CN112364577A - Numerical simulation analysis method for plate diving thermal structure parameters - Google Patents

Numerical simulation analysis method for plate diving thermal structure parameters Download PDF

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CN112364577A
CN112364577A CN202011380542.8A CN202011380542A CN112364577A CN 112364577 A CN112364577 A CN 112364577A CN 202011380542 A CN202011380542 A CN 202011380542A CN 112364577 A CN112364577 A CN 112364577A
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Abstract

The invention discloses a numerical simulation analysis method for plate diving thermal structure parameters, which is based on the mass, momentum and energy conservation equation of Navigstokes, adjusts and modifies model parameters after a plate starts diving from a sea ditch to the current shape and depth and reaches a stable state so that a calculated value of a surface thermal flowmeter reaches an observed value, and accordingly obtains the result of an optimal model. According to the method, on the basis of known plate depth and diving speed data, a three-dimensional temperature field, plate water content, dehydration rate and rock phase change distribution of a diving zone can be calculated and expressed. The calculation result can be further used for researching the earth deep temperature field, the rock phase change turning-back process, the underground fluid field of volcanic rock pulp and the investigation and development of metamorphic rock mineral products.

Description

Numerical simulation analysis method for plate diving thermal structure parameters
Technical Field
The invention relates to the technical field of plate diving geodynamics thermal numerical simulation, in particular to a numerical simulation analysis method for plate diving thermal structural parameters.
Background
The plate depression zone is an important link for material and energy circulation on the surface and deep part of the earth and is also a main zone for seismic energy release. The block dive is the expression form of convection of a mantle on the ground surface, low-density land shell substances in a dive land or ocean block are turned back into an ultrahigh pressure metamorphic zone, or molten fluid is developed under the high temperature of an overlying mantle to reach the base of the land shell to form a magma effect, and deep structures and substance interaction with each other with various characteristics are formed (a sympathy of luck musical instrument and the like, 2018).
At present, a plate diving thermal numerical model in the world is mainly of a two-dimensional structure, and the three-dimensional structure is less; the three-dimensional simulation of the plate temperature structure and the rock phase change calculation result is more deficient. The core bottleneck is the coding and modeling of the three-dimensional shape and the three-dimensional diving speed of the plate.
How to more accurately calculate the plate diving thermal structure and simultaneously realize the simulation expression based on the three-dimensional model result becomes a problem to be solved by practitioners of the same industry.
Disclosure of Invention
In view of the above, the present invention has been developed in order to provide a method for numerical simulation analysis of parameters of a plate dive thermal structure that overcomes or at least partially solves the above mentioned problems.
The embodiment of the invention provides a numerical simulation analysis method for a plate diving thermal structure parameter, which comprises the following steps:
calculating initial conditions of the plate boundary temperature according to the dive age and the plate free cooling model;
according to the depth and the diving speed of the plate, setting the regionalization and the speed field of the substances in the plate, and giving relevant parameters of each region of the model, wherein the relevant parameters comprise: density, viscosity, thermal conductivity, specific heat capacity, thermal expansion and thermal emissivity;
according to the initial condition of the boundary temperature and the related parameters, the mass, the temperature, the speed and the energy field of each dive step are calculated in an iterative mode by using a NaviStokes equation of conservation of mass, momentum and energy;
when the diving process is finished and the stable temperature state is reached, obtaining a final quality field, a temperature field, a speed field and an energy field;
comparing the earth surface heat flow observed values, and adjusting relevant parameters of each area of the given model to enable the temperature field to accord with the observed values:
calculating the water content, dehydration rate and rock phase change distribution result of the plate according to the temperature field and the speed field;
and carrying out three-dimensional drawing according to the calculated water content, dehydration rate, rock phase change distribution result and the temperature field.
Further, according to the initial condition of the boundary temperature and the related parameters, the mass, the temperature, the speed and the energy field of each diving step are calculated in an iterative mode by utilizing a NaviStokes equation of conservation of mass, momentum and energy; the method comprises the following steps:
constructing a three-dimensional numerical model:
conservation of mass:
Figure BDA0002808358440000021
conservation of momentum:
Figure BDA0002808358440000022
conservation of energy:
Figure BDA0002808358440000023
wherein rho is density and subscript s is adiabatic state; z is depth, v is velocity, P is pressure, x is displacement, i, j represents coordinate directions 1 and 2, τ is stress; ra0＝ρsg, g is the acceleration of gravity, and alpha is the thermal expansion rate; t is temperature and δ is a Crohn's function; cpIs a constant pressure specific heat capacity; t is time, k is thermal conductivity; eta is viscosity, HrIs the internal radiant heat energy per unit mass,
Figure BDA0002808358440000024
to strain rate, veRepresenting the surface erosion rate;
the initial temperature condition is calculated according to the temperatures of the overlying rock ring and the diving rock ring under the free cooling half space;
initial temperature of overburden rock circle:
Figure BDA0002808358440000031
initial temperature of nose-down rock ring:
Figure BDA0002808358440000032
wherein T is temperature, subscript 0 is upper mantle reference value, erf is error function, z is depth, TcontThe age of the overlying plate is in million years; k is thermal conductivity, CpAt a constant pressure specific heat capacity, tsIndicates age of nose-down block, g is density, α indicates thermal expansion rate, zdRepresenting the depth at which the bottom of the nose-down rockring reaches the reference temperature;
the boundary conditions of the numerical model are that the top T is 0, the upper covering plate and the soft flow ring on the front left side and the front right side are free sliding boundaries, the bottom boundary is a permeability boundary, and the rear side boundary is a curve convergence boundary;
starting from the initial condition of the plate boundary temperature, the convergence rate of the rear side boundary is the actual diving speed; the temperature boundary condition is that the top of the model is at a fixed temperature of 0 ℃, and the boundary condition of the side surfaces at the periphery is that the temperature gradient in the horizontal direction is zero; the bottom boundary adopts an external boundary fixed temperature condition 1600K;
and (4) performing iterative calculation of the mass, temperature, speed and energy fields of each diving step.
Further, the temperature stable state is that the temperature error is lower than a preset threshold value; the preset threshold value is 0.1% -10%.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
according to the numerical simulation analysis method for the plate diving thermal structure parameters, provided by the embodiment of the invention, based on the mass, momentum and energy conservation equation of Navigstokes, after the plate starts to dive from a sea ditch to the current shape and depth and reaches a stable state, model parameters are adjusted and modified so that the calculated value of the earth surface thermal flow reaches an observed value, and accordingly, the result of an optimal model is obtained. According to the method, on the basis of known plate depth and diving speed data, a three-dimensional temperature field, plate water content, dehydration rate and rock phase change distribution of a diving zone can be calculated and expressed. The calculation result can be further used for researching the earth deep temperature field, the rock phase change turning-back process, the underground fluid field of volcanic rock pulp and the investigation and development of metamorphic rock mineral products.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
fig. 1 is a flowchart of a numerical simulation analysis method for parameters of a plate diving thermal structure according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an embodiment of the present invention
FIG. 3 is a schematic rotation diagram of the Philippine sea block in southwest Japan; .
FIG. 4 is a schematic view of the squeeze and double dive of a marine panel under Kanto, Japan;
FIG. 5 is a schematic diagram of the pitch down temperature field and seismic profile in North and Central Chilean;
fig. 6 is a schematic diagram of the distribution of surface heat flow values of the Tibet plateau.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure 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 disclosure to those skilled in the art.
Referring to fig. 1, a method for numerically simulating and analyzing parameters of a plate diving thermal structure includes:
s10, calculating the initial condition of the plate boundary temperature according to the dive age and the plate free cooling model;
s20, setting regionalization and velocity fields of substances in the plate according to the plate depth and the diving speed, and giving relevant parameters of each region of the model, wherein the relevant parameters comprise: density, viscosity, thermal conductivity, specific heat capacity, thermal expansion and thermal emissivity;
s30, according to the boundary temperature initial condition and the related parameters, by using a NaviStokes equation of mass, momentum and energy conservation, iteratively calculating the mass, temperature, speed and energy field of each diving step;
s40, when the diving process is finished and the stable temperature state is achieved, obtaining a final quality field, a temperature field, a speed field and an energy field; the temperature stable state is that the temperature error is lower than a preset threshold value; the preset threshold is 0.1% -10%, and a proper threshold can be selected according to the temperature field data of a specific plate.
S50, comparing the earth surface heat flow observed values, adjusting relevant parameters of each area of the given model, and enabling the temperature field to accord with the observed values:
s60, calculating the water content, the dehydration rate and the rock phase change distribution result of the plate according to the temperature field and the speed field;
and S70, performing three-dimensional drawing according to the calculated water content, dehydration rate, rock phase change distribution result and the temperature field.
The embodiment of the invention solves the technical problem by using a three-dimensional numerical model based on seismic wave tomography data and plate three-dimensional dive speed, can calculate the plate dive thermal structure more accurately, and simultaneously realizes the simulation expression of a model result. On the basis of known plate depth (longitude, latitude and depth) and diving speed (longitude, latitude and speed) data, a three-dimensional temperature field of a diving zone, plate moisture content, dehydration rate and rock phase change distribution can be calculated and represented. The calculation result can be further used for researching the earth deep temperature field, the rock phase change turning-back process, the underground fluid field of volcanic rock pulp and the investigation and development of metamorphic rock mineral products.
The method is based on the mass, momentum and energy conservation equation of the Navistokes, and after the plate is dived from the sea ditch to the current shape and depth and reaches a stable state, model parameters are adjusted and modified so that the calculated value of the surface thermal flow reaches an observed value, and the result of the optimal model is obtained according to the observed value.
In order to facilitate the explanation of the technical scheme of the present invention, the indian plate at the bottom of Qinghai-Tibet plateau is taken as an example for the depression, and the detailed explanation is made.
A three-dimensional numerical model of the depression of indian plates at the bottom of the Qinghai-Tibet plateau is constructed, and the temperature structure, the distribution characteristics of high-temperature phase-change rocks and the dynamic characteristics of a mantle flow field of the depression plates are calculated, which is shown in figure 2.
A. Model code development
The thermal structure model has less consideration to irregular change of the plate shape in the direction of the sea ditch and neglects calculation errors existing when the diving angle is complex so far. Such as: when the dive speed direction is not parallel to the two-dimensional calculation section, the third-dimensional component of the speed brings dive increment or decrement but is not considered; when the plate shape shows a bend in a third dimension, the influence of adjacent physical fields of the calculated cross section on the cross section is ignored. The thermal structure models of Wada et al (2015) and Rosas et al (2015) also do not reflect the spatial three-dimensional variation in pitch velocity. Through the previous extended development research on numerical model code Stag3d (Tackley and Xie,2003), the three-dimensional shape and speed of the plane ocean plate are introduced as shown in fig. 3, and the plane ocean plate is applied to the thermal structure of the plane ocean plate plane including east japan (shown in fig. 4), northwest of the united states, north island of new zealand and north middle of chile (shown in fig. 5), so that the background fields including plane temperature structure, dehydration distribution, rock phase change process, plane interface earthquake and slow earthquake distribution are successfully obtained.
Wherein the southwest japanese model (fig. 3) focuses on simulating irregular dive of a plate, such as first rotation then dive of a philippine sea plate; the east japan model (fig. 4) focuses on analyzing the interactions between different plates, such as the extrusion and double dive of pacific and philippine sea plates under kanto in japan; the north-middle Chile model (fig. 5) focuses on the fine structure of the dive plate, including temperature field, velocity field, earthquake, slow glide and volcano distribution. These studies have addressed the key technology of two-dimensional to three-dimensional conversion, enabling dual three-dimensionality of the dive plate shape and speed. Wherein, the gray scale of the panel in FIG. 5 represents the size of the dive velocity, the cone represents the volcano, the sphere represents the Centennal directory of M >5.5 in 1900-2000 and the IRIS directory of M >0 in 2000-2010, the arrow represents the dive velocity field, and the circle represents the earthquake concentration area M8.
B. Slab shape and velocity data collection and import
The plate age (global seabed age database, Muller et al.2008), plate morphology (Slab2, Hayes et al.,2018, Science), plate relative motion speed (Morvel, DeMets et al.,2010) and the like of the depression interface of the India plate in Qinghai-Tibet plateau are introduced to construct the Indian plate rockwell area in depression, and reasonable density and viscosity setting are given. The length of the plate is continuously extended according to the diving speed in each calculation step until the plate crosses the model boundary at the side of the continental plate, and the temperature field is enabled to reach a stable state.
C. Model parameter selection and configuration
The model solution time can be set to 50-65 million years or other predecessor research results in conjunction with the dive process of the Tise ocean closure and the continental transformation. Following the principles of conservation of mass of incompressible masses, stokes' equations, and kinetic energy conservation, etc. (e.g., Gerya, 2010; Yoshioka and Murakami, 2007; Li, 2014; Li et al, 2012,2013,2014,2015,2016,2017,2019; Li loy sea, 2014; Li loy sea, etc., 2015; Chen, 2014; Chen et al, 2013,2014,2016,2017) and visco-plastic rheological property constitutive relations and viscosity coefficients (Ranalli,1995, etc.), the present invention can construct a three-dimensional numerical model:
conservation of mass:
Figure BDA0002808358440000071
conservation of momentum:
Figure BDA0002808358440000072
conservation of energy:
Figure BDA0002808358440000073
wherein rho is density and subscript s is adiabatic state; z is depth, v is velocity, P is pressure, x is displacement, i, j represents coordinate directions 1 and 2, τ is stress; ra0＝ρsg, g is the acceleration of gravity, and alpha is the thermal expansion rate; t is temperature and δ is a Crohn's function; cpIs a constant pressure specific heat capacity; t is time, k is thermal conductivity; eta is viscosity, HrIs the internal radiant heat energy per unit mass,
Figure BDA0002808358440000074
to strain rate, veRepresenting the surface erosion rate;
the initial temperature condition is calculated according to the temperatures of the overlying rock ring and the diving rock ring under the free cooling half space;
initial temperature of overburden rock circle:
Figure BDA0002808358440000075
initial temperature of nose-down rock ring:
Figure BDA0002808358440000076
wherein T is temperature, subscript 0 is upper mantle reference value, erf is error function, z is depth, TcontThe age of the overlying plate is in million years; k is thermal conductivity, CpAt a constant pressure specific heat capacity, tsIndicates age of nose-down block, g is density, α indicates thermal expansion rate, zdRepresenting the depth at which the bottom of the nose-down rockring reaches the reference temperature;
the boundary conditions of the numerical model are that the top T is 0, the upper covering plate and the soft flow ring on the front left side and the front right side are free sliding boundaries, the bottom boundary is a permeability boundary, and the rear side boundary is a curve convergence boundary;
starting from the initial condition of the plate boundary temperature, the convergence rate of the rear side boundary is the actual diving speed; the temperature boundary condition is that the top of the model is at a fixed temperature of 0 ℃, and the boundary condition of the side surfaces around the model is that the temperature gradient in the horizontal direction is zero (zero heat flow); the bottom boundary adopts an external boundary fixed temperature condition 1600K; can be dynamically changed according to model evolution. Differences between continental and marine plates, such as cooling age, thickness, rock composition and rheology, will be considered and discussed as an important aspect in this study as reasonable model parameters.
D. Model constraint conditions
As basic constraint conditions of the thermal structure model, a global earth surface heat flow observed value database obtained by means of BSR and the like and a global value (figure 6) obtained by Curie point depth derivation give reference values of surface heat flow in a dive zone. Furthermore, the tomography results have a reference effect on the dive sheet dewatering position and possible ascending magma paths etc. (Nabelek et al, 2009; Zhang et al, 2018, etc.); the geodetic survey provides a ground surface strain field and conjectures the deformation of the crust and the convection coupling of the crust mantle and the like (Klemperer, S.L., 2006 and the like), the space age distribution of the dive slab can be conjectured by the geomagnetism result, the evidence that the dive rock turns back and rises to the ground surface after the phase change can be provided by the geological research, and thus the phase distribution of metamorphic rocks such as the durite and the olivine can be estimated. The rear collision magma of Qinghai-Tibet plateau is acted to form potassium, ultra-potassium, volcanic rock, potassium adaptite, light granite and potassium calcium alkaline granite, and is intensively developed in the magma zone of Ozobottom structure and the south of Tibet.
In fig. 6, the left part is the global heat flow value derived from the curie point depth, the right part is the global earth surface heat flow value observed by means of BSR and the like, the dotted line represents the model area, the solid circle represents the observation point, the curve represents the equal-depth line of every 20km on the diving plate, and the arrow represents the diving speed of the indian plate.
E. Calculated output of model operation
Under the condition of geophysical parameter selection and constraint, numerical simulation calculation is carried out on high-performance parallel equipment through repeated debugging and optimal configuration, and the distribution rule of the India plate three-dimensional temperature field and the high-temperature phase change rock at the bottom of the Qinghai-Tibet plateau can be obtained. The output comprises the following steps: the system comprises an India plate depression three-dimensional temperature field, a vertical section depression temperature structure, a horizontal section depression temperature structure, an India plate three-dimensional temperature field database, an India plate depression high-temperature high-pressure metamorphic rock facies three-dimensional distribution, a vertical section high-temperature high-pressure metamorphic rock facies distribution, a horizontal section high-temperature high-pressure metamorphic rock facies distribution, an India plate high-temperature high-pressure metamorphic rock facies three-dimensional distribution database, a mantle flow three-dimensional distribution and the like.
Due to the fact that the precision of a two-dimensional dive thermal numerical model of predecessors is low, the result difference among different models is large, the temperature error is as high as 200-600 ℃, and the difference between the temperature error and an earth surface heat flow observation value is large, and the research of a dive zone deep thermal structure is stagnated. The failure to introduce three-dimensional plate shapes and velocity fields, while lacking three-dimensional representation, is one of the major causes of temperature errors. The method for analyzing the plate diving thermal structure parameters provided by the embodiment of the invention can overcome the bottleneck that a diving numerical model cannot introduce the three-dimensional plate shape and the three-dimensional diving speed, so that the objective correction of the three-dimensional diving thermal structure of the plate is possible, the calculated three-dimensional plate temperature field, the plate water content, the dehydration rate and the rock phase change distribution are obviously improved compared with the two-dimensional model, and the temperature error is reduced to be below 100 ℃. The underground fluid and rock phase change distribution calculated on the basis of the three-dimensional temperature structure has higher precision and reliability, and can provide reference for the investigation and development of metamorphic rock mineral products.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (3)

1. A numerical simulation analysis method for plate diving thermal structure parameters is characterized by comprising the following steps:
calculating initial conditions of the plate boundary temperature according to the dive age and the plate free cooling model;
according to the depth and the diving speed of the plate, setting the regionalization and the speed field of the substances in the plate, and giving relevant parameters of each region of the model, wherein the relevant parameters comprise: density, viscosity, thermal conductivity, specific heat capacity, thermal expansion and thermal emissivity;
according to the initial condition of the boundary temperature and the related parameters, the mass, the temperature, the speed and the energy field of each dive step are calculated in an iterative mode by using a NaviStokes equation of conservation of mass, momentum and energy;
when the diving process is finished and the stable temperature state is reached, obtaining a final quality field, a temperature field, a speed field and an energy field;
comparing the earth surface heat flow observed values, and adjusting relevant parameters of each area of the given model to enable the temperature field to accord with the observed values:
calculating the water content, dehydration rate and rock phase change distribution result of the plate according to the temperature field and the speed field;
and carrying out three-dimensional drawing according to the calculated water content, dehydration rate, rock phase change distribution result and the temperature field.
2. The method for numerical simulation analysis of thermal structure parameters of sheet metal dive according to claim 1, wherein the mass, temperature, velocity and energy fields of each dive step are iteratively calculated using mass, momentum and energy conservation navistokes equations according to the boundary temperature initial conditions and the related parameters; the method comprises the following steps:
constructing a three-dimensional numerical model:
conservation of mass:
Figure FDA0002808358430000011
conservation of momentum:
Figure FDA0002808358430000012
conservation of energy:
Figure FDA0002808358430000013
wherein rho is density and subscript s is adiabatic state; z is depth, v is velocity, P is pressure, x is displacement, i, j represents coordinate directions 1 and 2, τ is stress; ra0＝ρsg, g is the acceleration of gravity, and alpha is the thermal expansion rate; t is temperature and δ is a Crohn's function; cpIs a constant pressure specific heat capacity; t is time, k is thermal conductivity; eta is viscosity, HrIs the internal radiant heat energy per unit mass,
Figure FDA0002808358430000021
to strain rate, veRepresenting the surface erosion rate;
the initial temperature condition is calculated according to the temperatures of the overlying rock ring and the diving rock ring under the free cooling half space;
initial temperature of overburden rock circle:
Figure FDA0002808358430000022
initial temperature of nose-down rock ring:
Figure FDA0002808358430000023
wherein T is temperature, subscript 0 is upper mantle reference value, erf is error function, z is depth, TcontThe age of the overlying plate is in million years; k is thermal conductivity, CpAt a constant pressure specific heat capacity, tsIndicates age of nose-down block, g is density, α indicates thermal expansion rate, zdRepresenting the depth at which the bottom of the nose-down rockring reaches the reference temperature;
the boundary conditions of the numerical model are that the top T is 0, the upper covering plate and the soft flow ring on the front left side and the front right side are free sliding boundaries, the bottom boundary is a permeability boundary, and the rear side boundary is a curve convergence boundary;
starting from the initial condition of the plate boundary temperature, the convergence rate of the rear side boundary is the actual diving speed; the temperature boundary condition is that the top of the model is at a fixed temperature of 0 ℃, and the boundary condition of the side surfaces at the periphery is that the temperature gradient in the horizontal direction is zero; the bottom boundary adopts an external boundary fixed temperature condition 1600K;
and (4) performing iterative calculation of the mass, temperature, speed and energy fields of each diving step.
3. A method for numerical simulation analysis of thermal structural parameters of a panel diving according to claim 1, characterized in that said temperature steady state is a temperature error below a preset threshold; the preset threshold value is 0.1% -10%.
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