## 5aUW9. Numerical implementation of the three-dimensional one-way wave propagator using the third-order Thiele approximation on a hexagonal grid.

### Session: Friday Morning, December 6

### Time: 9:40

**Author: Mattheus J. N. van Stralen**

**Location: Lab. of Electromagnetic Res., Delft Univ. of Technol., P.O. Box 5031, 2600 GA Delft, The Netherlands**

**Author: Maarten V. de Hoop**

**Location: Colorado School of Mines, Golden, CO 80401-1887**

**Author: Hans Blok**

**Location: Delft Univ. of Technol., 2600 GA Delft, The Netherlands**

**Abstract:**

The Bremmer series solution of the 3-D acoustical wave equation in
generally inhomogeneous media, requires the introduction of pseudodifferential
operators. These operators describe the (de)composition, propagation and
interaction of the up- and downgoing waves. In this paper, a sparse matrix
representation of the propagator is derived. In a similar way the matrix
representations of the (de)composition and interaction of the up- and downgoing
waves can be derived. The focus is on designing sparse matrices, keeping the
accuracy high at the cost of ignoring any critical scattering-angle phenomena.
Such matrix representations follow from well-known rational approximations of
the vertical slowness, the Laplace operator and the vertical derivative. To
reduce artificial azimuthal anisotropy a hexagonal prism-type grid is employed
for the 3-D configuration. An optimization procedure is followed to minimize the
errors in phase and group slowness, in the high-frequency limit for a given
discretization rate. Through the Bremmer series it also accounts for the
backscattered field. The resulting algorithm provides an improvement of the
parabolic equation method. Numerical results will be presented at the
conference.

ASA 132nd meeting - Hawaii, December 1996