Ground-penetrating radar (GPR) is a mature geophysical methodology with a plethora of applications ranging from landmine detection and non-destructive testing to glaciology and and environmental science. GPR is gaining an increased popularity the last decade in planetary science and in particular in Lunar and Martian exploration. In-situ GPR was firstly used in planetary science in 2013 as part of the scientific payloads of Yutu-1, the planetary rover of the Chinese Chang'E-3 mission. Since then, GPR was employed in Yutu-2 rover from the Chang'E-4 mission, Perseverance from Mars 2020, Zhurong rover from Tianwen-1, and the landers of the Chang'E-5 and Chang'E-6 missions. Moreover, GPR is planned to be used in the future missions Chang'E-7 and ExoMars. ## Ground Penetrating Radar (GPR) - Basic Principles Here are the main principles of GPR that will be useful for this competition: - **Electromagnetic Waves:** GPR emits short pulses of electromagnetic waves (usually in the microwave range) into the ground through an antenna. These waves travel into the subsurface and are partially reflected back to the surface in the presence of a target with different material properties than the background. - **Dielectric properties:** The properties of matter that affect GPR are the so called dielectric properties i.e. the electric permittivity (ε), the electric conductivity (σ) and the magnetic susceptibility (μ). We mostly care about ε and σ, since μ is considered to be equal with the susceptibility of free space most of the times. - **Electric permittivity:** Usually is measured relatively to the permittivity of free space i.e. relative permittivity. Is affected primarily by the presence of liquid water and the density of the formations. For planetary radar, since liquid water is absent from the Lunar and Martian surface, the permittivity of the subsurface formations is approximated (based on samples from the Apollo missions) by $$\log (\epsilon) = 0.28 \rho$$, where ρ is the density. -**Velocity:** The velocity of the formation can be approximated by $$v = \frac{c}{\sqrt{\epsilon}}$$, where *v* is the velocity of the medium, *c* is the velocity of light, and ε is the relative permittivity of the medium. -**Reflectivity:** The reflectivity of subsurface targets is proportional to the contrast of the permittivity of the target compared to the permittivity of the background. -**Electromagnetic losses**: The electric conductivity affects the electromagnetic losses i.e. how fast a wave attenuates inside a formation. The conductivity is affected primarily by liquid water, and secondary by some oxides such as ilmenite. In general, in both Lunar and Martian setups, the conductivity is low, which increases the overall penetration depth of GPR compared to Terrestrial applications. -**Common-offset:** In the common-offset measurement configuration, GPR systems commonly use two antennas: a transmitting antenna and a receiving antenna. These antennas are positioned at a fixed distance apart from each other while moving along the measuring line. -**Multi-offset:** This configuration refers to using multiple transmitters and receivers. -**Central Frequency:** The pulses used in GPR have a wide range of frequencies, and the most dominant frequency is called the central frequency of the pulse. The central frequency is proportional to the resolution of the scan, and inversely proportional to the penetration depth. A low central frequency will have bigger penetration depth and low resolution, while a high central frequency will have high resolution with smaller penetration depth. -**B-Scan:** Bscan refers to an image that integrates multiple traces/scans along the measuring line. B-Scan is also referred to as radagram. ## Competition Details GPR has been used in the following planetary missions: - Chang'E-3 (Moon - Common Offset - 500 and 60 MHz central frequency) - Chang'E-4 (Moon - Common Offset - 500 and 60 MHz central frequency) - Chang'E-5 (Moon - Multi Offset - 2 GHz central frequency) - Chang'E-6 (Moon - Multi Offset - 2 GHz central frequency) - Tianwen-1 (Mars - Common Offset - 500 and 60 MHz central frequency) - Perseverance (Mars - Common Offset - 500 MHz central frequency) In the current competition we will explore the potential of using a low frequency multi-offset system utilising the lander as a receiver in a rover-lander cooperation ([AGU Abstract](https://agu.confex.com/agu/fm22/meetingapp.cgi/Paper/1061377)). The description of the problem in an abstract manner is outlined below: - Measurements are taken uisng one-shot multi-offset configuration. - Using the reciprocity theorem, one receiver (lander) with multiple transmitters (rover in different positions) is the equivalent of having a transmitter in the location of the receiver and multiple receivers on the locations of the transmitters. In other words we will have one transmitter at the position of the lander, and multiple receivers along the measuring line of the rover. - The subsurface will consist of low permittivity and conductivity materials, the permittivity will vary ε < 10, consistent with the returned samples from the Apollo missions. To simplify the problem, we assume a correlation between the relative permittivity and conductivity σ = ε/10000, following the rationale that the abnormally high permittivity value of titanium oxides and their dispersive properties will increase both the overall permittivity and electromagnetic losses of a Lunar formation. - The subsurface will consists of sequential layers with stochastic variations of dielectric properties, and distinct targets within them. This geometry aims at simulating ejecta layers and thin flood basalts expected in the Lunar near subsurface. ## Description of the training Data - Overview The data consist of 4400 synthetically generated B-Scans and their corresponding 4400 ground truth models, which are the 2D permittivity structures for each model. The data are saved in numpy arrays (.npy) in the folders Training_Bscan and Training_Labels. The B-Scans of the training data consist of 230 equidistant traces positioned every 20 cm from the transmitter. The discretisation step of the time domain is 3.0434 ns and the total time steps are 230 i.e. the time window of the measurements equals with 700 ns. The only processing applied to the data is a time varying gain i.e. every trace A(t) was multiplied by $$A(n\cdot dt) = A(n\cdot dt)*n^{3}$$, where *n* is the time index of the FDTD simulation i.e. n = t/dt, where dt = 0.0467 ns (the discretisation step of the FDTD based on the Courant limit). Conclusively, the B-Scans are 2D gray images with 230x230 dimensions. These images will be the inputs in the machine learning model. Notice that the B-Scans are not scaled! The ground truth data consist of 2D gray images with 224x224 dimensions. The discretisation step of the x-axis is 22.32 cm, and the discretisation step of the y-axis is 9.82 cm i.e. the whole domain is 50.02x22 meters. The values of the relative permittivities vary from 1 (relative permittivity of free space) to 10, which is an approximation of the upper permittivity value we expect to find in Lunar and Martian environments. **!! Description of the problem in a simplified and abstract manner for non-geophysicists: we need to develop an image-to-image translation that will take a B-Scan (230x230 gray image) as input and give the ground truth (224x224 gray image) as output. !!** **!! Notice that the B-Scans in the training data are complete, while the B-Scans in the evaluation/testing set have many missing traces !!** ## Description of the data - FDTD Details Below are the FDTD parameters used to synthetically generate the models (more info in the Notebook *gprMax_Simulations.ipynb*) - Spatial step: dx = dy = dz = 0.02 cm - Domain: 2D 50.02 x 24 meters - Time step: 0.99 Courant limit - PML layers: 60 - Source characteristics: randomly selected pulses with central frequency that varies from 60 - 100 MHz and different types of pulses. ## Description of the data - Geometry The models consist of randomly generated layers with different permittivities, different stochastic distributions of permittivities, different sampling rates between min and max permittivity, and different stochastic surfaces. The number of layers and their parameters are chosen randomly in each execution resulting to a wide range of models with complex geometries and stochastic formations. More information can be found in the Notebook *gprMax_Simulations* and in the notebook *Open and Explore Data*. More information can be found in the paper **Giannakis, I., Warren, C., Giannopoulos, A., Leontidis, G., Su, Y., Zhou, F., Martin-Torres, J., Diamanti, N., "Investigating the Capabilities of Deep Learning for Processing and Interpreting One-Shot Multi-offset GPR Data: A Numerical Case Study for Lunar and Martian Environments", arXiv:2410.14386, 2024** https://doi.org/10.48550/arXiv.2410.14386