| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
CARNEGIE INSTITUTION OF WASHINGTON DEPARTMENT OF TERRESTRIAL MAGNETISM, WASHINGTON, D.C.
OBSERVATORIO CHARACATO UNIVERSIDAD NACIONAL DE SAN AGUSTIN, AREQUIPA, Peru
CARNEGIE SEISMIC ANALYSIS CENTER, LIMA, Peru
Abstract
Mathematical instability in four-parameter least squares hypocenter solutions arises primarily from the fact that the four computed variables—origin time (T0), focal depth (h), latitude (
), and longitude (
)—are not strictly independent. Specifically, T0 exhibits a non-independent relationship with the geometric parameters. For small networks (< 10–15 stations), the lack of independence between T0 and the other variables results in unstable least-squares solutions. This instability is manifest most clearly by the fact that different station subsets of the observational network produce significantly different solutions for the same earthquake. The instability can be eliminated by computing T0 independently for each station using the formula
 |
where Tp = P-wave arrival time, Vk = S-P velocity, Vp = P-wave velocity, and Ts-p = time interval between P and S arrivals. An average value of T0 can be obtained from the individually calculated origin times and the P-wave travel times calculated. The variables 
, and z are then computed by the usual least-squares procedure using P-wave travel times only. The method is iterative and an average T0 is recalculated in the course of each iteration.
Fundamental properties of travel times within the Earth impose definite limitations upon the accuracy of the locations. Low values of the derivative dTp/dh at epicentral distances of a few degrees introduce a large uncertainty in focal depth, particularly for shallow (0–60 km) earthquakes. There is normally little error in epicenter, however, even for solutions in which depth is poorly determined. The dimensions and geometric configuration of the network in relation to the epicenter and the proximity of the epicenter to any one station are controlling factors in predicting the minimum uncertainty for any given hypocenter solution.
This article has been cited by other articles:
|
|
 |
|
  J.-M. Chiu, S.-C. C. Chiu, and S. G. Kim The significance of the crustal velocity model in local earthquake locations from a case example of a PANDA experiment in the central United States Bulletin of the Seismological Society of America, December 1, 1997; 87(6): 1537 - 1552. [Abstract] [PDF]
|
|
|
|
|
|
S. Y. SCHWARTZ and G. D. NELSON Loma Prieta aftershock relocation with S-P travel times: Effects of 3-D structure and true error estimates Bulletin of the Seismological Society of America, October 1, 1991; 81(5): 1705 - 1725. [Abstract] [PDF]
|
|
|
|
|
|
D. E. JAMES and M. K. SAVAGE Reply to comment by C. H. Thurber on "A search for seismic reflections from the top of the oceanic crust beneath Hawaii" Bulletin of the Seismological Society of America, June 1, 1991; 81(3): 1035 - 1041. [PDF]
|
|
|
|
|
|
J. S. GOMBERG, K. M. SHEDLOCK, and S. W. ROECKER The effect of S-wave arrival times on the accuracy of hypocenter estimation Bulletin of the Seismological Society of America, December 1, 1990; 80(6A): 1605 - 1628. [Abstract] [PDF]
|
|
|
|
|
|
C. NICHOLSON and D. W. SIMPSON Changes in Vp/Vs with depth: Implications for appropriate velocity models, improved earthquake locations, and material properties of the upper crust Bulletin of the Seismological Society of America, August 1, 1985; 75(4): 1105 - 1123. [Abstract] [PDF]
|
|
|
|
|
|
J. P. MCLAREN and C. FROHLICH Model calculations of regional network locations for earthquakes in subduction zones Bulletin of the Seismological Society of America, April 1, 1985; 75(2): 397 - 413. [Abstract] [PDF]
|
|
|
|
|
|
T. M. BOYD, J. A. SNOKE, I. S. SACKS, and A. RODRIGUEZ B. High-resolution determination of the Benioff zone geometry beneath southern Peru Bulletin of the Seismological Society of America, April 1, 1984; 74(2): 559 - 568. [Abstract] [PDF]
|
|
|
|
|
|
D. CACCAMO and G. NERI A new analytic procedure to determine hypocentral parameters of local seismic events Bulletin of the Seismological Society of America, April 1, 1984; 74(2): 655 - 667. [Abstract] [PDF]
|
|
|
|
|
|
E. G. C. SMITH Comments on "A fast epicenter location program" Bulletin of the Seismological Society of America, June 1, 1978; 68(3): 845 - 846. [PDF]
|
|
|
|
|
|
R. BULAND The mechanics of locating earthquakes Bulletin of the Seismological Society of America, February 1, 1976; 66(1): 173 - 187. [Abstract] [PDF]
|
|
|
|
|
|
W. D. SMITH Upper mantle velocities determined from local observations of deep earthquakes Bulletin of the Seismological Society of America, June 1, 1973; 63(3): 807 - 817. [Abstract] [PDF]
|
|
|
|
|
|
P. L. WARD and S. GREGERSEN Comparison of earthquake locations determined with data from a network of stations and small tripartite arrays on Kilauea Volcano, Hawaii Bulletin of the Seismological Society of America, April 1, 1973; 63(2): 679 - 711. [Abstract] [PDF]
|
|
|
|
|
|
R. J. WETMILLER An earthquake swarm on the Queen Charlotte Islands Fracture Zone Bulletin of the Seismological Society of America, December 1, 1971; 61(6): 1489 - 1505. [Abstract] [PDF]
|
|
|
|
|
|
F. J. GUMPER and C. SCHOLZ Microseismicity and tectonics of the Nevada Seismic Zone Bulletin of the Seismological Society of America, October 1, 1971; 61(5): 1413 - 1432. [Abstract] [PDF]
|
|
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
