Velocity structure of the Wellington region, New Zealand, from local earthquake data and its implications for subduction tectonics

Geoph-vs. J. R. a m . Soc. (1983) 75,335-359

Velocity structure of the Wellington region, New
Zealand, from local earthquake data and its
implications for subduction tectonics

Russell Robinson Geophysics Division, DSIR, BOX              1320, Wellington,
New Zealand

                                                                                   Downloaded from by guest on September 11, 2015
Received 1983 March 7 ; in original form 1982 November 1 7

Summary. The technique of inversion of arrival time data from local earth-
quakes to determine hypocentres and velocity structure simultaneously
has been applied t o the Wellington region, New Zealand. The subducting
Pacific plate lithosphere, which here has a thicker than normal and somewhat
continent-like crust, lies at 20-40 km under the area. The overlying Indian
plate is broken by several major faults, one of which separates it from the
accretionary border. The data used were P and S arrival times for 93 local
earthquakes, four explosions, and three regional events as recorded on the 12
station telemetered Wellington seismograph network. The inversion procedure
involved multiple iterations with progressively decreasing damping and an
approximate, but quite good, three-dimensional ray tracing scheme. A major
problem is the choosing of appropriate velocity blocks and assessing the
effect of possibly inaccurate choices on the derived velocities. Starting with
simple models and gradually increasing the complexity leads to a good
appreciation of the information in the data and its limitations. The final
velocity model is two-dimensional (plus station terms), the block boun-
daries drawn on the basis of seismicity and results of preceding simpler
models. Both P and S velocities were determined with good resolution. This
model reduces the variance of the travel-time residuals by 60 per cent
compared to the one-dimensional model now used for routine processing and
greatly increases the self-consistency of hypocentre determinations. The
results show that the crust east of the Wairarapa fault, part of the accre-
tionary border, has relatively low velocity, especially for S-waves, and high
heterogeneity compared to the crust of the Indian plate proper. The proba-
bility of anisotropy in the mid- and lower-crust of the Indian plate compli-
cates the interpretation, especially of a velocity reversal for S-waves from 15
to 25km depth. The gently dipping band of relatively intense seismicity
parallel to the plate interface is found to be a region of high seismic velocity
(an average of 7.37 km s-' for P) and is interpreted as the lower crust of
the subducting Pacific plate, the upper crust having been accreted to the plate
boundary further east. Events at greater depth are occurring in mantle
336             R. Robinson
                material with a P-wave velocity of 8.69km s-l and are probably related to
                bending of the subducted lithosphere.

In recent years there has been a proliferation of relatively dense networks of sensitive
seismographs that record numerous local events at the microearthquake level with hgh
precision. The arrival time data generated by such networks allows the distribution of local
hypocentres to be determined if a velocity model can be assumed. This provides much
insight into the local geological structure and tectonics. However, there exists in such data
the potential for simultaneously solving for both the hypocentres and the velocity structure.
The seismic velocities so determined provide important constraints on the geological
structure and allow the more accurate, or at least more internally consistent, routine
determination of hypocentres. This paper reports on the application of this inversion
technique to a region of plate convergence and of moderate seismic activity, the Wellington

                                                                                                           Downloaded from by guest on September 11, 2015
region of New Zealand.


The North Island of New Zealand lies within a zone of oblique plate convergence that results
in the subduction of the oceanic Pacific plate under the continental Indian plate (Fig. 1).
The subducted plate is manifested by a zone of sub-crustal earthquakes dipping to the north-
west and reaching depths of about 300 km (Adams & Ware 1977). This zone of earthquakes
shoals somewhat from north to south and there is a transition to continent-continent
convergence in the South Island resulting in the uplift of the Southern Alps. However, at
the latitude of Wellington the zone of sub-crustal earthquakes is still well developed
(Fig. 2). Under Wellington itself this zone of earthquakes lies at relatively shallow depth,
from about 20 to 45 km deep, and dips at about 10' (Robinson 1978). Its projection to
the surface off the east coast coincides with the position of the Hikurangi Trough.
   The plate convergence in the Wellington region has resulted in intense deformation of the
overlying Indian plate (Walcott 1978). The major structural elements are shown in Fig. 3.


Figure 1. Tectonic setting of central New Zealand. Triangles represent active volcanoes. The convergence
rate at the latitude of Wellington is 50 mni yr-'. The dashed box is the area shown in Fig. 3.
Velocity structure o f the Wellington region                337
                        NW                                   Network                          SE
                      01              I            I            I
                                                                         :   / L -Hikurangi

                     100   -

                     200   -

                                                                                                             Downloaded from by guest on September 11, 2015
Figure 2. NW-SE cross-section through Wellington showing subcrustal earthquakes greater than 100 km
deep as relocated by Adams & Ware (1977) (their cross-sections D and E), the band of relatively intense
seismicity located by t h e Wellington seismograph network, and the position of the Hikurangi Trough off
the east coast of the North Island.


Figure 3. Map of the Wellington region showing position of the seismograph stations of the network
(triangles), and the Wairau and Wairarapa faults. Generalized surface geology is indicated by diagonal
shading (schist), dotted shading (triassic greywacke), and n o shading (mixed outcrops of Jurassic grey-
wacke, Cenozoic sediments, and recent basin fill). The area enclosed by the solid line is roughly the area
modelled in this study. The cross near the bottom is t h e coordinate origin used in the inversion
338            R. Robinson
To the west of the Wairarapa fault the near surface rock is everywhere greywacke of Triassic
age except west of the inferred northward extension of the Wairau fault where it is schist,
the metamorphic equivalent of the greywacke. The terrain east of the Wairarapa fault is
generally considered to be part of an accretionary border (eg. Cole & Lewis 1981). In this
area there are mixed outcrops of Jurassic greywacke and more recent Cenozoic sediments
with recent basin fill in the Wairarapa depression immediately east of the fault. It is not clear
what proportion of the rocks in this eastern region were originally part of the Pacific plate
crust or are remnants of the Indian plate border or some combination of the two. Van der
Lingen (1982) notes the absence of typical oceanic sediments and describes the area as
perhaps formed from a pre-subduction borderland now being squeezed together. However,
the sea depth off the east coast is much less than normal for oceanic lithosphere and Bennett
(1983) has argued from seismic reflection data that greywacke type rocks are present there
in the upper crust rather than typical oceanic basalts. The unusually high elevation of the
accretionary border also suggests that the crust of the subducting lithosphere is thicker and

                                                                                                    Downloaded from by guest on September 11, 2015
lighter (more continent-like) than that of normal oceanic lithosphere.
   The largest historical earthquake in the Wellington region, that of 1855 with magnitude
8 (Eiby 1968), was accompanied by an offset on the Wairarapa fault. However, it seems
probable that the major faulting was on the shallow dipping plate interface and that the
movement on the Wairarapa fault was only secondary imbricate thrusting as observed in
the 1964 Alaska earthquake (Plafker & Rubin 1978).
   The extension of the structures on the North Island south-west across Cook Strait is
problematical. It is generally thought that a major fault zone immediately west of Kapiti
Island is the extension of the Wairau fault of the South Island although Walcott (1978)
argues that the Wairau fault curves abruptly east through Cook Strait itself. All the terrain
south-east of the Wairau fault in the South Island is very similar geologically to the
accretionary terrain east of the Wairarapa fault. Thus it seems that the basically two-
dimensional geological structure of the southern North Island is disrupted in the Cook
Strait region. This apparent complexity and the lack of suitable seismograph coverage
places a south-western limit on the area to be studied in this investigation, as shown in Fig. 3.


The Wellington seismograph network consists of 12 stations, the seismic signals being
telemetered back to a central recording site and recorded on 16mm film. The positions of
these stations are shown in Fig. 3. Data from station CCW will not be used due to the
complex structures in the Cook Strait region. All stations sense the vertical component of
motion only except for WEL which has a N-S oriented horizontal seismometer and a low-
gain vertical seismometer. The system frequency response peaks at 10 Hz, the displacement
gains ranging from 100 000 to 700 000.
   Typically, three to four events per day are recorded sufficiently well to be located; their
magnitudes ranging down t o about 1.0. Epicentres for the year 1981 are shown in Fig. 4. A
cross-section (NW-SE) is shown in Fig. 5 for well-observed events occurring during the
period 1980 January-1981 June and that lie within the area to be studied here. The
majority of the events define a band of activity in the centre of the network about 10 km
thick and dipping at 9" to the north-west. It seems likely that this delineates the top region
of the subducted Pacific plate since it projects eastward to the Hikurangi Trough and west-
ward to the deeper activity located by the national network (Fig. 2). Prominent reflected
phases from local quarry blasts have been shown by more detailed reflection surveys to
originate from an interface somewhat above this band, probably within the Pacific plate crust
Velocity structure of the Wellington region            339


                                                                                                       Downloaded from by guest on September 11, 2015
Figure 4. Routinely determined epicentres for the year 1981, all depths. Larger dots are events with
magnitude gteater than 4.

                             100                    WEL                       0       SE
                                                     A                            I 1


                    80        1

Figure 5. NW-SE cross-section of well observed events for the period 1980 January-I981 June, and
within the region studied.

(Davey & Smith 1982). Below this band of activity there is less intense and more diffuse
activity that increases to the north-west with some indication of a second band of activity.
Within the overlying Indian plate the activity is relatively less intense and generally does not
correspond well with the major faults. There is one zone of relatively intense shallow activity
off the west coast but it lies well to the west of the inferred position of the Wairau fault
340             R. Robinson
  The velocity model used to locate events on a routine basis is a simple one-dimensional
model based on an unreversed seismic refraction profile running north-east from Wellington
(Garrick 1968; see Fig. 9 of this paper).

The inversion technique
The simultaneous inversion of arrival time data from a suite of local earthquakes to obtain
both the hypocentres and the velocity structure has been described by many authors
although the details of their methods vary a good deal (Crosson 1976; Aki & Lee 1976;
Pavlis & Booker 1980; Spencer & Gubbins 1980; Hawley, Zandt & Smith 1981; Hirahara
1981 ; Roeker 1982; Takanami 1982). For those unfamiliar with the technique, a simplified
discussion will be given of the version used here; reference to the above authors can be made
for mathematical details.
   In principle the idea of simultaneous inversion is simple: one first parameterizes the

                                                                                                  Downloaded from by guest on September 11, 2015
velocity model in some way (usually by blocks of constant velocity as in this study) and
includes these parameters together with the hypocentral coordinates in an iterative least
squares formulation that minimizes the travel-time residuals. If there are N earthquakes
producing M observations of arrival time and there are P velocity parameters, then we
wish to minimize the quantity

p2 =   I At-AAx 1'

where Ax is the ( 4 N + P x 1) vector of hypocentre and velocity adjustments, A t is the
( M x 1) vector of travel-time residuals, and A is a ( M x 4 N +P)matrix of travel-time partial
derivatives with respect to the hypocentre and velocity parameters. The least squares
solution that minimizes pz leads to the usual normal equations

AAAx     =A"nt.
The matrix Z A is then of size ( 4 N + P x 4 N + P).
   One could theoretically solve this system of equations directly for Ax by inverting
Z A , modify the trial hypocentres and velocity parameters appropriately, and go through
the same process until it converged. In practice several major problems arise:
    (1) Since a large number of events must be included to sample adequately a complex
velocity structure, the matrix Z A becomes very large. This poses problems for computer
storage and, as it must be inverted, computer time.
    (2) Numerical imprecision and the inherent non-linearity of the problem (the travel
times are not linear functions of changes in hypocentre or velocity) produce unstable results
if some parameters are less than perfectly constrained by the data.
    (3) Three-dimensional ray tracing is required.
    The solution to the first problem is found in the fact that although the matrix &lis
large, it is mostly filled with zeros (the hypocentres are, to first order, independent of
one another). This leads naturally t o partitioning schemes (e.g. Cleary & Hales 1966;
Herrmann, Park & Wang 1981; Spencer & Gubbins 1980) that reduce the inversion of
one large matrix into the problem of inverting many smaller ones. This saves a lot of time
and the zeros do not have to be stored, but there is still a lot of matrix manipulation
involved. It may seem tempting to try decoupling the hypocentre and velocity parts of the
problem: solve for the hypocentres with a fixed velocity model, then use the travel-time
residuals to solve for a new velocity model, recalculate the hypocentres, etc. Unfortunately
Velocity structure of the Wellington region           34 1
 this seldom works: even if convergence occurs the result is often physically implausible and
 depends strongly on the starting model. This decoupling was not used in this study.
    The second problem can be eliminated by suitable pre-inversion conditioning of the
matrices involved (e.g. by column scaling), by not being overly ambitious in the complexity
of the velocity model, and by use of some form of damping of the least-squares adjust-
Fents. The simplest way t o introduce damping is to add a diagonal matrix, 0, t o the matrix
AA with the result that, upon inversion, the contribution of eigenvectors with eigenvalues
less than the corresponding element of 0 are suppressed. The choice of 0 is somewhat a
matter of taste. In the so-called ‘stochastic’ inversion technique each element of 0 has the
value of oN/oM, the ratio of a guess at the noise variance to a guess at the model variance
(Aki & Richards 1980, p. 695). Thus the elements of 0 are different for each sort of para-
meter: velocity, spatial coordinate and origin time. Another approach is simply to determine
by trial-and-error minimum values of these three different elements that result in stable
convergence. This is the method used in this study.

                                                                                                 Downloaded from by guest on September 11, 2015
    The introduction of damping means that the solution obtained for A x is only an estimate
of the true least squares solution: the resolution of one parameter from another is no longer
perfect. For this reason it is desirable to keep the damping as small as possible consistent
with stability. However, as the damping becomes less and the resolution sharper, the
standard errors increase so it is necessary to keep an eye on both the covariance matrix
C(which gives the standard errors) and the resolution matrix R given by

R = (ZA +0)-’ZA        and    C = o’(2A   + 0)-’R
 where u2 is the variance of the data. If the diagonal element of R corresponding to a given
 parameter is one, that parameter is perfectly resolved; generally values less than about
0.75 are considered as indicating poor resolution. In this study the ultimate changes in
 velocity from the initial model were quite large so that fairly heavy damping of the velocity
parameters was used in the first iteration. However, the damping was reduced in each
successive iteration. In the final iteration it was quite small. Damping of the hypocentre
parameters was initially small and reduced to zero in the final iteration. In all inversions,
except for test cases, there were ten iterations.
    The problem of three-dimensional ray tracing is not straightforward. Any of the several
possible exact ray tracing schemes would be very expensive in terms of computer time. It
was decided, therefore, to try first the approximate method described by Thurber &
Ellsworth (1980). Briefly, their method involves three steps: (1) compute an average one-
dimensional slowness model based on the velocity structure between the earthquake and
station in question; (2) find the least time ray path through this model in the usual way; (3)
integrate along this ray path through the three-dimensional model to get the travel time.
Despite its simplicity the method was shown by Thurber & Ellsworth to give very good
estimates of the travel time even in quite complex structures and is much less susceptible
than exact methods to becoming trapped in local minima of the travel time. It also has the
advantage here of making it easy to calculate estimates of the travel-time derivatives with
respect to both hypocentre changes and velocity parameters. This ray tracing method has
recently been used by Taylor & Scheimer (1982) in an inversion study with satisfactory
results .
   In order to test the accuracy of the approximate ray-tracing method in a situation similar
to that expected in the Wellington region, the times predicted by it and an exact ray- tracing
scheme were compared for a hypothetical model with large (20 per cent) lateral velocity
changes in the upper 20 km and dipping layers at greater depths. The approximate method
did very well: for 200 observations (for P-waves) the average absolute error was 0.016s
343,            R. Robinson
                                                                 4                  /

                       0 krn

                       5 krn

                                                                                                              Downloaded from by guest on September 11, 2015
                       30 krn

                                I                     I                      ,I
                                          VpIVs       =
Figure 6 . Simple two-dimensional velocity model used to test the inversion program. Velocities in k m s-'.

with a standard deviation of 0.018 s. The largest error was 0.075 s. Since the estimated
reading error for P arrivals in this study is 0.05s, it was judged that the approximate ray-
tracing method was sufficient. It should be noted that this test has not verified that the time
spent in each individual velocity block is a good estimate of the real time spent there and
hence the partial derivatives could be more in error than the small errors in travel time would
suggest. This could affect the rate of convergence of the inversion procedure.
    Based on the ideas discussed above, a computer program was written to carry out the
inversion process. It was executed on a VAX 11/780 computer and required about 7 min per
iteration for an inversion involving 100 earthquakes and 40 velocity parameters. In order to
test the program for errors and also to test the approximate ray-tracing method further, a
very simple test case was constructed using the two-dimensional velocity model shown in
Fig. 6 and the station configuration of the Wellington network. The synthetic data consisted
of nine P-wave arrivals and one S-wave arrivaI for each of 75 randomly positioned hypo-
centres. The times were perturbed by random errors between k0.05 s. The trial hypocentres

 Table 1. Inversion results for a two-dimensional test case.

  Block        Starting                Velocity after iteration number                  R*       Real
  number       velocity         1         2            3         4          5                    velocity
               km s-'                                                                            k m s"
 1             5 .OO            4.67           4.51       4.47       4.47   4.47        0.99     4.50
 2             6.25             6.00           6.00       6.01       6.01   6.01        1 .OO    6.00
 3             8.25             8.20           8.07       8.02       8.01   8.01        0.98     8.00
 4             5 .OO            5.39           5.44       5.45       5.46   5.46        0.99     5.50
 5             6.25             6.41           6.47       6.49       6.50   6.50        1.00     6.50
 6             8.25             8.20           8.33       8.41       8.45   8.46        0.98     8.50

 * R = corresponding diagonal element of the resolution matrix.
Velocity structure o f the Wellington region               343
were determined using these times and a one-dimensional velocity model. Damping was
applied in this inversion. The results are shown in Table 1 . The computed velocities converge
to values close to the true ones after only a few iterations, confirming that the program is
performing correctly. An interesting point to note, however, is that for block 6 the velocity
change computed in the first iteration is opposite in sign to that required; only in later
iterations does it converge to the correct value. This suggests that the single iteration inver-
sions sometimes performed in order to avoid three-dimensional ray tracing must be inter-
preted with caution.

Application of the technique

The arrival-time data used in this study were generated by 93 local earthquakes, four explo-
sions of known position but unknown origin time, and three regional events whose hypo-

                                                                                                         Downloaded from by guest on September 11, 2015
centres (but not origin times) were fixed t o those determined by the national seismograph
network. Of the regional events, two were at shallow depth 250 km to the north-east and the
other, also at shallow depth, 250km to the south-west. The inclusion of the explosions
provides a fixed reference point (similar to the master event in joint hypocentre determi-
nation schemes) while the regional events help to constrain the deeper structure. The
epicentres of the local events are shown in Fig. 7 and in NW-SE cross-section in Fig. 8.
Note that in these figures and subsequent ones the horizontal coordinate axes have been
rotated 45" from north-south and east-west in order to conform to the regional strike of
the geology and seismicity and the internal coordinate system of the inversion computer


                    E    50



                              0                       50                      100

                                                    X, km
Figure 7. Epicentres of events used in the inversion. Note that the coordinate system has been rotated
45" from north. Blasts are shown by open circles.
3 44

                               0-             8 W
                                                    .. .. :. .
                                                         I   ;.ow           I         s             I        ,
                                                                                                                 0 .
                                                                                                                       3       ,c       I            I   1

                                              ..                                                         .
                                                                                                                                0   .

                                               $0                                      0                 .                      0 .
                              20 -

                                                              .*                      *.


                                                                                                   . . .   .-
                                                                                                                         5 .

                                                                                                . .
                                                                            *.*                     *.                   ***                0.
                     1                              .0
                                                     .                  .*

                     5-    40      -          0 %
                                                                                                                                                 0       -
                     a                                                            0        .
                     a                                                                         0.
                                                                    0   .
                              60 -                                                    *.

                              a0   -
                                           ..  *.

                                                                                                                                                             Downloaded from by guest on September 11, 2015
Figure 8. NW-SE crosssection of events used in the inversion. Blasts are shown by open circles. The
extent of the seismograph network is indicated by t h e stations TCW and BLW.

                                                         One Dimensional Velocity Models

                                       5.59 2.97                                 5.61 2.98                                     5.43 (3.14)
                                                                                 5.77 3.54                                     6.21 (3.59)
                                       5.72   3.48
                          15                                                     6.04 3.53
                                       6.17 3.52
               1          25                                                     6.13 3.59                                     6.46 (3.73)
                                       6.82 3.88
                a,        35                                                     7.37 4.34
                                       7.97 4.79
                          45                                                     8.12 4.87                                     8.04 (4.65)
                                       (8.50) 4.79
                          55                                                    ((9.2)) 4.79

                                        Model 1                                 Model l b                                Standard Model

Figure 9. Comparison of one-dimensional models showing P and S velocities, in km s-*, in the various
layers. Uncertain values (poor resolution) are bracketed as are the S velocities for t h e standard model
since they are based o n assuming a P to S velocity ratio of 1.73. The P velocity in the lowest layer of
model 1B is unstable. Standard errors and resolution data are shown in Table 2.

program. The origin for this rotated coordinate system is shown in Fig. 3 . These events do
not represent a typical distribution of hypocentres but were chosen to produce a spatially
homogeneous set of events, as judged by eye. However, the natural distribution of events
precludes an ideal data set: there are no deep events in the south-eastern part of the region
studied. On average, there were 8.1 P readings and 1.6 S readings for each event, all phases
being weighted equally in the following inversions. All the arrival times were those made
during routine processing of the events, except for the blasts and regional events which were
read especially for this study. The estimated reading error is 0.05 s for P. The error for S is
no doubt larger but is difficult to estimate as it includes the effect of phase mis-identifi-
cation. The initial trial hypocentres were determined using the standard one-dimensional
velocity model used for routine processing (see Fig. 9). This model does not make use of
station corrections. The standard deviation of the travel-time residuals for the 93 local events
was 0.132 s using this model.
Velocit?,structure of the Wellington region       345

While it would have been possible to postulate initially a complex configuration of velocity
blocks based on the surface geology and distribution of seismicity, it was decided to start
simply and gradually increase the complexity of the model as results dictated. This proce-
dure leads to a better appreciation of the information present in the data and its limitations.
The small number of stations in the Wellington network can be expected to place severe
limits on the model complexity.

Table 2. (a) Inversion results for model 1.

Block              VP                SE            R             VS             SE      R
                       5.59         0.03           0.99              2.97       0.06    0.97
                       5.72         0.03           0.99              3.48       0.02    1 .oo
                       6.17         0.04           0.98              3.52       0.03    0.99

                                                                                                  Downloaded from by guest on September 11, 2015
                       6.82         0.07           0.96              3.88       0.05    0.98
                       7.97         0.08           0.95              4.79       0.08    0.95
                       8.50         0.22           0.6 1             4.79       0.08    0.95

Station terms
Station           P                  SE            R             S              SE      R
KIW                -0.10            0.03           0.99          -0.30          0.09    0.94
CAW                  0.07           0.02           1.oo          -              -       -

MTW                  0.11           0.04           0.99            0.58         0.08    0.95
TCW                -0.39            0.03           0.99          -0.87          0.06    0.97
MRW                -0.04            0.02           1.00          -0.07          0.04    0.99
WDW                  0.03           0.02           1 .oo           0.02         0.05    0.98
WEL                  0               -              -              0            -       -

WHW                  0.04           0.03           0.99            0.03         0.05    0.98
BLW                  0.33           0.03           0.99            0.96         0.06    0.97
BHW                - 0.04           0.02           1.oo          -0.02          0.05    0.98
MOW                  0.30           0.03           0.99            0.72         0.07    0.96

(b) Inversion results for model 1B.
Block               VP              SE             R             vs             SE      R
1                      5.61         0.02           1.oo              2.98       0.06    0.97
2                      5.77         0.05           0.98              3.54       0.03    0.99
3                      6.04         0.04           0.99              3.53       0.03    0.99
4                      6.13         0.1 1          0.89              3.59       0.05    0.98
5                      7.37         0.08           0.95              4.34       0.06    0.97
6                      8.12         0.1 1          0.89              4.87       0.09    0.94
7                      9.20         0.22           0.58              4.79       0.12    0.88

Station terms
Station            P                SE             R             S              SE      R
KIW                -0.1 1           0.03           0.99          -0.28          0.09    0.94
CAW                  0.07           0.02           1 .oo                                -

MTW                  0.13           0.04           0.99            0.69         0.08    0.94
TCW                -0.37            0.03           0.99          -0.80          0.06    0.96
MRW                - 0.04           0.02           1.oo          -0.06          0.04    0.99
WDW                  0.04           0.02           1.oo            0.05         0.05    0.98
WEL                  0              -               -              0            -       -

WHW                  0.05           0.03           0.99            0.08         0.05    0.98
BLW                  0.41           0.03           0.99            1.04         0.06    0.97
BHW                -0.03            0.02           1.oo            0.01         0.05    0.98
MOW                  0.32           0.03           0.99            0.74         0.07    0.96
3 46           R . Robinson
    The first step in the application of the inversion technique to the Wellington region was
to derive a one-dimensional model with station terms using the data described above (except
the regional events which were added later). By 'one-dimensional', it is meant that the Earth
was divided into flat layers of constant velocity. The thicknesses of the layers were taken as
shown in Fig. 9: the topmost is 5 km thick, the others 10 km thick down to a half-space at
45 km depth. There are thus velocity boundaries at roughly the depths indicated by the
refraction data used to derive the standard model. The parameters to be determined in the
inversion were the P and S velocities in each layer and P and S station terms. The station
terms at WEL were fixed to zero; this is necessary due to the unconstrained trade-off
between the origin times and station terms that would otherwise result.
    The results of the inversion (model 1) are shown in Fig. 9 and Table 2. All the para-
meters, except for the bottom half-space, were well resolved and stable (diagonal elements
of the resolution matrix are shown in Table 2 also). In interpreting these results it is
necessary to remember that an inappropriate geometry will manifest itself in the derived

                                                                                                    Downloaded from by guest on September 11, 2015
velocities in complex and unknown ways. That the one-dimensional geometry is indeed
inappropriate for the region as a whole is indicated by the wide range in station terms: from
-0.39 to + 0.36 s for P and from -0.87 to + 0.96 s for S. Still, three points are of interest.
First, the velocity in the half-space is quite high, 8.50 km s-' for P. The highest velocity in
the standard model is 8.04 km s-'. Secondly, the S-wave velocity seems to increase only
slightly in the depth range 5-35 km. Thirdly, the standard deviation of the travel-time
residuals has been decreased to 0.090, a reduction of 54 per cent in terms of variance
(Table 6).
    In order to examine the effect of different layer boundaries, a second inversion was
carried out with the two uppermost layers both 5 km thick, the deeper layers 10 km thick
down to a half-space at 5Okm depth. The results are likewise shown in Fig. 9 and Table 2
(model IB). It can be seen that the results of the two inversions are generally in accord.
Still, there are some differences from what would be expecSed from simple averaging across
boundaries, pointing out the importance of caution in interpreting relatively minor velocity
features that may in reality be artefacts of the model geometry. Another point to note is
that the velocities in the half-space are no longer stable in the second inversion. This was a
problem that later required the introduction of the regional events into the data set.
    The station terms determined in the one-dimensional inversion provide an important
clue as to the next step in the evolution of a velocity model. They are plotted in Fig. 10,
from which it can be seen that there are three distinct classes of stations: (1) the six stations
situated between the Wairau and Wairarapa faults whose station terms are near zero; ( 2 ) the
three stations east of the Wairarapa fault (on the accretionary border) whose station terms
are large and positive (late arrivals); (3) the one station, TCW, west of the Wairau fault with
large negative station terms (early arrivals). This distribution of station terms together with
the two-dimensional nature of the geology suggests that a more appropriate velocity model
would have NE-SW trending boundaries corresponding to the Wairau and Wairarapa faults.
 Thus the next inversion (model 2) was based on the geometry shown in Fig. 11. Vertical
boundaries striking N45'E at approximately the positions of these faults have been added
to the one-dimensional model and extended down to 35 km depth. Again, the parameters t o
be determined were the P and S velocity of each block and P and S station terms.
    The results of this this two-dimensional inversion are shown in Table 3 and Fig. 1 1 . It is
clear that this model is a better representation of the real Earth by the reduction in the
standard deviation of the station terms: from 0.40s for the one-dimensional case to
0.22s for the two-dimensional model. However, the station terms for TCW, west of the
Wairau fault, are still large. This was a bit unexpected because TCW is the only station
Velocity structure of the Wellington region           347
                                   1 .o        I                  I



                         c             o

                                                              /        WDW

                                                                                                               Downloaded from by guest on September 11, 2015


                                             -0.5                 0                 0.5
                                                      P station term, s e c .
 Figure 10. Plot of S station term versus P station term for model 1. There appear to be three separate
 groups of stations.

      0   3                            2                                        I                  1
               561 325                               566 295                          538 263
      5 - -
                                       5                                       4
               571 354                               574 353                          554 335
               -                                                                                       -_
E                                      8                                        7
                573 329                              604 353                          6 17 3 4 0
fQ   25--                                                                                              - _
:         1?

               (6 67) 3 69
                                       I 1

                                                     649 366

                                                                                      663 397
     35   --                       I                                       I                           - -

                                                     7.99 4.79
     45   - -                                                                                          - _

                                                    (8.38) 4.71
Figure 11. Results of the first two-dimensional inversion, model 2, showing P and S velocities for each
block, in km s". Standard errors and resolution data are shown in Table 3. Bracketed values have poor
resolution. Block numbers are indicated by the small figures in t h e upper left corner.
348               R. Robinson
Table 3. Inversion results for model 2

Block              VP               SE        R             vs             SE            R
 1                     5.38         0.05      0.98             2.63        0.15          0.79
 2                     5.66         0.03      0.99             2.95        0.06          0.97
 3                     5.61         0.14      0.82             3.25        0.08          0.94
 4                     5.54         0.04      0.99             3.35        0.03          0.99
 5                     5.74         0.03      0.99             3.53        0.02          1.oo
 6                     5.71         0.09      0.93             3.54        0.06          0.97
 7                     6.17         0.05      0.98             3.40        0.04          0.98
 8                     6.04         0.05      0.98             3.53        0.04          0.99
 9                     5.73         0.12      0.87             3.29        0.10          0.90
10                     6.63         0.10      0.92             3.97        0.07          0.95
11                     6.49         0.09      0.93             3.66        0.06          0.97
12                     6.67         0.16      0.75             3.69        0.14          0.83
13                     7.99         0.07      0.95             4.79        0.07          0.95

                                                                                                  Downloaded from by guest on September 11, 2015
14                     8.38         0.22      0.56             4.71        0.09          0.93

Station t e m s
St at io n         P                SE        R            S               SE           R
KIW                -0.09            0.03      0.99          -0.32          0.09         0.93
CAW                  0.04           0.02      1.oo          -              -            -
MTW                -0.13            0.05      0.98          -0.09          0.15         0.80
TCW                -0.38            0.06      0.97          -0.61          0.12         0.87
MRW                -0.02            0.02      1.oo          -0.02          0.04         0.99
WDW                  0.00           0.02      1.oo          -0.19          0.06         0.97
WEL                  0              -         -               0            -            -
WHW                  0.05           0.03      0.99            0.00         0.05         0.98
BLW                  0.13           0.05      0.98            0.29         0.14         0.81
BHW                - 0.09           0.02      1 .oo         - 0.20         0.06         0.97
MOW                  0.09           0.04      0.99            0.1 1        0.14         0.82

overlying block 3; it would not have been surprising to see a tradeaff between the velocity
in block 3 and the TCW station terms. However, an examination of the resolution matrix
shows that this is not the case for P to any great extent; for S there is some trade-off. This
result indicates that the structure under TCW that results in early arrivals does not extend
very far to the NE. There is supporting evidence for a change in structure NE of TCW from
the distribution of epicentres for shallow earthquakes. There are no shallow events near
TCW but they are quite common further to the NE.
   Another point to note is that the velocity in block 12 is not very well resolved. This is
an example of the fact that block size must increase with depth, with a consequently
coarser model, if good resolution is to be maintained. This is further illustrated by the very
poor P-wave velocity resolution for the bottom half-space. It was this observation that lead
to the addition of the regional events to the data set. Arrivals from these events travel in
part horizontally through the half-space and very effectively constrain the velocity. Since
there were no usable observations of S for these events, the P to S velocity ratio in the half-
space was fixed to 1.73.
   Up to this point the models considered have had horizontal boundaries. However, the
distribution of local earthquakes (Fig. 5) clearly indicates that at deep levels dipping boun-
daries would be more appropriate. Thus for the final inversion (model 3) the model geometry
shown in Fig. 12 was adopted, the positions of the dipping boundaries being taken so as to
delimit distinct seismic regions (Fig. 5). The model is still two-dimensional (plus station
terms): attempts at inversions with separate blocks underlying TCW proved t o be unstable.
Velocity structure o f the Wellington region               349

                                              5.68 3 04

                                              5.77    3.60                     5.57 3.37

                                6.03 3.34

                                                                                                              Downloaded from by guest on September 11, 2015
                                                     8.69 (5.03)

Figure 12. Results of the final inversion, model 3, showing P and S velocities for each block, in km s".
Standard errors and resolution data are shown in Table 4.

Table 4. Inversion results for model 3.

Block              VP               SE                R            vs               SE            R
 1                     5.40         0.04              0.98             2.72         0.17          0.76
 2                     5.68         0.02              1 .oo            3.04         0.07          0.96
 3                     5.88         0.13              0.85             3.39         0.08          0.94
 4                     5.57         0.05              0.98             3.37         0.03          0.99
 5                     5.71         0.05              0.98             3.60         0.02          1 .oo
 6                     5.71         0.10              0.92             3.62         0.07          0.96
 7                     6.1 1        0.06              0.97             3.29         0.05          0.98
 8                     6.03         0.06              0.97             3.34         0.05          0.98
 9                     6.93         0.06              0.97             4.36         0.08          0.95
10                     7.50         0.06              0.97             4.1 3        0.06          0.97
11                     7.25         0.07              0.96             3.92         0.07          0.96
12                     8.07         0.07              0.96             5.03         0.06          0.97
13                     8.69         0.05              0.98             5.03         -             -

Station terms
Station            P                SE                R            S                SE            R
KIW                -0.01            0.03              0.99         -0.10            0.09          0.94
CAW                  0.03           0.02              1 .oo        -                -             -

MTW                -0.06            0.04              0.99         -0.10            0.15          0.81
TCW                -0.21            0.05              0.98         -0.18            0.12          0.89
MRW                -0.01            0.02              1.oo           0.04           0.04          0.99
WDW                -0.02            0.02              1 .oo        -0.22            0.06          0.97
WEL                  0              -                 -              0              -             -

WHW                  0.04           0.03              0.99           0.03           0.05          0.98
BLW                  0.22           0.04              0.99           0.50           0.1 5         0.82
BHW                -0.10            0.02              1.oo         -0.21            0.06          0.97
MOW                  0.12           0.03              0.99           0.23           0.14          0.83
350            R. Robinson
                                                      Iteration Number

                                          S   1   2 3 4        5 6 7 8 910
                                          1   1   1    1   1   1 1 1 1 1 1

                                   -‘-I                                          I
                  Block 1     Vp

                    ock 2 Vp

                                                                                                       Downloaded from by guest on September 11, 2015
                  S Sta. Term
                  Figure 13. Examples of convergence of the parameters for model 3.

   The results of this inversion are shown in Table 4 and Fig. 12. In all cases the parameters
converge toward well-defined final values although as the damping was reduced to quite
small amounts in the final iterations they may oscillate slightly. Some examples of the
nature of the convergence are shown in Fig. 13. The first example illustrates again the danger
of one iteration inversions: the starting and final values are nearly the same but the initial
perturbation was quite large. The second example is probably ‘typical’. The third example is
for one of the best behaved parameters while the fourth example is for one the least well
behaved .
   It is of interest to test the effect of different initial velocity models. In the previous inver-
sions the starting velocities were taken from the standard one-dimensional model with zero
station terms. If the velocities and station terms are now taken to be those from the one-
dimensional inversion (model l), the difference in the results are shown in Table 5 . The
average absolute difference for the velocity parameters is only 0.03 km s-l and for the
station terms 0.03 s. In only four cases were the differences greater than the standard error
for model 3 , and then by little. Thus in the discussion to follow, the results of inversion 3
will be taken as the final model.
   Examination of the resolution matrix diagonal values (Table 5 ) shows that all parameters
of the velocity model are very well resolved (diagonal terms of 0.90 or more: mostly 0.95 or
more) except for the P velocity in block 3 ( O X ) , the S velocity in block 1 (0.76) and the
S station terms for MTW, TCW, BLW and MOW (0.81, 0.89, 0.82, 0.83). In particular, the
velocity in the half-space is now well constrained by the data, presumably because of the
addition of the distant events. In regard t o the block 1 S velocity and the S station terms for
the three eastern stations. it is clear from the full resolution matrix that these parameters
Velocity structure of the Wellington region           351
                        Table 5. Difference between models 3 and 3B.

                        Block                  VP                      vs
                         1                       0.03                    0.07
                         2                       0.00                    0.01
                         3                     -0.06                     0.00
                         4                     -0.08                   -0.01
                         5                     -0.09                   -0.01
                         6                     -0.13                   -0.01
                         I                     -0.02                     0.01
                         8                       0.02                  -0.01
                         9                     -0.11                   -0.02
                        10                       0.00                  -0.02
                        11                       0.02                  -0.02
                        12                       0.01                    0.01
                        13                       0.00                    0.00

                                                                                                    Downloaded from by guest on September 11, 2015
                       Station terms
                       Station                 P                       S
                       KIW                     -0.03                   -0.04
                       CAW                       0 .oo                 -
                       MTW                       0.01                    0.09
                       TCW                     - 0.04                    0.00
                       MRW                     -0.01                   -0.02
                       WDW                       0.00                    0.04
                       WEL                     -                       -
                       WHW                         0.00                -0.01
                       BLW                         0.03                  0.09
                       BHW                         0.01                  0.02
                       MOW                         0.02                  0.12

are not fully resolved from one another. Nevertheless, all these parameters manifest the
shallow S-wave velocity and it is clear that this is quite low. The situation near TCW is more
complex, with the P and S velocities in block 3 and the P and S station terms for TCW all
interacting. Still, it seems likely, as discussed above, that the shallow velocities near TCW are
significantly higher than those further to the NE (which are probably not much different
from those in block 2). Improvements in the resolution in this area would require at least
one off-shore seismograph.

Discussion of the velocity model

Before passing to the implications of the final velocity model in terms of geology and
tectonics, it would be well t o consider the degree to which it is a better representation of
the real Earth than the other models, not just a better predictor of travel times for the suite
of earthquakes used. Certainly if the model makes testable and correct predictions other
than of the travel times of local events, it can be taken to be more valid physically. Unfortu-
nately, most other observable geophysical effects would depend not only on the velocity
model but also on its extension downward and laterally and on parameters not directly
contained in the model. Teleseismic travel-time residuals would be affected by structures
deeper in the subducted Pacific plate lithosphere. Gravity anomalies depend on assuming
some velocity-density relationship and the spatial extrapolation of the model. However,
there is some support in gravity data for at least part of the model - the dipping high
352             R. Robinson
velocity layers at depth and the region of high velocity near TCW. The observed Bougher
gravity anomaly is more or less two-dimensional with a steady positive gradient of about
1.6 mgal km-' from NW t o SE (Reilly, Whiteford & Doone 1977). This would be expected
from the dipping high velocity (and hence high density) layers, corresponding to crustal
thinning. An interface dipping at 9" to the NW with a density contrast of 0.3 g cm-3 would
produce a gradient of 2.0 mgal km-' (Nettleton 1976, p. 202). The lower density of the
crust east of the Wairarapa fault would reduce this gradient somewhat. A one-dimensional
model with station terms converted to shallow velocity variations would predict a small
gradient in the opposite sense. The offshore gravity data also show an abrupt decrease not
far NE of TCW, corresponding to the inferred change in velocity there (F. J. Davey, private
   In general, however, it seems that the velocity model must stand or fall on its own merits.
To the degree that the model better predicts local travel times, it can reasonably be taken as
a more valid physical model also, although contrived cases can be imagined where this is not

                                                                                                             Downloaded from by guest on September 11, 2015
necessarily true. There can be little doubt that the two-dimensional models (number 2 or 3
above) are better able to match the observed data. This is indicated both by the reduction in
variance of the travel-time residuals (Table 6) and by the improved stability of hypocentre
determinations. On the basis of the travel-time variances either model 2 or 3 would be

Table 6. Standard deviation and variance of travel-time residuals

Model                     Standard dev.                  Variance                    Vdriance/variance
                                                                                     of standard model
Standard                  0.132                          0.0174                      1 .oo
1                         0.090                          0.0081                      0.47
2                         0.085                          0.0072                      0.41
3                         0.083                          0.0069                      0.40

                                               50                   55
                                                      X . krn
Figure 14. Scatter of computed epicentres using minimal subsets of arrival time data for a deep local
event. The cross is the position determined using all available phases and the velocities in model 3 . Two
data sets produced no stable epicentre when using the standard velocity model but were stable using
the other models.
Velocity structure of the Wellington region             3 53
preferred over the standard model and, although less strongly, over the one-dimensional
model 1. The superiority of the two-dimensional models, however, becomes evident when
considering the scatter in hypocentres computed for a single event using different subsets
of the arrival time data. Fig. 14 shows the scatter of epicentres computed for a deep event
using: (1) the standard model, (2) the one-dimensional model with station terms (model l),
and ( 3 ) the two-dimensional model with dipping layers (model 3). All epicentres were
computed using random combinations of four P arrivals and one S arrival and so would
normally be considered as poor locations (the actual number of observations was 10 Ps and
3 Ss). The standard model produced epicentres with a relatively large scatter and, moreover,
several data sets were completely unstable and did not yield any solution. The one-
dimensional model with station terms also produced a relatively large scatter but no data
sets were unstable. The two-dimensional model produced the least scatter with again no
instabilities. However, analyses such as this show very little difference between models 2 and
3 (without or with dipping layers) and so the preference for model 3 must be based on the

                                                                                                    Downloaded from by guest on September 11, 2015
fact that its velocity boundaries delimit distinct seismic regions and on the gravity data.

Structural,tectonic, physical implications
 One of the major reasons for carrying out this study was t o gain more insight into the local
 structure and tectonics than is available from hypocentre distributions alone. It has already
 been seen that, as far as velocity is concerned, the major crustal discontinuities correspond
 to the Wairau and Wairarapa faults. The discontinuity associated with the Wairarapa fault
 extends down to about 15 km depth and separates rocks of the accretionary border from the
 old Indian plate. The heterogeneous velocity structure east of the Wairarapa fault, as
indicated by the range in station terms despite all stations being sited on basement grey-
wacke, is consistent with the idea that the crustal rocks there were previously part of the
Pacific plate accreted on to the plate boundary or, alternatively, part of a now compressed
borderland. Those processes would certainly be expected to produce heterogeneity. Between
the Wairarapa and the Wairau faults, on the old Indian plate proper, the shallow structure
appears to be much more homogeneous. Further west, the Wairau fault separates the high
velocity rocks near TCW (schists) from the greywacke rocks in the central part of the region.
There also appears to be a N W S E trending velocity boundary, perpendicular to the Wairau
fault, that delimits the high velocity near TCW in the NE direction (the famous ‘Cook Strait
fault’, northern branch, of local geological legend?).
    There are two additional features of interest concerning the crustal velocities. First, there
is a discrepancy between the standard velocity model based on an unreversed refraction
profile running NE from Wellington (corresponding to blocks 2, 5 and 8) and the inversion
results. The P velocity between 5 and 25 km depth is substantially lower in the inversion
model than in the refraction model, an average of 5.90km s-l compared to 6.35 km s-’. It is
unlikely that the refraction based velocity is much in error due to a dipping interface as it
runs parallel t o the regional strike. Moreover, nearly the same velocity of 6.2 km s-’ at about
5 km depth has been observed elsewhere in a similar terrain near Arthur’s Pass in the South
Island (Davey & Broadbent 1980, fig. 8). The change in velocity in the standard model from
the mid-5 s to 6.2 km s-l at about 5 km depth is usually attributed to a transition from
greywacke to schists similar t o those observed at the surface near TCW. The explanation for
this discrepancy may thus lie in anisotropy. Laboratory and field measurements have shown
that the velocity in the schist is highly anisotropic (15 per cent, Garrick & Hatherton 1973).
Wherever they are exposed on the surface their fabric is aligned preferentially in the NE-SW
direction. Thus the refraction profile would have sensed their fastest direction. The inversion
procedure, however, would have to some degree sensed all directions but primarily vertically.
3 54           R. Robinson
 It is to be expected then that the inversion velocity would be less than the refraction profile
velocity. It would also be more suitable for locating local earthquakes on the whole.
     The second point of interest concerning the crust is the S-wave velocity profile - there
is a reversal in velocity from 15 to 25 km deep. Reports of P velocity reversals in the
 continental crust are now common (Landisman, Mueller & Mitchell 1971). Christensen
(1979) has shown on the basis of laboratory data that they should not be unexpected given
reasonable temperature gradients. However, the inversion model contains no velocity reversal
 for P-waves. Since the S-wave velocity, under crustal conditions, is no more sensitive to
temperature than P velocity (Hughes & Maurette 1956, 1957) it is not possible to ascribe the
S velocity reversal to high temperatures. This conclusion is supported by the fact that heat
 flow along the east coast of the North Island is generally lower than normal (Pandey 1981).
 However, the situation is made more complex by the probability of anisotropy as discussed
above. S-wave velocity anisotropy for upper mantle rocks is very much less than P-wave
velocity anisotropy (Verma 1960; Christensen & Salisbury 1979; Clowes & Au 1982). How-

                                                                                                   Downloaded from by guest on September 11, 2015
ever, the opposite is true for many metamorphic rocks likely to form the lower crust
(Christensen 1965, 1966). About all that can be said is that for mainly near-vertical ray
paths there is a reversal in S velocity but not for P, probably due to a change in compo-
sition or fabric with depth rather than a temperature effect. The substantial increase in both
 P-and S-wave velocity at about 25 km depth could be the cause of the strong reflections
observed from the lower crust under Wellington (Davey & Smith 1982).
    Another interesting feature of the velocity model lies somewhat deeper. The zone of
relatively intense seismicity dipping t o the north-west (corresponding t o blocks 10 and 11)
is shown to have quite a high seismic velocity, up to 7.50 km s-l for P and 4.13 km s-l for
S. As discussed in the introduction, this zone of activity very likely marks the top of the
subducting Pacific plate lithosphere, which at the latitude of Wellington is likely to have a
crust thicker and more continent-like in petrology than normal oceanic type lithosphere. An
interpretation of these high velocities depends critically on how appropriate the velocity
block boundaries are. It could be argued that the velocity boundaries chosen on the basis of
seismicity could encompass several distinct velocity layers (for example, the old Pacific plate
lower crust plus some of the upper mantle) so that the derived velocity represents some
sort of average. As long as the inversion procedure assigns the velocity boundaries as initial
and fixed conditions there is no way this possibility can be ruled out. However, the
apparent mechanical homogeneity of the region, as reflected by the seismicity (Fig. 5),
seems likely to reflect a homogeneity in velocity also. It likewise could be argued that the
prominent band of seismicity is really a single planar interface made to look thicker by
location errors. The focal mechanisms of the majority of the events, however, exhibit no
nodal planes of corresponding orientation (they are of normal fault type - Robinson 1978).
The boundaries used, then, seem likely t o delineate true velocity boundaries.
    What then do these results imply about the nature of the seismic band? Given the other
evidence that the subducting Pacific plate crust is thicker than normal, it seems most likely
that the seismic band represents the lower crust, which might well be about lOkm thick,
the upper crust having been left behind - accreted on to the plate boundary. The velocity
(an average of 7.37 km s-l for P and 4.02 km s-l for S) is appropriate for the lower crust of
either an oceanic type or continental type lithosphere, especially if phase changes have
occurred, as seems likely. Typical oceanic lower crust (gabbro) has a velocity of 7.1 km sfl
on average (Hyndman 1979) but increasing pressure and, more importantly, phase changes
during subduction would increase that velocity substantially. Amphibolites and some high
grade schists, such as might be found in the lower continental crust, exhibit P velocities
as high as 7.2-7.7kms-' (Christensen 1965). The S velocity for oceanic gabbro is about
3.7 km s-l (Hyndman 1979) and for amphibolites about 4.0 km s-l (Christensen 1966).
Velocity structure of the Wellington region              3 5s
  If the upper crust of the Pacific plate has been accreted, the absence of typical oceanic
 sediments within the exposed part of the accretionary border can be explained by either
 the semi-continenta! nature of the Pacific plate near Wellington or by assuming that any
 such sediments lie offshore nearer the Hikurangi Trough, as suggested by Van der Lingen
     It must be asked why the velocity in this seismic band does not increase with depth due
 to increasing pressure and probable phase changes during subduction. Compression alone
 would cause a relatively small increase in velocity, about 0.05 to 0.10 km s-l for an increase
 in depth of 10 km. However, a decrease of 0.25 km s-' is actually observed. There are three
 possible explanations: (1) frictional heating along the plate interface; (2) an increase in crack
 density due to the relatively intense seismicity; ( 3 ) a change in time of the composition of
 the rock undergoing subduction. Frictional heating alone seems an unlikely explanation
 since a temperature increase of about 650°C would be required. This would take the rock
 well into the ductile deformation regime, in conflict with the observed seismicity. Theo-

                                                                                                     Downloaded from by guest on September 11, 2015
 retical models that relate seismic velocity to crack density (e.g. Toksoz, Cheng & Timur
 1976) indicate that an increase in crack density of about a factor of 3 would be required
 to explain the observed velocity decrease. This seems reasonable. It could be proposed that
 as the Pacific plate lithosphere subducts from east to west, phase changes in the lower crust
begin to occur and serve to trigger the earthquakes. These events in turn progressively
 increase the crack density as the plate continues to move westward, thereby progressively
 decreasing the velocity westward and more than compensating for the expected increase due
to phase changes. However, an explanation in terms of change in rock composition cannot
be ruled out. Velocity variations of the same sort of magnitude as observed here have been
measured in the lower sections of different ophiolite sections by Christensen & Salisbury
(1982), presumably reflecting the variations to be expected in the lower oceanic crust. No
doubt similar heterogeneity would exist in a more continental-like lower crust. It is
interesting to note that the seismic activity within the band starts rather abruptly and is
most intense under the Wairarapa depression, immediately east of the Wairarapa fault.
Rodgers (1982) has postulated that phase changes in the subducting crust can cause down-
warps in the overlying plate. This is consistent with observations here, as is the mechanism
of the events - normal faulting.
     The resolution of the data was not sufficient to subdivide the next lower layer or the
half-space in order to check on any lateral changes in velocity. This is because of the lack
of deeper events in the south-eastern half of the region. The velocity in block 12,
8.07 km s-' for P-waves, is typical of either oceanic or continental uppermost mantle. The
P-wave velocity in the half-space is quite high, 8.69 km s-' , but not unexpectedly so. Haines
(1979) also found a high value (8.50 km s-') when studying P, propagation along the east
coast of the North Island. The average oceanic lithosphere model of Kosminskaya & Kapustain
(1976) has a P-wave velocity of 8.60 km s-' 5 km below the Moho. The deepest events are
clearly occurring at significant depth in the mantle of the subducting plate. The fact that
they increase in number to the NW suggests that they may be related to the downward
bending of the plate that must begin just west of the modelled area. Reyners (1980) came to
a similar conclusion for an area 150-200km further north based on temporary micro-
earthquake surveys. He suggested that phase changes within the mantle of the subducting
plate may be responsible for initiating the bending.

Shift of hypocentres
One of the products of the simultaneous inversion process is, of course, new hypocentres. It
is of interest to see the degree of shift introduced by the final velocity model. Fig. 15 shows
356             R. Robinson
                            1     I      1        I   1
                                                            I      I      1      I     I


                                                                                                           Downloaded from by guest on September 11, 2015

                          0                               50                               100
Figure 15. Comparison of epicentres for events used in the inversion using the standard model and model
3 , the arrow pointing from the former to the latter. Dashed lines are the positions of the Wairau fault
(top) and Wairarapa fault (bottom).

the shift in epicentres from those of the standard model and Fig. 16 shows the shift in depth
on a NM-SE cross-section. The average epicentre shift is 1.78 km; the average hypocentre
shift is 3.17 km. The epicentre shifts appear to be random in direction but their magnitude
increases towards the boundaries of the network, as would be expected. As to the depth, on
the whole the deeper events do not shift much whereas the shallower events (depth
Velocity structure of the Wellington region                  357
           NW                                                                                         SE



                                                                                                           Downloaded from by guest on September 11, 2015


                100                                 50                                   0
                                                     Y , km
Figure 16. Comparison of depths calculated for events used in the inversion using the standard model and
model 3, the arrow pointing from the former to the latter. Boundaries of velocity blocks used in model 3
are shown by light lines.

The technique of inverting arrival time data of local earthquakes to simultaneously deter-
mine hypocentres and velocity is able to supply important information on the structure and
tectonics of the Wellington region. The approximate three-dimensional ray- tracing scheme of
Thurber & Ellsworth (1980) seems to be adequate for this technique. The major problem is
probably the difficulty in choosing appropriate velocity block boundaries and assessing how
possibly incorrect choices affect the resulting velocities. Starting with simple models and
gradually increasing the complexity leads to a better appreciation of the information in the
data and its limitations. The use of multiple iterations clearly shows the danger of the single
iteration inversions sometimes performed in order to avoid three-dimensional ray tracing:
the initial adjustments may sometimes cause a velocity parameter t o diverge from the final
value despite damping.
   The final velocity model determined for the Wellington region is two-dimensional (plus
station corrections). This model reduces the variance of the travel-time residuals by 60 per
cent compared to the standard model used for routine processing and also greatly improves
the self-consistency of hypocentre determinations. The results show that the crust east of
the Wairarapa fault, part of the accretionary border, has a relatively low velocity, especially
for S-waves, and high heterogeneity compared t o the crust of the Indian plate proper. The
probability of anisotropy in the mid- and lower crust of the Indian plate complicates the
interpretation, especially of a velocity reversal for S-waves from 15 to 25 km depth. The
gently dipping band of relatively intense seismicity marking the plate interface is found to
You can also read
NEXT SLIDES ... Cancel