Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed problem. In the framework of Tikhonov regularization theory, in order to replace an ill-posed problem by a well-posed one and to get a unique and stable solution, a stabilizing functional (stabilizer) has to be introduced. The stabilizer selects the desired solution from a class of solutions with a specific physical and/or geometrical property; e.g., the existence of sharp boundaries separating media with different petrophysical parameters. Usually stabilizers based on maximum smoothness criteria are used during the inversion process; in these cases the solutions provide smooth images which, in many situations, do not describe the examined objects properly. Recently a new algorithm of direct minimization of the Tikhonov parametric functional with minimum support stabilizer has been introduced; it produces clear and focused images of targets with sharp boundaries. In this research we apply this new technique to real radar tomographic data and we compare the obtained result with the solution generated by the more traditional minimum norm stabilizer.
Multistatic ground-penetrating radar (GPR) signals can be imaged tomographically to produce three-dimensional distributions of image intensities. In the absence of objects of interest, these intensities can be considered to be estimates of clutter. These clutter intensities spatially vary over several orders of magnitude, and vary across different arrays, which makes direct comparison of these raw intensities difficult. However, by gathering statistics on these intensities and their spatial variation, a variety of metrics can be determined. In this study, the clutter distribution is found to f…
We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ to within its assigned errors.
In the present paper, the solution of the seismic data inversion problem through multi-objective optimization with NSGA II is addressed. The seismic inversion consists of estimating the slowness of rocks in the subsurface from the travel times of the waves through the transmitters and receivers of the seismic waves. The inversion process uses the multi-objective optimization technique, in which it is necessary to estimate the trade-off between the misfit functional and the stabilizing constraint. The constraint used was the classic first-order Tikhonov. A synthetic model of inclined layers was…
The three electromagnetic properties appearing in Maxwell's equations are dielectric permittivity, electrical conductivity and magnetic permeability. The study of point diffractors in a homogeneous, isotropic, linear medium suggests the use of logarithms to describe the variations of electromagnetic properties in the earth. A small anomaly in electrical properties (permittivity and conductivity) responds to an incident electromagnetic field as an electric dipole, whereas a small anomaly in the magnetic property responds as a magnetic dipole. Neither property variation can be neglected without …
Geophysical methods offer several key advantages over conventional subsurface measurement approaches, yet their use for hydrologic interpretation is often problematic. Here, we introduce theory and concepts of a novel Bayesian approach for high-resolution soil moisture estimation using traveltime observations from crosshole Ground Penetrating Radar (GPR) experiments. The recently developed Multi-try DiffeRential Evolution Adaptive Metropolis with sampling from past states, MT-DREAM(ZS) is being used to infer, as closely and consistently as possible, the posterior distribution of spatially dist…
Solving or resolving global tomographic models with spherical wavelets, and the scale and sparsity of seismic heterogeneity
Princeton University（普林斯顿大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）；GéoAzur Université de Nice（尼斯大学地理与地球物理实验室）；Program in Applied and Computational Mathematics Princeton University（普林斯顿大学应用与计算数学项目）
Shandong University（山东大学）；University of Leeds（利兹大学）
A DNN architecture referred to as GPRInvNet was proposed to tackle the challenges of mapping the ground-penetrating radar (GPR) B-Scan data to complex permittivity maps of subsurface structures. The GPRInvNet consisted of a trace-to-trace encoder and a decoder. It was specially designed to take into account the characteristics of GPR inversion when faced with complex GPR B-Scan data, as well as addressing the spatial alignment issues between time-series B-Scan data and spatial permittivity maps. It displayed the ability to fuse features from several adjacent traces on the B-Scan data to enhanc…
Hydrogeological flow and transport strongly depend on the connectivity of subsurface properties. Uncertainty concerning the underlying geological setting, due to a lack of field data and prior knowledge, calls for an evaluation of alternative geological conceptual models. To reduce the computational costs associated with inversions (parameter estimation for a given conceptual model), it is beneficial to rank and discard unlikely conceptual models prior to inversion. Here, we demonstrate an approach based on a quantitative comparison of ground-penetrating radar (GPR) sections obtained from fiel…
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating these surface recordings to actual Earth properties is non-trivial. Tomographic techniques use only a small amount of the information contained in the full seismogram and result in relatively low resolution images. Other methods use a larger amount of the seismogram but are based on either linearization of the problem, an expensive statistical search over a limi…
Ionospheric tomography using GPS data has been reported in the literature and even the application to radar altimeter calibration was succesfully carried out in a recent work. We here present a new software tool, called Global Ionospheric Stochastic Tomography software (GIST), and its powerful capability for ingesting GPS data from different sources (ground stations, receivers on board LEO for navigation and occultation purposes) and other data such as altimetry data to yield global maps with dense coverage and inherent calibration of the instruments. We show results obtained including 106 IGS…
In groundwater hydrology, geophysical imaging holds considerable promise for improving parameter estimation, due to the generally high resolution and spatial coverage of geophysical data. However, inversion of geophysical data alone cannot unveil the distribution of hydraulic conductivity. Jointly inverting geophysical and hydrological data allows us to benefit from the advantages of geophysical imaging and, at the same time, recover the hydrological parameters of interest. We have applied a coupling strategy between geophysical and hydrological models that is based on structural similarity co…
A strategy is presented to incorporate prior information from conceptual geological models in probabilistic inversion of geophysical data. The conceptual geological models are represented by multiple-point statistics training images (TIs) featuring the expected lithological units and structural patterns. Information from an ensemble of TI realizations is used in two different ways. First, dominant modes are identified by analysis of the frequency content in the realizations, which drastically reduces the model parameter space in the frequency-amplitude domain. Second, the distributions of glob…
Global probabilistic inversion within the latent space learned by a Generative Adversarial Network (GAN) has been recently demonstrated. Compared to inversion on the original model space, using the latent space of a trained GAN can offer the following benefits: (1) the generated model proposals are geostatistically consistent with the prescribed prior training image (TI), and (2) the parameter space is reduced by orders of magnitude compared to the original model space. Nevertheless, exploring the learned latent space by state-of-the-art Markov chain Monte Carlo (MCMC) methods may still requir…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
In the workflow of Full-Waveform Inversion (FWI), we often tune the parameters of the inversion to help us avoid cycle skipping and obtain high resolution models. For example, typically start by using objective functions that avoid cycle skipping, like tomographic and image based or using only low frequency, and then later, we utilize the least squares misfit to admit high resolution information. We also may perform an isotropic (acoustic) inversion to first update the velocity model and then switch to multi-parameter anisotropic (elastic) inversions to fully recover the complex physics. Such …
Geophysical inversion should ideally produce geologically realistic subsurface models that explain the available data. Multiple-point statistics is a geostatistical approach to construct subsurface models that are consistent with site-specific data, but also display the same type of patterns as those found in a training image. The training image can be seen as a conceptual model of the subsurface and is used as a non-parametric model of spatial variability. Inversion based on multiple-point statistics is challenging due to high nonlinearity and time-consuming geostatistical resimulation steps …
Most geophysical inverse problems are nonlinear and rely upon numerical forward solvers involving discretization and simplified representations of the underlying physics. As a result, forward modeling errors are inevitable. In practice, such model errors tend to be either completely ignored, which leads to biased and over-confident inversion results, or only partly taken into account using restrictive Gaussian assumptions. Here, we rely on deep generative neural networks to learn problem-specific low-dimensional probabilistic representations of the discrepancy between high-fidelity and low-fid…
Estimating the spatially varying microstructures of heterogeneous and locally anisotropic media non-destructively is necessary for the accurate detection of flaws and reliable monitoring of manufacturing processes. Conventional algorithms used for solving this inverse problem come with significant computational cost, particularly in the case of high dimensional non-linear tomographic problems. In this paper, we propose a framework which uses deep neural networks (DNNs) with full aperture, pitch-catch and pulse-echo transducer configurations to reconstruct material maps of crystallographic orie…
An explicit expression for P-wave velocity is proposed to develop a novel tomographic technique in a spherically symmetric model of the Earth (MZY). The distribution of the P velocity structure in the mantle is determined using only 34 P- and 2 PcP-observed traveltimes. By applying a non-linear inversion, the P-residuals in the range between 0 and 100 degrees are minimised up to a maximum value of 0.015 s. Furthermore, from the high quality computation of PcP traveltimes, with residuals much better than 0.13 s, it is possible to infer the existence of a brief low velocity layer in the D" regio…
We present a Bayesian tomography framework operating with prior-knowledge-based parametrization that is accelerated by surrogate models. Standard high-fidelity forward solvers solve wave equations with natural spatial parametrizations based on fine discretization. Similar parametrizations, typically involving tens of thousand of variables, are usually employed to parameterize the subsurface in tomography applications. When the data do not allow to resolve details at such finely parameterized scales, it is often beneficial to instead rely on a prior-knowledge-based parametrization defined on a …
