Ground-penetrating radar (GPR) measures the velocity (VG) of electromagnetic waves in a subsurface material. In a low-loss material, VG depends primarily on the porosity (φ) and water saturation (Sw) of the material. Therefore, it is impossible to estimate φ and Sw uniquely from VG without additional information. The seismic P-wave velocity (VP) 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 VG and VP to invert for φ and Sw in shallow sediments. The complex refractive index model (CRIM) for VG and Gassmann-Biot model for VP are used to relate these velocities to φ and Sw. Each model presents a nonlinear equation in φ and Sw. The two equations are solved simultaneously to estimate φ and Sw from VG-VP 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 VG-VP measurements in various soil types collected from the literature. Inversion results show that inverted φ values for most data points fell around 0.4, which is the critical porosity in sandy soils, while inverted Sw values generally agreed with reported saturations for most of the data points. Few data points resulted in unrealistic φ and Sw values when a sandy soil matrix was assumed. We found that perturbing the matrix properties for these points resulted in shifting the inverted φ and Sw to more realistic values.

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