A Simple Model Generator for Radar Sounding Applications Based on Stochastic Media Model and gprMax

Ground penetrating radar (GPR), or more generically called radar sounding, is an established technique for probing subsurface objects and sublayer structures. Simulating pre-constructed models and comparing with the real-world observations can contribute to retrieve the geometrical and physical properties of subsurface objects. However, most GPR simulations are limited to geometrically simple models with homogeneous physical properties of subsurface media which are generally unable to represent the real-world situations. In this paper, we develop a simple model generator by combining the stochastic media model and gprMax, an open-source software for electromagnetic simulations, to jointly generate models with geometrically random fragments, which are forward models with minimum human intervention. These easily prepared and simulated models can enrich the model training datasets which can be further utilized in machine learning for GPR retrieval algorithms.


Introduction
As one of the most effective non-destructive techniques, radar has been widely used for many diverse applications in geophysical fields.Examples include Ground Penetrating Radar (GPR) for assessing buried infrastructures [1], Ice Sounding Radar (ISR) for locating potential diverse hypersaline subglacial hydrological environment [2], and Lunar Penetrating Radar (LPR) onboarded by the "Yutu" rover to study the lunar sublayer structures and regolith properties [3], all of which are based on collected radargrams.However, the understanding of how electromagnetic waves propagate through complex subsurface medium and the interpretation of radargrams for the subsurface targets is quite challenging although certain prior knowledge may be available.Traditionally, forward modeling is widely used to assist the understanding of radargram.For example, gprMax [4], an open-source software, was developed to simulate electromagnetic wave propagation in the subsurface domain.Although it is capable of building 2D and 3D heterogeneous models, it relies on the random distribution of water content which leads to heterogeneous dielectric constant of underground soils following the Peplinski model [5].This simplified approximation works fine with the GPR detection on Earth, however, strictly speaking, it cannot be applied to the lunar regolith modelling because lunar soil arguably does not contain any water.Given this situation, we develop a simple model generator that combines stochastic medium modelling with gprMax, to jointly create models with subsurface fragments with random shapes and distributions, which can realistically represent lunar subsurface environment.Furthermore, we design a graphical user interface (GUI) in MATLAB which can handle key geometrical and dielectric settings of the random fragments, and automatically proceed and interact with gprMax.

Principles for the random model generation
Any complicated subsurface intrusive fragments can be split into several simple composition blocks.In this study, our generator is designed to produce stochastic models contain both the creation of random shapes and the process of setting their random distribution.
Circle is a uniform symmetrical pattern determined by the center coordinate and radius, which specifies its location and size, respectively.Therefore, our generator first produces random circles with the realistic radius and density range determined by the real-world applications.We define all the random numbers following the pseudo-random number generator Mersenne Twister (MT) algorithm, which is based on the twisted generalized feedback shift register (TGFSR).

Random circle.
The generator creates the evenly spaced points in the interval of the given radius range.For each radius, we use the MT algorithm to set the random number and x-y coordinates of the circle, so as to assure that all circles are distributed uniformly.

Base shapes.
Based on the circle shape, we define another three base shapes, i.e., triangle, rectangle, and sector, as shown in Figure 1(a).In every random circle, we consider the centre as the origin of the polar coordinates, with the polar axis horizontal.From 0 to 2π, the generator generates different angles to form noncoincident points, which defines the corresponding shape.Provided with the random location and radius, the regenerated random distributions of triangle, rectangle, and sector are displayed in Figure 1(b).

Multi-shape combination.
Based on the random distributions of our base shapes of non-overlapped ones or overlapped ones, in order to make sure of the randomness of multi-shape combinations, we first sample k unique observations uniformly for each type of base shapes and then we generate the base shape inside the radius of those circles.It is noted that the number k is generated by MT algorithm and the complexity of the entire model may vary according to the overlapping degree, such as, overlapping area and overlapping angle.By doing so, the combination of random shapes can be more complex, which is intentionally to be more realistic, as illustrated in Figure 1(c).Provided with the random location and radius, the regenerated random distributions of triangle, rectangle, and sector are displayed in Figure 1(b).

Workflow of the model generator
The proposed Stochastic Model Generator workflow consists of three parts, i.e., data input block, data output block, and model simulation and analysis block, as displayed in Figure 2(a).3 By running the quick-start function, the GUI will be launched, as Figure 2(b) displays, where two procedures are worthy of attention.Firstly, the user needs to specify the basic information required by gprMax, such as the file name, material definition, the parameters related to the computational domain, the discretization step of the model, the time window, and the type of: excitation waveform.Secondly, the user needs to define the stochastic parameters of the model, such as the type of the base shape with its size and density, the combination type and the (non-)overlapped choice.In addition, the background medium of our model can also define as an inhomogeneous medium, by either the stratified density [6], or randomly distributed water content with the aid of Peplinski model [5].
After confirming the input parameters, our model will directly follow the gprMax command protocols and automatically generate ".in" files, which will be fed to the gprMax solver without further manual operation.This automatic procedure can save enormous time and effort in writing gprMax scripts, which can be rather complicated for stochastic media models.Finally, within the GUI, the simulated results can be displayed and stored in the widely-supported HDF5 format.

Simulation experiment
The experiments are conducted to simulate the lunar subsurface domain filled with randomly distributed fragments, that may mainly originate from meteorite impact, cosmic rays and solar wind [7].With these fragments, a variety of radar clutters can be visualized in the radargram, within which a surface target represented by the hyperbola can be clearly identified in region A of Figure 3(a).
In order to mimic this scenario, we setup the stochastic media model by our designed model generator.As displayed in Figures 3b(i-iii), we define three models that represent: i) a round artificial rock buried in the stratified regolith, ii) random fragments in the stratified regolith, and iii) a round artificial rock  buried in the stratified regolith with random fragments, respectively.The computational domain is set as 5 × 5 × 0.01 m, the discretization is 0.01 m for each direction, the time window is 60 μs and the Ricker waveform with the center frequency of 500 MHz (same as the LPR [7] in Chang'E-4) is specified.We define the relative permittivity ( r  ) of the background lunar regolith by the empirical formula for the Apollo core sample [8], which is a function of depth (z): ( z 12.2)/( z 18) 1.92 r 1.919 It is clear in Figures 3(b-c)(ii-iii) that the randomly distributed fragments produce many clutters, which is similar to those in the LPR observed radargram.It therefore validates the potential of our designed model generator in imitating the real lunar subsurface environment.It shall be emphasized that such models are not generated by the traditional way of applying the heterogeneous dielectric constant of subsurface soils following the Peplinski model [5].Instead, our model generator can define the elementary shapes of subsurface fragments with their random distribution readily adjustable.Furthermore, with such model generator, we can automatically produce vast number of random models that can be fed in advanced machine learning algorithms, by which the true subsurface environment can be accurately portrayed.

Conclusions
In this study, we develop a simple model generator based on our stochastic media model and gprMax.The stochastic media model not only creates random shapes based on four basic shapes, but also defines their random distribution.Such model is further combined with gprMax in a simplified workflow and GUI.In our validation simulation experiments, we successfully generate several realistic stochastic media models, and the generated clutters can mimic the fragments in the CE-4 LPR observed radargram, as well as the artificial object with clear hyperbola signature.With such ready model generator, numerous complex models can be automatically generated and proceeded to establish a sample library for machine learning in the future.

Figure 1 .
Figure 1.Procedure of generating multi-shape random distribution of fragments.(a) Base shapes created from the circle shape; (b) Random distributions of four base shapes; (c) The overlapped and non-overlapped distributions of multi-shape combinations.

Figure 2 .
Figure 2. Workflow (a) and GUI (b) of the Stochastic Models Generator.

Figure 3 .
Figure 3. (a) Observed radargram from CE-4 LPR.(b)Simulation models, where relative permittivity of each object is identical to the color.(c)Simulation results corresponding to (b).Relative permittivity of fragments and the artificial block is 5 and 8, respectively.