scholarly journals Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. H19-H31 ◽  
Author(s):  
Knud Skou Cordua ◽  
Thomas Mejer Hansen ◽  
Klaus Mosegaard
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
A Priori ◽  
Waveform Inversion ◽  
Multiple Point ◽  
Full Waveform Inversion ◽  
A Posteriori ◽  
A Priori Information ◽  
Full Waveform ◽  
Priori Information

We present a general Monte Carlo full-waveform inversion strategy that integrates a priori information described by geostatistical algorithms with Bayesian inverse problem theory. The extended Metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear inverse problems, such as full-waveform inversion. Sequential Gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two-point (e.g., Gaussian) or multiple-point statistics. We outline the theoretical framework for a full-waveform inversion strategy that integrates the extended Metropolis algorithm with sequential Gibbs sampling such that arbitrary complex geostatistically defined a priori information can be included. At the same time we show how temporally and/or spatiallycorrelated data uncertainties can be taken into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data using multiple-point-based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full-waveform inverse problem. Benefits of the proposed methodology compared with deterministic inversion approaches include: (1) The a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information, which provides a means of obtaining resolution analysis. (2) Based on a posteriori realizations, complicated statistical questions can be answered, such as the probability of connectivity across a layer. (3) Complex a priori information can be included through geostatistical algorithms. These benefits, however, require more computing resources than traditional methods do. Moreover, an adequate knowledge of data uncertainties and a priori information is required to obtain meaningful uncertainty estimates. The latter may be a key challenge when considering field experiments, which will not be addressed here.

Improvements to elastic full-waveform inversion using cross-gradient constraints

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. R105-R115 ◽  
Author(s):  
Edgar Manukyan ◽  
Hansruedi Maurer ◽  
André Nuber
Keyword(s):  
Field Data ◽  
A Priori ◽  
Waveform Inversion ◽  
Structural Similarity ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
A Priori Information ◽  
Individual Parameter ◽  
Full Waveform ◽  
Priori Information

Seismic full-waveform inversion (FWI) is potentially a powerful method for obtaining high-resolution subsurface images, but the results are often distorted by nonlinear effects and parameter trade-offs. Such distortions can be particularly severe in the case of multiparameter FWI, such as elastic FWI, in which inversion is performed simultaneously for P- and S-wave velocities and density. The problem can be alleviated by adding constraints in the form of plausible a priori information. A usually well-justified constraint includes the structural similarity of different model parameters; i.e., an anomalous body likely exhibits variations in all elastic properties, although their magnitudes may be different. To consider such types of a priori information, we have developed a structurally constrained elastic FWI, which is based on minimization of the cross products of gradients of different model parameters. Our synthetic 2D experiments show that structurally constrained FWI can significantly improve model reconstruction. It is also demonstrated that our approach still leads to improved results, even when the structural similarity between the individual parameter types is not exactly met. Inversions of field data show that in comparison to conventional FWI, structurally constrained FWI is able to match the field data equally well while requiring less structural complexity of the subsurface.

scholarly journals A synthetic study to assess the applicability of full-waveform inversion to infer snow stratigraphy from upward-looking ground-penetrating radar data

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. WA213-WA223 ◽  
Author(s):  
Lino Schmid ◽  
Jürg Schweizer ◽  
John Bradford ◽  
Hansruedi Maurer
Keyword(s):  
Water Content ◽  
Liquid Water ◽  
A Priori ◽  
Waveform Inversion ◽  
Liquid Water Content ◽  
A Priori Information ◽  
Full Waveform ◽  
Snow Stratigraphy ◽  
Priori Information ◽  
Ground Penetrating

Snow stratigraphy and liquid water content are key contributing factors to avalanche formation. Upward-looking ground-penetrating radar (upGPR) systems allow nondestructive monitoring of the snowpack, but deriving density and liquid water content profiles is not yet possible based on the direct analysis of the reflection response. We have investigated the feasibility of deducing these quantities using full-waveform inversion (FWI) techniques applied to upGPR data. For that purpose, we have developed a frequency-domain FWI algorithm in which we additionally took advantage of time-domain features such as the arrival times of reflected waves. Our results indicated that FWI applied to upGPR data is generally feasible. More specifically, we could show that in the case of a dry snowpack, it is possible to derive snow densities and layer thicknesses if sufficient a priori information is available. In case of a wet snowpack, in which it also needs to be inverted for the liquid water content, the algorithm might fail, even if sufficient a priori information is available, particularly in the presence of realistic noise. Finally, we have investigated the capability of FWI to resolve thin layers that play a key role in snow stability evaluation. Our simulations indicate that layers with thicknesses well below the GPR wavelengths can be identified, but in the presence of significant liquid water, the thin-layer properties may be prone to inaccuracies. These results are encouraging and motivate applications to field data, but significant issues remain to be resolved, such as the determination of the generally unknown upGPR source function and identifying the optimal number of layers in the inversion models. Furthermore, a relatively high level of prior knowledge is required to let the algorithm converge. However, we feel these are not insurmountable and the new technology has significant potential to improve field data analysis.

scholarly journals Adding Prior Information in FWI through Relative Entropy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 599
Author(s):  
Danilo Cruz ◽  
João de Araújo ◽  
Carlos da Costa ◽  
Carlos da Silva
Keyword(s):  
Inverse Problem ◽  
Relative Entropy ◽  
Global Minimum ◽  
Prior Information ◽  
Waveform Inversion ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Full Waveform

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.

A Backward Monte Carlo method for fast-ion-loss simulations

2021 ◽  
Author(s):  
Filippo Zonta ◽  
Lucia Sanchis ◽  
Eero Hirvijoki
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
A Priori ◽  
Target Surface ◽  
A Priori Information ◽  
Ion Distributions ◽  
Plasma Facing Components ◽  
Priori Information ◽  
Fast Ion

Abstract This paper presents a novel scheme to improve the statistics of simulated fast-ion loss signals and power loads to plasma-facing components in fusion devices. With the so-called Backward Monte Carlo method, the probabilities of marker particles reaching a chosen target surface can be approximately traced from the target back into the plasma. Utilizing the probabilities as {\it a priori} information for the well-established Forward Monte Carlo method, statistics in fast-ion simulations are significantly improved. For testing purposes, the scheme has been implemented to the ASCOT suite of codes and applied to a realistic ASDEX Upgrade configuration of beam-ion distributions.

scholarly journals Ozone profile smoothness as a priori information in the inversion of limb measurements

2004 ◽  
Vol 22 (10) ◽  
pp. 3411-3420 ◽  
Author(s):  
V. F. Sofieva ◽  
J. Tamminen ◽  
H. Haario ◽  
E. Kyrölä ◽  
M. Lehtinen
Keyword(s):  
A Priori ◽  
Optimal Estimation ◽  
Maximum A Posteriori ◽  
A Posteriori ◽  
A Priori Information ◽  
Ozone Profile ◽  
Stellar Occultation ◽  
Atmospheric Profiles ◽  
Priori Information ◽  
Typical Measurement

Abstract. In this work we discuss inclusion of a priori information about the smoothness of atmospheric profiles in inversion algorithms. The smoothness requirement can be formulated in the form of Tikhonov-type regularization, where the smoothness of atmospheric profiles is considered as a constraint or in the form of Bayesian optimal estimation (maximum a posteriori method, MAP), where the smoothness of profiles can be included as a priori information. We develop further two recently proposed retrieval methods. One of them - Tikhonov-type regularization according to the target resolution - develops the classical Tikhonov regularization. The second method - maximum a posteriori method with smoothness a priori - effectively combines the ideas of the classical MAP method and Tikhonov-type regularization. We discuss a grid-independent formulation for the proposed inversion methods, thus isolating the choice of calculation grid from the question of how strong the smoothing should be. The discussed approaches are applied to the problem of ozone profile retrieval from stellar occultation measurements by the GOMOS instrument on board the Envisat satellite. Realistic simulations for the typical measurement conditions with smoothness a priori information created from 10-years analysis of ozone sounding at Sodankylä and analysis of the total retrieval error illustrate the advantages of the proposed methods. The proposed methods are equally applicable to other profile retrieval problems from remote sensing measurements.

scholarly journals The Neuroelectromagnetic Inverse Problem and the Zero Dipole Localization Error

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Rolando Grave de Peralta ◽  
Olaf Hauk ◽  
Sara L. Gonzalez
Keyword(s):  
Inverse Problem ◽  
Unique Solution ◽  
A Priori ◽  
Inverse Solution ◽  
Localization Error ◽  
A Priori Information ◽  
Dipole Localization ◽  
Inverse Solutions ◽  
Priori Information ◽  
Additional Constraints

A tomography of neural sources could be constructed from EEG/MEG recordings once the neuroelectromagnetic inverse problem (NIP) is solved. Unfortunately the NIP lacks a unique solution and therefore additional constraints are needed to achieve uniqueness. Researchers are then confronted with the dilemma of choosing one solution on the basis of the advantages publicized by their authors. This study aims to help researchers to better guide their choices by clarifying what is hidden behind inverse solutions oversold by their apparently optimal properties to localize single sources. Here, we introduce an inverse solution (ANA) attaining perfect localization of single sources to illustrate how spurious sources emerge and destroy the reconstruction of simultaneously active sources. Although ANA is probably the simplest and robust alternative for data generated by a single dominant source plus noise, the main contribution of this manuscript is to show that zero localization error of single sources is a trivial and largely uninformative property unable to predict the performance of an inverse solution in presence of simultaneously active sources. We recommend as the most logical strategy for solving the NIP the incorporation of sound additional a priori information about neural generators that supplements the information contained in the data.

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