Full-waveform inversion of ground-penetrating radar data and its indirect joint petrophysical inversion with shallow-seismic data

Both full-waveform inversion (FWI) of ground-penetrating radar (GPR) and shallow-seismic data have received special attention in the past decade because they allow the reconstruction of seismic and electromagnetic (EM) properties at high resolution. Research on the two FWIs includes: FWI of single geophysical data and joint FWI of multiple geophysical data. In this dissertation, I focus on GPR FWI in the former and joint petrophysical inversion (JPI) in the latter.

In GPR FWI, the high computational costs and frequency-independent assumption are two problems that limit its development. To reduce computational costs, I apply a subset FWI (SFWI) to multi-offset GPR data. SFWI uses the data simulated on a model subset to approximate the data simulated on an entire model. Thus it obtains theoretical speedup and memory saving factor equal to the size ratio of the model and its subset. SFWI has higher or lower than expected speedups when combined with the source parallelization and model domain parallelization, respectively. The model subset depends on the illumination of the acquisition geometry used, for which I give rules of thumb by quantifying its effect on the simulation and inversion. ... mehrBoth 2-D synthetic and field data validate that SFWI provides results comparable to FWI but requires much lower computational costs than FWI. This study makes FWI an affordable technique for general users and promotes its application in addressing near-surface problems.

The second problem means that dielectric permittivity and electrical conductivity are supposed to be frequency independent in most GPR FWI, which may lead to false estimates if they strongly depend on frequency. I develop frequency-dependent GPR FWI to solve this problem. Using the $\tau$-method introduced from the seismic community, I define the permittivity attenuation parameter to quantify the attenuation resulting from the complex permittivity. The new parameter acts as a low-pass filter, distorting the waveform and decaying the amplitude of the EM waves. The use of permittivity attenuation reduces the number of reconstructed parameters in frequency-dependent GPR FWI. The 2-D synthetic examples illustrate that permittivity attenuation is necessary for reconstructing permittivity and conductivity models in frequency-dependent media. The 2-D field example shows that frequency-dependent GPR FWI provides a better fit to the observed data and a more robust conductivity reconstruction in a high permittivity attenuation environment than frequency-independent GPR FWI. This research greatly expands the application of GPR FWI in more complicated media.

Shallow-seismic and GPR FWI can provide complementary information for each other. Based on the sensitivity difference of the two data to petrophysical parameters, I propose indirect JPI, where seismic data are used for porosity reconstruction and GPR data are used for saturation reconstruction. Unlike conventional JPI, I first update the seismic and GPR parameters using non-petrophysical parametrizations and then transform the most reliable estimates to petrophysical parameters. The 2-D synthetic tests show that indirect JPI can provide more accurate and consistent results than conventional JPI. In addition, due to the rational use of the sensitivity of geophysical data to parameters, indirect JPI is more robust when uncertainties exist in petrophysical $a\;priori$ knowledge. More importantly, indirect JPI is flexible to integrate different types of seismic and EM waves and acquisition geometries depending on the target of interest, resulting in the best solution. Indirect JPI has been proven to be a promising approach for multiparameter reconstructions.

To validate if indirect JPI can solve the real problem, I apply it for the first time to Love-wave and multi-offset surface GPR field data. It provides consistent imaging of near-surface targets with good accuracy by estimating seismic, EM, and petrophysical models. The inversion results are validated by direct-push technology and borehole measurements. This application suggests that indirect JPI can avoid conflicting geological interpretations that may arise in individual inversions and shows higher efficiency of information exchange than joint structural inversion. Furthermore, this method is robust with different petrophysical initial models and coefficients, for instance, Archie's coefficients. The study verifies the feasibility of using indirect JPI to invert multiple geophysical field data and promotes the broader applicability of petrophysical methods.

In summary, this dissertation (1) reduces the computational costs of GPR FWI and extends GPR FWI to frequency-dependent media, and (2) proposes a new joint strategy to combine GPR and shallow-seismic data and validates its performance through 2-D synthetic and field examples.