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We tested the amplitude correction at the boundary condition by
downward propagating a shot and picking the amplitudes of the
wavefield recorded at a certain depth. Since our particular purpose of using
WEMVA is finding velocity anomalies that generate focusing-effect AVO
Vlad and Biondi (2002), we used the same focusing-generating
velocity model as that presented in the lower right panel of Figure 6 of
Vlad (2002). For convenience, we present it in the
upper panel of Figure 4, also tracing wavefronts through it
for a better visualization of the kinematics of propagation. The time
delays induced by the presence of the low-velocity slab
have not been shown because they are under the common picking
threshold - this is a typical focusing-effect AVO case.
To obtain the curves in the lower panel of Figure 4, for
each of the three methods, we propagated a wavefield through the
velocity model in the upper panel of the figure (with the low-velocity
slab), and another wavefield through the constant-velocity
background only. For each *x* location, we picked the maximum
amplitudes of each wavefield at the depth of 6000m, and we divided the
amplitudes obtained from the model with the slab by the amplitudes obtained from
the constant-velocity background. A deviation from the value of 1
indicates the presence of the wavefield scattered by the slab.
We performed this procedure using
three different algorithms: (1) - Linearized downward continuation with
no amplitude correction applied; (2) - Linearized downward
continuation with boundary condition amplitude correction applied at
the surface; (3) - Pseudospectral wave propagation
Biondi (2002), for reference. The application of the boundary condition
correction has brought the values closer to those of the reference
curve. A possible shot-profile formulation of WEMVA would therefore
benefit from the application of the boundary condition correction.

**g3
**

Figure 4 **Top panel:** Velocity model for testing the amplitude
behavior of the linearized downward continuation operator. A shot
has been generated at (0,0) and the wavefield is recorded at a depth
of 6 km. The thin slab has a velocity of 1647 m/s, contrasting to the background of 1830
m/s. Wavefronts have been traced for better visualization of
propagation kinematics. **Bottom panel:** Curve ``-L'' - Linearized
downward continuation with no amplitude correction applied; Curve ``+L'' -
Linearized downward continuation with boundary condition amplitude
correction; Curve ``Ref'' - Pseudospectral wave
propagation.

** Next:** The propagation operator correction
** Up:** Application to linearized downward
** Previous:** Linearized downward continuation -
Stanford Exploration Project

5/23/2004