## Abstract

This PhD study examines the use of seismic technology for the problem of detecting underground facilities, whereby a seismic source such as a sledgehammer is used to generate seismic waves through the ground, sensed by an array of seismic sensors on the ground surface, and recorded by the digital device. The concept is similar to the techniques used in exploration seismology, in which explosions (that occur at or below the surface) or vibration wave-fronts generated at the surface reflect and refract off structures at the ground depth, so as to generate the ground profile of the elastic material properties such as the elastic wave speeds and soil densities. One processing method is casting the estimation problem into an inverse problem to solve for the unknown material parameters. The forward model for the seismic signals used in the literatures include ray tracing methods that consider only the first arrivals of the reflected compressional P-waves from the subsurface structures, or 3D elastic wave models that model all the seismic wave components. The ray tracing forward model formulation is linear, whereas the full 3D elastic wave model leads to a nonlinear inversion problem.

In this PhD study, both the linear and nonlinear inverse problems are investigated, in order to solve the problem to locate the position of an underground tunnel. One practical limitation of geophysics inversion problem is the high dimension of the unknown parameter space, such as the elastic wave speeds, soil density values of the discretized ground medium, which leads to time-consuming computations and instability behaviour of the inversion process. In addition, the geophysics inverse problem is generally ill-posed due to non-exact forward model that introduces errors. The Bayesian inversion method through the probability density function permits the incorporation of a priori information about the parameters, and also allow for incorporation of theoretical errors. This opens up the possibilities of application of inverse paradigm in the real-world geophysics inversion problems.

In this PhD study, the Bayesian inversion paradigm for the tunnel localization problem was investigated. A formulation of the mathematical framework of the inverse problem to solve the specific tunnel localization problem defined in the PhD study has been proposed. On this basis, two optimization algorithms, namely the Monte Carlo Metropolis Hasting and Simulated Annealing have been studied, and a new reduced modelling scheme to reduce the dimension of the ground material elastic parameter space has been proposed. Also, the linear ray tracing and nonlinear 3D elastic wave models have been examined using the Bayesian inversion algorithms and conventional source localization beamforming algorithms. Additionally, an experiment validation of the inversion framework is performed through conducting seismic measurements at an underground tunnel site using an array of geophones deployed on the ground surface and using a surface seismic source.

The examples show with the field data, inversion for localization is most advantageous when the forward model completely describe all the elastic wave components as is the case of the FDTD 3D elastic model. The simulation results of the inversion of the soil density values show that both the global optimization method, i.e., Monte Carlo Metropolis Hasting algorithm and Simulated Annealing, are able to provide fairly good estimates which agree with the investigations in the literatures that focus only on geo-inversion of the elastic medium. The results of Monte Carlo Metropolis Hasting inversion to solve the source localization problem, i.e., invert for source depth and source range, display large fluctuations in the range and depth samples generated. However the point MAP estimates derived from 5000 runs of the Metropolis Hasting method are relatively close to the true values. The results of the Simulated Annealing using an initial guess as the MAP estimate calculated from a small number of runs of the Monte Carlo Metropolis Hasting algorithm (in the simulation, we use 50 runs), is able to improve the accuracy of the range and depth estimate of the source. The field results of the joint inversion of material elastic parameters and tunnel location show an agreement with the simulated results. The PDF curves of range and depth derived from Monte Carlo Metropolis Hasting samples shows multi-modal distribution behaviour, which made the mean estimate not a suitable parameter for processing the Monte Carlo samples. The MAP estimates derived from both the Monte Carlo Metropolis Hasting and Simulated Annealing methods however match well against the location of the underground tunnel. These results reflect that the point MAP estimate, in agreement with the simulation results, provides a more accurate representation for the location parameters exhibiting multi-modal distribution behaviour.

In this PhD study, both the linear and nonlinear inverse problems are investigated, in order to solve the problem to locate the position of an underground tunnel. One practical limitation of geophysics inversion problem is the high dimension of the unknown parameter space, such as the elastic wave speeds, soil density values of the discretized ground medium, which leads to time-consuming computations and instability behaviour of the inversion process. In addition, the geophysics inverse problem is generally ill-posed due to non-exact forward model that introduces errors. The Bayesian inversion method through the probability density function permits the incorporation of a priori information about the parameters, and also allow for incorporation of theoretical errors. This opens up the possibilities of application of inverse paradigm in the real-world geophysics inversion problems.

In this PhD study, the Bayesian inversion paradigm for the tunnel localization problem was investigated. A formulation of the mathematical framework of the inverse problem to solve the specific tunnel localization problem defined in the PhD study has been proposed. On this basis, two optimization algorithms, namely the Monte Carlo Metropolis Hasting and Simulated Annealing have been studied, and a new reduced modelling scheme to reduce the dimension of the ground material elastic parameter space has been proposed. Also, the linear ray tracing and nonlinear 3D elastic wave models have been examined using the Bayesian inversion algorithms and conventional source localization beamforming algorithms. Additionally, an experiment validation of the inversion framework is performed through conducting seismic measurements at an underground tunnel site using an array of geophones deployed on the ground surface and using a surface seismic source.

The examples show with the field data, inversion for localization is most advantageous when the forward model completely describe all the elastic wave components as is the case of the FDTD 3D elastic model. The simulation results of the inversion of the soil density values show that both the global optimization method, i.e., Monte Carlo Metropolis Hasting algorithm and Simulated Annealing, are able to provide fairly good estimates which agree with the investigations in the literatures that focus only on geo-inversion of the elastic medium. The results of Monte Carlo Metropolis Hasting inversion to solve the source localization problem, i.e., invert for source depth and source range, display large fluctuations in the range and depth samples generated. However the point MAP estimates derived from 5000 runs of the Metropolis Hasting method are relatively close to the true values. The results of the Simulated Annealing using an initial guess as the MAP estimate calculated from a small number of runs of the Monte Carlo Metropolis Hasting algorithm (in the simulation, we use 50 runs), is able to improve the accuracy of the range and depth estimate of the source. The field results of the joint inversion of material elastic parameters and tunnel location show an agreement with the simulated results. The PDF curves of range and depth derived from Monte Carlo Metropolis Hasting samples shows multi-modal distribution behaviour, which made the mean estimate not a suitable parameter for processing the Monte Carlo samples. The MAP estimates derived from both the Monte Carlo Metropolis Hasting and Simulated Annealing methods however match well against the location of the underground tunnel. These results reflect that the point MAP estimate, in agreement with the simulation results, provides a more accurate representation for the location parameters exhibiting multi-modal distribution behaviour.

Original language | English |
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Publisher | Technical University of Denmark, Department of Electrical Engineering |
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Number of pages | 157 |

Publication status | Published - 2014 |