Shallow morphology of the subducted Pacific plate along the Hikurangi margin, New Zealand

PHYSICS O F T H E EARTH AND PLANETARY INTERIORS

ELSEVIER

Physics of the Earth and Planetary Interiors 93 (1996) 3-20

Shallow morphology of the subducted Pacific plate along the Hikurangi margin, New Zealand J . H . A n s e l l a,1, S.C. B a n n i s t e r b,. a

Research School of Earth Sciences, I/ictoria University of Wellington, Wellington, New Zealand b Institute of Geological and Nuclear Sciences, Wellington, New Zealand

Received 30 August 1994; revision accepted 19 July 1995

Abstract Along the east coast of the North Island, New Zealand, the Pacific plate is subducted beneath the Australian plate. The seismicity associated with this subduction has been determined using the results from a number of temporary and permanent microearthquake networks. A synthesis of the microearthquake seismicity, the depths of thrust events, the depth of S to P conversions, and deep reflection seismic studies leads to a coherent picture of the subducting slab, both in terms of its mechanical structure and in terms of the general morphology. The slab is initially subducted at a low angle of a few degrees, is bent through a circular arc of few hundred kilometre radius and then becomes planar again below 120 km depth. The radius of curvature varies along strike from about 280 km, just north of Wellington, to 240 km, north of Hawke Bay. The slab shape, between depths of 15-45 km, is thus approximately conical. It also approximates, within the errors of hypocentre location, a surface of constant Gaussian curvature, as would be geometrically expected from the simple bending of a thin spherical lithospheric shell. Observed seismicity is primarily concentrated within what is interpreted as the subducted crust of the Pacific plate, with a lower level of activity within the subducted mantle. Normal fault mechanisms at the top of the plate probably reflect tensional stress associated with the plate bending whereas thrust events observed at the lower bound of the observed seismicity probably reflect compression below the neutral plane.

1. Introduction

The east coast of the North Island, New Zealand, is an ideal location to study the geometry and seismic structure of a subducting slab. Along this coast, which is part of the Hikurangi

* Corresponding author. 1 Deceased.

margin and which lies south of the Kermadec region, the Pacific plate is subducted beneath the Australian plate. Here the interface between the plates is in a depth range of 10-30 km. Significant historic earthquakes in the region include the 1855 Wellington event of M = 8, the 1931 Hawkes Bay event of M--7.75 and the 1934 Pahiatua event of M = 7.5 (Eiby, 1968). A national network of seismographs began in 1900 and gradually developed, but the intersta-

0031-9201/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0031-9201(95)03085 -9

4

J.14. Ansell, S.C. Bannister/Physics of the Earth and Planetary Interiors 93 (1996) 3-20

Fig. 1. Map of North Island, New Zealand, showing the location of line profiles used in Surveys A - H (see text). The Hikurangi Trough marks the onset of north-westerly subduction and also shown is the 200 km depth contour of the Benioff zone. Also marked is the along-strike profile XY, N40°E at its centre. The inset shows the direction of absolute plate motions. The landmass is stippled and bathymetry is in kilometres.

tion spacing of over 100 km did not allow accurate depth determinations for shallower earthquakes. Since 1971, 12 microearthquake surveys have been undertaken along the margin, using both portable seismographs and the permanent microearthquake network which was established around Wellington in 1976. Abundant information on the shallow seismicity is thus now available. The Pacific plate is subducted towards the north-west along the Hikurangi Trough (Fig. 1). To the east of the trough the plate is covered by 1-3 km of fiat-lying sediments under a water depth of between 2 and 3 km (Davy, 1992). These shallow sediments possibly consist of turbidites overlying older open ocean pelagic sediments. The plate also carries a significant number of volcanic knolls, some of which are exposed on the

sea-bed whereas others are covered by sediment. The knolls, which have a vertical dimension of the order of 2 kin, are older than mid-Miocene but have apparently been active into the PlioPleistocene (Lewis and Bennett, 1985). However, gravity modelling in this region, known as the Hikurangi-Chatham plateau, indicates a crustal thickness, exclusive of sediment, of 10-15 km (Davy and Wood, 1994). This crustal thickness could indicate that the ocean crust was formed in a region where the spreading centre intersected a region of hotter than normal mantle (White et al., 1992). The age of the crust is unknown, but may be at least as old as Mesozoic, though to the north-east of the Plateau the crustal age is of order 100 Myr (Smith et al., 1989; Davy, 1992). The onset of subduction along the Hikurangi Trough is obscured by up to 4 km of flat-lying sediment (Davy, 1992) and hence there is not a significant bathymetric trench comparable with the Kermadec Trench to the north. On some seismic reflection profiles the subduction of buried volcanic knolls is apparent (Lewis and Bennett, 1985). The subducted plate has been traced by deep seismic profiling from well offshore to close to the east coast by Davey et al. (1986), who found that, following subduction, "The oceanic crust dips at only about 3° under the accreting sedimentary sequences of the overriding plate". A low-velocity layer, approximately 1 km thick, was observed at the top of the subducting plate and identified with older subducted sediments. The top of this layer was about 14 km deep near the coast, near Lines D and E of Fig. 1. The Pacific plate is then subdueted beneath the east coast and down into the mantle to a depth of more than 350 km. The lower edge of the continuous seismicity associated with the plate increases in depth from 200 km at 41°S to 350 km at 37°S, then shallows by 100 km before increasing in depth again to the north in the Kermadec Region (Ansell and Adams, 1986). The deep seismic zone under the North Island is almost planar below a depth of 120 km, strikes about N45°E, and is only about 9 km thick (Ansell and Smith, 1975; Ansell, 1978), although the apparent shape may be affected by the velocity

J.H. Ansell, S. C Bannister ~Physics of the Earth and Planetary Interiors 93 (1996) 3-20

model. This thickness is slightly less than that of the oceanic crust currently being subducted, estimated at 10-15 km. At the southern end of the region the absolute motion of the Pacific plate in the hot-spot reference frame is N52°W at 82 mm year-1 and that of the Australian plate is N5°E at 32 mm year-1 (Minster and Jordan, 1978). Hence, relative to the Australian plate, the motion of the Pacific plate is N89°W at 47 mm year-1. Thus the normal to the deep seismic zone is close to the direction of the absolute motion of the Pacific plate, rather than the direction of relative plate motion. In this study, we now elucidate the shallow geometry of the subducting plate, at depths of 10-90 km, between the offshore accretionary complex and the back-arc region, using the extensive database of microearthquake observations. We shall use seismicity distributions, thrust focal mechanisms, S to P conversions and seismic velocity studies to constrain the shallow subduction geometry.

2. Microearthquake datasets Nine datasets labelled A - I were used in this study of the 400 km region from Gisborne to Wellington (Fig. 1). The profiles used by the original researchers for vertical cross-sections are shown in Fig. 1 and their azimuths are given below. In general, the hypocentres were projected from up to 50 km either side of the profiles, except for Profile H, where the hypocentres were projected up to 100 km from the north-east. The datasets and the details of the seismic surveys involved are specified below. Dataset A is primarily derived from the north-eastern half of two surveys carried out by Bannister (1988). The surveys involved recordings over a total period of 60 days using 15 portable seismograph stations (vertical component only) with 350 events eventually being located. Of these only 117 high-quality events are included in Dataset A, with an average of 11 stations recording, and an average local magnitude of 1.8. The profile used in plot projections was N50°W. Un-

5

derthrusting focal mechanisms were interpreted by Bannister near the interpreted plate interface and thrust mechanisms at 55-60 km depth. S to P conversions were interpreted on the basis of observations of a phase which arrived between P and S from local earthquakes, recorded on the vertical component. This phase was often larger in amplitude than P and about the same size as S, and was often distinctive. These conversions were modelled by Bannister to obtain the estimated depth of the conversion location. Joint hypocentre and velocity determinations were also carried out using the P and S seismic arrival times. Also included in Dataset A are deeper subduction zone events located using a portable microearthquake array by Richardson (1989). Dataset B is formed by 107 events from the south-western half of the surveys described above. The same analysis was carried out as for Dataset A. Dataset C is the data obtained from the survey of Chong (1982). This survey was carried out over 15 days using 11 portable seismograph stations, with 145 local events recorded. The profile used for projection was the same as that used for Datasets A and B. Similar analysis to that described above was carried out by Chong, examining observed S to P conversions and relocating events following joint hypocentre and velocity inversion. Dataset D is the data from the two surveys of Reyners (1980). The first survey was carried out at the south-east end of the profile, with recording over 23 days using five portable seismograph stations, locating 267 local events. The second survey was at the north-west end of the profile, recording over 30 days using 12 portable stations, and locating 133 events. The profile used for plot projections was N49°W. Also included in Dataset D are several deeper subduction zone earthquakes which were located from a portable instrument survey carried out by Olson (1985). Her survey was primarily focused on volcanic events associated with the Mt. Ruapehu volcano (located near the north-west end of the Dataset C profile; Fig. 1). These shallow-depth volcanic events are not included in Dataset D. Dataset E represents events located in the

6

J.H. Ansell, S.C. Bannister/Physics of the Earth and Planetary Interiors 93 (1996) 3-20

north-eastern half of the region covered by two surveys by Kayal (1984, 1986). The first of the two surveys, at the north-east end of the region, used nine portable seismograph stations over a period of 14 days, locating 20 portable stations over 12 days, with about 100 events eventually located. Kayal used a plot projection of N45°W for plots of the data. Underthrusting focal mechanisms were interpreted by Kayal from composite focal mechanisms of first motions from several events. Dataset F, one of the earlier microearthquake surveys, represents the data from the survey of Arabasz and Lowry (1980). This survey involved nine seismograph stations which were occupied over 11 days, with 142 local events eventually being located. Arabasz and Lowry used a profile projection of N49°W. Dataset G is the data from the south-west half of the region covered by the two surveys described in Dataset E. Underthrusting focal mechanisms were reported by Kayal (1984). S to P conversions were observed from some events and some attempt was made by Kayal to model these phases (Kayal, 1986). Dataset H is the data from the north-eastern half of the very extensive Wellington network survey, by Robinson (1986). This is by far the most detailed of the data sets, with recording over a 5 year period by 12 permanent stations spread around the Wellington region. A total of 7231 events are included in the data set, and were plotted using a N40°W projection. Joint NW

hypocentre and velocity determinations were carried out by Robinson using the best quality events, with subsequent relocation of all of the events. Dataset I is the data from the survey of Smith (1979). This early survey used five portable seismographs over a period of 17 days, 49 events being located. Smith plotted events using a N45°W projection. The locations are not very well constrained owing to the low number of stations, and no use is made of this data in the present study. Our interpretation thus covers the section of the subduction zone between Gisborne and Wellington. There are only limited data to the north of this section, where further work is required. To the south, Robinson (1986) has proposed a break in the plate, but part of the region is offshore and the station coverage (at that time) limited the accuracy of the locations. Again, further work is required. In using hypocentral estimates for earthquakes it is important to appreciate both the systematic and random errors involved. The most accurate hypocentre estimates come from joint hypocentre and velocity determinations, and these are available for four datasets--A, B, C and H - - which also proved to provide the best constraints in modelling. Further, Chong (1982) has shown that, within a seismograph array, the effect of using horizontal layered models in the location procedure instead of dipping layered models (more appropriate for the subducted slab) is relatively small if the horizontal model has appropriate

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J.H. Ansel~ S.C. Bannister ~Physics of the Earth and Planetary Interiors 93 (1996) 3-20

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8

J. tl. Ansell, S.C. Bannister / Physics of the Earth and Planetary Interiors 93 (1996) 3-20

velocities. This is the case in the datasets considered here. Thus an analysis of the location methods used in the datasets and the work of Chong (1982), Bannister (1988) and Robinson (1986) indicates that the horizontal and vertical standard errors owing to random error are about 2 km, and there is the possibility of systematic error of about the same magnitude for events shallower than 35 km near the centre of the array. Events at the edge of the array, or at very shallow or deep depths, may have twice this error.

3. Individual analyses In each of the original studies the researchers essentially used the seismicity data from their own surveys to determine the location of the interface between the subducting plate and the overlying crust. This process may be straightforward if the survey is over several years and involves thousands of hypocentres, as in Dataset H, but the process is not well defined for a survey with a 2 or 3 week duration. In the latter case, the temporal variation of seismicity may well not reveal a clear or accurate picture of the long-term seismicity. The plate interfaces estimated by the original researchers for Datasets A - I are plotted in Fig. 2, using the normal of the N40°E XY line in Fig. 1 to obtain a common projection. Although there is some similarity among the estimates, there is also considerable divergence, which we believe results from the inadequate constraints imposed by the seismicity of the single datasets. The depth contours from these interface estimates have been plotted without reinterpretation by Smith et al. (1989) and appear to indicate significant topography of up to 10 km on the interface along its strike. However, in Fig. 3 we have projected all the data, except those from Datasets F and H, onto a vertical plane which strikes N40°E and passes through Wellington, the line XY of Fig. 1. Only events within 55 km south-east and 8 km northwest of this vertical plane are included. Noting the limited nature of the dataset, there is really

no evidence either for or against lateral variation of the plate interface in the order of 10 km. We consider that a joint consideration of the datasets should provide a simpler, clearer picture.

4. General structure A coherent generalized structure of the region emerges from a joint consideration of the seismicity, the velocities determined by inversions, the depths of thrust events, the depths of S to P conversions, deep reflection seismic studies, and the structural interpretation of the oceanic crust seaward of the trench. In Fig. 4, using Datasets A, B and C, we have plotted histograms of the projection of the focal depths of earthquakes, focal depths of events with underthrusting focal mechanisms, and depths of interpreted S to P conversions onto a vertical plane passing through the line XY of Fig. 1. We restrict the dataset to those data lying within a small distance range of the line XY, not including events more than 50 km south-east or north-west of that line. Moreover, as the events occur within a dipping structure, and we are projecting events from up- and down-dip within that structure, we attempt to allow for that dip during the projection by making an approximate (sine) depth correction based on the distance of the event from the line XY and using an 11 ° dip as an approximation of the dip of the subducted plate. We note from the figure that the thrust events are localized in depth but the S to P conversions occur over a wider range of depths. Also, the seismicity in the top 20 km, interpreted as the overlying Australian plate crust, is considerably less than that in the upper part of the subducting plate.

4.1. Overlying Australian plate In the crust of the overlying Australian plate, low seismicity is observed. This seismicity extends throughout the whole thickness of the crust above the subducting plate. To the west, where the subducted plate is deeper, we find the seismicity extends down to the presumed Moho (discussed

J.H. Ansell, S.C. Bannister~Physics of the Earth and Planetary Interiors 93 (1996) 3-20

in a later section). There is some lateral variation in this crustal seismicity along the strike of the zone, with an almost aseismic zone under Wellington. The crustal microseismicity is diffuse and not concentrated along fault zones.

S-wave arrival times from local microearthquakes, the exact velocity depending on the layer thickness. Similar low-velocity zones at the equivalent depth have also been interpreted off the south coast of the North Island near Profile H and with thickness 1.4 km (Luo, 1992), and, at a shallower depth, offshore near Profile D with thickness about 1 km (Davey et al., 1986). The exact nature and thickness of the interplate thrust zone may be expected to vary along strike and down-dip, and the precise definition of the zone is restricted by the error in the earthquake locations. The nature of the zone and its lateral variation may be important in the seismogenesis of interplate earthquakes. Physically, the zone may represent a crush zone together with sub-

4.2. Plate interface and interplate thrust zone Below the overlying crust is the interpreted interplate thrust zone which is associated with a significant increase in seismicity, with thrust events and with the low-velocity zone of thickness (in the order of) 3 km found by Bannister (1988) in Dataset A. This low-velocity zone was found by Bannister to have a P-wave velocity between 3 and 4.7 km s -1 from the inversion of P- and

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10

J.H. Ansell, S.C. Bannister/Physics of the Earth and Planetary Interiors 93 (1996) 3-20

ducted sediments, volcanic knolls and debris, as seen offshore at the onset of subduction. Although the exact thickness of the zone and its variability are not yet well defined, it is modelled here as 3 km. For convenience, the top of the interplate thrust zone is defined as the 'plate interface'. This plate interface also represents the upper limit of the S to P conversion depths and may be associated with deep reflections reported under Wellington (approximately 20 km depth) by Davey and Smith (1983) and offshore (approximately 14 km depth) by Davey et al. (1986) (Fig. 5(b)).

4.3. Subducted Pacific plate Immediately below the interplate thrust zone is a band of more intense seismicity of between 11 and 15 km thick, with highest seismicity near the centre. The thickness is comparable with the thickness of seismic activity observed down-dip the subducted plate by AnseU and Smith (1975) and the offshore crustal thickness estimated in gravity modelling by Davy and Wood (1994). Reported S to P conversion depths occur in the depth range of the intense seismicity and are not confined to the interplate thrust zone. Physically, this band of seismicity may represent subducted, thickened, oceanic crust. Below this seismic band is a region of decreased seismicity which we identify with the upper part of the subducted mantle. The overall thickness of the seismically active part of the subducted crust and mantle, including the interface zone, varies along strike between 35 and 45 km (see Fig. 3 and Fig. 6 below).

5. Projection onto the plane NS0°W Comparing the depth to the plate interface in the Wellington region (Dataset H) with that in the Hawkes Bay (Datasets A and B), we find that the subduction zone strikes approximately N40°E (as drawn by the line XY of Fig. 1), as a first rough approximation. The hypocentres from the central Datasets C, D and E were projected onto a vertical plane

perpendicular to the line XY of Fig. 1, and plotted in Fig. 5(a). Shown in this figure are the thrust events from the datasets, the projected location of Wellington seismograph station (Wellington, WEL), the location of the back-arc volcanoes and the coastline in the vicinity of Profiles C, D and E. In Fig. 5(b) we show results from three deep seismic reflection studies, plotted on the same projection. To the north-west, in Section (i), we show a migrated line drawing of reflections interpreted from data collected on a marine multichannel seismic survey (Stern, 1990), carried out to the north-west of Datasets F and G. We see coherent reflectors in the crust of the Australian plate down to the Moho (which is identified using the deepest seismic reflector), together with north-westerly dipping reflectors associated with the top of the subducting Pacific plate (Stern and Davey, 1989). In the neighbourhood of this seismic line, Stern and Davey also noted a negative correlation between the density of reflectors in the overlying crust and the seismicity, a feature also noted elsewhere (Ansell et al., 1986). In the centre of the figure, Section (ii), is the interpreted shallow structure and deep reflectors found from a crustal seismic refraction-deep reflection survey carried out along a northwestsoutheast profile centred on Wellington (Davey and Smith, 1983). We note that this survey is 150-200 km south of Datasets C, D and E. Offshore, to the south-east of Datasets C, D and E, Section (iii), we show the position of a deep reflection horizon seen on a marine multichannel seismic profile. This horizon is associated with a d6collement surface in the sediments overlying the subducting plate (Davey et al., 1986). Using the seismicity and deep seismic reflection information in Figs. 5(a) and 5(b) we have sketched in Fig. 5(a) a first approximation of the generalized plate interface, as the continuous line. For these datasets we find the shape of this interface between depths of 15 and 60 km can be described by a cylinder which has a radius of 265 + 35 km. Marked in Fig. 5(a) is the projection of a cylinder which has radius 260 km and centre 275 km deep and 70 km to the south-east of the line XY. The Appendix details the appropriate

J.H. Ansell, S.C. Bannister~Physics of the Earth and Planetary Interiors 93 (1996) 3-20

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Fig. 6. Individual Datasets A - H with cross-sections of the conical model interface (continuous line) with radius of curvature varying from 240 km in Region A to 280 km in Region H. Also marked are the locations of thrust mechanisms (e) and S to P conversions ( r, ). A 33 km deep Moho is marked for the Australian plate (left). (Datasets A - G are projected onto the line N130OE and H onto N135°E.)

12

J.H. Ansell, S.C. Bannister/Physics of the Earth and Planetary Interiors 93 (1996) 3-20

Table 1 Calculated radii for the conical model, and offset of centre of curvature as measured from the XY line of Fig. 1 Distance

Radius

Offset of radius

Depth of centre

0 56 72 155 184 225 272 330

280.0 273.2 271.3 261.2 257.7 252.7 247.0 240.0

72.0 71.0 70.7 69.2 68.7 67.9 67.1 66.0

292.5 286.7 285.0 275.4 271.8 266.4 259.9 251.5

Distance is that measured along XY from each profile to Wellington. The offset of the centre is with respect to XY of Fig. 1.

calculations of the depth contours for a cylinder beneath a sphere (Eqs. (A9) and (A10)). The depth contours are, as expected, convex ocean175 °

ward with the right sense of curvature in the down-dip direction. Also shown in Fig. 5(a) are parallel curves marking the bottom of the 3 km interplate thrust zone and the lower limit of observed seismicity. If each of the Datasets A - H is now examined with relation to this model (Fig. 6) we find that the radius and centre of curvature of the crosssections of the interface appear to change along the strike of the subduction zone. Further, the strike of the deeper plate (N45°E; Ansell and Smith, 1975) is oblique to the strike of the shallower seismicity (N40°E) and so a simple cylindrical model appears not to be the best approximation. At the south end, Dataset H, the cross-section of the plate interface is best fitted by a circle of radius 280 _+ 30 km (Table 1). The radius of curvature required to fit the data sets then de.,--"-t

179 °

I"Y

I I iI

i- 40 °

40 °"

/ / /

I

'

175 ° I

,

179 ° I

42 ° _

Fig. 7. Depth isobaths (in km) from the Earth's surface to the fitted conical slab model beneath the North Island. X a n d Y are as in Fig. 1. Offshore to the east are shown the frontal thrusts of the accretionary prism (Lewis and Bennett, 1985).

J.It. Ansell, S.C. Bannister~Physics of the Earth and Planetary Interiors 93 (1996) 3-20

creases to the north, to 240 + 40 km for Dataset A. A radius of 258 _+35 km fits Dataset D. Taking into account the observed change in the radius and the centre of curvature along strike (Table 1), the shape of the interface can be described to a good approximation by a cone (see Eqs. (A5), (A6) and (All)). Cross-sections of such a cone have been overlaid on each of the datasets in Fig. 6, using the parameters shown in Table 1. The approximation of the interface by a cone appears to be appropriate for the depth range 15-45 km (although it is still consistent with the available data down to 60 km depth). To the south-east, at depths shallower than 15 kin, the

\

13

cross-section of the interface may be approximated by a tangent to the circular cross-section of the cone. The actual dip and position of this tangent were constrained by the use of offshore seismic reflection profiles. Below 60 km depth the interface may be smoothly extended to tie in with deeper events (which are planar at depths below 120 km). Fig. 7 shows how the depth to the fitted interface varies with lateral position across the east coast. The north-westerly curvature of the isobaths demonstrates the effect of the depth variation between the gently conical slab model and the Earth's spherical surface (following the Appendix). Fig. 8 shows a perspective of the sub-

\ \

\.\ \

q

.

\

\

\

-

\ \

\ \

\ 60kin

;I /

AUSTRALIAN PLATE ,Ig

/ ////

J

/

/

/

f

/

/

/

/

/

J

/

PACIFIC PLATE

I1/.

/ I

lOOkm

.J

/ / f

Fig. 8. A perspective of the subducted plate with respect to the overlying Australian plate and the landmass of the North Island of New Zealand. Also shown is the shallow seismicity in the Wellington region, the 20 km and 60 km plate depth contours, and the position of the thrust faulting in the Hikurangi Trough to the east.

14

J.H. Ansell, S.C. Bannister/Physics of the Earth and Planetary Interiors 93 (1996) 3-20

ducted plate with respect to the overlying Australian plate and the landmass of the North Island of New Zealand.

6. Rolled ball model

The change in radius of curvature of the zone to the north-east leads to the approximation of the surface of the subducted plate by a section of a cone. The data and the conical model agree within the errors of location and the possible errors owing to projection. Future improvements in location accuracy and precise determinations of the interface position will lead to a refinement of the conical model. The axis of the cone, determined from the centres of curvature, plunges from north-east to south-west, and so the vertical cross-sections used are not exactly normal to the axis. Further development of the current model will need to take this detailed geometry into account. Now, although the thick subducting plate described above does not physically resemble a thin shell, it has been shown by Yamoaka et al. (1986) that, in general, the shape of a Wadati-Benioff zone can be simulated largely by a "simple bending of a spherical shell without surface deformation". That study suggested that, on the large scale, Gaussian curvature is essentially conserved for coherent slabs. One simple example of a deformed spherical shell is the shape achieved by rolling up a section of the shell into a cigar shape or a rolled ball (see the Appendix). The centre of the rolled ball is cylindrical and the extremities essentially (but not exactly) conical. (The variation of the radius of curvature along the shape is related to an elliptic integral.) We find that, within the errors of location of the surface of the subducted slab, our conical model is nearly equivalent to that expected for the near-conical section of a rolled ball, with the Gaussian curvature of the Earth. (The mathematical details will be presented elsewhere.) As noted above, such a surface may be geometrically expected from the simple bending of a spherical lithospheric shell, but only in the absence of stretching, shrinking or tearing. AI-

though the geometry of the subducted plate examined in the present study, in the 15-50 km depth range, appears to be consistent with this geometrical model, the extensions of the plate to the north-east, south-west and up-dip need to be also considered. To the south-west, for example, the Gaussian curvature may not remain invariant; Robinson (1986) interpreted a 7 km vertical offset in the plate interface along a NW-SE line through Cook Strait, south of Wellington, from relocated hypocentres. To the north-east, one might expect similar segmentation at, for example, the transition between the Hikurangi subduction and the Kermadec subduction zone, as implied by Hatherton and Syms (1975). Up-dip, however, there is no evidence to suggest that the Gaussian curvature would not remain invariant, and the geometry of our model is consistent with the geometry of the trench; the shallow 12-15 km depth contours of the conical model beneath the Earth's surface (Fig. 7) begin to parallel the shape of the trench (as vaguely indicated by the strike of the offshore frontal thrusts of the accretionary prism).

7. Constraints on rheology

Seismicity is observed throughout the overlying crust of the Australian plate, from the Earth's surface down to the interface of the subducted plate, in the region where the overlying crust is directly in contact with the subducted crust. This probably indicates that the temperature in the overlying crust is lower than 350 + 100°C, the limiting temperature for ductile deformation within continental crust (Chen and Molnar, 1983). Such a cool crust might be expected from the combined effects of heat loss at the Earth's surface and heat loss for at least 5 Myr (Ansell and Adams, 1986) to the subducting plate below through both convection of cooler migrating water and conduction. Similarly, as seismicity is observed immediately above the interface, we conclude that the long-term effect of shear heating at the interface itself does not dominate the effects of cooling.

J.H. AnseU, S.C. Bannister~Physics of the Earth and Planetary Interiors 93 (1996) 3-20

Further to the west we find, surprisingly, that the crust is seismically active and hence brittle down to the presumed depth of Moho, about 33 km (Fig. 5). The reason for this is not fully understood but several mechanisms are possible, including the presence of a "mafic lower crust of diabase composition" (Shudofsky et al., 1987) or an earlier episode of underthrusting by cool material. It is possible, for example, that the lower crust consists of former Pacific oceanic crust, covered with Triassic-Jurassic sediment, with the Dun Mountain Ophiolite terrane running through the west of the region (Korsch and Wellman, 1988). Within the subducted plate the maximum depth of the seismicity is between 35 and 45 km below the interface, with variation along strike and down-dip (Figs• 4 and 5(a)). This 'seismogenic thickness' is of the same order as other physical thicknesses found for old oceanic lithosphere• For example, the seismic thickness found from long-range seismic refraction studies is between 38 and 42 km (Nagumo et al., 1981; Shimamura et al., 1983); whereas anisotropic inversions of surface-wave data (Anderson and Regan, 1983)

15

indicate a thickness of 47 km for 50-100 Myr old lithosphere. Similarly, estimates of the long-term elastic thickness of oceanic lithosphere, made by examination of flexure resulting from loading and subduction, suggest elastic thicknesses between 36 and 46 km for 100 Myr oceanic crust (Bodine et al., 1981). The simple picture of the subducted lithosphere strained by bending and by the excess weight of the down-dip slab qualitatively fits the data. Normal faulting events at the top of the plate reflect tensional stress associated with the bending whereas the thrust events at the lower bound of the observed seismicity reflect the compression below the neutral plane. Superimposed is the effect of down-dip slab pull as evidenced by focal mechanisms from events within the deeper subducted plate beneath Central North Island described by Harris (1982), the effect of which is to lower the neutral surface. From focal mechanisms (Chong, 1982; Bannister, 1988) in the northern section we find the neutral surface at a depth of approximately 35 km below the plate interface, with tensional events above and thrust events below (Fig. 9).

distance (km) -25

0

25

;.~.~:~:;~.~:~::;/.~:~::;~!:~::;~.~:.~:;~!:~::;~!:.::;~:~:~;~.~:~::;~.~!:~::;..~!:.::;~.~:~::;...!:~:!~!:.~:;~.~:~::;~:~::!~!:~::;~!:.::;~!:~:~;~:::~.:

II..., ........................

~!i{::i!i{::i!~!::~!i!::i:~i!::iii!::i.~i!::i!i!::i..i!::i!~!::~!i!::i!~!::~!i!::~:~.:.:.. ,.........., ........ ~

:-~:-:.MO~..::.:.~

~

.- " -

==" ® =

.---"

.... '~ " . . . .

~

i ;.i!~:i: i !~ii; i !~ii~i !i~::".i!~ii~i !i:i ~i !~!i'.i!i iiiiiiii ~

-o

Z

ooo []

• ,

•.•'•" •

•,

.°•°

• ••"

•.

~

D O W N D I P

TENSION

•

•

•

•

.

• . ,

•

• . . °

°

°

°

°

'

....

•"

0

I

20 km I

Fig. 9. Strain direcUons determined for events below the Hawkes Bay region (Chong, 1982; Bannister, 1988). Thrust events (e) are observed along the plate interface zone, normal fau|Ung ([]), with down-dip tension, is observed within the subducted crust, and thrust events ( • ) , with down-dip compression, arc observed at approximately 50-55 km deep, 30-45 km below the interface.

16

J.H. Ansell, S.C. Bannister / Physics of the Earth and Planetary Interiors 93 (1996) 3-20

At the southern end of the zone only tensional mechanisms are observed (Robinson, 1986), indicating that the neutral surface is below the lower limit of seismicity. However, because of the limited depth of seismicity the neutral surface could equally well be at the same depth at the southern end of the zone as it is in the northern section. The number of factors involved cause some difficulty in deducing precise details of the stress profile and rheology of the subducted plate from the observed seismicity distribution and the neutral plane. The seismicity and the position of the neutral plane are affected by the curvature of the plate, which changes both along strike and downdip, by the strength of the rock (the stress yield envelope), which is strongly dependent on temperature, strain rate and geochemical composition (e.g. Shudofsky et al., 1987), and by the level of intraplate stress, which is also likely to change along strike (e.g. Harris, 1982). If, for example, as is possible, the rheology within the subducted plate is depth dependent, then the stress yield envelope will be asymmetric and the neutral plane will not necessarily lie in the centre of the plate. Changes in the stress

yield envelope will also affect the position of zones of anelastic deformation, and associated seismicity. Changes in curvature of the subducted plate along strike and down-dip, as found in this study and used by Galea (1992), will result in vertical migration of the neutral plane through the plate. Also, as the subducting plate begins to bend in the down-dip direction beneath the east coast, at around 15 km depth, there will be an associated increase in strain. The change of seismicity in the region 40-50 km south-east of line XY (Fig. 6) could be associated with this change in curvature; the position at which the model tangent representing the shallower plate interface touches the model cone.

8. Conclusion

A synthesis of the microearthquake seismicity recorded on temporary and permanent microearthquake networks leads to a coherent picture of the subducting slab beneath the east coast of the North Island, New Zealand, both in terms

O I

Fig. A1. An axisymmetricalfigure with radius r(x) lies within a sphere of radius R and centre 0'. We consider the radial depth d of the upper surface of the axisymmetricfigure from a point P on the sphere.

J.H. Ansell, S.C. Bannister/Physics of the Earth and Planetary Interiors 93 (1996) 3-20

of its mechanical structure and in terms of the general morphology. The defined slab shape is consistent with that of a gently tapering cone, with radius varying from 280 to 240 km, and intercepting tangential planes. This shape approximates the conical section of a rolled ball and thus, described mathematically, can be used as a reference model for comparison in future studies. Fine details of the structure, such as lateral variations in the thickness and nature of the interface zone, may be important for seismogenesis but remain to be determined. The quantity and quality of data required may well be forthcoming from a recent array deployment by Memphis State University, Leeds University and the Institute of Geological and Nuclear Sciences Limited.

Acknowledgements

17

A.2. The coordinate system We consider a sphere of radius R, with a centre O'. The axisymmetric figure has radius r(x) on cross-sections perpendicular to its axis of symmetry which is taken as the x axis. The origin O is the point on the x axis closest to O' and the z axis is along the outward radius O'O. The y axis makes up the right-handed x, y, z set. The radial distance from O to O' is p and the radial depth of O below the sphere is h, so

p = IO'Ol = R - h A general radial line through O' intersects the upper surface of the axisymmetric figure at Q(x, y, z) and the sphere at P(X, Y, Z). The coordinates (x, y, z) and (X, Y, Z) are both referred to the same axes and satisfy the equations X 2 + y2 + ( Z +p)2 = R 2

Thanks are due to Sally Rowe and Carolyn Hume for draughting figures, Russel Robinson for data, and the seismologists who originally recorded the microearthquake data. Thanks also go to Hugh Bibby, Ling-Yun Chiao and an anonymous reviewer for their comments and suggestions. The N.Z. Lottery Science Board and the VUW Internal Grants Committee assisted with funding.

Appendix A.1. Depth from a sphere to an axisymmetric figure

and y2 + z 2 = r(x)2

(A1)

where r(x) is the radius function. The radius r(x) is zero for a straight line, constant for a cylinder, varies linearly with x for a cone and varies smoothly with x for a rolled ball.

A.3. The radial depth d The radial depth d of Q below P is given by

d= leal The determination of the depth from the surface of the Earth to the subducting plate involves three-dimensional geometry. If the upper surface of the subducting plate can be approximated by an axisymmetric figure, then the relevant simplified geometric problem is the depth from a sphere to this axisymmetric figure. Here we derive some general results on the variation of depth with position and illustrate them with respect to four relevant axisymmetric figures: (1) a straight line; (2) a cylinder; (3) a cone; (4) a rolled ball (see Fig. A1).

Thus d can be considered as a function of (x, y, z), the coordinates of Q, or (X, Y, Z), the coordinates of P. These coordinates are themselves related:

x=X(R-d)/R,

y=Y(R-d)/R,

(z + p) = ( Z + p)(R - d ) / R

(A2)

Now, as the point Q(x, y, z) lies both on the upper surface of the axisymmetric figure and on a sphere with centre O' and the radius R - d , the

l8

J.H. Ansell, S. C, Bannister/Physics of the Earth and Planetary Interiors 93 (1996) 3-20

coordinates x, y and z simultaneously satisfy the equations (for z >/0) y2 + z2 = r ( x ) 2

and d =R-

(p2 + x 2 ) 1/2 = h + p - (p2 + x 2 ) '/2

(A3)

= h - x Z / 2 p for small x and x 2 +y2 + (z +p)2 = (REliminating z, we find equations

d) 2 x,

y

(A4) and

d

satisfy the

x 2 + r 2 ( x ) + 2p[r2(x) - y 2 ] 1/2 = ( R - d )

2-p2

(AS) These equations can also be written in terms of X, Y and Z by using Eq. (A2).

The depth contours for constant depth d can be plotted in the x, y plane using Eq. (A5). These contours illustrate the variation of depth with position in the x - y plane. Alternatively, the same equation for fixed x gives the depth profile perpendicular to the axis of symmetry and for fixed y gives the depth profile along a section parallel to the plane of symmetry, y = 0. Eq. (A5) can also be rewritten, for d < R,

+/3 2

+ 2p[r2(x)--y2]

The depth along the line decreases from the maximum depth of h at the centre x = 0 to zero when the line intersects the sphere at x = + ( R 2 - 02) 1/2. For small x the variation is quadratic in x, as in Eq. (A8), whereas for x near + ( R 2 p2)a/2 it is linear. This pattern of depth variation along a straight line is also relevant to any line or generator in a general axisymmetric figure.

A.5.2. Cylinder For a cylinder the radius r(x) is a constant, r, say. We take 0 ~
A.4. Depth contours

d=R-{rZ(x)

(A8)

1/2

+X2) 1/2

(A6)

(R -d) 2 _p2 _ r 2

(A9)

and

d=R-

[r2 + 2 p ( r 2 - y 2 ) 1 / 2 + p 2

+x2]'/2 (A10)

from which we can plot contours and depth profiles for particular values of r, p and R. For fixed y, we have a straight line in the cylinder and the depth decreases quadratically away from the centre x = 0.

A.5.3. Cone For a cone the radius r(x) varies linearly with

which reduces on the plane y = 0 to d = R - { [ r ( x ) + / 0 ] 2 + X2} 1/2

X 2 + 2 p ( r 2 - - y 2 ) 1/2 =

X~

(A7)

r( x) = b - ax (a, b constants)

(All)

A.5. Examples of axisymmetric figures

the apex is at x = b / a and the depth contours and profiles are given by Eqs. (A5) and (A6) with r(x) as in Eq. (All):

A.5.1. Straight line

dr(x)

A straight line has radius r(x)= 0 and equation

dx

y =0=z

A.5.4. Rolled ball

Hence from Eqs. (A5) and (A6), with 0 ~
If a section of a sphere or ball is rolled up around an axis, an axisymmetric figure is formed with an unchanged Gaussian curvature. Such a

x 2 = (R-d)

2-p2

J.H. Ansell, S.C. Bannister~Physics of the Earth and Planetary Interiors 93 (1996) 3-20

rolled ball can be formed from an inextensible spherical cap (Struik, 1961). The rolled ball shape is therefore possibly relevant to the shape of oceanic lithosphere, which on subduction is, in the down-dip direction, initially bent around a smaller radius. The shape of the rolled ball is expressed in terms of an elliptic integral, with a parameter 0 and constants c, r and Re. We find (Struik, 1961) r(x), the radius of the axisymmetric figure, is given by r ( x ) = r cos 0

(A12)

where x / R e = f0°(1 - k E sinE~b)1/2 d e - c / R e

(A13)

and - r r / 2 ~<0 < 7r/2 and k = r / R e . The initial radius of the ball is Re. The maxima radius of the roiled ball perpendicular to the axis is r, when 0 = 0 and x = - c . r ( x ) tends to zero as 0 tends to + 7r/2: dr(x)

k s i n 0 / ( 1 - k 2 sin E 0) 1/2

(A14)

dx Near the centre of the rolled ball the shape is approximately cylindrical whereas toward the ends the shape is approximately conical. The appropriate depth contours of the roiled ball inside a sphere can be found directly through Eqs. (A5), (A6), (A12) and (A13), or by using a cylindrical or conical approximation.

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19

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Shudofsky, G.N., Cloetingh, S., Stein, S. and Wortel, R., 1987. Unusually deep earthquakes in East Africa: constraints on the thermo-mechanical structure of a continental rift system. Geophys. Res. Lett., 14: 741-744. Smith, E.G.C., 1979. A micro-earthquake survey of the Rangitikei and Manawatu Basins. N.Z.J. Geol. Geophys., 22: 473-478. Smith, E.G.C., Stern, T.A. and Reyners, M., 1989. Subduction and back-arc activity at the Hikurangi convergent margin, New Zealand. Pageophys., 129: 203-231. Stern, T.A., 1990. The deep seismic expression of south Taranaki basin (New Zealand). In: B. Pinet and C. Bois (Editors), The Potential of Deep Seismic Profiling for Hydrocarbon Exploration, Technip, Paris, pp. 265-274. Stern, T.A. and Davey, F.J., 1989. Crustal structure and origin of basins formed behind the Hikurangi subduction zone, New Zealand. Geophys. Monogr. Am. Geophys. Union, 48: 73-85. Struik, D.J., 1961. Lectures on Classical Differential Geometry, 2nd edn. Addison Wesley, Reading, MA. White, R.S., McKenzie, D. and O'Nions, R.K., 1992. Oceanic crustal thickness from seismic measurements and rare earth element inversions. J. Geophys. Res., 97: 1968319715. Yamaoka, K., Fukao, Y. and Kumazawa, M., 1986. Spherical shell tectonics: effects of sphericity and inextensibility on the geometry of the descending lithosphere. Rev. Geophys., 24: 27-53.