scholarly journals Characterizing seismic scattering in 3D heterogeneous Earth by a single parameter

2020 ◽  
Author(s):  
Jagdish Chandra Vyas ◽  
Martin Galis ◽  
Paul Martin Mai
Keyword(s):  
Standard Deviation ◽  
Correlation Length ◽  
Hurst Exponent ◽  
Seismic Waves ◽  
The Other ◽  
Small Scale ◽  
Seismic Scattering ◽  
Von Karman ◽  
Velocity Variations ◽  
Von Kármán

<p>We analyze the power spectral density (PSD) of von Karman autocorrelation function (ACF) to derive a theoretical parameter which characterizes the scattering of seismic wavefield due to random heterogeneities in 3D Earth structure. We then verify our analytical findings by performing ground-motion simulations. We characterize scattering using root-mean-square (RMS) fluctuations of normalized seismic wave speed, which represents wavefield scattering due to random heterogeneities in 3D Earth under the diffraction condition. The isotropic von Karman ACF is parameterized by correlation length a, standard deviation σ, and Hurst exponent H. To compute the RMS value, we simplify the von Karman PSD for three regimes: k·a ≫ 1 (λ ≪ a), k·a ≈ 1 (λ ≈ a) and k·a ≪ 1 (λ ≫ a), where λ is wavelength and k wavenumber of the seismic waves. The analysis of the RMS values reveals that 1) scattering is proportional to the standard deviation σ of small-scale velocity variations in all three regimes, 2) scattering is inversely proportional to the correlation length in the k·a ≫ 1 regime, but directly proportional to the correlation length in the other two regimes, 3) a small Hurst exponent H for the k·a ≫ 1 regime leads to scattering controlled solely by the standard deviation of small-scale velocity variations (for the other two regimes, it leads to weaker scattering). The seismic scattering effectively vanishes for H approaching zero. Our theoretical findings are purely physics based and are furthermore verified by 3D high resolution numerical simulations. Hence, we developed solid physics-based understanding of 3D seismic scattering due to random heterogeneities in the Earth which will be helpful for future modeling studies.</p>

scholarly journals Characterizing Seismic Scattering in 3D Heterogeneous Earth by a Single Parameter

2021 ◽  
Author(s):  
Jagdish Chandra Vyas ◽  
Martin Galis ◽  
Paul Martin Mai
Keyword(s):  
Correlation Length ◽  
Small Scale ◽  
Ground Acceleration ◽  
Seismic Scattering ◽  
Von Karman ◽  
Power Spectral ◽  
Scattering Effects ◽  
Seismic Wave Scattering ◽  
Elastic Rock ◽  
Von Kármán

ABSTRACT We derive a theoretical parameter for three seismic scattering regimes where seismic wavelengths are either much shorter, similar, or much longer than the correlation length of small-scale Earth heterogeneities. We focus our analysis on the power spectral density (PSD) of the von Karman autocorrelation function (ACF), used to characterize the spatial heterogeneity of small-scale variations of elastic rock parameters that cause elastic seismic-wave scattering. Our analysis is based on the assumption that the PSD of the medium heterogeneities at the corresponding wavenumber is related to the wavefield scattering. Our theoretical findings are verified by numerical simulations. The seismic scattering effects in our simulations are assessed by examining attenuation of peak ground acceleration. We discover (1) that seismic scattering is proportional to the standard deviation of velocity variations in all three regimes, (2) that scattering is inversely proportional to the correlation length for the regime where seismic wavelengths are shorter than correlation length, but directly proportional to the correlation length in the other two regimes, and (3) that scattering effects are weak due to heterogeneities characterized by a gentle decay of the von Karman ACF for regimes where seismic wavelengths are similar or much longer than the correlation length.

Hydrodynamics and behaviour of Simuliidae larvae (Diptera)

1986 ◽  
Vol 64 (6) ◽  
pp. 1295-1309 ◽  
Author(s):  
M. M. Chance ◽  
D. A. Craig
Keyword(s):  
Boundary Layer ◽  
Lower Boundary ◽  
The Body ◽  
The Other ◽  
Avoidance Reaction ◽  
Larval Body ◽  
Video Recordings ◽  
Von Karman ◽  
Von Kármán ◽  
Lower Boundary Layer

Detailed water flow around larvae of Simulium vittatum Zett. (sibling IS-7) was investigated using flow tanks, aluminium flakes, pigment, still photography, cinematography, and video recordings. Angle of deflection of a larva from the vertical has a hyperbolic relationship to water velocity. Velocity profiles around larvae show that the body is in the boundary layer. Frontal area of the body decreases as velocity increases. Disturbed larvae exhibit "avoidance reaction" and pull the body into the lower boundary layer. Longitudinal twisting and yawing of the larval body places one labral fan closer to the substrate, the other near the top of the boundary layer. Models and live larvae were used to demonstrate the basic hydrodynamic phenomenon of downstream paired vortices. Body shape and feeding stance result in one of the vortices remaining in the lower boundary layer. The other rises up the downstream side of the body, passes through the lower fan, then forms a von Karman trail of detaching vortices. This vortex entrains particulate matter from the substrate, which larvae then filter. Discharge of water into this upper vortex remains constant at various velocities and only water between the substrate and top of the posterior abdomen is incorporated into it. The upper fan filters water only from the top of the boundary layer. Formation of vortices probably influences larval microdistribution and filter feeding. Larvae positioned side by side across the flow mutually influence flow between them, thus enhancing feeding. Larvae downstream of one another may use information from the von Karman trail of vortices to position themselves advantageously.

scholarly journals On the phenomenon of vortex street breakdown

1971 ◽  
Vol 48 (3) ◽  
pp. 507-527 ◽  
Author(s):  
William W. Durgin ◽  
Sture K. F. Karlsson
Keyword(s):  
The Other ◽  
Vortex Street ◽  
Wake Flow ◽  
Karman Vortex Street ◽  
Von Karman ◽  
Von Karman Vortex Street ◽  
Kármán Vortex Street ◽  
Karman Vortex ◽  
The Individual ◽  
Von Kármán

A von Kármán vortex street generated in the usual way was subjected to a deceleration, thereby changing the ratio of longitudinal to lateral spacing between the vortices. Distortion of the individual vortices followed which resulted in annihilation of concentrated vortex regions and creation of a stationary wake flow. This wake flow was itself dynamically unstable and developed into a new vortex street of a different frequency from the initial one. The breakdown of the initial vortex street is qualitatively explained by considering the convection of a concentrated vortex region due to the motion imposed by all the other vortices.

scholarly journals Flight Data-Based Wind Disturbance and Air Data Estimation

Atmosphere ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 470
Author(s):  
Zhenxing Gao ◽  
Haofeng Wang ◽  
Zhiwei Xiang ◽  
Debao Wang
Keyword(s):  
Turbulence Model ◽  
Wind Field ◽  
Estimation Accuracy ◽  
Small Scale ◽  
Prevailing Wind ◽  
Wind Disturbance ◽  
Flight Data ◽  
Von Karman ◽  
Wide Range ◽  
Von Kármán

The instantaneous wind field and air data, including true airspeed, angle of attack, angle of sideslip, cannot be measured and recorded accurately in wind disturbance. A new air data and wind field estimation method is proposed based on flight data in this study. Since the wind field is the horizontal prevailing wind added by turbulence, the slowly time-varying prevailing wind and small-scale turbulence are described by the exponentially correlated stochastic wind model and von Karman turbulence model, respectively. The system update equation of air data is built based on inertial measurements instead of the complex aerodynamic and aero-engine model of aircraft. Benefitted by the post-analysis characteristics of flight data, a forward–backward filtering algorithm was designed to improve the estimation accuracy. Simulation results indicate that the forward–backward filter integrated with the von Karman turbulence model can reduce the estimation error and ensure filtering stability. A further test with actual flight data shows that the forward–backward filter is not only able to track the wide-range change in prevailing wind but also reduce the adverse effects of uncertain disturbance on estimation accuracy.

Instability, coalescence and fission of finite-area vortex structures

1973 ◽  
Vol 61 (2) ◽  
pp. 219-243 ◽  
Author(s):  
J. P. Christiansen ◽  
N. J. Zabusky
Keyword(s):  
Growth Rate ◽  
Small Scale ◽  
Two Dimensional ◽  
Large Area ◽  
Finite Area ◽  
Inviscid Fluids ◽  
Von Karman ◽  
Long Time ◽  
The Stability ◽  
Von Kármán

We have made computational experiments to study the stability and long-time evolution of two-dimensional wakes. We have used the VORTEX code, a finite-difference realization of two-dimensional motions in incompressible inviscid fluids. In the first experiment an initial shear-unstable triangular velocity profile evolves into a non-homogeneous, finite-area, asymmetric vortex array and like-signed regions attract andfuse(or coalesce). Enhanced transport across the profile is due to ‘capture’ and convection of small-scale vortex regions by larger opposite-signed vortex regions. In the following experiments we study the stability of an asymmetric four-vortexfinite-areasystem corresponding to a von Kármán street of point vortices. Here the critical parameter isb/a, the initial transverse-to-longitudinal separation ratio of vortex centres. At\[ b/a = 0.281 \]the four-vortex system is stable and we observe that large-area vortex regions develop elliptical (m= 2), triangular (m= 3), etc. surface modes owing to mutual interactions. Atb/a= 0 the measured growth rate is smaller than that for the corresponding von Kármán system and atb/a= 0·6 the measured growth rate is larger. Atb/a= 0 one vortex undergoes fission in the high-shear field produced by two nearest-neighbour opposite-signed vortex regions. Heuristic comparisons are made with the two-dimensional tunnel experiments of Taneda and others.

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