scholarly journals Robust full-waveform inversion with Radon-domain matching filter

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R707-R724 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
Radon Transform ◽  
Waveform Inversion ◽  
Delta Function ◽  
Measured Data ◽  
Dirac Delta Function ◽  
Full Waveform Inversion ◽  
Dirac Delta ◽  
Full Waveform ◽  
Matching Filter ◽  
Filter Approach

Cycle skipping is a severe issue in full-waveform inversion. One option to overcome it is to extend the search space to allow for data comparisons beyond the “point-to-point” subtraction. A matching filter can be computed by deconvolving the measured data from the predicted ones. If the model is correct, the resulting matching filter would be a Dirac delta function in which the energy is focused at zero lag. An optimization problem can be formulated by penalizing this matching filter departure from a Dirac delta function. Because the matching filter replaces the local sample-by-sample comparison with a global one using deconvolution, it can reduce the cycle-skipping problem. Because the matching filter is computed using the whole trace of the measured and predicted data, it is prone to unwanted crosstalk of different events. We perform the deconvolution in the Radon domain to reduce crosstalk and improve the inversion. We first transform the measured and the predicted data into the [Formula: see text] domain using the local Radon transform. We then perform deconvolution for the trace indexed by the same slope value. The main objective of the proposal is to use the slope information embedded in the Radon-transform representation to separate the events and reduce the crosstalk in the deconvolution step. As a result, the objective function tends to be more convex and stabilizes the inversion process. The result obtained for the modified Marmousi model demonstrates the proposed Radon-domain matching-filter approach can converge to a meaningful model given data without the low frequencies of less than 3 Hz and a [Formula: see text] initial model. Compared to the conventional time-space matching-filter approach, the Radon-domain approach indicates fewer artifacts in the model and better fitting of the measured data. The result corresponding to the Chevron 2014 benchmark data set also indicates the good performance of the proposed approach.

scholarly journals The application of an optimal transport to a preconditioned data matching function for robust waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R923-R945 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
High Resolution ◽  
Probability Distribution ◽  
Transport Theory ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
Delta Function ◽  
Dirac Delta Function ◽  
Dirac Delta ◽  
Matching Filter ◽  
Optimal Transport Theory

Full-waveform inversion (FWI) promises a high-resolution model of the earth. It is, however, a highly nonlinear inverse problem; thus, we iteratively update the subsurface model by minimizing a misfit function that measures the difference between the measured and the predicted data. The conventional [Formula: see text]-norm misfit function is widely used because it provides a simple, high-resolution misfit function with a sample-by-sample comparison. However, it is susceptible to local minima if the low-wavenumber components of the initial model are not accurate. Deconvolution of the predicted and measured data offers an extended space comparison, which is more global. The matching filter calculated from the deconvolution has energy focused at zero lag, like an approximated Dirac delta function, when the predicted data matches the measured one. We have introduced a framework for designing misfit functions by measuring the distance between the matching filter and a representation of the Dirac delta function using optimal transport theory. We have used the Wasserstein [Formula: see text] distance, which provides us with the optimal transport between two probability distribution functions. Unlike data, the matching filter can be easily transformed to a probability distribution satisfying the requirement of the optimal transport theory. Though in one form, it admits the conventional normalized penalty applied to the nonzero-lag energy in the matching filter, the proposed misfit function is metric and extracts its form from solid mathematical foundations based on optimal transport theory. Explicitly, we can derive the adaptive waveform inversion (AWI) misfit function based on our framework, and the critical “normalization” for AWI occurs naturally per the requirement of a probability distribution. We use a modified Marmousi model and the BP salt model to verify the features of the proposed method in avoiding cycle skipping. We use the Chevron 2014 FWI benchmark data set to further highlight the effectiveness of the proposed approach.

Quantitative conductivity and permittivity estimation using full-waveform inversion of on-ground GPR data

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. H79-H91 ◽  
Author(s):  
Sebastian Busch ◽  
Jan van der Kruk ◽  
Jutta Bikowski ◽  
Harry Vereecken
Keyword(s):  
Quantitative Estimation ◽  
Waveform Inversion ◽  
Measured Data ◽  
Optimization Approach ◽  
Full Waveform Inversion ◽  
Near Surface ◽  
Full Waveform ◽  
Novel Approach ◽  
Wide Range ◽  
Starting Model

Conventional ray-based techniques for analyzing common-midpoint (CMP) ground-penetrating radar (GPR) data use part of the measured data and simplified approximations of the reality to return qualitative results with limited spatial resolution. Whereas these methods can give reliable values for the permittivity of the subsurface by employing only the phase information, the far-field approximations used to estimate the conductivity of the ground are not valid for near-surface on-ground GPR, such that the estimated conductivity values are not representative for the area of investigation. Full-waveform inversion overcomes these limitations by using an accurate forward modeling and inverts significant parts of the measured data to return reliable quantitative estimates of permittivity and conductivity. Here, we developed a full-waveform inversion scheme that uses a 3D frequency-domain solution of Maxwell’s equations for a horizontally layered subsurface. Although a straightforward full-waveform inversion is relatively independent of the permittivity starting model, inaccuracies in the conductivity starting model result in erroneous effective wavelet amplitudes and therefore in erroneous inversion results, because the conductivity and wavelet amplitudes are coupled. Therefore, the permittivity and conductivity are updated together with the phase and the amplitude of the source wavelet with a gradient-free optimization approach. This novel full-waveform inversion is applied to synthetic and measured CMP data. In the case of synthetic single layered and waveguide data, where the starting model differs significantly from the true model parameter, we were able to reconstruct the obtained model properties and the effective source wavelet. For measured waveguide data, different starting values returned the same wavelet and quantitative permittivities and conductivities. This novel approach enables the quantitative estimation of permittivity and conductivity for the same sensing volume and enables an improved characterization for a wide range of applications.

scholarly journals 2.5D crosshole GPR full-waveform inversion with synthetic and measured data

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. H71-H82
Author(s):  
Amirpasha Mozaffari ◽  
Anja Klotzsche ◽  
Craig Warren ◽  
Guowei He ◽  
Antonios Giannopoulos ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Waveform Inversion ◽  
Computational Effort ◽  
Measured Data ◽  
Superior Performance ◽  
Full Waveform Inversion ◽  
High Contrast ◽  
Model Errors ◽  
Full Waveform ◽  
2D Data

Full-waveform inversion (FWI) of cross-borehole ground-penetrating radar (GPR) data is a technique with the potential to investigate subsurface structures. Typical FWI applications transform 3D measurements into a 2D domain via an asymptotic 3D to 2D data transformation, widely known as a Bleistein filter. Despite the broad use of such a transformation, it requires some assumptions that make it prone to errors. Although the existence of the errors is known, previous studies have failed to quantify the inaccuracies introduced on permittivity and electrical conductivity estimation. Based on a comparison of 3D and 2D modeling, errors could reach up to 30% of the original amplitudes in layered structures with high-contrast zones. These inaccuracies can significantly affect the performance of crosshole GPR FWI in estimating permittivity and especially electrical conductivity. We have addressed these potential inaccuracies by introducing a novel 2.5D crosshole GPR FWI that uses a 3D finite-difference time-domain forward solver (gprMax3D). This allows us to model GPR data in 3D, whereas carrying out FWI in the 2D plane. Synthetic results showed that 2.5D crosshole GPR FWI outperformed 2D FWI by achieving higher resolution and lower average errors for permittivity and conductivity models. The average model errors in the whole domain were reduced by approximately 2% for permittivity and conductivity, whereas zone-specific errors in high-contrast layers were reduced by approximately 20%. We verified our approach using crosshole 2.5D FWI measured data, and the results showed good agreement with previous 2D FWI results and geologic studies. Moreover, we analyzed various approaches and found an adequate trade-off between computational complexity and accuracy of the results, i.e., reducing the computational effort while maintaining the superior performance of our 2.5D FWI scheme.

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.

Elastic Full Waveform Inversion With a Permanent Seismic Source ACROSS: Towards Hydrocarbon Reservoir Monitoring

2014 ◽  
Author(s):  
Mamoru Takanashi ◽  
Ayato Kato ◽  
Junzo Kasahara ◽  
Stefan Luth ◽  
Christopher Juhlin
Keyword(s):  
Waveform Inversion ◽  
Seismic Source ◽  
Full Waveform Inversion ◽  
Hydrocarbon Reservoir ◽  
Full Waveform ◽  
Reservoir Monitoring
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