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.

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>

Dynamical evolution of the seismic coda wave increments during the 2011-2012 Santorini's caldera unrest. A Non-Extensive Statistical Physics approach.

2020 ◽  
Author(s):  
Theodoros Aspiotis ◽  
Ioannis Koutalonis ◽  
Georgios Michas ◽  
Filippos Valianatos
Keyword(s):  
Statistical Physics ◽  
Distribution Functions ◽  
Coda Waves ◽  
Coda Wave ◽  
Tectonic Activity ◽  
Volcanic Complex ◽  
Dynamical Structure ◽  
Gaussian Shape ◽  
Caldera Unrest ◽  
Seismic Coda

<p>Santorini's caldera being unrest during 2011-2012, led several studies to raise the important question of whether seismicity is associated with an impending and potential volcanic eruption or it solely relieves the accumulated tectonic energy. In the present work we study seismic coda waves generated by local earthquake events prior, during and after the seismic crisis that occurred within the caldera area. Coda waves are interpreted as scattered seismic waves generated by heterogeneities within the Earth, i.e. by faults, fractures, velocity and/or density boundaries and anomalies, etc. In particular, we utilize the three components of the seismograms recorded by three seismological stations on the island of Santorini and estimate the duration of the coda waves by implementing a three step procedure that includes the signal-to-noise ratio, the STA/LTA method and the short time Fourier transform. The final estimation was verified or reestimated manually due to the existent ambient seismic noise. Due to the nature and the path complexity of the coda waves and towards achieving a unified framework for the study of the immerse geo-structural seismotectonic complexity of the Santorini volcanic complex, we use Non-Extensive Statistical Physics (NESP) to study the probability distribution functions (pdfs) of the increments of seismic coda waves. NESP forms a generalization of the Boltzmann-Gibbs statistical mechanics, that has been extensively used for the analysis of semi-chaotic systems that exhibit long-range interactions, memory effects and multi-fractality. The analysis and results demonstrate that the seismic coda waves increments deviate from the Gaussian shape and their respective pdfs could adequately be described and processed by the q-Gaussian distribution. Furthermore and in order to investigate the dynamical structure of the volcanic-tectonic activity, we estimate the q-indices derived from the pdfs of the coda wave time series increments during the period 2009 - 2014 and present their variations as a function of time and as a function of the local magnitude (M<sub>L</sub>) of the events prior, during and after the caldera unrest.</p> <p> </p> <p><strong> Acknowledgments. </strong>We acknowledge support by the project “HELPOS – Hellenic System for Lithosphere Monitoring” (MIS 5002697) which is implemented under the Action “Reinforcement of the Research and Innovation Infrastructure”, funded by the Operational Programme "Competitiveness, Entrepreneurship and Innovation" (NSRF 2014-2020) and co-financed by Greece & European Union (ERDF)</p>

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.

Time-reverse imaging with limited S-wave velocity model information

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. MA33-MA40 ◽  
Author(s):  
Brian Steiner ◽  
Erik H. Saenger ◽  
Stefan M. Schmalholz
Keyword(s):  
Energy Density ◽  
Wave Velocity ◽  
Wave Energy ◽  
Velocity Model ◽  
Body Waves ◽  
P Wave ◽  
S Wave ◽  
Velocity Models ◽  
Wave Energy Density ◽  
Wavefield Extrapolation

Time-reverse imaging is a wave propagation algorithm for locating sources. Signals recorded by synchronized receivers are reversed in time and propagated back to the source location by elastic wavefield extrapolation. Elastic wavefield extrapolation requires a P-wave as well as an S-wave velocity model. The velocity models available from standard reflection seismic methods are usually restricted to only P-waves. In this study, we use synthetically produced time signals to investigate the accuracy of seismic source localization by means of time-reverse imaging with the correct P-wave and a perturbed S-wave velocity model. The studies reveal that perturbed S-wave velocity models strongly influence the intensity and position of the focus. Imaging the results with the individual maximum energy density for both body wave types instead of mixed modes allows individual analysis of the two body waves. P-wave energy density images render stable focuses in case of a correct P-wave and incorrect S-wave velocity model. Thus, P-wave energy density seems to be a more suitable imaging condition in case of a high degree of uncertainty in the S-wave velocity model.

scholarly journals Two-Dimensional Full-Waveform Joint Inversion of Surface Waves Using Phases and Z/H Ratios

2021 ◽  
Vol 11 (15) ◽  
pp. 6712
Author(s):  
Chao Zhang ◽  
Ting Lei ◽  
Yi Wang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Wave Velocity ◽  
Joint Inversion ◽  
Waveform Inversion ◽  
Small Scale ◽  
Imaging Method ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Full Waveform

Surface-wave dispersion and the Z/H ratio are important parameters used to resolve the Earth’s structure, especially for S-wave velocity. Several previous studies have explored using joint inversion of these two datasets. However, all of these studies used a 1-D depth-sensitivity kernel, which lacks precision when the structure is laterally heterogeneous. Adjoint tomography (i.e., full-waveform inversion) is a state-of-the-art imaging method with a high resolution. It can obtain better-resolved lithospheric structures beyond the resolving ability of traditional ray-based travel-time tomography. In this study, we present a systematic investigation of the 2D sensitivities of the surface wave phase and Z/H ratio using the adjoint-state method. The forward-modeling experiments indicated that the 2D phase and Z/H ratio had different sensitivities to the S-wave velocity. Thus, a full-waveform joint-inversion scheme of surface waves with phases and a Z/H ratio was proposed to take advantage of their complementary sensitivities to the Earth’s structure. Both applications to synthetic data sets in large- and small-scale inversions demonstrated the advantage of the joint inversion over the individual inversions, allowing for the creation of a more unified S-wave velocity model. The proposed joint-inversion scheme offers a computationally efficient and inexpensive alternative to imaging fine-scale shallow structures beneath a 2D seismic array.

scholarly journals Identifying recharge under subtle ephemeral features in flat-lying semi-arid region using a combined geophysical approach

2020 ◽  
Author(s):  
Brady A. Flinchum ◽  
Eddie Banks ◽  
Michael Hatch ◽  
Okke Batelaan ◽  
Luk Peeters ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Arid Region ◽  
Geophysical Methods ◽  
P Wave ◽  
Seismic Survey ◽  
Small Scale ◽  
S Wave ◽  
Near Surface ◽  
Semi Arid Region ◽  
Semi Arid

Abstract. Identifying and quantifying recharge processes linked to ephemeral surface water features is challenging due to their episodic nature. We use a unique combination of well-established near-surface geophysical methods to provide evidence of a surface and groundwater connection under a small ephemeral recharge feature in a flat, semi-arid region near Adelaide, Australia. We use a seismic survey to obtain P-wave velocity through travel-time tomography and S-wave velocity through the multichannel analysis of surface waves. The ratios between P-wave and S-wave velocities allow us to infer the position of the water table. A separate survey was used to obtain electrical conductivity measurements from time-domain electromagnetics and water contents were acquired by downhole nuclear magnetic resonance. The combined geophysical observations provide evidence to support a groundwater mound underneath a subtle ephemeral feature. Our results suggest that recharge is localized and that small-scale ephemeral features play an important role in groundwater recharge. Furthermore, we show that a combined geophysical approach can provide a unique perspective that helps shape the hydrogeological conceptualization of a semi-arid region.

scholarly journals Identifying recharge under subtle ephemeral features in a flat-lying semi-arid region using a combined geophysical approach

2020 ◽  
Vol 24 (9) ◽  
pp. 4353-4368 ◽  
Author(s):  
Brady A. Flinchum ◽  
Eddie Banks ◽  
Michael Hatch ◽  
Okke Batelaan ◽  
Luk J. M. Peeters ◽  
...  
Keyword(s):  
Surface Water ◽  
Wave Velocity ◽  
Arid Region ◽  
P Wave ◽  
Seismic Survey ◽  
Small Scale ◽  
S Wave ◽  
Geophysical Surveys ◽  
Semi Arid Region ◽  
Semi Arid

Abstract. Identifying and quantifying recharge processes linked to ephemeral surface water features is challenging due to their episodic nature. We use a combination of well-established near-surface geophysical methods to provide evidence of a surface and groundwater connection under a small ephemeral recharge feature in a flat, semi-arid region near Adelaide, Australia. We use a seismic survey to obtain P-wave velocity through travel-time tomography and S-wave velocity through the multichannel analysis of surface waves. The ratios between P-wave and S-wave velocities are used to calculate Poisson's ratio, which allow us to infer the position of the water table. Separate geophysical surveys were used to obtain electrical conductivity measurements from time-domain electromagnetics and water contents from downhole nuclear magnetic resonance. The geophysical observations provide evidence to support a groundwater mound underneath a subtle ephemeral surface water feature. Our results suggest that recharge is localized and that small-scale ephemeral features may play an important role in groundwater recharge. Furthermore, we show that a combined geophysical approach can provide a perspective that helps shape the hydrogeological conceptualization of a semi-arid region.

S-Wave Velocity Tomography: Small-Scale Laboratory Application

2005 ◽  
Vol 28 (4) ◽  
pp. 12638 ◽  
Author(s):  
L David Suits ◽  
TC Sheahan ◽  
J-S Lee ◽  
AL Fernandez ◽  
JC Santamarina
Keyword(s):  
Wave Velocity ◽  
Small Scale ◽  
S Wave ◽  
Velocity Tomography

Shear wave velocity from inter-source interferometry

2021 ◽  
Author(s):  
Tom Eulenfeld
Keyword(s):  
Wave Field ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Ambient Noise ◽  
Cross Correlation ◽  
Coda Wave ◽  
Earthquake Catalog ◽  
Seismic Coda ◽  
The Cross

<p>Ambient noise correlation uses the recordings of multiple, statistically distributed seismic sources (the noise sources) at two seismometers. By cross-correlating this signal, one obtains a wave traveling between two seismometers. Due to the principle of reciprocity it is possible to interchange the role of sources and receivers. This cannot be done with ambient noise, but another stochastic signal, the seismic coda is used. Using a cross-correlation of the seismic coda of two earthquakes recorded at multiple seismometers, it is possible to construct a seismic wave traveling between the two earthquakes in depth (inter-source interferometry). Here, I use the the time lag of the maxima in the cross-correlation of the coda wave field to measure the shear wave velocity in the source volume of swarm earthquakes. This technique is different from previous studies analyzing the decorrelation of the coda wave field of nearby events or using the cross-correlation for relocation purposes.</p><p>The technique is applied to five event clusters of the 2018 West Bohemia earthquake swarm. With the help of a high quality earthquake catalog, I was able to determine the shear wave velocity in the region of the five clusters separately. The shear wave velocities range between 3.5 km/s and 4.2 km/s. The resolution of this novel method is given by the extent of the clusters and better than for a comparable classical tomography. The method can be incorporated into a tomographic inversion to map the shear wave velocity in the source region with unprecedented resolution. The influence of focal mechanisms and the attenuation properties on the polarity and location of the maxima in the cross-correlation functions is discussed.</p>

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