PyLith 2.2.1 用户手册：地球动力学数值模拟

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"PyLith 2.2.2 用户手册是针对地球动力学数值模拟研究的专业指南，由 Brad Aagaard, Matthew Knepley 和 Charles Williams 编写，并在 geodynamics.org 发布。手册涵盖了软件的使用、文档约定、引用、支持以及对 PyLith 设计和有限元方法的详细解释。" PyLith 是一款用于地球动力学数值模拟的软件，主要服务于科学研究和教育领域。这个用户手册详细介绍了 PyLith 的各个方面，包括它的工作流程、设计原理和解决方案方法，以便于研究人员理解和应用。在介绍部分，手册提供了关于 PyLith 版本 2.2.1 的新特性、历史背景以及 PyLith 的基本工作流程。PyLith 的设计基于 Pyre 框架，利用了 PETSc（Portable, Extensible Toolkit for Scientific Computation）库来实现高效的并行计算。这使得 PyLith 能够处理大规模的地球动力学模型。在理论部分，手册详细讲解了控制方程，尤其是弹性方程的推导，包括索引记号和向量记号两种表示方式。对于有限元方法的阐述，不仅涉及索引记号的表述，也包括向量记号的表达，从而帮助用户理解如何将弹性方程转化为有限元形式。对于静态问题的求解方法，手册提供了详细步骤，而动态问题的解决方案则进一步涉及到时间积分和波动方程的处理。这些内容对于理解 PyLith 如何模拟地壳的变形和地震动力学过程至关重要。此外，手册还提到了文档的约定，如命令行参数、文件名和目录的处理、Unix Shell 命令的使用，以及配置文件的摘录，这些信息对于实际操作 PyLith 是非常实用的。同时，手册鼓励用户提供反馈，以持续改进软件和文档。 PyLith 2.2.2 用户手册是一部全面的参考指南，对于使用 PyLith 进行地球动力学数值模拟的研究人员来说，它提供了深入的理论知识和实践指导，帮助他们有效地进行复杂地质现象的模拟分析。

xii CONTENTS

C File Formats 267

C.1 PyLith Mesh ASCII Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

C.2 SimpleDB Spatial Database Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

C.2.1 Spatial Database Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

C.2.1.1 Cartesian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

C.2.1.2 Geographic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

C.2.1.3 Geographic Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

C.2.1.4 Geographic Local Cartesian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

C.3 SimpleGridDB Spatial Database Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

C.4 TimeHistory Database Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

C.5 User-Speciﬁed Time-Step File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

C.6 PointsList File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

D Alternative Material Model Formulations 275

D.1 Viscoelastic Formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

D.1.1 Effective Stress Formulation for a Linear Maxwell Viscoelastic Material . . . . . . . . . . . . . . . . . . 275

E Analytical Solutions 277

E.1 Traction Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

E.1.1 Solutions Using Polynomial Stress Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

E.1.2 Constant Traction Applied to a Rectangular Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

F PyLith Software License 281

List of Figures

1.1 Workﬂow involved in going from geologic structure to problem analysis. . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 PyLith dependencies. PyLith makes direct use of several other packages, some of which have their own depen-

dencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Pyre Architecture. The integration framework is a set of cooperating abstract services. . . . . . . . . . . . . . . . 4

3.1 Guide for selecting the appropriate installation choice based on a hardware and intended use. The installation

options are discussed in more detail in the following sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 PyLith requires a ﬁnite-element mesh (three different mechanisms for generating a mesh are currently sup-

ported), simulation parameters, and spatial databases (deﬁning the spatial variation of various parameters).

PyLith writes the solution output to either VTK or HDF5/Xdmf ﬁles, which can be visualized with ParaView

or Visit. Post-processing is generally done using the HDF5 ﬁles with Python or Matlab scripts. . . . . . . . . . . 28

4.2 Linear cells available for 2D problems are the triangle (left) and the quadrilateral (right). . . . . . . . . . . . . . . 31

4.3 Linear cells available for 3D problems are the tetrahedron (left) and the hexahedron (right). . . . . . . . . . . . . 32

4.4 Global uniform mesh reﬁnement of 2D and 3D linear cells. The blue lines and orange circles identify the edges

and vertices in the original cells. The purple lines and green circles identify the new edges and vertices added

to the original cells to reﬁne the mesh by a factor of two. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.5 General layout of a PyLith HDF5 ﬁle. The orange rectangles with rounded corners identify the groups and

the blue rectangles with sharp corners identify the datasets. The dimensions of the data sets are shown in

parentheses. Most HDF5 ﬁles will contain either vertex_fields or cell_fields but not both. . . . . . . 50

4.6 Screenshot of PyLith Parameter Viewer in web browser upon startup. . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.7 Screenshot of Version tab of the PyLith Parameter Viewer with sample JSON parameter ﬁle. . . . . . . . . . . . 57

4.8 Screenshot of Parameters tab of the PyLith Parameter Viewer with sample JSON parameter ﬁle before select-

ing a component in the left panel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

4.9 Screenshot of Parameters tab of the PyLith Parameter Viewer with sample JSON parameter ﬁle with the

z_neg facility selected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.1 Spring-dashpot 1D representations of the available 3D elastic and 2D/3D viscoelastic material models for

PyLith. The top model is a linear elastic model, the middle model is a Maxwell model, and the bottom model

is a generalized Maxwell model. For the generalized Maxwell model, λ and µ

tot

are speciﬁed for the entire

model, and then the ratio µ

/µ

tot

is speciﬁed for each Maxwell model. For the power-law model, the linear

dashpot in the Maxwell model is replaced by a nonlinear dashpot obeying a power-law. . . . . . . . . . . . . . . 69

6.1 Orientation of a fault surface in 3D, where φ denotes the angle of the fault strike, δ denotes the angle of the

fault dip, and λ the rake angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

xiii

xiv LIST OF FIGURES

6.2 Sign conventions associated with fault slip. Positive values are associated with left-lateral, reverse, and fault

opening motions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.3 Example of cohesive cells inserted into a mesh of triangular cells. The zero thickness cohesive cells control slip

on the fault via the relative motion between the vertices on the positive and negative sides of the fault. . . . . . . 94

6.4 Example of how faults with buried edges must be described with two sets of vertices. All of the vertices on

the fault are included in the fault group; the subset of vertices along the buried edges are included in the

fault_edge group. In 2-D the fault edges are just a single vertex as shown in Figure 6.3 on page 94(a). . . . . 94

7.1 Mesh composed of two linear triangular cells used in the example problems. . . . . . . . . . . . . . . . . . . . . . 114

7.2 Color contours and vectors of displacement for the axial displacement example using a mesh composed of two

linear triangular cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7.3 Color contours and vectors of displacement for the shear displacement example using a mesh composed of two

linear triangular cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.4 Color contours and vectors of displacement for the kinematic fault example using a mesh composed of two

linear triangular cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.5 Mesh composed of two bilinear quadrilateral cells used for the example problems. . . . . . . . . . . . . . . . . . 118

7.6 Color contours and vectors of displacement for the axial displacement example using a mesh composed of two

bilinear quadrilateral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.7 Color contours and vectors of displacement for the shear displacement example using a mesh composed of two

bilinear quadrilateral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

7.8 Color contours and vectors of displacement for the kinematic fault example using a mesh composed of two

bilinear quadrilateral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.9 Color contours and vectors of displacement for the axial traction example using a mesh composed of two

bilinear quadrilateral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.10 Mesh composed of two linear tetrahedral cells used for example problems. . . . . . . . . . . . . . . . . . . . . . . 123

7.11 Color contours and vectors of displacement for the axial displacement example using a mesh composed of two

linear tetrahedral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.12 Color contours and vectors of displacement for the kinematic fault example using a mesh composed of two

linear tetrahedral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.13 Mesh composed of two trilinear hexahedral cells used for the example problems. . . . . . . . . . . . . . . . . . . 126

7.14 Color contours and vectors of displacement for the axial displacement example using a mesh composed of two

trilinear hexahedral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7.15 Color contours and vectors of displacement for the shear displacement example using a mesh composed of two

trilinear hexahedral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

7.16 Color contours and vectors of displacement for the kinematic fault example using a mesh composed of two

trilinear hexahedral cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7.17 Mesh composed of two linear tetrahedral cells in a georeferenced coordinate system used for the example

problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.18 Color contours and vectors of displacement for the kinematic fault example using a mesh composed of two

linear tetrahedral cells in a georeferenced coordinate system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

7.19 Mesh composed of linear tetrahedral cells generated by LaGriT used for the example problems. The different

colors represent the different materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

LIST OF FIGURES xv

7.20 Color contours and vectors of displacement for the axial displacement example using a mesh composed of

linear tetrahedral cells generated by LaGriT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

7.21 Color contours and vectors of displacement for the kinematic fault example using a mesh composed of linear

tetrahedral cells generated by LaGriT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.22 Mesh composed of trilinear hexahedral cells generated by CUBIT used for the suite of example problems. The

different colors represent the two different materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.23 Displacement ﬁeld for example step01 visualized using ParaView. The mesh has been distorted by the computed

displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . . . . . . . . . . . 143

7.24 Displacement ﬁeld for example step02 visualized using ParaView. The mesh has been distorted by the computed

displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . . . . . . . . . . . 145

7.25 Displacement ﬁeld for example step03 visualized using ParaView. The mesh has been distorted by the computed

displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . . . . . . . . . . . 146

7.26 Displacement ﬁeld for example step04 at t = 200 years visualized using ParaView. The mesh has been distorted

by the computed displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . 149

7.27 Displacement ﬁeld for example step05 at t = 40 years visualized using ParaView. The mesh has been distorted

by the computed displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . 150

7.28 Displacement ﬁeld for example step06 at t = 300 years visualized using ParaView. The mesh has been distorted

by the computed displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . 153

7.29 Displacement ﬁeld (color contours) and velocity ﬁeld (vectors) for example step07 at t = 300 years visualized

using ParaView. The mesh has been distorted by the computed displacements (magniﬁed by 500), and the

vectors show the computed velocities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

7.30 The XY-component of strain (color contours) and displacement ﬁeld (vectors) for example step08 at t = 150

years visualized using ParaView. For this visualization, we loaded both the step08-lower_crust.xmf

and step08-upper_crust.xmf ﬁles to contour the strain ﬁeld, and superimposed on it the displacement

ﬁeld vectors from step08.xmf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

7.31 The XY-component of strain (color contours) and displacement ﬁeld (vectors) for example step09 at t = 150

years visualized using ParaView. For this visualization, we loaded both the step09-lower_crust.xmf

and step09-upper_crust.xmf ﬁles to contour the strain ﬁeld, and superimposed on it the displacement

ﬁeld vectors from step09.xmf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.32 Magnitude of tractions on the fault for example step10 visualized using ParaView. . . . . . . . . . . . . . . . . . 160

7.33 Magnitude of tractions on the fault for example step10 visualized using ParaView. Vectors of fault slip are

also plotted. Note that PyLith outputs slip in the fault coordinate system, so we transform them to the global

coordinate system using the Calculator in ParaView. A more general approach involves outputing the fault

coordinate system information and using these ﬁelds in the Calculator. . . . . . . . . . . . . . . . . . . . . . . . . 161

7.34 Displacement ﬁeld for example step12 at t = 200 years visualized using ParaView. The mesh has been distorted

by the computed displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . 162

7.35 Displacement ﬁeld for example step13 at t = 200 years visualized using ParaView. The mesh has been distorted

by the computed displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . 163

7.36 Displacement ﬁeld for example step14 at t = 200 years visualized using ParaView. The mesh has been distorted

by the computed displacements (magniﬁed by 500), and the vectors show the computed displacements. . . . . . 164

7.37 Displacement ﬁeld for example step15 at t = 200 years visualized using ParaView. The z-component of the

displacement ﬁeld is shown with the color contours, and the vectors show the computed displacements. . . . . . 166

7.38 Stress ﬁeld (xx-component) for example step16 at t = 200 years visualized using ParaView. Note that for this

example, Stress_xx = Stress_yy = Stress_zz, and there is no vertical displacement throughout the simulation.

Also note that the stresses appear as four layers since we have used CellFilterAvg for material output. . . . . . . 167

xvi LIST OF FIGURES

7.39 Displacement ﬁeld for example step17 at t = 200 years visualized using ParaView. The z-component of the

displacement ﬁeld is shown with the color contours, and the vectors show the computed displacements. Note

the larger displacements compared with example step15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

7.40 Displacement ﬁeld for example step18 visualized using ParaView. The vectors show the displacement ﬁeld

while the colors in the wireframe correspond to the z-component of the displacement ﬁeld. . . . . . . . . . . . . 170

7.41 Stress ﬁeld (zz-component) for example step19 at t = 200 years visualized using ParaView. The stresses appear

as four layers since we have used CellFilterAvg for material output. . . . . . . . . . . . . . . . . . . . . . . . . . . 171

7.42 Displacement magnitude for example step20 visualized using ParaView. . . . . . . . . . . . . . . . . . . . . . . . 172

7.43 A slip impulse and the resulting point displacement responses visualized using ParaView. . . . . . . . . . . . . . 174

7.44 Cartoon of subduction zone example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

7.45 Diagram of fault slip and boundary conditions for each step in the subduction zone example. . . . . . . . . . . . 175

7.46 Variable resolution ﬁnite-element mesh with triangular cells. The nominal cell size increases at a geometric

rate of 1.2 away from the region of coseismic slip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

7.47 Solution for Step 1. The colors indicate the magnitude of the displacement, and the deformation is exaggerated

by a factor of 1000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

7.48 Solution for Step 2 at 100 years. The colors indicate the magnitude of the displacement, and the deformation is

exaggerated by a factor of 1000. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

7.49 Solution for Step 3 at 150 years (immediately following the earthquake rupture). The colors indicate the mag-

nitude of the displacement, and the deformation is exaggerated by a factor of 1000. . . . . . . . . . . . . . . . . . 179

7.50 Solution for Step 4. The colors indicate the magnitude of the displacement. . . . . . . . . . . . . . . . . . . . . . 180

7.51 Solution for Step 5 at the end of the simulation. The colors indicate the magnitude of the x-displacement

component and the deformation has been exaggerated by a factor of 10,000. . . . . . . . . . . . . . . . . . . . . . 182

7.52 Cumulative slip as a function of time and depth in Step 5. The red lines indicate slip every 10 time steps. . . . . 182

7.53 Solution for Step 6 at the end of the simulation. The colors indicate the magnitude of the x-displacement

component and the deformation has been exaggerated by a factor of 10,000. . . . . . . . . . . . . . . . . . . . . . 184

7.54 Cumulative slip as a function of time and depth in Step 6. The red lines indicate slip every 10 time steps. . . . . 184

7.55 Domain for shear wave propagation in a 8.0 km bar with 400 m cross-section. We generate a shear wave via

slip on a fault located in the middle of the bar while limiting deformation to the transverse direction. . . . . . . . 185

7.56 Mesh composed of triangular cells generated by CUBIT used for the example problem. . . . . . . . . . . . . . . 186

7.57 Displacement ﬁeld in the bar at 3.0 s. Deformation has been exaggerated by a factor of 800. . . . . . . . . . . . . 187

7.58 Mesh composed of hexahedral cells generated by CUBIT used for the example problem. . . . . . . . . . . . . . . 188

7.59 Displacement ﬁeld in the bar at 3.0 s. Deformation has been exaggerated by a factor of 800. . . . . . . . . . . . . 188

7.60 Velocity ﬁeld in the bar at 3.0 s for the static friction fault constitutive model. Deformation has been exaggerated

by a factor of 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

7.61 Velocity ﬁeld in the bar at 3.0 s for the slip-weakening friction fault constitutive model. Deformation has been

exaggerated by a factor of 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

7.62 Velocity ﬁeld in the bar at 3.0 s for the rate- and state-friction fault constitutive model. Deformation has been

exaggerated by a factor of 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

7.63 Mesh composed of tetrahedral cells generated by LaGriT used for the example problem. . . . . . . . . . . . . . . 192

7.64 Displacement ﬁeld in the bar at 3.0 s. Deformation has been exaggerated by a factor of 800. . . . . . . . . . . . . 193

7.65 Mesh composed of hexahedral cells generated by CUBIT used for the example problem. . . . . . . . . . . . . . . 194

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