A Recursive Algorithm for Computing Ray-Parameter Derivatives

Abstract

Under the assumption of high frequency, wave propagation can be described by the ray method. Many quantities in wave phenomena are characterized by some ray parameters and their derivatives. For example, the slope of arrival time-offset curve is characterized by the emergence angle of a ray; the curvature is characterized by derivative of that angle, and the amplitude of the signal is characterized by the derivative of the taking-off angle. In this paper, we give a recursive algorithm for ray-parameter derivatives, when the medium is made up of constant-velocity layers separated by arbitrary, smooth interfaces. The algorithm uses derivatives of interfaces, intersection points of rays with the interfaces, and angles of incidence and transmission, all of which are easily computed. A conclusion of these formulas is that no ray caustic exists for transmission or for the reflection from any one of the reflectors when the interfaces are flat.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
May 20, 1991
Accession Number
ADA241005

Entities

People

  • Zhenyue Liu

Organizations

  • Colorado School of Mines

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Amplitude
  • Availability
  • Classification
  • Curvature
  • Differential Geometry
  • Earth Models
  • Equations
  • Geometry
  • Mathematics
  • Reflection
  • Reflectors
  • Security
  • Wave Phenomena
  • Wave Propagation

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering