spatial partial derivative of f can be written as:
wherein,
to representSpatial derivative of direction, DγRepresenting the spatial derivative in the gamma direction, △ t is the time step,
and △Gamma is respectively
Grid step length in direction and gamma direction, amRepresenting a finite difference operator, superscript n representing a time coordinate, and subscripts i, j representing a space coordinate;
carrying out numerical value dispersion by using a full-staggered grid mechanism under a curved fan coordinate system;
the recurrence format of the wavefield update is:
wherein,
step 6: through the absorption boundary module, the artificial boundary reflection is absorbed under the three-direction absorption boundary condition under the curved fan coordinate system, and the curved fan coordinate system comprises three boundaries: an outer boundary, an inner boundary and an angle boundary;
for the outer boundary, adopting a complex frequency shift perfect matching layer in the radius direction under a curved fan coordinate system to carry out artificial boundary reflection pressing; for the inner boundary, at the relief of the tunnel space:
substituting equation (7) into equation (2) yields the undulation free surface boundary condition:
for the corner boundary, there are two cases, the first case is a closed model, θ ∈ [0,2 π ], then the boundary condition is satisfied:
the second case is a non-closed model, theta belongs to [0, theta ∈max],θmax<2 pi, pressing artificial boundary reflection by adopting a complex frequency shift perfect matching layer in the angle direction under a curved fan coordinate system;
and 7: transforming the wave field snapshot into a Cartesian coordinate system through a coordinate inverse transformation module;
and 8: and outputting the shot records and the wave field snapshots of the space model of the fluctuating tunnel through an output module.
3. The undulating tunnel space forward modeling method based on irregular sector mesh subdivision as claimed in claim 2, wherein: in step 4, the two-dimensional elastic velocity stress wave equation under the cartesian coordinate system is:
wherein v isxAnd vzVelocity, τ, of the horizontal and vertical components, respectivelyxx，τzz，τxzIs the stress field, t is the time; rho is density, and lambda and mu are Lame constants; transforming the equation (10) into a fan-shaped coordinate system, wherein the elastic wave fluctuation equation in the fan-shaped coordinate system is as follows:
wherein v isθAnd vrThe velocity of the angular component and the radial component, respectively; tau isrr，τθθ，τrθIs an auxiliary stress field under a fan-shaped coordinate system; applying the chain rule, equation (11) in the curved fan coordinate system can be expressed as:
wherein the partial derivative
And
can be obtained by the following formula:
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| CN113740901B (en) * | 2020-05-29 | 2024-01-30 | 中国石油天然气股份有限公司 | Land seismic data full-waveform inversion method and device based on complex undulating surface |
| CN112230277B (en) * | 2020-09-30 | 2021-10-29 | 山东大学 | Tunnel seismic wave propagation numerical simulation method and system based on cylindrical coordinate system |
| CN113435074B (en) * | 2021-03-24 | 2024-02-09 | 中国地震局工程力学研究所 | M-UFSPML model, construction method, intelligent terminal and server |
| CN117826237B (en) * | 2024-01-04 | 2024-08-06 | 深地科学与工程云龙湖实验室 | Method for predicting earthquake wave propagation induced by shield machine work in tunnel |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5996726A (en) * | 1998-01-29 | 1999-12-07 | Gas Research Institute | System and method for determining the distribution and orientation of natural fractures |
| CN102062875A (en) * | 2010-11-30 | 2011-05-18 | 中国石油集团川庆钻探工程有限公司 | Forward modeling method for fluctuating surface elastic wave equation |
| EP2778724A2 (en) * | 2013-03-15 | 2014-09-17 | Paradigm Sciences Ltd. | Systems and methods for building axes, co-axes and paleo-geographic coordinates related to a stratified geological volume |
| CN106353797A (en) * | 2015-07-17 | 2017-01-25 | 中国石油化工股份有限公司 | High-precision earthquake forward modeling method |
| CN106772590A (en) * | 2017-03-17 | 2017-05-31 | 中国地质科学院地球物理地球化学勘查研究所 | A kind of free earth's surface finite-difference forward modeling system and method that acutely rises and falls |
| CN106814390A (en) * | 2015-11-27 | 2017-06-09 | 中国石油化工股份有限公司 | Staggered-mesh the Forward Modeling based on time-space domain optimization |
-
2018
- 2018-09-17 CN CN201811079748.XA patent/CN109188512B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5996726A (en) * | 1998-01-29 | 1999-12-07 | Gas Research Institute | System and method for determining the distribution and orientation of natural fractures |
| CN102062875A (en) * | 2010-11-30 | 2011-05-18 | 中国石油集团川庆钻探工程有限公司 | Forward modeling method for fluctuating surface elastic wave equation |
| EP2778724A2 (en) * | 2013-03-15 | 2014-09-17 | Paradigm Sciences Ltd. | Systems and methods for building axes, co-axes and paleo-geographic coordinates related to a stratified geological volume |
| CN106353797A (en) * | 2015-07-17 | 2017-01-25 | 中国石油化工股份有限公司 | High-precision earthquake forward modeling method |
| CN106814390A (en) * | 2015-11-27 | 2017-06-09 | 中国石油化工股份有限公司 | Staggered-mesh the Forward Modeling based on time-space domain optimization |
| CN106772590A (en) * | 2017-03-17 | 2017-05-31 | 中国地质科学院地球物理地球化学勘查研究所 | A kind of free earth's surface finite-difference forward modeling system and method that acutely rises and falls |
Non-Patent Citations (2)
| Title |
|---|
| "Variable-coordinate forward modeling of irregular surface based on dual-variable grid";Huang Jian-Ping 等;《APPLIED GEOPHYSICS》;20150331;第12卷(第1期);第101-110页 * |
| "时间域起伏自由地表正演模拟综述";李振春 等;《地球物理学进展》;20161231;第31卷(第1期);第0300-0309页 * |
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