scholarly journals Coda-wave decorrelation sensitivity kernels in 2-D elastic media: a numerical approach

2020 ◽  
Vol 223 (2) ◽  
pp. 934-943
Author(s):  
Alejandro Duran ◽  
Thomas Planès ◽  
Anne Obermann
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Numerical Approach ◽  
Coda Waves ◽  
Coda Wave ◽  
Elastic Media ◽  
S Wave ◽  
Velocity Changes

SUMMARY Probabilistic sensitivity kernels based on the analytical solution of the diffusion and radiative transfer equations have been used to locate tiny changes detected in late arriving coda waves. These analytical kernels accurately describe the sensitivity of coda waves towards velocity changes located at a large distance from the sensors in the acoustic diffusive regime. They are also valid to describe the acoustic waveform distortions (decorrelations) induced by isotropically scattering perturbations. However, in elastic media, there is no analytical solution that describes the complex propagation of wave energy, including mode conversions, polarizations, etc. Here, we derive sensitivity kernels using numerical simulations of wave propagation in heterogeneous media in the acoustic and elastic regimes. We decompose the wavefield into P- and S-wave components at the perturbation location in order to construct separate P to P, S to S, P to S and S to P scattering sensitivity kernels. This allows us to describe the influence of P- and S-wave scattering perturbations separately. We test our approach using acoustic and elastic numerical simulations where localized scattering perturbations are introduced. We validate the numerical sensitivity kernels by comparing them with analytical kernel predictions and with measurements of coda decorrelations on the synthetic data.

Simulation of seismic wave scattering for the computation of probabilistic coda-wave sensitivity kernels

2020 ◽  
Author(s):  
Tuo Zhang ◽  
Christoph Sens-Schönfelder
Keyword(s):  
Wave Velocity ◽  
Wave Scattering ◽  
Random Medium ◽  
Coda Waves ◽  
Coda Wave ◽  
Small Scale ◽  
Model Parameters ◽  
S Wave ◽  
Seismic Coda ◽  
Wave Sensitivity

<p>Scattered seismic coda waves are frequently used to characterize small scale medium heterogeneities, intrinsic attenuation or temporal changes of wave velocity. Spatial variability of these properties raises questions about the spatial sensitivity of seismic coda waves. Especially the continuous monitoring of medium perturbations using ambient seismic noise led to a demand for approaches to image perturbations observed with coda waves. An efficient approach to localize the property variations in the medium is to invert the observations from different source-receiver combinations and different lapse times in the coda for the location of the perturbations. The key of such an inversion is calculating the coda-wave sensitivity kernels which describe the connection between observations and the perturbation. Most discussions of sensitivity kernels use the acoustic approximation and assume wave propagation in the diffusion regime.</p><p>We model 2-D  elastic multiple nonisotropic scattering in a random medium with spatially variable heterogeneity and attenuation. The Monte Carlo method is used to numerically solve the radiative transfer equation that describes the wave scattering process here. Recording of the specific intensity of the wavefield <strong><em>I</em>(<em>r,n,t</em>)</strong> which contains the complete information about the energy at position <strong><em>r</em></strong> at time <em>t</em> with the propagation direction <strong><em>n</em></strong> allows us to calculate sensitivity kernels according to rigorous theoretical derivations. We investigate sensitivity kernels that describe the relationships between changes of the model parameters P- and S-wave velocity, P- and S-wave attenuation, and the strength of fluctuation on the one hand and the observables envelope amplitude, travel time changes and decorrelation on the other hand. These sensitivity kernels reflect the effect of the spatial variations of medium properties on wavefield. Our work offers a direct approach to compute these new expressions and adapt them to spatially variable heterogeneities. The sensitivity kernels we derived are the first step in the development of an inversion approach based on coda waves.</p>

scholarly journals Ultrasonic monitoring of stress and cracks of the 1/3 scale mock-up of nuclear reactor concrete containment structure

2021 ◽  
pp. 147592172110347
Author(s):  
Qi Xue ◽  
Eric Larose ◽  
Ludovic Moreau ◽  
Romain Thery ◽  
Odile Abraham ◽  
...  
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Structural Changes ◽  
Nuclear Reactor ◽  
Temporal Variations ◽  
Coda Waves ◽  
Coda Wave ◽  
Apparent Velocity ◽  
Exterior Surface ◽  
Velocity Changes

To evaluate the stress level and damage of a reinforced concrete containment wall (similar to those used in nuclear power plants) and its reaction to pressure variations, we conducted successive ultrasonic experiments on the exterior surface of the containment wall in the gusset area for three consecutive years (2017, 2018 and 2019). During each experiment, the pressure inside the containment wall increased gradually from 0 MPa to 0.43 MPa and then decreased back to 0 MPa. From the analysis of the ultrasonic coda waves obtained in the multiple scattering regime (80–220 kHz), we performed Coda Wave Interferometry to calculate the apparent velocity changes in the structure (denoted by dV/ V a) and Coda Wave Decorrelation (DC) measurements to produce 3D cartographies of stress and crack distribution. From three source–receiver pairs, located at the top, middle and bottom of the experimental region, we observe that coda waves dilate, shrink and remain almost unchanged, respectively. This corresponds to the decreasing, increasing and invariant pressure inside the concrete. The comparison of 3 years’ results demonstrates that the variation of dV/ V a and DC under the same pressure test increases through the years, which indicates the progressive deterioration and ageing of the concrete. From a large collection of source–receiver pairs at different times, the spatial–temporal variations of dV/ V a and DC are then used to produce a map of the structural velocity and scattering changes, respectively. We observe a decreasing velocity on the top part and an increasing in the middle one, which is in line with the dV/ V a analysis. The reconstructed scattering changes (or structural changes) highlight the active region during the inflation–deflation procedure, corresponding to the opening and closing (and sometimes the development) of cracks. The larger magnitude in 2019 than in 2017 indicates the increasing damage in the concrete.

Prestack waveform inversion based on analytical solution of the viscoelastic wave equation

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. R45-R61
Author(s):  
Yuanqiang Li ◽  
Jingye Li ◽  
Xiaohong Chen ◽  
Jian Zhang ◽  
Xin Bo
Keyword(s):  
Analytical Solution ◽  
Seismic Reflection ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Low Frequency ◽  
S Wave ◽  
Single Interface ◽  
Wave Velocities ◽  
Avo Inversion ◽  
Viscoelastic Wave

Amplitude-variation-with-offset (AVO) inversion is based on single interface reflectivity equations. It involves some restrictions, such as the small-angle approximation, including only primary reflections, and ignoring attenuation. To address these shortcomings, the analytical solution of the 1D viscoelastic wave equation is used as the forward modeling engine for prestack inversion. This method can conveniently handle the attenuation and generate the full wavefield response of a layered medium. To avoid numerical difficulties in the analytical solution, the compound matrix method is applied to rapidly obtain the analytical solution by loop vectorization. Unlike full-waveform inversion, the proposed prestack waveform inversion (PWI) can be performed in a target-oriented way and can be applied in reservoir study. Assuming that a Q value is known, PWI is applied to synthetic data to estimate elastic parameters including compressional wave (P-wave) and shear wave (S-wave) velocities and density. After validating our method on synthetic data, this method is applied to a reservoir characterization case study. The results indicate that the reflectivity calculated by our approach is more realistic than that computed by using single interface reflectivity equations. Attenuation is an integral effect on seismic reflection; therefore, the sensitivity of seismic reflection to P-and S-wave velocities and density is significantly greater than that to Q, and the seismic records are sensitive to the low-frequency trend of Q. Thus, we can invert for the three elastic parameters by applying the fixed low-frequency trend of Q. In terms of resolution and accuracy of synthetic and real inversion results, our approach performs superiorly compared to AVO inversion.

scholarly journals Sensitivity kernels for static and dynamic tomography of scattering and absorbing media with elastic waves: a probabilistic approach

2021 ◽  
Vol 225 (3) ◽  
pp. 1824-1853
Author(s):  
Tuo Zhang ◽  
Christoph Sens-Schönfelder ◽  
Ludovic Margerin
Keyword(s):  
Energy Density ◽  
Wave Velocity ◽  
Probabilistic Approach ◽  
Coda Waves ◽  
Isotropic Scattering ◽  
Coda Wave ◽  
Small Scale ◽  
Practical Calculation ◽  
S Wave ◽  
Seismic Coda

SUMMARY Scattered seismic coda waves are frequently used to characterize small scale medium heterogeneities, intrinsic attenuation or temporal changes of wave velocity. Spatial variability of these properties raises questions about the spatial sensitivity of seismic coda waves. Especially the continuous monitoring of medium perturbations using ambient seismic noise led to a demand for approaches to image perturbations observed with coda waves. An efficient approach to localize spatial and temporal variations of medium properties is to invert the observations from different source–receiver combinations and different lapse times in the coda for the location of the perturbations. For such an inversion, it is key to calculate the coda-wave sensitivity kernels which describe the connection between observations and the perturbation. Most discussions of sensitivity kernels use the acoustic approximation in a spatially uniform medium and often assume wave propagation in the diffusion regime. We model 2-D multiple non-isotropic scattering in a random elastic medium with spatially variable heterogeneity and attenuation using the radiative transfer equations which we solve with the Monte Carlo method. Recording of the specific energy density of the wavefield that contains the complete information about the energy density at a given position, time and propagation direction allows us to calculate sensitivity kernels according to rigorous theoretical derivations. The practical calculation of the kernels involves the solution of the adjoint radiative transport equations. We investigate sensitivity kernels that describe the relationships between changes of the model in P- and S-wave velocity, P- and S-wave attenuation and the strength of fluctuation on the one hand and seismogram envelope, traveltime changes and waveform decorrelation as observables on the other hand. These sensitivity kernels reflect the effect of the spatial variations of medium properties on the wavefield and constitute the first step in the development of a tomographic inversion approach for the distribution of small-scale heterogeneity based on scattered waves.

Estimation of seismic source parameters in 3D elastic media using the reciprocity theorem

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R963-R976
Author(s):  
Petr V. Petrov ◽  
Gregory A. Newman
Keyword(s):  
Heterogeneous Media ◽  
Source Parameters ◽  
Synthetic Data ◽  
Seismic Source ◽  
Optimization Methods ◽  
Geothermal Field ◽  
Second Order ◽  
Order Moment ◽  
Elastic Media ◽  
Moment Tensors

We have developed a novel method based upon reciprocity principles to simultaneously estimate the location of a seismic event and its source mechanism in 3D heterogeneous media. The method finds double-couple (DC) and non-DC mechanisms of microearthquakes arising from localized induced and natural seismicity. Because the method uses an exhaustive search of the 3D elastic media, it is globally convergent. It does not suffer from local minima realization observed with local optimization methods, including Newton, Gauss-Newton, or gradient-descent algorithms. The computational efficiency of our scheme is derived from the reciprocity principle, in which the number of 3D model realizations corresponds to the number of measurement receivers. The 3D forward modeling is carried out in the damped Fourier domain with a 3D finite-difference frequency-domain fourth- and second-order code developed to simulate elastic waves generated by seismic sources defined by forces and second-order moment density tensors. We evaluate the results of testing this new methodology on synthetic data for the Raft River geothermal field, Idaho, as well as determine its applicability in designing optimal borehole monitoring arrays in a fracking experiment at the Homestake Mine, South Dakota. We also find that the method proposed here can retrieve the moment tensors of the space distributed source with data arising from spatially restricted arrays with limited aperture. The effects of uncertainties on the source parameter estimation are also examined with respect to data noise and model uncertainty.

Liver Radioembolization: An Analysis of Parameters that Influence the Catheter-Based Particle-Delivery via CFD

2020 ◽  
Vol 27 (10) ◽  
pp. 1600-1615 ◽  
Author(s):  
Jorge Aramburu ◽  
Raúl Antón ◽  
Alejandro Rivas ◽  
Juan C. Ramos ◽  
Bruno Sangro ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Particle Distribution ◽  
Numerical Approach ◽  
Radioactive Microspheres ◽  
Tumor Bearing ◽  
Hemodynamic Pattern ◽  
Valuable Treatment ◽  
Catheter Tip ◽  
Radiation Induced ◽  
Computational Fluid Dynamics Cfd

Radioembolization (RE) is a valuable treatment for liver cancer. It consists of administering radioactive microspheres by an intra-arterially placed catheter with the aim of lodging these microspheres, which are driven by the bloodstream, in the tumoral bed. Even though it is a safe treatment, some radiation-induced complications may arise. In trying to detect or solve the possible incidences that cause nontarget irradiation, simulating the particle- hemodynamics in hepatic arteries during RE by computational fluid dynamics (CFD) tools has become a valuable approach. This paper reviews the parameters that influence the outcome of RE and that have been studied via numerical simulations. In this numerical approach, the outcome of RE is regarded as successful if particles reach the artery branches that feed tumor-bearing liver segments. Up to 10 parameters have been reviewed. The variation of each parameter actually alters the hemodynamic pattern in the vicinities of the catheter tip and locally alters the incorporation of the particles into the bloodstream. Therefore, in general, the local influences of these parameters should result in global differences in terms of particle distribution in the hepatic artery branches. However, it has been observed that under some (qualitatively described) appropriate conditions where particles align with blood streamlines, the local influence resulting from a variation of a given parameter vanishes and no global differences are observed. Furthermore, the increasing number of CFD studies on RE suggests that numerical simulations have become an invaluable research tool in the study of RE.

Coda Waves for Health Monitoring of Composites Under Low-Velocity Impact

2021 ◽  
Author(s):  
Subal Sharma ◽  
Vinay Dayal
Keyword(s):  
Ultrasonic Waves ◽  
Coda Waves ◽  
Low Velocity Impact ◽  
Coda Wave ◽  
Low Velocity ◽  
Fibrous Composite Material ◽  
Velocity Impact ◽  
Isotropic Composite ◽  
The Impact ◽  
Impact Damages

Abstract Coda waves have been shown to be sensitive to lab-controlled defects such as very small holes in fibrous composite material. In the real world, damages are subtler and more irregular. The main objective of this work is to investigate coda wave capability to detect low-velocity impact damages. The emphasis is to detect the presence of barely visible impact damages using ultrasonic waves. Detection of incipient damage state is important as it will grow over the life of the structure. Differential features, previously used in similar work, have been utilized to detect realistic impact damages on carbon fiber composites. Quasi-isotropic composite laminates were subjected to low-velocity impact energy ranging from 2J to 4.5J. Two differential features reported could be used detect the presence of damage. It is also observed that ply orientation can be a deterministic factor for indicating damages. The size and shape of the impact damage has been characterized using ultrasonic C-scans. Results indicate that coda waves can be used for the detection of damage due to low-velocity impact.

A least squares method for earthquake mechanism determination using S-wave data

1964 ◽  
Vol 54 (6A) ◽  
pp. 2037-2047
Author(s):  
Agustin Udias
Keyword(s):  
Least Squares ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Numerical Approach ◽  
Focal Mechanisms ◽  
Least Square ◽  
S Wave ◽  
Double Couple ◽  
Earthquake Mechanism

abstract In this paper a numerical approach to the determination of focal mechanisms based on the observation of the polarization of the S wave at N stations is presented. Least-square methods are developed for the determination of the orientation of the single and double couple sources. The methods allow a statistical evaluation of the data and of the accuracy of the solutions.

scholarly journals Discussion on the Theoretical Basis for Cross-Over Method Applied to Downhole Wave Velocity Test

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Qing Dong ◽  
Zheng-hua Zhou ◽  
Su Jie ◽  
Bing Hao ◽  
Yuan-dong Li
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Wave Velocity ◽  
Theoretical Basis ◽  
Influence Factors ◽  
P Wave ◽  
Engineering Practice ◽  
S Wave ◽  
Simulation Results ◽  
The Cross

At engineering practice, the theoretical basis for the cross-over method, used to obtain shear wave arrival time in the downhole method of the wave velocity test by surface forward and backward strike, is that the polarity of P-wave keeps the same, while the polarity of S-wave transforms when the direction of strike inverted. However, the characteristics of signals recorded in tests are often found to conflict with this theoretical basis for the cross-over method, namely, the polarity of the P-wave also transforms under the action of surface forward and backward strike. Therefore, 3D finite element numerical simulations were conducted to study the validity of the theoretical basis for the cross-over method. The results show that both shear and compression waves are observed to be in 180° phase difference between horizontal signal traces, consistent with the direction of excitation generated by reversed impulse. Furthermore, numerical simulation results prove to be reliable by the analytic solution; it shows that the theoretical basis for the cross-over method applied to the downhole wave velocity test is improper. In meanwhile, numerical simulations reveal the factors (inclining excitation, geophone deflection, inclination, and background noise) that may cause the polarity of the P-wave not to reverse under surface forward and backward strike. Then, as to reduce the influence factors, we propose a method for the downhole wave velocity test under surface strike, the time difference of arrival is based between source peak and response peak, and numerical simulation results show that the S-wave velocity by this method is close to the theoretical S-wave velocity of soil.

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