Annual Report 2000 - WIT

“
Ã
Æ
³
244
0
0.5
[km]
0 0.5 1.0 1.5 2.0
0.3
0.25
0.2
0.15
0.05
0.1
0
0.5
[km]
0 0.5 1.0 1.5 2.0
0.5
0.45
0.4
0.35
0.3
0
0.5
[km]
0 0.5 1.0 1.5 2.0
0.6
0.55
0.65
0.55
[km]
1.0
0.35
[km]
1.0
[km]
1.0
0.5
1.5
2.0
0.4
0.45
0.5
1.5
2.0
0.45
0.5
1.5
2.0
0.6
0.55
Figure 3: Wavefronts in a horizontally layered model; J Ã ‚ -slices with offset 0 km
(left), 1 km (middle) and 1.3 km from the source.
TRAVELTIME PERTURBATION
To compute traveltimes for arbitrary anisotropic media, a perturbation scheme can be
embedded into the FD eikonal solver. We consider a model with arbitrary anisotropy
as a perturbed model with respect to an elliptically anisotropic reference model. The
formula for traveltime correction derived by jCervený (1982) is used:
•
¢:‘ k ‹ l`’ † Ã Ç
¢S‹
where:
X
—–
É ÿ”“
³ÖẼš
Æ
š Ö ˜œ›
¾ –
³Ö.Ẽšžš
with ³Ö.š as density normalized elastic coefficients of the anisotropic medium, Æ ³ are
the components of the slowness vector, and – Ö are the components of the polarization
vector of the considered type of (Ÿ…k wave Ÿ(l Ú
, Ÿ…l¡ or ). The vectors and ¢ depend
o
on to the reference ellipsoidal medium.
Theoretically these corrections can be of arbitrary order. However, for practical
applications in most cases a first-order correction as above is used. To minimize the
errors in the perturbation approach the reference medium should be chosen close to the
given anisotropic medium. Formulas for a best-fitting ellipsoidal reference medium
were derived by (Ettrich et al., 2000). In these formulas it is supposed that the polarization
vector is substituted by the phase normal. Therefore only for weak anisotropy
the phase velocity of the P-wave is well approximated.
We now consider the case of strong anisotropy. Following (Burridge et al., 1993)
there are three possibilities to simplify orthorhombic or transversely isotropic symmetry
to ellipsoidal one. The othorhombically anisotropic medium has an elliptical
—–
† –
³Ö˜£š š
³ÖẼšžš