Joint Inversion of Ground-Penetrating Radar and Seismic Velocities for Porosity and Water Saturation in Shallow Sediments

Ground-penetrating radar (GPR) measures the velocity (V_G) of electromagnetic waves in a subsurface material. In a low-loss material, V_G depends primarily on the porosity (ρ) and water saturation (S_w) of the material. Therefore, it is impossible to estimate ρ and S_w uniquely from V_G without additional information. The seismic P-wave velocity (V_P) in the same material can provide the extra information required for the inversion. In this study, an approach is described for a closed-form solution of V_G and V_P to invert for ρ and S_w in shallow sediments. The complex refractive index model (CRIM) for V_G and Gassmann-Biot model for V_P are used to relate these velocities to ρ and S_w. Each model presents a nonlinear equation in ρ and S_w. The two equations are solved simultaneously to estimate ρ and S_w from V_G-V_P measurements. Testing of the inversion procedure in the presence of errors in assuming the properties of the soil matrix showed that these errors can drastically affect the inverted water saturation and porosity, especially in dry, low-porosity sediments. The approach is applied on many V_G-V_P measurements in various soil types collected from the literature. Inversion results show that inverted ρ values for most data points fell around 0.4, which is the critical porosity in sandy soils, while inverted S_w values generally agreed with reported saturations for most of the data points. Few data points resulted in unrealistic ρ and S_w values when a sandy soil matrix was assumed. We found that perturbing the matrix properties for these points resulted in shifting the inverted ρ and S_w to more realistic values.