Book contents
- Frontmatter
- Contents
- Foreword by Michael Berry
- Introduction
- 1 The Semiclassical Trace Formula
- 2 Wave Chaos for the Helmholtz Equation
- 3 The Unreasonable Effectiveness of Random Matrix Theory for the Vibrations and Acoustics of Complex Structures
- 4 Gaussian Random Wavefields and the Ergodic Mode Hypothesis
- 5 Short Periodic Orbit Theory of Eigenfunctions
- 6 Chaotic Wave Scattering
- 7 Transfer Operators Applied to Elastic Plate Vibrations
- 8 Mesoscopics in Acoustics
- 9 Diagrammatic Methods in Multiple Scattering
- 10 Time-Reversed Waves in Complex Media
- 11 Ocean Acoustics: A Novel Laboratory for Wave Chaos
- 12 Mesoscopic Seismic Waves
- 13 Random Matrices in Structural Acoustics
- 14 The Analysis of Random Built-Up Engineering Systems
- References
- Index
12 - Mesoscopic Seismic Waves
Published online by Cambridge University Press: 05 October 2010
- Frontmatter
- Contents
- Foreword by Michael Berry
- Introduction
- 1 The Semiclassical Trace Formula
- 2 Wave Chaos for the Helmholtz Equation
- 3 The Unreasonable Effectiveness of Random Matrix Theory for the Vibrations and Acoustics of Complex Structures
- 4 Gaussian Random Wavefields and the Ergodic Mode Hypothesis
- 5 Short Periodic Orbit Theory of Eigenfunctions
- 6 Chaotic Wave Scattering
- 7 Transfer Operators Applied to Elastic Plate Vibrations
- 8 Mesoscopics in Acoustics
- 9 Diagrammatic Methods in Multiple Scattering
- 10 Time-Reversed Waves in Complex Media
- 11 Ocean Acoustics: A Novel Laboratory for Wave Chaos
- 12 Mesoscopic Seismic Waves
- 13 Random Matrices in Structural Acoustics
- 14 The Analysis of Random Built-Up Engineering Systems
- References
- Index
Summary
This chapter presents recent developments of multiple scattering and mesoscopic concepts in seismology. After a brief review of classical elastic wave propagation in the Earth, we focus on the scattered waves that form the tail or coda of the signal. The stabilization of vertical to horizontal kinetic energy ratios in the coda is illustrated with data from small crustal earthquakes recorded at a temporary network in California. Using a priori geological data, we show that the measurements agree very well with the equipartition principle applied to a layered elastic medium. This confirms that the formation of the coda results from the multiple scattering of elastic waves by Earth's heterogeneities. The concepts of equipartition, diffusion, and energy stabilization are carefully discussed and distinguished with the aid of numerical Monte Carlo simulations. We underline that energy stabilization occurs much earlier than equipartition because the latter concept asks for an isotropic energy flux distribution. Having established the importance of multiple scattering in the Earth we explore the role of interference in random seismic wavefields. A brief review of recent experimental and theoretical works on the weak localization of seismic waves is presented. We further explore mesoscopic concepts by demonstrating the close relations between long-time correlation of random seismic waves and the Green's function. Using data from a permanent seismic network in the Alps, we give strong experimental evidence that the correlation of seismic noise contains not only ballistic but also multiply scattered seismic waves.
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- Chapter
- Information
- New Directions in Linear Acoustics and VibrationQuantum Chaos, Random Matrix Theory and Complexity, pp. 188 - 205Publisher: Cambridge University PressPrint publication year: 2010