Introduction

Plans for Computer Programs in Seismology are as follow:

Version	Release Data	Goals
3.15	01 FEB 2002	Inversion of surface-wave and/or recvier functions for earth structure. Includes tools for determining dispersion and receiver functions
3.16	01 JUN 2002	Fix bugs in 3.15, rewrite and improve documentation for inversion for Earth structure
3.19	01 AUG 2002	Source parameter inversion from surface-wave radiation patterns (Herrmann) and waveform inversion (Ammon)
3.20	01 SEP 2002	Fig bugs and 3.19
3.25	01 DEC 2002	Transverse Isotropy synthetics and perhaps inversion

As an initial step toward Version 3.25, I have implemented wavenumber integration code for TI media. Computation of modal synthetics and surface-wave dispersion for TI media must be programmed. Computation of generalized ray synthetics requires a much, much smarter routine to follow the more complex Cagniard paths.

Green's Functions

The following figures present the Green's functions for a TI and best approximation Isotropic media (Dahlen and Tromp, p 321 8.191 - 8.192). The MODEL96 isotropic model is:

MODEL.01
Modified Van der Heiden beryl TI model - Isotropic approximation Dahlen and Tromp
ISOTROPIC
KGS
FLAT EARTH
1-D
CONSTANT VELOCITY
LINE08
LINE09
LINE10
LINE11
      H(KM)   VP(KM/S)   VS(KM/S) RHO(GM/CC)    QP         QS       ETAP       ETAS      FREFP      FREFS
     1.0000     5.8383    3.3408     2.7000   0.00       0.00       0.00       0.00       1.00       1.00    

The TI model used is a modified version based on the TI material properties of beryl. The modification was to reduce the velocities to be approximately 6.0 km/sec for P and 3.5 km/sec for S

MODEL.01
Modified Van der Heiden beryl TI model
TRANSVERSE ISOTROPIC
KGS
FLAT EARTH
1-D
CONSTANT VELOCITY
LINE08
LINE09
LINE10
LINE11
      H(KM)  VPV(KM/S)  VSV(KM/S) RHO(GM/CC)    QP         QS       ETAP       ETAS      FREFP      FREFS
             VPH(KM/S)  VSH(KM/S)  VPF(KM/S)                                                                  
    1.0000     5.7530     3.0220     2.7000   0.00       0.00       0.00       0.00       1.00       1.00    
               6.1430     3.4730     3.0430

The comparisons to follow consist of a source at depth 0 km, and receivers placed beneath the source on the arc of a circle with radius of 3.5 km. The receivers locations are at takeoff angles of 35 - 55 degrees from the downward vertical. The convention is that the vertical motion is positive up, the radial is positive away for the source and that the transverse is positive in a clockwise sense when looking in the positive downward z-direction. The range of angles for the receivers was chosen to highlight and to understand the arrivals fromthe different wavefront surfaces. At smaller or greater angles, the synthetics consist of essentially just the Quasi-P and Quasi-Z arrivals.

The first two figures give the Z, R and T record sections for a point horizontal force the direction of North with the receivers along an azimuth of 45 degrees.

Isotropic Media Synthetics - Left Vertical, Center Radial, Right Transverse <

Transverse Isotropic Media Synthetics - Left Vertical, Center Radial, Right Transverse

In the process of writing the wavenumber integration code in a cylindrival coordinate system, I first computed the synthetic response for oriented point forces in a cartesian coordinate system by direct application of a 4-dimensional inverse Fourier transforms - three over wavenumber and one over frequency. These were speedily run on Lupei Zhu's 2.0GHz PC under LINUX. The following two figures compare the cartesian and cylindrical coordiate solutions:

Point force Green's functions computed by 4 dimensional inverse Fourier tranforms. The 9 panels are as follow: left to right - Z, R and T components of motion. Top to bottom - horizontal force in X-direction, Y direction and Z-direction. Within each panel, the receiver position varies from 0 to 90 degrees in increments of 5 degrees.

Point force Green's functions computed using Fourier-Hankel transforms in a cylindrical coordinate system. The difference in vertical component motion for the point vertical source is due to slight differences in corrdinate system definitions.

The agreement of the 4-D (x,y,z) synthetics and the (r, theta, z) synthetics supports the coding done in tspec96!

The following figures compare all Green's functions - the first 10 are used for moment tensor sources and the last five for point force responses.

Isotropic	Transverse Isotropic

Last Changed 03 May 2002