## Validation of 3D synthetic seismograms
based on the ray-Born approximation

**Libor Sachl**
### Summary

The first-order Born approximation is a weak scattering perturbation method which is
a powerful tool. The combination of the Born approximation and the ray theory enables to
extend the applicability of the ray theory in terms of the required smoothness of the model
and ensures faster computations than with, e.g., the finite difference method. We are
motivated to describe and explain the effects of the numerical discretization of the Born
integral on the resulting seismograms.

We focus on forward modelling and study the cases in which perturbation from the
background model contains the interface. We restrict ourselves to isotropic models that
contain two homogeneous layers. We compare the 2D and 3D ray-based
Born-approximation seismograms with the ray-theory seismograms.

The Born seismograms are computed using a grid of finite extent. We anticipate that
the computational grid should contain an appropriate number of gridpoints, otherwise the
seismogram would be inaccurate. We also anticipate that the limited size of the
computational grid can cause problems.

We demonstrate numerically that an incorrect grid can produce significant errors in
the amplitude of the wave, or it can shift the seismogram in time. Moreover, the grid
boundaries work as interfaces, where spurious waves can be generated. We also attempt
to explain these phenomena theoretically. We give and test the options of removing the
spurious waves. We show that it is possible to compute the Born approximation in
a sparser grid, if we use elastic parameters averaged from some dense grid.

### Keywords

Born approximation, ray theory, velocity model, perturbation.

### Whole paper

The reprint is available in
PDF (745 kB).

*Stud. geophys. geod.*, **57** (2013), 84-102.