THEORETICAL CALCULATION OF THE SPECTRUM OF FIRST ARRIVALS IN LAYERED ELASTIC MEDIA

Abstract

A practical method for the calculation of the spectral parameters of first-arriving signals in seismology has been the object of much theoretical work in recent years. The difficulty has been in the fact that the first arrival usually behaves as an imperfectly trapped mode. A practical technique is proposed. By a change of variable, the twice transformed solution is separated into a product of the form f(u).e raised to the -iuR power. This can be integrated with respect to the phase variable u, using standard quadrature methods, with the real part of u changing most rapidly along the integration path. By making the frequency complex, it is possible to displace any singularities away from the vicinity of the contour. This gives the spectrum of the signal as viewed through an exponentially decaying time window, making it possible to work with the first arrival by itself.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1965
Accession Number
AD0617746

Entities

People

  • Robert A. Phinney

Organizations

  • Princeton University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Complex Variables
  • Computer Programming
  • Computers
  • Data Analysis
  • Differential Equations
  • Elastic Waves
  • Equations
  • Frequency
  • Geometry
  • Group Velocity
  • Phase Velocity
  • Refraction
  • Surface Waves
  • Travel Time
  • Wave Propagation
  • Waves

Readers

  • Systems Analysis and Design
  • Theoretical Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.