Geometrical spreading of seismic body waves in laterally inhomogeneous media with curved interfaces of the second order

1975 ◽  
Vol 19 (3) ◽  
pp. 298-299
Author(s):  
Vlastislav ěrvený ◽  
Ivan Pšenčík ◽  
J. Vaněk
Keyword(s):  
Inhomogeneous Media ◽  
Second Order ◽  
Body Waves ◽  
Geometrical Spreading ◽  
Seismic Body Waves

Computation of ray amplitudes of seismic body waves in vertically inhomogeneous media

1977 ◽  
Vol 21 (3-4) ◽  
pp. 248-255 ◽  
Author(s):  
Vlastislav Červený ◽  
Věnceslava Pretlová ◽  
I. Pšenčik
Keyword(s):  
Inhomogeneous Media ◽  
Body Waves ◽  
Seismic Body Waves

Offset‐dependent geometrical spreading in a layered medium

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 492-496 ◽  
Author(s):  
Bjørn Ursin
Keyword(s):  
Point Source ◽  
Taylor Series ◽  
Layered Medium ◽  
Exact Expression ◽  
Second Order ◽  
Geometrical Spreading ◽  
Approximate Expressions

The geometrical spreading for a point source in a horizontally layered medium has been computed by Ursin (1978) and Hubral (1978) as a Taylor series in the offset coordinate. The coefficients in the Taylor series depend on the thicknesses and the velocities of the layers. Here, I start with the exact expression for geometrical spreading and show that it can be expressed as a function of the velocity in the first layer, the offset, and the first‐ and second‐order traveltime derivatives. A shifted hyperbolic traveltime approximation (Castle, 1988) and the usual hyperbolic traveltime approximation are used to derive approximate expressions for geometrical spreading. These expressions can also be derived from a truncated Taylor series by making additional approximations, but this procedure is not so obvious.

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