Effizienz der Lax-Wendroff-Korrektur bei der akustischen Finiten-Differenzen Modellierung seismischer Wellen

Based on the first-order acoustic wave equation in stress-velocity formulation the
Lax-Wendro↵ scheme is used to develop a temporal high-order finite-di↵erence sche-
me on the staggered grid. Direct discretization of temporal high-order derivations
are numerical unstable, however the discretization of spatial ones is stable. With
the use of the Lax-Wendro↵ scheme temporal derivations are rewritten to spatial
ones, using the acoustic wave equation. For reasons of simplification in this work
only a homogeneous case is addressed. In 1D I present an explicit FD-scheme with
arbitrary order in space and time. For the 2D case a temporal fourth-order and spa-
tial high-order FD-scheme is shown. The dispersion relation of the phase velocity
is calculated, derived from the boundedness of the dispersion relation the stability
condition is analyzed as well. Using analytical solutions as a reference the accuracy
of the FD-schemes are investigated by numerical simulations. Comparison of accu-
racy and computational time are used to determine the eciency of the presented
FD-schemes among each other.