Study And Application On Full Waveform Inversion Based On Multi-offset Ground Penetrating Radar Data

Ground penetrating radar(GPR)is an important near-surface prospecting technique utilized to reveal the electromagnetic properties of subsurface.It has been widely applied to geotechnical investigation,engineering quality inspection,groundwater contamination monitoring,polar exploration,lunar probe etc.With the development of GPR methods,the exploration mission has extended from simply describing the position,shape and interfaces of the abnormal body to accurately inverting the subsurface electrical structures.At present,the construction methods for dielectric model with GPR data mainly include velocity analysis,tomography,and full waveform inversion(FWI).Among them,velocity analysis and ray-based tomography only utilize the travel time of the electromagnetic wavefield,which theoretically limits the accuracy and resolution of the inversion results.Under the framework of the least-squares theory,full waveform inversion makes use of the complete waveform information,such as the travel time,amplitude and phase etc.It minimizes the difference between the observed and the synthetic GPR data to obtain well-defined geological structures and quantitative rock physical properties in the subsurface.GPR full-waveform inversion comprehensively utilize the kinematic and dynamic characteristics of the electromagnetic wavefield to develop its potentials in determining the occurrence state of near-surface objects and quantifying the subsurface electrical attributes(permittivity and conductivity).However,surface-to-surface acquisition configuration is easily affected by the near surface;in addition,due to the frequency-dependent attenuation mechanisms,higher frequencies do not penetrate as far as lower frequencies,all results in a low signal-to-noise ratio(SNR)of the GPR data.Therefore,it has become a research focus to develope the high-resolution,high-precision GPR FWI and apply it to the processing and interpretation of the field data.In this paper,two issues in the process of GPR FWI are discussed.First,the inversion accuracy gradually decreases from shallow to deep,the reconstruction quality at depth is relatively poor.Second,in the context of the multi-parameter FWI,the sensitivity difference of GPR data to permittivity and conductivity will cause a serious deviation between the calculated and the true steepest-descent directions,which will greatly increase the nonlinearity of the inverse problem.Here,reasonable and effective solutions are put forward to solve these two problems.For the first problem,we propose a model-based layer stripping strategy to improve and optimize the conventional data-based layer stripping method from aspects of calculation efficiency,layer selection and application scope,etc.For the second problem,we deeply investigate the variation law of the perturbation wavefields of different perturbation models in the on-ground multi-offset GPR acquisition configuration,further conclude the phase relationship between the responses(scattered wavefield)of two-parameter perturbations and the responses of single-parameter perturbations.The main methods proposed in this paper and the main results achieved can be summarized as follows:(1)A model-based layer stripping full waveform inversion(MLS FWI)method is proposed in the time domain.From top to bottom in the model domain,the relative permittivity is updated layer by layer.Differing from conventional layer stripping FWI,which uses an offset and/or temporal window to extract partially observed data for calculating a partial gradient,a spatial Hanning window in the model domain is applied to the overall gradient calculated from the entire gathers for getting the gradient of a layer.It minimized the objective function of each window in the gather from top to bottom to ensure that the total objective function was the smallest.Most importantly,when combined with the source encoding technique,this MLS FWI fundamentally solves the problem that forward simulation of all source positions is required when adding the window in a data-based layer stripping FWI,and thus greatly improves the calculation efficiency,saves the memory and the stochastic attributes can help to suppress the “crosstalk noise”.In the frame of the frequency multi-scale scheme,a new stepped inversion sequence is proposed to improve the inversion at depth,this stepped inversion sequence helps reduce the frequency order between any two adjacent layers,greatly smooths the frequency gaps existing in the conventional inversion sequence.It can effectively strengthen the inversion accuracy at depth and appears to provide better coverage than the other methods.(2)A phase correction frequency-domain full-waveform inversion method is proposed for simultaneously updating permittivity and conductivity.We first probe into the problem of inaccurate updating directions in the multi-parameter FWI through the most fundamental local optimization algorithm,namely the steepest descent method,and further attribute the unreliability of the steepest-descent directions in the two-parameter inversion to the adjoint source;Then analyze the phase relationship between the scattered wavefield of two-parameter ?-? perturbations and of mono-parameter ? or ? perturbations and further investigate the phase difference between two perturbation wavefields with the change of the relative perturbation ratio in permittivity and conductivity.Here,a phase correction method is derived based on a modified loss tangent formula in low-loss media to adjust the adjoint source from the perspective of phase so that the adjoint source of the ?-? perturbations can be consistent with that of the two single-parameter perturbations in phase,respectively.The proposed method can effectively improve the accuracy and stability of the steepest-descent updating directions in the contect of multi-parameter FWI,thus reliable and high-precision inversion results are expected.(3)To verify the practicability of the methods proposed in this paper,we further study on the full waveform inversion based on the multi-offset GPR field data.Firstly,the original data is analyzed and preprocessed in detail,then we suppresse,remove or compensate the unreasonable contents in the original data to improve the quality of the data.In the data preprocessing,a wavelet inversion method based on the particle swarm optimization is proposed.In this method,we first select several characteristic points in the air direct wave which can control the main shape of the waveform as the matching references,then establish the objective functions based on amplitude and time,respectively.A global optimization algorithm is used due to the small amount of calculation in one simulation.This wavelet inversion method can effectively reduce the inversion error caused by inaccurate wavelet estimation.Multi-parameter full waveform inversion of the field data is carried out in the time domain,utiliaze the layer stripping scheme and the quasi-Newton method to complete the iterative updating of different parameter models.The full-waveform inversion can depict the spatial distribution of the pollutants in the study area,provide detailed information such as underground small-scale structures,and effectively identify electrical properties changes in soil caused by hydrocarbon pollution.