Since the original version of HYPOCENTER was published. (Lienert et al., 1986), it has been used primarily to locate earthquakes using data collected by small ...
A ComputerProgram for Locating Earthquakes Both Locallyand Globally Barry R. Lienert Hawaii Institute of Geophysics and Planetology
Jens Havskov Institute for Solid Earth Physics University of Bergen, Bergen Norway
INTRODUCTION Since the original version of HYPOCENTER was published (Lienert et al., 1986), it has b e e n used primarily to locate earthquakes using data collected by small networks of seismometers (e.g., A m b o s et al., 1985). In its original form it suffered from m a n y of the same limitations as its predecessors (HYPO71, HYPOINVERSE, etc.). It could not use azimuth data, was unable to force the calculation of specific phases (P,,, Pc, etc.) and was limited to locating events at station distances of less than about 500 km, due to a "fiat earth" velocity m o d e l and coordinate system. The increasing use of portable t h r e e - c o m p o n e n t seismometers has m a d e it possible to determine the azimuth of a given event in addition to the arrival times of both primary and secondary phases. In principle, this allows single-station locations to be obtained, provided that the location software can use azimuth data. Global location capability is useful in processing data from regional networks, as it allows preliminary global locations to be m a d e in emergencies such as for tsunami warning. We therefore u n d e r t o o k a major revision of the original HYPOCENTER c o d e to address these limitations. The majority of the work has b e e n p e r f o r m e d at the University of Bergen, which operates an on-line seismic network of m o r e than 30 instruments distributed over 106 km 2. Data from this network has b e e n used to test the n e w program. The program has n o w b e e n in routine use for m o r e than three years at the University of Bergen. It has also b e e n u s e d extensively by regional seismic networks in m o r e than 20 countries as part of the SEISAN software p a c k a g e (Havskov and Utheim, 1992, Havskov and Lindholm, 1994). In this paper, we describe the n e w p r o g r a m and its features, as well as d e m o n strating its capability with selected examples.
PROGRAM CAPABILITIES 1. Local event location using a user-specified layered velocity model, with either a first arrival or any combination of the phases P, Pg, Pb, P,, S, S8, &, S,,, Lg or Rg. 2. Distant event location using an arbitrary spherically-
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symmetric earth model (presently IASPEI91). The phase set presently includes P, Pa~ PKP, PkiKP, pP, PPag,
pPKP, pPKiKP, sP, sPcl~, sPKP, sPKiKP, PP, P~F , S, Saef, SKS, pS, pSd@ pSKS, sS, sSct~, sSKS, SS, S IS I, PS, PKS, SP, SKP, SKiKP, PeP, PcS, ScP, ScS, PKKP, PKKS, SKKP, and SKKS. 3. Use of azimuth observations from one or several stations, allowing single station location. 4. Specifying initial values for, or fixing, any of the hypocentral parameters. 5. Robust weighting of outliers using bisquare residual weighing. 6. Use of arrival time differences ( S - P,, or Lg - Pg, etc.). 7. Station elevation corrections using either a constant velocity or layered model. 8. Statistics for sets of events, including station residuals, average root m e a n square (r.m.s.) residual and differences from previous locations. 9. Individual p a r a m e t e r files for each event, allowing the use of different velocity models and magnitude scales for a single set of data. 10. Calculation of Me, Mr, Ms or Mb magnitudes. 11. Elliptical confidence region calculations incorporating prior information on travel time error statistics.
PROGRAM DESCRIPTION HYPOCENTER is written in FORTRAN77, one of the most machine-independent high-level languages. We have successfully c o m p i l e d o u r p r e s e n t s o u r c e c o d e on SUN Sparcstations and IBM-compatible PC's (DOS 5.0 or better, 4MB RAM, 386 or better CPU). The program can therefore be run on the vast majority of machines used to process earthquake data. The IASPEI91 software (Buland and Chapman, 1983; Kennett and Engdahl, 1991) for calculating global travel times is also written in FORTRAN77, which m a d e it straightforward to interface into HYPOCENTER. A flowchart showing the major steps in the program appears in Figure 1. These steps are described in detail below:
Seismological Research Letters Volume 66, Number 5, September-October 1995
PROGRAM FLOWCHART
Iget initial parameters & stations I
r
.... Figure 1 Flowchart showing the main computational steps inHYPOCENTER.
I
I
get header record for new event
I
.1 /
"
no
locate? yes
T
/1'
I get phases I enough valid phases?
no
I yes
Iconsistency test I I
/
I starting location I
r-,
Itravel times & derivatives
/
I
-,
I
Iresidual weighting & rms I I
return to previous solution increase damping
I
-, /
I
rrns decrease? no
Iapply corrections I
I yes
I calculate hypocenter corrections & errors
1 convergence?
Tyes I output solution
I
... no
/
I
1. Input and Output Formats
3.
The program's default is to read the NORDIC input format (Havskov, 1990) and to provide an output in the same format containing the output hypocenter and its residuals. The NORDIC format is then capable of acting as a hypocentral database for each event. HYPOCENTER outputs the hypocenters in HYP071 summary file format for compatibility with existing plotting packages. A detailed print file is also generated for each event. This can be examined interactively during location of individual events in a large set.
Iterative location programs commonly start at a point near the station recording the first arrival. This can lead to problems when using least-squares techniques, which converge very slowly, or sometimes not at all, for events outside the limits of a regional network (Buland, 1976). Also, for small elongated networks, two potential solutions may exist at equal distances from the long axis. A starting location close to the first-arrival station can then bias the final location to the corresponding side of such a network. Although this bias is usually on the correct side, any systematic error in the firstarrival station's time can have a disproportionately large effect on the final location. In the new version of HYPOCENTER, a starting location algorithm analyzes the available phase data and uses the following information to determine a starting location: (a) Similar phases at different stations are used to determine the apparent velocity and azimuth of a plane-wave, using linear regression on the arrival times with respect to the horizontal station coordinates (i.e., latitude and longitude). For the Bergen network, reasonable azimuths of distant events could usually be determined from plane-wave regression. However, distances estimated using the variation of slowness predicted by the IA5PEI91 model were rather poor. To improve their accuracy, we used a stepwise search proce-
2.
Travel Time Consistency Tests
A single bad arrival time, due to a bad pick, a bad dock, or a data entry error, can seriously bias the starting location as well as the least-squares solution. The outlier problem has been discussed byJeffreys (962) and Anderson (982), who both used residual weighing to improve the robustness of their least-squares solutions. Before applying such residual weighting, we initially check the phase data set for obviously bad arrivals (misread phases, etc.) using two tests. First, we test that secondary phases (5, L, R, etc.) do occur after their primary parent phases (usually P) at each individual station. Secondly, we test that the arrival time differences for similar phases at pairs of adjacent stations are less than the calculated travel times between them (Johnson, 1979).
Starting Location
Seismological Research Letters Volume 66, Number 5, September-October 1995
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dure, increasing or decreasing the distance and azimuth at intervals of I degree while searching for a minimum in the travel time residual r.m.s. With first-arrivals from the Bergen network, this procedure has p r o v e d remarkably successful, often obtaining starting locations of distant (A > 100 ~ earthquakes that are within 100 k m of the ISC locations. (b) Different phases at the s a m e station ( S - P, L - P, etc.) give approximate distances to the event and are very useful where absolute times are questionable. When such distances are available, the p r o g r a m calculates the intersections of pairs and uses these as potential starting locations. (c) Azimuth information is frequently available from three-component stations,, as well as from seismic arrays such as NORSAR and ARCESS and provides useful constraints on a starting location. A starting location is then obtained either from the intersection of two azimuths at different stations, or from a single azimuth and a multi-phase distance. The latter case m a k e s it feasible to locate epicenters using a single station. (d) Depth phases, w h e n identified, give a time difference from their primary parent phase. This time difference is multiplied by a user-specified constant (nominally 5 km/s) to calculate a starting depth. The m e a n of all such depths is then used as the starting depth. To prevent a single bad depth phase from biasing this mean, outliers having a deviation of more than twice the r.m.s, deviations of all the depths are excluded and the m e a n recalculated. The best of all the starting locations in (a)-(d) is selected by calculating the r.m.s, of their travel time residuals and taking the location with the m i n i m u m r.m.s.
4.
Travel time and derivative calculations
W h e t h e r or not the u s e r - s p e c i f i e d l a y e r e d m o d e l or IASPEIgl software is used is d e t e r m i n e d by a user-specified distance, whose default value is 1500 km. If all the distances from an event are less than this, the layered model is used to calculate travel times and their derivatives. The layered model subroutine is similar to the original HYPOCENTER subroutine (Lienert et al., 1986) but has b e e n modified to force the calculation of Pg, Pb, P,,, etc., w h e n these are specified. It also uses geocentric coordinates enabling approximate P,, and Pe times to be calculated even at large distances. However, if the distance indicator in the header record of the NORDIC format is "L," the layered model will always be used for that event. If the distance of any station exceeds the user-specified limit, or the NORDIC distance indicator is "D," the IASPEI91 s o f t w a r e (Kennett a n d Engdahl, 1991) is used to calculate the travel times and their derivatives. To calculate distance, w e convert geographic latitudes and longitudes to geocentric latitudes and longitudes on a sphere having the earth's equatorial radius (6378.2 km). We then apply corrections for the ellipticity of the earth for each p h a s e using the p r o c e d u r e of Dziewonski and Gilbert (1976). Selection of phases by the IASPEI91 software has b e e n implemented as follows: (a) If the phase is a single P or S, it is assumed that it is
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the first arriving IASPEI91 p h a s e having the same first letter (e.g., P could be matched with P, and Swith 3", or at large distances, P w i t h PKPab and S w i t h SKSab). (b) If PKP, SKS, PKSor SKPare specified, the first-arrival branches of the first IASPEI91 p h a s e matching the first three letters is used, e.g. if the user specifies SKP, the program would select SKPab, SKPbc, etc. If the p h a s e is a depth phase (e.g., sP, pPKP, etc.), the first p h a s e matching the second to fourth letters is selected. (c) All other phases are m a t c h e d with the first IASPEIgI phase which matches the specified 8-character phase ID. The derivatives of travel time with respect to epicentral 1
distance, A = (x~ +x~) ~ (geocentric radians), and depth, x 3 (positive down in km), calculated b y the IASPEI9I software are used to obtain at/axl, at/axa and at/ax 3 using r the backazimuth at the source, the longitude, Xl and latitude, x2 (all in geocentric radians). The azimuthal derivatives (Bratt and Bache, 1988) are then a~/axa = - cos ~ cos I latitude I/sin A ar = sin r D ar
5.
x3 = o
Elevation corrections and Depth Origin
In the global case, we correct for station elevation by using the slowness of the incoming wave, at/aA and the uppermost IASPEI91 velocity. These are then used to calculate the vertical slowness and hence the additional travel time to the station. The default depth origin is always placed at sea-level for global location. However, for local events, it is possible to set the depth origin at the elevation of the highest station. In this case, the layered velocity m o d e l is used to calculate the station elevation corrections.
6.
Residual Weighting
For global events, we weight the travel time residuals using Anderson's (1982) bisquare method, i.e., an absolute residual-based taper, normalized to 4.685 times the median of the absolute residuals and starting at a minimum residual of 0.1 seconds. We found that a m i n o r adaptation of this method resulted in a considerable i m p r o v e m e n t in its performance. The arrival time mean, on which the weights are based, can be biased to one side by the presence of a single large positive or negative outlier causing a similar bias in the residual weights. We therefore recalculate the weighted m e a n value of the residuals a s e c o n d time using the first set of residual weights and recalculate the weights a second time using this n e w mean. Since any severe outlier is weighted out the second time around, the recalculated weights are unaffected by it.
7.
Hypocentral Corrections
We have used the a d a p t i v e l y - d a m p e d least squares algorithm described by Lienert et al. (1986). Although it did not
SeismologicalResearch Letters Volume 66, Number 5, September-October 1995
affect the operation of the original HYPOCENTER program, the original paper contained several errors in the centering equations. We therefore give these centering equations again below, using a slightly different notation. We define the n travel time differences as
at, = t, - T,- to
To further improve numerical stability, the weighted and centered partial derivative matrix
(1)
where t~ is the ith arrival time, T,. is its calculated travel time and to is the origin time. Each travel time is assigned a weight, 0 < (o~ _
