scholarly journals On the Potential of 3D Transdimensional Surface Wave Tomography for Geothermal Prospecting of the Reykjanes peninsula

2021 ◽  
Author(s):  
Amin Rahimi Dalkhani ◽  
Xin Zhang ◽  
Cornelis Weemstra
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Velocity Structure ◽  
Voronoi Tessellation ◽  
Three Dimensional ◽  
Seismic Network ◽  
Two Dimensional ◽  
Travel Times ◽  
Model Resolution ◽  
Reykjanes Peninsula

Seismic travel time tomography using surface waves is an effective tool for three-dimensional crustal imaging. Historically, these surface waves are the result of active seismic sources or earthquakes. More recently, however, also surface waves retrieved through the application of seismic interferometry are exploited. Conventionally, two-step inversion algorithms are employed to solve the tomographic inverse problem. That is, a first inversion results in frequency-dependent, two-dimensional maps of phase velocity, which then serve as input for a series of independent, one-dimensional frequency-to-depth inversions. As such, a two-dimensional grid of localized depth-dependent velocity profiles are obtained. Stitching these separate profiles together subsequently yields a three-dimensional velocity model. Relatively recently, a one-step three-dimensional non-linear tomographic algorithm has been proposed. The algorithm is rooted in a Bayesian framework using Markov chains with reversible jumps, and is referred to as transdimensional tomography. Specifically, the three-dimensional velocity field is parameterized by means of a polyhedral Voronoi tessellation. In this study, we investigate the potential of this algorithm for the purpose of recovering the three-dimensional surface-wave-velocity structure from ambient noise recorded on and around the Reykjanes Peninsula, southwest Iceland. To that end, we design a number of synthetic tests that take into account the station configuration of the Reykjanes seismic network. We find that the algorithm is able to recover the 3D velocity structure at various scales in areas where station density is high. In addition, we find that the standard deviation on the recovered velocities is low in those regions. At the same time, the velocity structure is less well recovered in parts of the peninsula sampled by fewer stations. This implies that the algorithm successfully adapts model resolution to the density of rays. Also, it adapts model resolution to the amount of noise on the travel times. Because the algorithm is computationally demanding, we modify the algorithm such that computational costs are reduced while sufficiently preserving non-linearity. We conclude that the algorithm can now be applied adequately to travel times extracted from (time-averaged) station-station cross correlations by the Reykjanes seismic network.

scholarly journals On the Potential of 3D Transdimensional Surface Wave Tomography for Geothermal Prospecting of the Reykjanes Peninsula

2021 ◽  
Vol 13 (23) ◽  
pp. 4929
Author(s):  
Amin Rahimi Dalkhani ◽  
Xin Zhang ◽  
Cornelis Weemstra
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Velocity Structure ◽  
Voronoi Tessellation ◽  
Three Dimensional ◽  
Velocity Model ◽  
Seismic Network ◽  
Travel Times ◽  
Model Resolution ◽  
Reykjanes Peninsula

Seismic travel time tomography using surface waves is an effective tool for three-dimensional crustal imaging. Historically, these surface waves are the result of active seismic sources or earthquakes. More recently, however, surface waves retrieved through the application of seismic interferometry have also been exploited. Conventionally, two-step inversion algorithms are employed to solve the tomographic inverse problem. That is, a first inversion results in frequency-dependent, two-dimensional maps of phase velocity, which then serve as input for a series of independent, one-dimensional frequency-to-depth inversions. As such, a set of localized depth-dependent velocity profiles are obtained at the surface points. Stitching these separate profiles together subsequently yields a three-dimensional velocity model. Relatively recently, a one-step three-dimensional non-linear tomographic algorithm has been proposed. The algorithm is rooted in a Bayesian framework using Markov chains with reversible jumps, and is referred to as transdimensional tomography. Specifically, the three-dimensional velocity field is parameterized by means of a polyhedral Voronoi tessellation. In this study, we investigate the potential of this algorithm for the purpose of recovering the three-dimensional surface-wave-velocity structure from ambient noise recorded on and around the Reykjanes Peninsula, southwest Iceland. To that end, we design a number of synthetic tests that take into account the station configuration of the Reykjanes seismic network. We find that the algorithm is able to recover the 3D velocity structure at various scales in areas where station density is high. In addition, we find that the standard deviation of the recovered velocities is low in those regions. At the same time, the velocity structure is less well recovered in parts of the peninsula sampled by fewer stations. This implies that the algorithm successfully adapts model resolution to the density of rays. It also adapts model resolution to the amount of noise in the travel times. Because the algorithm is computationally demanding, we modify the algorithm such that computational costs are reduced while sufficiently preserving non-linearity. We conclude that the algorithm can now be applied adequately to travel times extracted from station–station cross correlations by the Reykjanes seismic network.

The diffraction of an obliquely incident surface wave by a vertical barrier of finite depth

1966 ◽  
Vol 62 (4) ◽  
pp. 829-838 ◽  
Author(s):  
T. R. Faulkner
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Deep Sea ◽  
Small Amplitude ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Finite Depth ◽  
Two Dimensional ◽  
Obliquely Incident ◽  
Vertical Barrier

The effect of a vertical barrier, fixed in an infinitely deep sea, on normally incident surface waves of small amplitude was first considered by Ursell (1) and generalizations which retain the two-dimensional aspects of the problem have subsequently been considered by John (2) and Lewin (3). The fluid motion due to the flexural vibrations of a barrier of finite depth has been considered by Alblas (4), the motion in this case being three-dimensional.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Steady State Motion and Surface Waves

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Steady State ◽  
Surface Wave ◽  
Surface Waves ◽  
Existence And Uniqueness ◽  
Wave Speed ◽  
Wave Theory ◽  
Two Dimensional ◽  
Elastic Materials ◽  
Steady State Motion ◽  
Anisotropic Elastic

The Stroh formalism for two-dimensional elastostatics can be extended to elastodynamics when the problem is a steady state motion. Most of the identities in Chapters 6 and 7 remain applicable. The Barnett-Lothe tensors S, H, L now depend on the speed υ of the steady state motion. However S(υ), H(υ), L(υ) are no longer tensors because they do not obey the laws of tensor transformation when υ≠0. Depending on the problems the speed υ may not be prescribed arbitrarily. This is particularly the case for surface waves in a half-space where υ is the surface wave speed. The problem of the existence and uniqueness of a surface wave speed in anisotropic materials is the crux of surface wave theory. It is a subject that has been extensively studied since the pioneer work of Stroh (1962). Excellent expositions on surface waves for anisotropic elastic materials have been given by Farnell (1970), Chadwick and Smith (1977), Barnett and Lothe (1985), and more recently, by Chadwick (1989d).

THREE‐DIMENSIONAL SEISMIC MODEL STUDIES

Geophysics ◽  
1955 ◽  
Vol 20 (1) ◽  
pp. 19-32 ◽  
Author(s):  
F. K. Levin ◽  
H. C. Hibbard
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Wave ◽  
Surface Waves ◽  
Shear Waves ◽  
Three Dimensional ◽  
Seismic Model ◽  
Model Studies ◽  
Ground Roll ◽  
Detector Configurations

Elastic wave propagation in a two‐layer section has been studied with a solid two‐bed model and records resembling seismograms obtained for the four possible source‐detector configurations. Numerous events are identified. Among these, the shear waves are found to be surprisingly prominent. The amplitude of the ground roll falls off approximately as [Formula: see text] This is the amplitude‐range dependence expected for a surface wave. The ability of two in‐line detectors to reduce surface waves has been demonstrated.

A note on the total reflexion or transmission of surface waves in the presence of parallel obstacles

1975 ◽  
Vol 67 (3) ◽  
pp. 465-472 ◽  
Author(s):  
D. V. Evans
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Water Wave ◽  
Wave Theory ◽  
Two Dimensional ◽  
Total Transmission ◽  
Vertical Barriers ◽  
Total Reflexion ◽  
Dimensional Surface

It is shown how a two-dimensional surface wave can be either totally reflected or totally transmitted in the presence of two parallel vertical barriers each containing a small gap. Total transmission of a surface wave past obstacles has been known to occur in many situations in water-wave theory, but total reflexion is a comparatively new phenomenon which could be of practical use in the design of breakwaters.

Unsteady Reynolds-averaged Navier–Stokes investigation of free surface wave impact on tidal turbine wake

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200703
Author(s):  
Zhisong Li ◽  
Kirti Ghia ◽  
Ye Li ◽  
Zhun Fan ◽  
Lian Shen
Keyword(s):  
Free Surface ◽  
Surface Wave ◽  
Surface Waves ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Wave Impact ◽  
Power Extraction ◽  
Tidal Turbine ◽  
Turbine Wake

Tidal current is a promising renewable energy source. Previous studies have investigated the influence of surface waves on tidal turbines in many aspects. However, the turbine wake development in a surface wave environment, which is crucial for power extraction in a turbine array, remains elusive. In this study, we focus on the wake evolution behind a single turbine and its interaction with surface waves. A numerical solver is developed to study the effects of surface waves on an industrial-size turbine. A case without surface wave and two cases with waves and different rotor depths are investigated. We obtain three-dimensional flow field descriptions near the free surface, around the rotor, and in the near- and far-wake. In a comparative analysis, the time-averaged and instantaneous flow fields are examined for various flow characteristics, including momentum restoration, power output, free surface elevation and vorticity dynamics. A model reduction technique is employed to identify the coherent flow structures and investigate the spatial and temporal characteristics of the wave–wake interactions. The results indicate the effect of surface waves in augmenting wake restoration and reveal the interactions between the surface waves and the wake structure, through a series of dynamic processes and the Kelvin–Helmholtz instability.

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