33. -
3 4. -
<u
- o5
35.
3 6. -
37. -
146.
147.
148.
149.
150.
151.
152.
Longitude
5.800
6.400
Figure 6.28 b) Crustal P-wave velocity model resulting from a 2-D inversion with initial Pn velocities set to the higher value of 8.1 km s"1. Note the is little change from previous results.
3-D Linear Inversion 6.58
biased somewhat by the initial model. It is important to know then what effect changing the
initial model has on the velocity maps.
Fig. 6.28a shows the Pn velocity map obtained from an inversion using an initial
upper Mantle velocity of 8.1 km s '1, instead of the usual 7.86 km s '1. The outermost
region, which is devoid of any data, has remained at the starting value, just as in the earlier
inversions. To make the diagram clearer, and to retain the same shading scale, we have
omitted the highest three contour intervals from the plot. The initial velocity of 8.1 km s '1
lies in the highest contour interval and all velocities have been perturbed downwards from
this value, indicating, rather unsurprisingly, that this initial value is much to high. Perhaps
the most interesting feature of the diagram is that it is actually very similar to the
corresponding models generated with an initial Pn velocity of 7.86 km s '1, shown in Figs.
6.23c & 6.26b. The contour pattem in anomalies are virtually identical, however the new
velocity map has essentially a uniform increase in velocities of about four contour intervals,
or 0.16 km s '1 over that in Fig. 6.26b.
45000 S 40000 £ 35000 30000 25000 Iteration
Figure 6.29 Misfit reduction curves for inversion beginning at a different upper Mantle P-wave velocity. The inversion A was performed with an initial Pn velocity of 7.86 km s '1 while inversion B had a value of 8.1 km s’1.
3-D Linear Inversion 6.59
Comparing the 'convergence curves' of the two inversions, shown in Fig. 6.29, we
see that the '8.1' inversion has obviously been started at a much poorer initial model,
however the misfit is quickly reduced and in fact falls slightly below that of the 7.86'
inversion. This suggests that the two inversions are not heading for the same model, but
instead two models with the same relative structure, but displaced by a constant amount. It
would appear then that the property which distinguishes the two starting models has been
mapped into the two 'solution' models with about the same amplitude. The size of this d.c.
shift in velocities gives us an indication of the degree of non-uniqueness in the inversion,
since we know that an average velocity shift of 0.16 km s"1 does not affect the estimated
misfit function to a noticeable degree. Moreover this suggests a method by which we may
estimate the tolerance on all velocity parameters i.e. by repeating the inversion many times
over from different starting models (both Pg and Pn velocities) and examining the effect on
the solution. However this represents a considerable amount of effort since many tens of
inversions may be required before any comprehensive picture emerges, and, therefore, does
not seem to be warranted within the confines of the linear inversion. The upper Crustal P-
wave structure resulting from the same inversion is shown in Fig. 6.28b. Again we observe
the standard picture which indicates that the change in the upper Mantle velocity model has
not influenced the Crustal structure even though the two are linked via the hypocentral
parameters.
6.4.1.11 Inversions with the controlled source data
The rest of the inversions in the linear study have been performed with the inclusion
of the blast data. Figs. 6.30a to f show the resulting Crustal, upper Mantle P-wave, S-wave
and Moho depth parameters respectively. The Crustal P-wave velocity map seems to have
altered somewhat, especially to the far north-east where a large amount of travel times are
now available in an area which was previously almost totally devoid of rays. A prominent
3-D Linear Inversion 6.60
quarries north of Sydney. The data from the north-south running refraction line to the east
seems to have been responsible for the slight high now observed in this region. The features
prominent in the earlier inversion are still apparent in the new velocity map. The familiar
'saddle' type feature running on a northwest - southeast to northeast - southwest pair of
axes, which was prominent in all previous maps, appears in the new inversion only slightly
distorted. The high velocity arm along the northwest - southeast axis has been diminished in
amplitude, while the low velocity arm has broadened slightly. Also the shape of the
previous velocity low in the northeast has been elongated to the south.
The upper Mantle P-velocity map, Fig. 6.30b, exhibits some more complicated
changes. Essentially the double low in the northeast has diminished considerably in
amplitude and, while the upper portion has moved towards the northwest. The high to the
west of the network has increased in amplitude and now dominates the picture. The S-
velocities also show more structure in the north in response to the new data. The general
pattern of anomalies is very similar to the previous maps if not a little more abrupt. The
amplitudes are also higher in the current map which gives an appearance of a more patchy
model. The Moho depth map is also very similar to those from the earlier inversions. Again
the only new features appear in the far north of the region. Nearly all features seem to have
been reinforced by the introduction of the blast travel times, hence the slopes descending to
the south and north, or the central network region, have been increased.
The depth distribution of the earthquakes is shown in Fig. 6.30e. Again the number
of events at the shallow depths has increased. We would presume that this is due to the
inclusion of the controlled source data which provides extra constraint on the velocity
structure, especially in the near surface region, since many of the source-receiver separations
are quite small. The earthquake relocation map is displayed in Fig. 6.30f and again is
dominated by the movements in the north-east, a feature which has remained throughout all