A gradient-based model parametrization using Bernstein polynomials in Bayesian inversion of surface wave dispersion

2017 ◽  
Vol 211 (1) ◽  
pp. 528-540 ◽  
Author(s):  
Jeremy M. Gosselin ◽  
Stan E. Dosso ◽  
John F. Cassidy ◽  
Jorge E. Quijano ◽  
Sheri Molnar ◽  
...  
Keyword(s):  
Surface Wave ◽  
Bernstein Polynomials ◽  
Wave Dispersion ◽  
Bayesian Inversion ◽  
Surface Wave Dispersion ◽  
Gradient Based

scholarly journals Geodynamic tomography: constraining upper-mantle deformation patterns from Bayesian inversion of surface waves

2020 ◽  
Vol 224 (3) ◽  
pp. 2077-2099
Author(s):  
J K Magali ◽  
T Bodin ◽  
N Hedjazian ◽  
H Samuel ◽  
S Atkins
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Upper Mantle ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Bayesian Inversion ◽  
Model Parameters ◽  
Mantle Flow ◽  
Surface Wave Dispersion ◽  
Elastic Tensor

SUMMARY In the Earth’s upper mantle, seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of olivine due to mantle deformation. Large-scale observation of anisotropy in surface wave tomography models provides unique constraints on present-day mantle flow. However, surface waves are not sensitive to the 21 coefficients of the elastic tensor, and therefore the complete anisotropic tensor cannot be resolved independently at every location. This large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor. In this work, we propose to regularize the tomographic problem by using constraints from geodynamic modelling to reduce the number of model parameters. Instead of inverting for seismic velocities, we parametrize our inverse problem directly in terms of physical quantities governing mantle flow: a temperature field, and a temperature-dependent viscosity. The forward problem consists of three steps: (1) calculation of mantle flow induced by thermal anomalies, (2) calculation of the induced CPO and elastic properties using a micromechanical model, and (3) computation of azimuthally varying surface wave dispersion curves. We demonstrate how a fully nonlinear Bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields, without having to explicitly parametrize the elastic tensor. Here, we consider simple flow models generated by spherical temperature anomalies. The results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation. The solution to our inversion problem is an ensemble of models (i.e. thermal structures) representing a posterior probability, therefore providing uncertainties for each model parameter.

scholarly journals Geodynamic Tomography: Constraining Upper-Mantle Deformation Patterns from Bayesian Inversion of Surface Waves

2021 ◽  
Author(s):  
John Keith Magali ◽  
Thomas Bodin ◽  
Navid Hedjazian ◽  
Henri Samuel ◽  
Suzanne Atkins
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Upper Mantle ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Bayesian Inversion ◽  
Model Parameters ◽  
Mantle Flow ◽  
Surface Wave Dispersion ◽  
Elastic Tensor

<p>In the Earth’s upper mantle, seismic anisotropy mainly originates from the crystallographic preferred orientation (CPO) of olivine due to mantle deformation. Large-scale observation of anisotropy in surface wave tomography models provides unique constraints on present-day mantle flow. However, surface waves are not sensitive to the 21 coefficients of the elastic tensor, and therefore the complete anisotropic tensor cannot be resolved independently at every location. This large number of parameters may be reduced by imposing spatial smoothness and symmetry constraints to the elastic tensor. In this work, we propose to regularize the tomographic problem by using constraints from geodynamic modeling to reduce the number of model parameters. Instead of inverting for seismic velocities, we parametrize our inverse problem directly in terms of physical quantities governing mantle flow: a temperature field, and a temperature-dependent viscosity. The forward problem consists of three steps: (1) calculation of mantle flow induced by thermal anomalies, (2) calculation of the induced CPO and elastic properties using a micromechanical model, and (3) computation of azimuthally varying surface wave dispersion curves. We demonstrate how a fully nonlinear Bayesian inversion of surface wave dispersion curves can retrieve the temperature and viscosity fields, without having to explicitly parametrize the elastic tensor. Here, we consider simple flow models generated by spherical temperature anomalies. The results show that incorporating geodynamic constraints in surface wave inversion help to retrieve patterns of mantle deformation. The solution to our inversion problem is an ensemble of models (i.e. thermal structures) representing a posterior probability, therefore providing uncertainties for each model parameter.</p>

Comparison of different regularization schemes for the 1D laterally constrained inversion of seismic surface wave data

2020 ◽  
Author(s):  
Julien Guillemoteau ◽  
Giulio Vignoli ◽  
Jennifer Barreto
Keyword(s):  
Inverse Problem ◽  
Surface Wave ◽  
Geophysical Methods ◽  
Model Space ◽  
Wave Dispersion ◽  
Sources Of Information ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Gradient Based ◽  
Inversion Procedure

<p>The 1D layered inversion of surface wave dispersion data is a powerful tool to characterize the vertical distribution of S-wave velocity. Its applications span from seismology to geotechnical engineering, going through exploration geophysics. As many others, also this non-linear inverse problem is considerably ill-posed. Thus, in the Tikhonov’s regularization framework, the associated non-uniqueness and instability of the solution with respect to the data and their uncertainty can be tackled by including prior information in the inversion process. However, for the case of the gradient-based deterministic inversion problem, only constraints enforcing smooth spatial variations of the S-velocities have been used, even when blocky targets were expected. This, clearly, generates results that might fit the observed data, but that are often not compatible with other sources of information. On the other hand, probabilistic approaches can be used to properly map the model space; however, they are still very computationally expensive to be used routinely, or to be easily integrated in a multi-physical inversion procedure involving other geophysical methods.</p><p>Our goal is to combine computer efficiency, capability of integration with other geophysical methods, and some exhaustiveness regarding the non-uniqueness of the inverse problem. For this, we developed a coherent set of tools for the deterministic inversion of dispersion curves that is capable of applying a quite large spectrum of constraints. This includes, for example, vertically and laterally constrained inversions with different levels and kinds of regularization (sharpness and/or smoothness). In this study, we evaluate the capabilities and the possible limitations of the different regularization approaches on various datasets.</p>

Improved Surface Wave Dispersion Models, Amplitude Measurements and Azimuth Estimates

2005 ◽  
Author(s):  
Jeffry L. Stevens ◽  
David A. Adams ◽  
G. E. Baker ◽  
Mariana G. Eneva ◽  
Heming Xu
Keyword(s):  
Surface Wave ◽  
Wave Dispersion ◽  
Dispersion Models ◽  
Surface Wave Dispersion

scholarly journals Imaging the subsurface using induced seismicity and ambient noise: 3-D tomographic Monte Carlo joint inversion of earthquake body wave traveltimes and surface wave dispersion

2020 ◽  
Vol 222 (3) ◽  
pp. 1639-1655
Author(s):  
Xin Zhang ◽  
Corinna Roy ◽  
Andrew Curtis ◽  
Andy Nowacki ◽  
Brian Baptie
Keyword(s):  
Surface Wave ◽  
Ambient Noise ◽  
Velocity Structure ◽  
Joint Inversion ◽  
Body Wave ◽  
Source Parameters ◽  
Wave Dispersion ◽  
Inversion Method ◽  
Surface Wave Dispersion ◽  
Wave Data

SUMMARY Seismic body wave traveltime tomography and surface wave dispersion tomography have been used widely to characterize earthquakes and to study the subsurface structure of the Earth. Since these types of problem are often significantly non-linear and have non-unique solutions, Markov chain Monte Carlo methods have been used to find probabilistic solutions. Body and surface wave data are usually inverted separately to produce independent velocity models. However, body wave tomography is generally sensitive to structure around the subvolume in which earthquakes occur and produces limited resolution in the shallower Earth, whereas surface wave tomography is often sensitive to shallower structure. To better estimate subsurface properties, we therefore jointly invert for the seismic velocity structure and earthquake locations using body and surface wave data simultaneously. We apply the new joint inversion method to a mining site in the United Kingdom at which induced seismicity occurred and was recorded on a small local network of stations, and where ambient noise recordings are available from the same stations. The ambient noise is processed to obtain inter-receiver surface wave dispersion measurements which are inverted jointly with body wave arrival times from local earthquakes. The results show that by using both types of data, the earthquake source parameters and the velocity structure can be better constrained than in independent inversions. To further understand and interpret the results, we conduct synthetic tests to compare the results from body wave inversion and joint inversion. The results show that trade-offs between source parameters and velocities appear to bias results if only body wave data are used, but this issue is largely resolved by using the joint inversion method. Thus the use of ambient seismic noise and our fully non-linear inversion provides a valuable, improved method to image the subsurface velocity and seismicity.

scholarly journals Reliable workflow for inversion of seismic receiver function and surface wave dispersion data: a “13 BB Star” case study

2019 ◽  
Vol 24 (1) ◽  
pp. 101-120
Author(s):  
Kajetan Chrapkiewicz ◽  
Monika Wilde-Piórko ◽  
Marcin Polkowski ◽  
Marek Grad
Keyword(s):  
Surface Wave ◽  
Inverse Problems ◽  
Receiver Function ◽  
Joint Inversion ◽  
Wave Dispersion ◽  
Receiver Functions ◽  
P Wave ◽  
Surface Wave Dispersion ◽  
Phase Velocity Dispersion ◽  
Wide Range

AbstractNon-linear inverse problems arising in seismology are usually addressed either by linearization or by Monte Carlo methods. Neither approach is flawless. The former needs an accurate starting model; the latter is computationally intensive. Both require careful tuning of inversion parameters. An additional challenge is posed by joint inversion of data of different sensitivities and noise levels such as receiver functions and surface wave dispersion curves. We propose a generic workflow that combines advantages of both methods by endowing the linearized approach with an ensemble of homogeneous starting models. It successfully addresses several fundamental issues inherent in a wide range of inverse problems, such as trapping by local minima, exploitation of a priori knowledge, choice of a model depth, proper weighting of data sets characterized by different uncertainties, and credibility of final models. Some of them are tackled with the aid of novel 1D checkerboard tests—an intuitive and feasible addition to the resolution matrix. We applied our workflow to study the south-western margin of the East European Craton. Rayleigh wave phase velocity dispersion and P-wave receiver function data were gathered in the passive seismic experiment “13 BB Star” (2013–2016) in the area of the crust recognized by previous borehole and refraction surveys. Final models of S-wave velocity down to 300 km depth beneath the array are characterized by proximity in the parameter space and very good data fit. The maximum value in the mantle is higher by 0.1–0.2 km/s than reported for other cratons.

Surface Wave Dispersion Imaging Using Improved τ-p Transform Approach

2013 ◽  
Vol 353-356 ◽  
pp. 1196-1202 ◽  
Author(s):  
Jian Qi Lu ◽  
Shan You Li ◽  
Wei Li
Keyword(s):  
Surface Wave ◽  
Phase Shift ◽  
Dispersion Curve ◽  
Wave Dispersion ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Narrow Frequency Range ◽  
Channel Analysis ◽  
Rayleigh Wave Dispersion

Surface wave dispersion imaging approach is crucial for multi-channel analysis of surface wave (MASW). Because the resolution of inversed S-wave velocity and thickness of a layer are directly subjected to the resolution of imaged dispersion curve. The τ-p transform approach is an efficient and commonly used approach for Rayleigh wave dispersion curve imaging. However, the conventional τ-p transform approach was severely affected by waves amplitude. So, the energy peaks of f-v spectrum were mainly gathered in a narrow frequency range. In order to remedy this shortage, an improved τ-p transform approach was proposed by this paper. Comparison has been made between phase shift and improved τ-p transform approaches using both synthetic and in situ tested data. Result shows that the dispersion image transformed from proposed approach is superior to that either from conventionally τ-p transform or from phase shift approaches.

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