Hypocentre Derivation

How earthquakes are located and their magnitudes determined.

Event completeness

Felt earthquakes are located within one hour of their origin time, and are given "Reviewed" status (STATUS_CODE is set to R). Other significant events are located every working day, and are also assigned "Reviewed" status; these generally have a magnitude of 3.5 or above. Once all data sources have been received by GeoNet, a full set of hypocentres is located and given "Provisional" status (STATUS_CODE is set to P). Since July 2008, this analysis is performed within one week of the occurrence of the events. After the hypocentres have been re-checked, they are given "Final" status (STATUS_CODE is set to F).

Timing arrangements

Origin times are given in Universal Time (U.T. or, more strictly, U.T.C., which is atomically kept time, adjusted when necessary by one second steps ("leap seconds") to agree with the astronomically determined time known as UT1). For most seismological and civil purposes this may be regarded as the Mean Solar Time of the Greenwich meridian. GeoNet seismographs are equipped with GPS receivers for timing purposes. A temperature compensated quartz crystal clock is synchronised hourly with GPS time. The GPS time is extremely precise (nanosecond accuracy) but the crystal clock may drift between synchronisations at a rate of a few milliseconds per day.

It is sometimes desirable to know the local civil time at which an earthquake occurred. The times used for civil purposes in New Zealand (except the Chatham Islands) are New Zealand Standard Time, and New Zealand Daylight Time, which are defined in the Time Act, 1974. New Zealand Standard Time is 12 hours, and New Zealand Daylight Time 13 hours, ahead of U.T. The period of Daylight Time is specified by Order in Council, as provided by the Act; currently Daylight Time is in effect from the beginning of the year until 02:00 NZST on the third Sunday in March, and from 02:00 NZST on the first Sunday in October until the end of the year.

The time observed in the Chatham Islands is 45 minutes in advance of that currently in use in New Zealand.

Determination of origins

For events located before January 1987 with a SOLN_CODE value of 1, earthquake origins are determined using the phases P, Pn, P*, Pg, and the corresponding S phases. The New Zealand Standard model is used to calculate travel-times of rays passing through and immediately beneath the crust, except for two regions of special study (Wellington 1978 to 1986, Pukaki 1975 to 1983).

For events located after September 1986 with a SOLN_CODE value of 2, earthquake origins are determined using P and S phases or first-arriving crustal P and S phases. Four different velocity/depth structures are used in different parts of the country.

Beneath the "Moho" defined by these models, velocities are smoothly merged with those of the Jeffreys-Bullen Tables (British Association for the Advancement of Science, 1958). The solutions are in all cases based upon uniform procedures applied to laterally homogeneous models.

Digital seismograms are displayed on high-resolution graphics monitor screens under the control of CUSP (Caltech-USGS Seismic Processor) interactive software, for an analyst to select phase onset times by positioning a cursor on the trace. The analyst also selects the amplitude maximum to be used in magnitude calculations. Whenever possible, locations are based exclusively on times of first-arriving P and S phases.

Weights are initially assigned to phase arrival times by analysts according to the precision of the measurement. The weight of readings is further modified by the location program, which, after each iteration, weights the residuals used to adjust the 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 are calculated (origin time, latitude, longitude, and focal depth). In some cases, however, the focal depth is not allowed to vary, but restricted to some chosen depth. This is most commonly done for crustal earthquakes. Unless there is 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 is usually assigned, according to the crustal phases present and the goodness of fit of the resulting solution. Less often, the depth is restricted to a smaller value, particularly when the strengths of locally reported felt intensities indicate an uncommonly shallow focus. The parameter Z_CODE takes a value of R if there is a restriction for any of the foregoing reasons. There are also times when data not suitable for input to the location program (e.g. overseas PKP readings), indicate the depth of focus; in such cases the depth is similarly fixed and the restriction shown by Z_CODE taking a value of G (to indicate intervention by a Geophysicist). When convergence of the location program fails for lack of enough data, both epicentre and depth are 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 are read to ensure that there will be enough data for a satisfactory solution. When enough near observations are available, arrival times recorded at stations more distant from the epicentre are excluded from the calculations. The analysts are free to completely reject data which they think to be unreliable, or to assign a low initial weight to it in the location program's procedure for minimising mean residuals. (See earlier details of how the weights are used).

The RMS 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,

RMS = sqrt [ Σi=1,...n { (wi ri)2 / (n - m) } ]

where r_i is the ith 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.) When the number of readings used and the number of parameters are the same, the standard errors ERT, ERLAT, ERLON, ERZ and RMS are not defined. The parameters N_PH and N_STN indicate the degree of constraint on the adopted origin: that is, N_PH phases from N_STN 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). DMIN is the distance from the epicentre to the nearest of these N_STN stations, DMAX is the distance from the epicentre to the furthest of them, and AZGAP is the greatest angular gap in their distribution about the epicentre. CORR is the correlation coefficient of the errors in latitude and longitude. It may be used to construct an epicentral confidence region. (See Flinn, E.A., 1965, "Confidence regions and error determinations for seismic event locations". Rev. Geophys. 3: 156-185.)

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 M_L 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 has been 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 = A0 R-N exp ( - α R )

where A is an amplitude recorded at an epicentral distance R, A₀ is a calibration function, N is a geometric spreading factor and α is an inelastic attenuation coefficient, has been 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:

MA = log10 A + 1.0 log10 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 can be justified on a priori grounds and provides a smooth connection with previously published New Zealand magnitudes. Station corrections are added to the individual estimates of magnitude, which are then averaged. The number of magnitude estimates contributing to this mean value, and an indication of their scatter, are provided (parameters N_MAG and ERMAG).