Attenuation Measurements by Multimode Synthetic Seismograms

1989 ◽  
pp. 79-115
Author(s):  
Giuliano F. Panza
Keyword(s):  
Synthetic Seismograms

On computing ray‐synthetic seismograms for anelastic media using complex rays

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 422-432 ◽  
Author(s):  
D. J. Hearn ◽  
E. S. Krebes
Keyword(s):  
Surface Layer ◽  
Plane Wave ◽  
Saddle Point ◽  
Viscoelastic Medium ◽  
Observation Point ◽  
Acute Angle ◽  
Synthetic Seismograms ◽  
Propagation Angle ◽  
Source Point ◽  
Complex Rays

A plane wave propagating in a viscoelastic medium is generally inhomogeneous, meaning that the direction in which the spatial rate of amplitude attenuation is maximum is generally different from the direction of travel. The angle between these two directions, which we call the “attenuation angle,” is an acute angle. In order to trace the ray corresponding to a plane wave propagating between a source point and a receiver point in a layered viscoelastic medium, one must know both the initial propagation angle (the angle that the raypath makes with the vertical) and the initial attenuation angle at the source point. In some recent literature on the computation of ray‐synthetic seismograms in anelastic media, values for the initial attenuation angle are chosen arbitrarily; but this approach is fundamentally unsatisfactory, since different choices lead to different results for the computed waveforms. Another approach, which is more deterministic and physically acceptable, is to deduce the value of the initial attenuation angle from the value of the complex ray parameter at the saddle point of the complex traveltime function. This value can be obtained by applying the method of steepest descent to evaluate approximately the integrals giving the exact wave field at the observation point. This well‐known technique results in the ray‐theory limit. The initial propagation angle can also be determined from the saddle point. Among all possible primary rays between source and receiver, each having different initial propagation and attenuation angles, the ray determined by the saddle point, which we call a “stationary ray,” has the smallest traveltime, a result which is consistent with Fermat’s principle of least time. Such stationary rays are complex rays, i.e., the spatial (e.g., Cartesian) coordinates of points on stationary raypaths are complex numbers, whereas the arbitrarily determined rays mentioned above are usually traced as real rays. We compare examples of synthetic seismograms computed with stationary rays with those from some arbitrarily determined rays. If the initial value of the attenuation angle is arbitrarily chosen to be a constant for all initial propagation angles, the differences between the two types of seismograms are generally small or negligible in the subcritical zone, except when the constant is relatively large in value, say, within 10 degrees or so of its upper bound of 90 degrees. In that case, the differences are significant but still not large. However, if the surface layer is highly absorptive, the differences can be quite large and pronounced. For larger offsets, i.e., in the supercritical zone, large phase discrepancies can exist between the waveforms for the stationary rays and those for the arbitrarily determined rays, even if the constant initial attenuation angle is not large and even for moderate absorptivity in the surface layer.

Seismogram synthesis for multi-layered media with irregular interfaces by global generalized reflection/transmission matrices method. II. Applications for 2D SH case

1995 ◽  
Vol 85 (4) ◽  
pp. 1094-1106
Author(s):  
Xiaofei Chen
Keyword(s):  
Present Article ◽  
Analytical Solutions ◽  
Scattering Problem ◽  
Layered Media ◽  
Synthetic Seismograms ◽  
Numerical Results ◽  
New Method ◽  
New Formulation ◽  
Series Study

Abstract As the second part of a series study attempting to present a new method of seismogram synthesis for the irregular multi-layered media problems, the present article is devoted to discussing the aspects of the implementation of our new formulation developed earlier in part I of this series study (Chen, 1990). In this article, we have verified the validity of the formulation by comparing our numerical results with the existing analytical solutions for the scattering problem of a semi-circular canyon, and have shown its applicability by computing the synthetic seismograms for several selected irregular multi-layered media cases. Finally, applying our algorithm to the Whittier-Narrows earthquake of 1987, we have successfully interpreted the observed records.

Dispersion interpretation from synthetic seismograms and multi-channel analysis of surface waves (MASW)

2012 ◽  
Author(s):  
J. Tyler Schwenk ◽  
Richard Miller ◽  
Julian Ivanov ◽  
Jason McKenna
Keyword(s):  
Surface Waves ◽  
Synthetic Seismograms ◽  
Channel Analysis

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

Generation of Synthetic Seismograms Using Linear Systems Theory

1971 ◽  
Vol 8 (11) ◽  
pp. 1409-1422 ◽  
Author(s):  
O. G. Jensen ◽  
R. M. Ellis
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Systems Theory ◽  
Linear Systems ◽  
Time Domain ◽  
Synthetic Seismograms ◽  
Elastic Wave Propagation ◽  
Arbitrary Angle ◽  
Teleseismic Events

The linear systems theory for elastic wave propagation in a multilayered crust has been extended to time domain solutions. Attenuation is specifically included. This direct time domain approach allows the computation of synthetic seismograms for P or SV waveforms incident at an arbitrary angle at the base of the crustal section. To demonstrate the utility of the technique, seismograms are computed for various conditions and comparisons made with teleseismic events recorded in central Alberta.

Sign in / Sign up

Export Citation Format

Share Document