Untitled Document
Multi arrival tomography
Juerg Hauser, Malcolm Sambridge and Nicholas Rawlinson
Research School of Earth Sciences, Australian National
University, Canberra, ACT 0200, Australia
Figure 1. a) Layered velocity model
and associated first arrival paths used in the inversion test.
Point sources are denoted by stars and receivers by triangles.
Note that paths also emanate from two impinging plane waves. b)
Relative error in percent between the true model and the inversion
result. Contour lines are plotted at 1.5% intervals.
In seismic imaging the focus has largely been on first arrivals, with
a wide variety of schemes developed for their calculation. However, later
arrivals often contribute to the length and shape of a recorded wave
train, particularly in regions of complex geology. They are likely to
contain additional information about seismic structure as their two point
paths, differs from that of the first arrival. If they can be used in
seismic tomography, improved images should result. Here we use the wavefront
construction principle as the basis of a new scheme for computing travel
times for first and later arrivals that arise from smooth variations
in both velocity structure and interface geometry.
To investigate the possibility of using later arrivals to improve seismic
imaging a numerical test is performed. We compare the results of first
and multi arrival tomography, when recovering a two layered crustal scale
structure characterised by two low velocity anomalies and a u-shaped
valley in the interface. The inversion is performed simultaneously for
interface and velocity structure. There are sources above and below the
interface and two incoming plane waves are also simulated. Figures 1.a
and 2.a show the ray path coverage of the structure, which we will try
to recover using travel times. Clearly the later arrivals not only contain
additional information about the two low velocity anomalies but also
about the shape of the valley in the interface. Figure 1.b shows the
difference between the inversion result and the true structure when only
first arrivals are used in the inversion. The trade off between interface
geometry and velocity anomaly is clearly not as well resolved compared
to when both first and later arrivals are used (figure 2.b).
This example demonstrates that multi arrival tomography has the potential
to lead to an improved recovery of structure. An important difference
between first and later arrivals is that the existence of a later arrival
is a function of the structure. This means that during the iterative
inversion procedure, the number of ray paths and hence data is not constant.
Using later arrival therefore makes the inverse problem much more non-linear,
which means that care must be taken to avoid instabilities in an iterative
non-linear approach.
Potential applications of multi arrival tomography include surface wave
tomography, where observations of multipathing has been a long recognised
phenomenon, with measurements and analysis using earthquake sources dating
back many decades.
Figure 2. a) Layered
velocity model and associated first and later arrival paths used
in the inversion test. Point sources are denoted by stars and receivers
by triangles. Note that paths also emanate from two impinging plane
waves. b) Relative error in percent between the true model and
the inversion result. Contour lines are plotted at 1.5% intervals.