Application of Laplace Domain Waveform Inversion to Cross-Hole Radar Data

Xu Meng,Lei Fu,Sixin Liu,Yi Xu

doi:10.3390/rs11161839

Abstract

Full waveform inversion (FWI) can yield high resolution images and has been applied in Ground Penetrating Radar (GPR) for around 20 years. However, appropriate selection of the initial models is important in FWI because such an inversion is highly nonlinear. The conventional way to obtain the initial models for GPR FWI is ray-based tomogram inversion which suffers from several inherent shortcomings. In this paper, we develop a Laplace domain waveform inversion to obtain initial models for the time domain FWI. The gradient expression of the Laplace domain waveform inversion is deduced via the derivation of a logarithmic object function. Permittivity and conductivity are updated by using the conjugate gradient method. Using synthetic examples, we found that the value of the damping constant in the inversion cannot be too large or too small compared to the dominant frequency of the radar data. The synthetic examples demonstrate that the Laplace domain waveform inversion provide slightly better initial models for the time domain FWI than the ray-based inversion. Finally, we successfully applied the algorithm to one field data set, and the inverted results of the Laplace-based FWI show more details than that of the ray-based FWI.

Highlights

Ground Penetrating Radar (GPR) is extensively applied in archaeological, environmental, hydrological and engineering investigations to detect subsurface structures [1]
By back-propagating the long-wavelength residuals in the Laplace domain, the results of the inversion can provide a smooth reconstruction of the velocity model as an initial model for the subsequent time or frequency domain Full-waveform inversion (FWI) [21]
We propose an adaptive Laplace domain waveform inversion of cross-hole radar data, which provides an alternative approach for obtaining initial models for the time domain FWI

Summary

Introduction

Ground Penetrating Radar (GPR) is extensively applied in archaeological, environmental, hydrological and engineering investigations to detect subsurface structures [1]. Conventional initial models in the cross-hole FWI are from ray-based inversions [2,3,4,5,6,7]. Shin and Cha [20] suggest using a Laplace domain waveform inversion to build an initial velocity model for FWI. By back-propagating the long-wavelength residuals in the Laplace domain, the results of the inversion can provide a smooth reconstruction of the velocity model as an initial model for the subsequent time or frequency domain FWI [21]. We propose an adaptive Laplace domain waveform inversion of cross-hole radar data, which provides an alternative approach for obtaining initial models for the time domain FWI. All images of the Laplace domain waveform inversion are compared with the respective ray-based results

Laplace-Transformed Wavefield

Inversion Problem

Results

Synthetic Data 1: A Simple Model