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Volume 12 Number 4
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

An analytical expression for the time‐distance curve of seismic waves travelling in a medium consisting of intrinsically anisotropic layers with arbitrarily dipping plane interfaces can be given in terms of the “co‐ordinates” of the interfaces (length of the perpendicular from the shotpoint to the interface, strike ν and dip α of the interface) if for each layer the velocity is given as a function of the orientation of the wave normal. The interpretation of the time‐distance curve is understood as the inverse process, namely finding an expression for the co‐ordinates in terms of some characteristics of the time‐distance curve, e.g. intercept times and apparent velocities. In addition, it is useful to know where the “limiting ray”, which is the ray connecting shotpoint and last geophone, enters and leaves a specific layer, for it is only on the medium between these two points that information can be obtained by interpretation. As ray and wave normal do not generally coincide in anisotropic media, the location of these points cannot be calculated from the co‐ordinates and the direction of the wave normal without recourse to the functional dependence between the directions of ray and wave normal.

An analytical solution of this problem would involve the solution of a number of equations, implicitly containing several parameters. Successive approximation would be rather cumbersome. Instead, a graphical method is proposed which yields all pertinent information without calculation.

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2006-04-27
2024-04-28

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