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Open AccessLetter

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

by 1, 2,*, 1 and 3
1
State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau, China
2
College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China
3
Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, China
*
Author to whom correspondence should be addressed.
Remote Sens. 2019, 11(16), 1839; https://doi.org/10.3390/rs11161839
Received: 11 June 2019 / Revised: 8 July 2019 / Accepted: 31 July 2019 / Published: 7 August 2019
(This article belongs to the Special Issue Recent Progress in Ground Penetrating Radar Remote Sensing)
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. View Full-Text
Keywords: cross-hole radar tomography; Laplace domain; waveform inversion; permittivity; conductivity cross-hole radar tomography; Laplace domain; waveform inversion; permittivity; conductivity
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MDPI and ACS Style

Meng, X.; Liu, S.; Xu, Y.; Fu, L. Application of Laplace Domain Waveform Inversion to Cross-Hole Radar Data. Remote Sens. 2019, 11, 1839.

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