Anisotropic velocity models
- We compute the
recorded wave field
in 3-D models composed of two homogeneous layers separated by
one curved interface with triclinic anisotropy in the upper layer.
The bottom layer is isotropic and has P-wave velocity
Vp= 3.6 km/s.
- The dimensions of the 3-D models were taken from
the 2-D Marmousi model and dataset (Versteeg & Grau, 1991).
- We perform the migration
in homogeneous models without curved interface:
a) Triclinic anisotropy (TA) representing dry
Vosges sandstone (Mensch & Rasolofosaon, 1997). Reflected two-point
rays propagate in 3-D volume.
b) Isotropic medium (ISO) with P-wave
velocity Vp2=
14.1 km2/s2
(equal to the vertical P-wave velocity in the TA model,
matrix element
A33).
c) VTI-1 is a transversely isotropic media
with a vertical symmetry axis (VTI).
We optimized velocities for vertical and near vertical P-waves to
obtain the best results of the migration. We fitted matrix element
A33
for vertical P-waves and elements
A13=
A23
(mean of triclinic elements
A13,
A23)
for near vertical P-waves
according to elastic moduli of triclinic anisotropy.
d) VTI-2 is similar to VTI-1,
we only decreased matrix element
A33=
14.1 km2/s2,
which is responsible for vertical P-wave velocity,
to A33=
11.6 km2/s2.
e) VTI-3 is similar to VTI-1,
we only decreased matrix elements
A11=
10.45 km2/s2
and A12=
0.65 km2/s2,
which are responsible for horizontal
P-wave velocity in the direction parallel with measurement lines,
to A11=
8.95 km2/s2
and A12=
-0.85 km2/s2.
f) HTI-1 is a transversely isotropic media
with a horizontal symmetry axis (HTI).
The symmetry axis is parallel with
the x1 coordinate axis.
We fitted matrix element
A33 for vertical
P-waves and element
A23 for near vertical
P-waves according to the elastic moduli of triclinic anisotropy.
The horizontal P-wave velocity, perpendicular to the profile lines
(A22),
is equal to the vertical P-wave
velocity (A33)
of the triclinic (TA) model.
g) HTI-2 is a transversely isotropic media
with a horizontal symmetry axis (HTI).
The symmetry axis is parallel with
the x2 coordinate axis.
We fitted matrix element
A33 for vertical
P-waves and element A13
for near vertical
P-waves according to the elastic moduli of triclinic anisotropy.
The horizontal P-wave velocity, parallel with the profile lines
(A11),
is equal to the vertical P-wave
velocity (A33)
of the triclinic (TA) model.