HYPO71 Discussion

Our experience indicates that locating local earthquakes accurately requires considerable efforts (see the discussion is given in the readme.txt file on the CD-ROM). As discussed in Lee and Stewart (1981, p. 130-139), earthquake location is a nonlinear problem, and there is no "fool-proof" method to locate an earthquake because the input data may be insufficient to constraint the problem. The HYPO71 program does not solve the equations in the Geiger's method by the traditional matrix inversion techniques as almost all other earthquake programs do. It uses a multiple stepwise regression method (Draper and Smith, 1966) to adjust hypocenter parameters only if it is statistically significant above a prescribed critical F-value. Obviously, this method reduces to the traditional technique if one set the critical F-value to zero. We believe that by studying the output results of a HYPO71 solution, one can gain some insight on what are the difficulties in reducing the residuals in solving a nonlinear problem by iterations.

We recommend interested students to read the mathematical procedures for earthquake location and computing travel times presented in Lee and Stewart (1981) [This book is reproduced in directory \17Lee1 on the Handbook CD].

Our experience indicates that locating local earthquakes accurately requires considerable efforts. One must have accurate station coordinates (better than 0.1 km if possible), a reasonable crustal structure model (e.g., from controlled explosions), and reliable P and S arrivals. Naturally no computer program will give correct answers if the input data contain errors, so careful checking is essential before any earthquake location program is run. One should also remember that small residuals and standard errors are not sufficient to guarantee accurate hypocenter solution.

HYP071 is designed to catch some common mistakes in the input data, but this should not be counted on to find all of the errors. HYP071 also provides an assessment of the quality of the hypocenter solution and information that may improve the solution. Users are urged to study the output carefully. We wish to emphasize that values for "TEST VARIABLES" in the input file must be carefully chosen for a given application because they influence how the program goes about locating the earthquakes. The standard values in the program were developed for the large and closely spaced network of seismic stations in central California (with over 100 stations and station separation usually less than 10 kilometers).

As discussed in Lee and Stewart (1981, p. 130-139), earthquake location is a nonlinear problem, and there is no "fool-proof" method to locate an earthquake because the input data may be insufficient to constraint the problem. The HYPO71 program does not solve the equations in the Geiger's method by the traditional matrix inversion techniques as almost all other earthquake programs do. It uses a multiple stepwise regression method (Draper and Smith, 1966) to adjust hypocenter parameters only if it is statistically significant above a prescribed critical F-value. Obviously, this method reduces to the traditional technique if one set the critical F-value to zero. We believe that by studying the output results of a HYPO71 solution, one can gain some insight on what are the difficulties in reducing the residuals in solving a nonlinear problem by iterations.

Boyd and Snoke (1984) discussed the error estimates in some commonly used earthquake location programs at that time, including HYPO71. Lienert et al. (1986) discussed their HYPOCENTER program and compared it with HYPO71 and HYPOINVERSE (see Chapter 85.8 by Klein). Because there are many earthquake location papers/programs written before and after HYPO71, serious students should study at least some of these papers . A few recent examples are: Shearer (1997), Waldhauser and Ellsworth (2000), and Schweitzer (2001). See also Chapter 85.7 by Lahr and Snoke, and Chapter 85.9 by Pujol.

Finally, one should select an earthquake location program or write one's own that is best suitable for one's data and purposes.

References

Boyd, T. M., and J. A. Snoke, (1984). Error estimates in some commonly used earthquake location programs, Earthq. Notes 55(2), 3-6.

Draper, N. R., and H. Smith (1966). Applied Regression Analysis, John Wiley & Sons, New York, 407 pp.

Lee, W. H. K. and S. W. Stewart (1981). Principles and Applications of Microearthquake Networks, Academic Press, New York, 293 pp. [See Handbook CD-ROM, under the directory of \17Lee].

Lienert, B. R., E. Berg, and L. N. Frazer (1986). HYPOCENTER: An earthquake location method using centered, scaled, and adaptively damped least squares, Bull. Seism. Soc. Am. 76, 771-783.

Schweitzer, J. (2001). HYPOSAT - An enhanced routine to locate seismic events. Pure appl. geophys. 158, 277-289.

Shearer, P. M. (1997). Improving local earthquake locations using the L1 norm and waveform cross correlation: application to the Whittier Narrows, California, aftershock sequence, J. Geophys. Res. 102, 8269-8283.

Waldhauser, T. and W. L. Ellsworth (2000). A double-difference earthquake location algorithm: method application to the northern Hayward fault, California, Bull. Seism. Soc. Am. 90, 1353-1368.