# Historical Location Information

## GROPE

Events in GeoNet's catalogue from 1987 to 2011 were determined using the GROPE technique.

For events located after September 1986 with an evaluationmethod of GROPE, earthquake origins were determined using P and S phases or first-arriving crustal P and S phases, in conjunction with a one-dimensional model of the crust shown in the table (earthmodel nz1dr). Four different velocity/depth structures were used in different parts of the country (Taupo network from 1987, Clyde network 1986 to 1996 only). Beneath the "Moho" defined by these models, velocities were smoothly merged, initially with those of the Jeffreys-Bullen Tables (British Association for the Advancement of Science, 1958), and subsequently the IASP91 model.

Earthquake analysts reviewed automated phase arrivals, as well as selecting the maximum amplitudes to be used in magnitude calculations. Weights on the phase arrival times were assigned or amended according to the errors in their measurement. The weight of readings was further modified by the location program, which, after each iteration, weighted the residuals used to adjust the computer-determined trial origin. The procedure (see Jeffreys, H., 1939: Probability Theory, Cambridge University Press) greatly reduces the weight given to phases with residuals greater than three standard errors.

In general, all four coordinates of the earthquake origin were calculated (origin time, latitude, longitude, and focal depth). In some cases, however, the focal depth was not allowed to vary, but restricted to some chosen depth. This was most commonly done for crustal earthquakes. Unless there was a station within 25 km of a shock in the upper crust, or within 50 km of a shock in the lower crust, a nominal depth of either 12 or 33 km was usually assigned, according to the crustal phases present and the goodness of fit of the resulting solution. Less often, the depth was restricted to a smaller value, particularly when the strengths of locally reported felt intensities indicated an uncommonly shallow focus. The parameter depthtype indicates if there is a restriction for any of the foregoing reasons. There were also times when data not suitable for input to the location program (e.g. overseas PKP readings), indicated the depth of focus; in such cases the depth was similarly fixed and the restriction noted in depthtype. When convergence of the location program failed for lack of enough data, both epicentre and depth were fixed at values consistent with the available information, and computation limited to finding a compatible origin time.

In routine origin determinations, sufficient of the stations nearest to the epicentre were read to ensure that there would be enough data for a satisfactory solution. When enough near observations were available, arrival times recorded at stations more distant from the epicentre were excluded from the calculations. The analysts were free to completely reject data which they thought to be unreliable, or to assign a low initial weight to it in the location program's procedure for minimising mean residuals.

The originerror parameter is the standard deviation of residuals (in seconds), and is an indication of how well the adopted origin reconciles the available data with the earth models used by the location program. Formally:

$$originerror = \sqrt{\sum_{i=1}^{n} \frac{ (w_i r_i)^2}{(n - m) } }$$

where $$r_i$$ is the $$i^{th}$$ residual, $$w_i$$ its weight, $$n$$ the number of readings and $$m$$ the number of parameters determined (4 for unrestricted depth, 3 when depth is restricted.) The parameters usedphasecount and usedstationcount indicate the degree of constraint on the adopted origin: that is, usedphasecount phases from usedstationcount stations were used in the determination of the origin. (All phases given non-zero weight are counted but stations which failed to provide such a phase are not). minimumdistance is the distance from the epicentre to the nearest of these usedstationcount stations, and azimuthalgap is the greatest angular gap in their distribution about the epicentre.

In using the earthquake catalogue, it is essential to keep in mind that the positions of earthquakes with epicentres outside the network of seismograph stations can be very uncertain, even though the mean residual is small.

### Magnitudes

The magnitudes assigned to local earthquakes are intended to be the values of ML as originally defined by C.F. Richter (Bull. Seism. Soc. Am. 25: 1-32, 1935), but his procedure for performing the magnitude calculation at other than the standard distance of 100 km was modified, to take account of the observed characteristics of energy propagation in New Zealand, including the effect of focal depth (Haines, A.J., Bull. Seism. Soc. Am. 71: 275-94, 1981).

For stations more than 100 km away from the epicentre, an amplitude-distance relationship of the form:

$$A = A_o R^{-N} exp( - α R )$$

where $$A$$ is an amplitude recorded at an epicentral distance $$R$$, $$A_o$$ is a calibration function, $$N$$ is a geometric spreading factor and α is an inelastic attenuation coefficient, was found appropriate for all parts of the country.

For all New Zealand crustal earthquakes $$N$$ is 2 and $$α$$ generally takes a value close to 0. With these values, the relationship describes head-wave propagation with no attenuation. In the Central Volcanic Region, however, α takes values of 0.8 deg$$^{-1}$$ for P waves and 1.05 deg$$^{-1}$$ for S waves. Adjustments are therefore made according to the distance travelled in the volcanic region.

For deep earthquakes in the Main Seismic Region the same parameters as for crustal earthquakes apply ($$N = 2, α = 0$$), provided that (i) $$R$$ now measures the slant distance from the focus to the base of the crust, and (ii) stations to the west of the Volcanic Region or south of the Main Seismic Region (south of a line between Cape Foulwind and Amberley) are not used, because the structure there necessitates different spreading and attenuation terms.

For deep earthquakes in Fiordland the same amplitude-distance relationship is used, with (i) $$N$$ given the value 1 (body wave propagation), (ii) $$α$$ increasing with focal depth, and (iii) stations in the North Island not used, because of variations of the coefficients $$N$$ and $$α$$.

For stations closer than 100 km to the epicentre, the formula:

$$M_A = log_{10}A+1.0log_{10}R+0.0029 R+ K$$

developed by R. Robinson (Pageoph 125: 579-596, 1987) is used, where $$A$$ is the maximum digital count, $$R$$ is the slant distance from the station to the earthquake focus (in kilometres) and $$K$$ is a station correction allowing for site factors.

Empirical corrections are applied to allow for differences in site effects. They are made in such a manner as to give the most consistent estimates of magnitude from the different stations, and their absolute level is adjusted to give a standard Wood-Anderson instrument at Wellington a zero correction, a procedure that provides a smooth connection with previously published New Zealand magnitudes. Station corrections are added to the individual estimates of magnitude, which are then weighted and averaged. Estimates from stations at distances less than 100 km are given half-weight, as are Fiordland stations for deep earthquakes. The number of magnitude estimates contributing to the mean value, and an indication of their scatter, are defined in parameters magnitudestationcount and magnitudeuncertainty.

### Velocity Models

Model (nz1dr) Upper Depth Boundary (km) Vp (km/s) Vs (km/s) Corners of region: latitude, longitude
New Zealand Standard 0.0 5.5 3.3
12.0 6.5 3.7
33.0 8.1 4.6
Taupo 0.0 3.00 1.70 35.6°S, 180.0°E
2.0 5.30 3.00 38.0°S, 177.5°E
5.0 6.00 3.50 39.7°S, 175.7°E
15.0 7.40 4.30 39.0°S, 175.0°E
33.0 7.78 4.39 37.0°S, 176.0°E
65.0 7.94 4.51 34.6°S, 178.5°E
96.4 8.08 4.52
Wellington 0.0 4.40 2.54 41.0°S, 178.0°E
0.4 5.63 3.16 43.5°S, 175.0°E
5.0 5.77 3.49 42.0°S, 173.0°E
15.0 6.39 3.50 39.7°S, 175.7°E
25.0 6.79 3.92
35.0 8.07 4.80
45.0 8.77 4.86
Clyde 0.0 4.4 2.6 45.5°S, 172.0°E
0.5 6.0 3.3 49.0°S, 167.0°E
12.0 6.5 3.7 44.5°S, 168.0°E
33.0 8.1 4.6 44.0°S, 169.0°E