Modeling and imaging of ground penetrating radar data

Ground Penetrating Radar (GPR) is an active and non-invasive exploration technique based on the propagation of electromagnetic waves in the subsurface. Modeling of GPR data is important because it helps us with data interpretation and forms the basis (solution to the forward problem) for most iterative inversion techniques. Conversely, migration (or imaging) is a type of inversion technique (backward propagation) that creates an image related to the subsurface reflectivity and can be used to estimate the model parameters of the media that affect the propagation of the waves. However, for practical applications, modeling and migration techniques must be fast, accurate and efficient. I have developed a fast, efficient and accurate GPR modeling technique for stratified media (isotropic and laterally homogeneous layers) based on the invariant imbedding or reflectivity technique. To test the results obtained with this technique, and have a general tool for modeling of GPR data in heterogeneous, dispersive and isotropic media, I have implemented a 3D explicit Finite Difference Time Domain (FDTD) technique. The FDTD formalism is presented in conjunction with a discussion of the electromagnetic dispersion mechanisms that affect the GPR signal in most geologic media. I show that the results obtained with the reflectivity and FDTD techniques are nearly identical for laterally homogeneous media. Real GPR data is used to study the capabilities and practical aspects that affect the accuracy of the reflectivity technique. I have developed a new technique for migration of GPR data in heterogeneous and lossy media. I have implemented the technique in 2D media and presented the formalism for its extension to 3D media. The new technique, based on the Split Step Fourier migration technique, allows us to efficiently include the dispersion and attenuation effects in the media. An approximation of homogeneous plane waves, which do not add new restrictions to the Split Step Fourier technique, gives greater stability to the imaging technique allowing us to migrate the data through thicknesses up to three times the characteristic skin depths of the media computed at the dominant frequency of the GPR signal.