gprMax3.0用户指南：探地雷达数值模拟

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"gprMax3.0原版英文说明书，由CraigWarren和AntonisGiannopoulos编写，发布于2017年3月3日，适用于探地雷达数值模拟学习者，涵盖安装、基本原理、使用方法及软件特性等内容。" gprMax是一款专门用于地面穿透雷达（Ground-Penetrating Radar, GPR）数值模拟的开源软件。这份3.0版本的用户指南详细介绍了如何操作和理解gprMax。 1. **gprMax是什么？** gprMax是一个基于FDTD（Finite-Difference Time-Domain）方法的GPR数值模拟工具，它允许用户模拟地下介质中的电磁波传播，帮助理解GPR数据并进行地质结构分析。 2. **软件包概述** gprMax包含了安装程序、模拟模型构建工具以及结果解析和可视化功能。用户可以根据需求创建复杂的地下环境模型，并设置不同的材料属性、源信号和边界条件。 3. **安装** 安装过程简单明了，用户按照指南中的步骤即可完成，包括下载软件包、解压缩和运行安装程序。 4. **启动gprMax** 安装完成后，用户可以按照指导启动gprMax，进行模型设置和模拟运行。软件界面直观，适合初学者和高级用户。 5. **更新gprMax** 用户可以通过内置的更新功能获取最新的软件补丁和功能升级，保持软件版本的最新状态。 6. **软件特点** - **新功能和变化**：用户可以在这一部分了解每个新版本引入的改进和新特性。 - **关键特性**：包括FDTD算法、吸收边界条件、对象构造命令、源信号定义、PML（Perfectly Matched Layers）边界条件等。 7. **GPR建模指导** - **基本概念**：解释了GPR的基本工作原理和电磁波在地下传播的物理现象。 - **坐标系统和约定**：描述了在gprMax中设定坐标系统的方式以及相关的模拟规则。 - **空间离散化**：讨论了将连续空间转化为离散网格的过程，用于数值计算。 - **吸收边界条件**：用于减少模拟边界对结果的影响，模拟无限大空间。 8. **输入文件命令** gprMax使用文本输入文件定义模型参数，包括基本命令、通用命令、材料定义、对象构造、源和输出设置以及PML设置。 9. **输出数据** 模拟完成后，软件可以生成多种输出数据，如场值、几何信息、A扫描（单通道数据）、B扫描（横截面图像）和天线参数。 10. **绘图** gprMax内置了数据可视化功能，能够绘制A扫描、B扫描，显示天线参数和内置波形，便于用户分析和解释结果。 11. **文件工具** 提供了一些实用脚本，如旧版输入文件转换和输出文件合并，方便用户管理和处理模拟数据。 12. **输入文件脚本** 用户可以利用Python脚本语言自定义输入文件，包括常量/变量定义和输入命令函数，增强了软件的灵活性和可编程性。 13. **并行执行** gprMax支持OpenMP和MPI两种并行计算模式，利用多核处理器或分布式计算资源加速模拟运算。这份gprMax3.0的用户手册为用户提供了一个全面的参考，无论你是初次接触GPR模拟还是寻求更高级的建模技巧，都能从中受益。通过深入学习和实践，你将能够运用gprMax进行精确的地下环境探测和分析。

gprMax User Guide, Release 3.0.18

Realistic soils, heterogeneous objects and rough surfaces

The inclusion of improved models of soils is important for many GPR simulations. gprMax can now be used to

create soils with more realistic dielectric and geometrical properties. A semi-empirical model, initially suggested

by [DOB1985], is used to describe the dielectric properties of the soil. The model relates relative permittivity of

the soil to bulk density, sand particle density, sand fraction, clay fraction and water volumetric fraction. Using this

approach, a more realistic soil with a stochastic distribution of the aforementioned parameters can be modelled.

The real and imaginary parts of this semi-empirical model can be approximated using a multi-pole Debye function

plus a conductive term. This can now be achieved in gprMax using the new dispersive material functionality. For

further details see the material commands section.

Fractals are scale invariant functions which can express the topography of the earth for a wide range of scales

with sufﬁcient detail [TUR1987]. For this reason fractals have been chosen to represent the topography of soils.

Fractals can be generated by the convolution of Gaussian noise with an inverse Fourier transform of

𝑘𝑏

, where

𝑘 is the wavenumber and 𝑏 is a constant related to the fractal dimension [TUR1997]. gprMax can now generate

heterogeneous volumes (boxes) with realistic soil properties that can have rough surfaces applied. For further

details see the fractal object building commands section.

Fractal correlated noise [TUR1997] is used to describe the stochastic distribution of the properties of soils. This

approach has been chosen because it has been shown that soil-related environmental properties frequently obey

fractal laws [BUR1981], [HILL1998]. For further details see the material commands section and the fractal object

building commands section.

Library of antenna models

gprMax now includes Python modules with pre-deﬁned models of antennas that behave similarly to commercial

antennas [WAR2011]. Currently models of antennas similar to Geophysical Survey Systems, Inc. (GSSI) (http:

//www.geophysical.com) 1.5 GHz (Model 5100) antenna, and MALA Geoscience (http://www.malags.com/) 1.2

GHz antenna are included. By taking advantage of Python scripting in input ﬁles, using such complex structures

in a model is straightforward without having to be built step-by-step by the user. For further details see the Python

section.

Anisotropic materials

It is possible to specify objects that have diagonal anisotropy which allows materials such as wood and ﬁbre-

reinforced composites, often imaged with GPR, to be more accurately modelled. Standard isotropic objects specify

one material identiﬁer that deﬁnes the same properties in x, y, and z directions. However, every volumetric object

building command can also be speciﬁed with three material identiﬁers, which allows properties for the x, y, and z

directions to be separately deﬁned.

Dielectric smoothing

At the boundaries between different materials in a model there is the question of what electric and magnetic

material properties to use?

• Should the last object to be deﬁned at that location dictate the electric and magnetic properties?

• Should an average set of electric and magnetic properties of the materials of the objects that share that

location be used?

This latter option is often referred to as dielectric smoothing and has been shown to result in more accurate

simulations [LUE1994] [BOU1996] [WHI2009]. To address this question gprMax includes an option to turn

dielectric smoothing on or off for volumetric object building commands. The default behaviour (if no option is

speciﬁed) is for dielectric smoothing to be on. The option can be speciﬁed with a single character y (on) or n (off)

given after the material identiﬁer in each object command. When dielectric smoothing is on gprMax calculates

the arithmetic mean of the electric and magnetic properties of the surrounding Yee cells, to use for the single Yee

cell edge (boundary) of interest.

12 Chapter 2. Software Features

gprMax User Guide, Release 3.0.18

Perfectly Matched Layer (PML) boundary conditions

With increased research into quantitative information from GPR, it has become necessary for models to be able to

have more efﬁcient and better-performing Perfectly Matched Layer (PML) absorbing boundary conditions. Since

2005 gprMax has featured PML absorbing boundary conditions based on the uniaxial PML (UPML) [GED1998]

formulation. A PML based on a recursive integration approach to the complex frequency shifted (CFS) PML

[GIA2012] has been adopted in the new version of gprMax. A general formulation of this RIPML, which can be

used to develop any order of PML, has been used to implement ﬁrst and second order CFS stretching functions.

One of the attractions of the RIPML is that it is easily applied as a correction to the ﬁeld quantities after the

complete FDTD grid has been updated using the standard FDTD update equations. gprMax now offers the ability

(for advanced users) to customise the parameters of the PML which allows its performance to be better optimised

for speciﬁc applications. Additionally, since the RIPML is media agnostic it can be used without change to

problems involving dispersive and anisotropic materials. For further details see the PML commands section.

Open source, robust, ﬁle formats

Alongside improvements to the input ﬁle there is a new output ﬁle format – HDF5 (http://www.hdfgroup.org/

HDF5/) – to manage the larger and more complex data sets that are being generated. HDF5 is a robust, portable

and extensible format with a number of free readers available. For further details see the output ﬁle section.

In addition, the Visualization Toolkit (VTK) (http://www.vtk.org) is being used for improved handling and viewing

of the detailed 3D FDTD geometry meshes. The VTK is an open-source system for 3D computer graphics,

image processing and visualisation. It also has a number of free readers available including Paraview (http:

//www.paraview.org). For further details see the geometry view command.

2.2. Key features 13

CHAPTER 3

Guidance on GPR modelling

Basic concepts

This section discusses some basic concepts of GPR modelling. gprMax solves Maxwell’s equations using the

Finite-Difference Time-Domain (FDTD) method. Detailed information about the use of FDTD for GPR modelling

can be found in [GIA1997] and general information on the FDTD method in [KUN1993] and [TAF2005].

All electromagnetic phenomena, on a macroscopic scale, are described by the well-known Maxwell’s equations.

These are ﬁrst order partial differential equations which express the relations between the fundamental electro-

magnetic ﬁeld quantities and their dependence on their sources.

∇ × E = −

𝜕B

𝜕𝑡

∇ × H =

𝜕D

𝜕𝑡

+ J

∇ · B = 0

∇ · D = 𝑞

𝑣

where 𝑡 is time (seconds) and 𝑞

𝑣

is the volume electric charge density (coulombs/cubic metre). In Maxwell’s

equations, the ﬁeld vectors are assumed to be single-valued, bounded, continuous functions of position and time.

In order to simulate the GPR response from a particular target or set of targets the above equations have to be

solved subject to the geometry of the problem and the initial conditions.

The nature of the GPR forward problem classiﬁes it as an initial value – open boundary problem. This means

that in order to obtain a solution you have to deﬁne an initial condition (i.e. excitation of the GPR transmitting

antenna) and allow for the resulting ﬁelds to propagate through space reaching a zero value at inﬁnity since, there

is no speciﬁc boundary which limits the problem’s geometry and where the electromagnetic ﬁelds can take a

predetermined value. Although the ﬁrst part is easy to accommodate (i.e. speciﬁcation of the source), the second

part cannot be easily tackled using a ﬁnite computational space.

The FDTD approach to the numerical solution of Maxwell’s equations is to discretize both the space and time

continua. Thus the discretization spatial ∆𝑥, ∆𝑦 and ∆𝑧 and temporal ∆𝑡 steps play a very signiﬁcant role –

since the smaller they are the closer the FDTD model is to a real representation of the problem. However, the

values of the discretization steps always have to be ﬁnite, since computers have a limited amount of storage and

ﬁnite processing speed. Hence, the FDTD model represents a discretized version of the real problem and is of

limited size. The building block of this discretized FDTD grid is the Yee cell [YEE1966] named after Kane Yee

who pioneered the FDTD method. This is illustrated for the 3D case in Fig. 3.1.

gprMax User Guide, Release 3.0.18

Fig. 3.1: 3D FDTD Yee cell

By assigning appropriate constitutive parameters to the locations of the electromagnetic ﬁeld components complex

shaped targets can be included easily in the models. However, objects with curved boundaries are represented

using a staircase approximation.

The numerical solution is obtained directly in the time domain by using a discretized version of Maxwell’s curl

equations which are applied in each FDTD cell. Since these equations are discretized in both space and time the

solution is obtained in an iterative fashion. In each iteration the electromagnetic ﬁelds advance (propagate) in

the FDTD grid and each iteration corresponds to an elapsed simulated time of one ∆𝑡. Hence by specifying the

number of iterations you can instruct the FDTD solver to simulate the ﬁelds for a given time window.

The price you have to pay for obtaining a solution directly in the time domain using the FDTD method is that

the values of ∆𝑥, ∆𝑦, ∆𝑧 and ∆𝑡 can not be assigned independently. FDTD is a conditionally stable numerical

process. The stability condition is known as the CFL condition after the initials of Courant, Freidrichs and Lewy

and is given by,

∆𝑡 ≤

𝑐



(Δ𝑥)

(Δ𝑦)

(Δ𝑧)

where 𝑐 is the speed of light. Hence ∆𝑡 is bounded by the values of ∆𝑥, ∆𝑦 and ∆𝑧. The stability condition for

the 2D case is easily obtained by letting ∆𝑧 −→ ∞.

One of the most challenging issues in modelling open boundary problems, such as GPR, is the truncation of the

computational domain at a ﬁnite distance from sources and targets where the values of the electromagnetic ﬁelds

can not be calculated directly by the numerical method applied inside the model. Hence, an approximate condition

known as absorbing boundary condition (ABC) is applied at a sufﬁcient distance from the source to truncate and

therefore limit the computational space. The role of this ABC is to absorb any waves impinging on it, hence

simulating an unbounded space. The computational space (i.e the model) limited by the ABCs should contain

all important features of the model such as sources and output points and targets. Fig. 3.2 illustrates this basic

difference between the problem to be modelled and the actual FDTD modelled space.

It is assumed that the half-space which contains the target(s) is of inﬁnite extent. Therefore, the only reﬂected

waves will be the ones originating from the target. In cases where the host medium is not of inﬁnite extent (e.g.

16 Chapter 3. Guidance on GPR modelling

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