Bayesian full waveform inversion designed for exploration during mechanized tunneling – A small-scale experiment

2022 ◽  
Author(s):  
M. Trapp
Keyword(s):  
Waveform Inversion ◽  
Small Scale ◽  
Full Waveform Inversion ◽  
Mechanized Tunneling ◽  
Full Waveform ◽  
Scale Experiment

Full-waveform inversion with wavefield gradients

2021 ◽  
Author(s):  
Sneha Singh ◽  
Yann Capdeville ◽  
Heiner Igel ◽  
Navid Hedjazian ◽  
Thomas Bodin
Keyword(s):  
Waveform Inversion ◽  
Effective Model ◽  
Small Scale ◽  
Full Waveform Inversion ◽  
Coupling Tensor ◽  
Full Waveform ◽  
Surface Topographies ◽  
Good For ◽  
Incorrect Model

<p>Wavefield gradient instruments, such as rotational sensors and DAS systems, are becoming more and more accessible in seismology. Their usage for Full Waveform Inversion (FWI) is in sight. Nevertheless, local small-scale heterogeneities, like geological inhomogeneities, surface topographies, and cavities are known to affect wavefield gradients. This effect is in fact measurable with current instruments. For example, the agreement between data and synthetics computed in a tomographic model is often not as good for rotation as it is for displacement.</p><p>The theory of homogenization can help us understand why small-scale heterogeneities strongly affect wavefield gradients, but not the wavefield itself. It tells us that at any receiver measuring wavefield gradient, small-scale heterogeneities cause the wavefield gradient to couple with strain through a coupling tensor <strong>J</strong>. Furthermore, this <strong>J</strong> is 1) independent of source, 2) independent of time, but 3) only dependent on the receiver location. Consequently, we can invert for <strong>J</strong> based on an effective model for which synthetics fit displacement data reasonably well. Once inverted, <strong>J</strong> can be used to correct all other wavefield gradients at that receiver.</p><p>Here, we aim to understand the benefits and drawbacks of wavefield gradient sensors in a FWI context. We show that FWIs performed with rotations and strains are equivalent to that performed with displacements provided that 1) the number of data is sufficient, and 2) the receivers are placed far away from heterogeneities. In the case that receivers are placed near heterogeneities, we find that due to the effect of these heterogeneities, an incorrect model is recovered from inversion. In this case therefore, the coupling tensor <strong>J</strong> needs to be taken into account for each receiver to get rid of the effect.</p>

Improvement of GPR Full-waveform inversion images using Cone Penetration Test data

Geophysics ◽  
2021 ◽  
pp. 1-74
Author(s):  
Zhen Zhou ◽  
Anja Klotzsche ◽  
Jessica Schmäck ◽  
Harry Vereecken ◽  
Jan van der Kruk
Keyword(s):  
Waveform Inversion ◽  
Cone Penetration Test ◽  
Small Scale ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
Penetration Test ◽  
Cone Penetration ◽  
Full Waveform ◽  
Effective Source

Detailed characterization of aquifers is critical and challenging due to the existence of heterogeneous small-scale high-contrast layers. For an improved characterization of subsurface hydrological characteristics, crosshole ground penetrating radar (GPR) and Cone Penetration Test (CPT) measurements are performed. In comparison to the CPT approach that can only provide 1D high resolution data along vertical profiles, crosshole GPR enables measuring 2D cross-sections between two boreholes. Generally, a standard inversion method for GPR data is the ray-based approach that considers only a small amount of information and can therefore only provide limited resolution. In the last decade, full-waveform inversion (FWI) of crosshole GPR data in time domain has matured, and provides inversion results with higher resolution by exploiting the full recorded waveform information. However, the FWI results are limited due to complex underground structures and the non-linear nature of the method. A new approach that uses CPT data in the inversion process is applied to enhance the resolution of the final relative permittivity FWI results by updating the effective source wavelet. The updated effective source wavelet possesses a priori CPT information and a larger bandwidth. Using the same starting models, a synthetic model comparison between the conventional and updated FWI results demonstrates that the updated FWI method provides reliable and more consistent structures. To test the method, five experimental GPR cross-section results are analyzed with the standard FWI and the new proposed updated approach. Both synthetic and experimental results indicate the potential of improving the reconstruction of subsurface aquifer structures by combining conventional 2D FWI results and 1D CPT data.

scholarly journals Multiscale seismic imaging with inverse homogenization

2021 ◽  
Author(s):  
N Hedjazian ◽  
Y Capdeville ◽  
T Bodin
Keyword(s):  
Seismic Imaging ◽  
Effective Properties ◽  
Waveform Inversion ◽  
Homogenization Theory ◽  
Small Scale ◽  
Full Waveform Inversion ◽  
Inverse Homogenization ◽  
Long Wavelength ◽  
Full Waveform ◽  
Scale Models

Summary Seismic imaging techniques such as elastic full waveform inversion (FWI) have their spatial resolution limited by the maximum frequency present in the observed waveforms. Scales smaller than a fraction of the minimum wavelength cannot be resolved, and only a smoothed, effective version of the true underlying medium can be recovered. These finite-frequency effects are revealed by the upscaling or homogenization theory of wave propagation. Homogenization aims at computing larger scale effective properties of a medium containing small-scale heterogeneities. We study how this theory can be used in the context of FWI. The seismic imaging problem is broken down in a two-stage multiscale approach. In the first step, called homogenized full waveform inversion (HFWI), observed waveforms are inverted for a smooth, fully anisotropic effective medium, that does not contain scales smaller than the shortest wavelength present in the wavefield. The solution being an effective medium, it is difficult to directly interpret it. It requires a second step, called downscaling or inverse homogenization, where the smooth image is used as data, and the goal is to recover small-scale parameters. All the information contained in the observed waveforms is extracted in the HFWI step. The solution of the downscaling step is highly non-unique as many small-scale models may share the same long wavelength effective properties. We therefore rely on the introduction of external a priori information, and cast the problem in a Bayesian formulation. The ensemble of potential fine-scale models sharing the same long wavelength effective properties is explored with a Markov chain Monte Carlo algorithm. We illustrate the method with a synthetic cavity detection problem: we search for the position, size and shape of void inclusions in a homogeneous elastic medium, where the size of cavities is smaller than the resolving length of the seismic data. We illustrate the advantages of introducing the homogenization theory at both stages. In HFWI, homogenization acts as a natural regularization helping convergence toward meaningful solution models. Working with fully anisotropic effective media prevents the leakage of anisotropy induced by the fine scales into isotropic macro-parameters estimates. In the downscaling step, the forward theory is the homogenization itself. It is computationally cheap, allowing us to consider geological models with more complexity (e.g. including discontinuities) and use stochastic inversion techniques.

Review of crosshole ground-penetrating radar full-waveform inversion of experimental data: Recent developments, challenges, and pitfalls

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. H13-H28 ◽  
Author(s):  
Anja Klotzsche ◽  
Harry Vereecken ◽  
Jan van der Kruk
Keyword(s):  
Experimental Data ◽  
High Resolution ◽  
Ground Penetrating Radar ◽  
Waveform Inversion ◽  
Measured Data ◽  
Transport Processes ◽  
Small Scale ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Ground Penetrating

Heterogeneous small-scale high-contrast layers and spatial variabilities of soil properties can have a large impact on flow and transport processes in the critical zone. Because their characterization is difficult and critical, high-resolution methods are required. Standard ray-based approaches for imaging the subsurface consider only a small amount of the measured data and suffer from limited resolution. In contrast, full-waveform inversion (FWI) considers the full information content of the measured data and could yield higher resolution images in the subwavelength scale. In the past few decades, ground-penetrating radar (GPR) FWI and its application to experimental data have matured, which makes GPR FWI an established approach to significantly improve resolution. Several theoretical developments were achieved to improve the application to experimental data from crosshole GPR FWI. We have determined the necessary steps to perform FWI for experimental data to obtain reliable and reproducible high-resolution images. We concentrate on experimental crosshole GPR data from a test site in Switzerland to illustrate the challenges of applying FWI to experimental data and discuss the obtained results for different development steps including possible pitfalls. Thereby, we acknowledge out the importance of a correct time-zero correction of the data, the estimation of the effective source wavelet, and the effect of the choice of starting models. The reliability of the FWI results is investigated by analyzing the fit of the measured and modeled traces, the remaining gradients of the final models, and validating with independently measured logging data. Thereby, we found that special care needs to be taken to define the optimal inversion parameters to avoid overshooting of the inversion or truncation errors.

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