The paper studies the effect of magnitude errors on heterogeneous catalogs, by applying the apparent magnitude theory (seeTinti andMulargia, 1985a), which proves to be the most natural and rigorous approach to the problem. Heterogeneities in seismic catalogs are due to a number of various sources and affect both instrumental as well as noninstrumental earthquake compilations.
The most frequent basis of heterogeneity is certainly that the recent instrumental records are to be combined with the historic and prehistoric event listings to secure a time coverage, considerably longer than the recurrence time of the major earthquakes. Therefore the case which attracts the greatest attention in the present analysis is that of a catalog consisting of a subset of higher quality data, generallyS 1, spanning the interval ΔT 1 (the instrumental catalog), and of a second subset of more uncertain magnitude determination, generallyS 2, covering a vastly longer interval ΔT 2 (the historic and/or the geologic catalog). The magnitude threshold of the subcatalogS 1 is supposedly smaller than that ofS 2, which, as we will see, is one of the major causes of discrepancy between the apparent magnitude and the true magnitude distributions. We will further suppose that true magnitude occurrences conform to theGutenberg-Richter (GR) law, because the assumption simplified the analysis without reducing the relevancy of our findings.
The main results are: 1) the apparent occurrence rate λ exceeds the true occurrence rate ρ from a certain magnitude onward, saym GR; 2) the apparent occurrence rate λ shows two distinct GR regimes separated by an intermediate transition region. The offset between the two regimes is the essential outcome ofS 1 being heterogeneous with respect toS 2. The most important consequences of this study are that: 1) it provides a basis to infer the parameters of the true magnitude distribution, by correcting the bias deriving from heterogeneous magnitude errors; 2) it demonstrates that the double GR decay, that several authors have taken as the incontestable proof of the failure of the GR law and of the experimental evidence of the characteristic earthquake theory, is instead perfectly consistent with a GR-type seismicity.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Ambraseys, N. N. andMelville, C. P. (1982),A history of Persian earthquakes. Cambridge Earth Science Series, Cambridge.
Båth, M. (1981),Earthquake recurrence of a particular type. PAGEOPH119, 1063–1079.
Caputo, M. (1976),Model and observed seismicity represented in a two dimensional space. Ann. Geofis.29, 277–288.
Cosentino, P. andLuzio, D. (1976),A generalization of the frequency-magnitude relation in the hypothesis of a maximum regional magnitude. Ann. Geofis.29, 3–8.
Davison, C. Jr. andScholz, C. H. (1985),Frequency-moment distribution of earthquakes in the Aleutian Arc: A test of the characteristic earthquake model. Bull. Seism. Soc. Am.75, 1349–1361.
Gutenberg, B. andRichter, C. F. (1944),Frequency of earthquakes in California. Bull Seism. Soc. Am.34, 185–188.
Howell, B. F. Jr. (1985),On the effect of too small a data base on earthquake frequency diagrams. Bull. Seism. Soc. Am.75, 1205–1207.
Ishimoto, M. andIida, K. (1939),Observations sur le séismes enregistrés par le microsismographe construit dernièrment. Bull. Earthquake Res. Inst., Univ. Tokyo17, 443–478.
Johnston, A. C. andNava, S. J. (1985),Recurrence rates and probability estimates for the New Madrid seismic zone. J. Geoph. Res.90, 6737–6753.
Lee, W. H. K. andBrillinger, D. R. (1979),On Chinese earthquake history—An attempt to model an incomplete data set by point process analysis. PAGEOPH117, 1229–1257.
Lomnitz-Adler, J. andLomnitz, C. (1978),A new magnitude-frequency velation. Tectonophysics49, 237–245.
Lomnitz-Adler, J. (1985a),Asperity models and characteristic earthquakes. Geophys. J. R. Astr. Soc.83, 435–450.
Lomnitz-Adler, J. (1985b),On the magnitude-frequency relation of asperity models. Tectonophysics120, 133–140.
Main, I. G. andBurton, P. W. (1986),Information theory and the earthquake frequency, magnitude distribution, Bull. Seism. Soc. Am.74, 1409–1426.
Makjanić, B. (1980),On the frequency distribution of earthquake magnitude and intensity. Bull. Seism. Soc. Am.70, 2253–2260.
Mulargia, F. andTinti, S. (1985),Seismic sample area defined from incomplete catalogues: An application to the Italian territory. Phys. Earth Planet. Int.40, 273–300.
Postpischl, D., editor, (1985),Catalogo dei terremoti italiani dall'anno 1000 al 1980. Progetto Finalizzato Geodinamica, CNR, Rome.
Schwartz, D. P. andCoppersmith, K. J. (1984),Fault behavior and characteristic earthquakes: Examples from the Wasatch and San Andreas faults. J. Geophys. Res.89, 5681–5698.
Singh, S. K., Rodriquez, M. andEsteva, L. (1983), Statistics of small earthquakes and frequency of occurrence of large earthquakes along the Mexican subduction zone. Bull. Seism. Soc. Am.73, 1779–1796.
Tinti, S. andMulargia, F. (1985a),Effects of magnitude uncertainties on estimating the parameters in the Gutenberg-Richter frequency-magnitude law. Bull. Seism. Soc. Am.75, 1681–1697.
Tinti, S. andMulargia, F. (1985b),Completeness analysis of a seismic catalog. Annales Geophysicae3, 407–414.
Tinti, S. andMulargia, F. (1985c),Application of the extreme value approaches to the apparent magnitude distribution of the earthquakes. PAGEOPH123, 199–220.
Tinti, S., Rimondi, R. andMulargia, F. (1986),On the frequency-apparent magnitude relations. Annales Geophysicae4, 467–472.
Tinti, S., Vittori, T. andMulargia, F. (1986),Regional intensity-magnitude relationships for the Italian territory. Tectonophysics127, 129–154.
Vered, M. (1977),Relations between isoseismic area and magnitude for Italian earthquakes. Boll. Geofis. Teor. Appl.20, 290–293.
Wesnousky, S. G., Scholz, C. H. andShimazaki, K. (1982),Deformation of an Island Arc: Rates of moment release and crustal shortening in intraplate Japan determined from seismicity and Quaternary faulting. J. Geophys. Res.87, 6829–6852.
Wesnousky, S. G., Scholz, C. H., Shimazaki, K. andMatsuda, T. (1983),Earthquake frequency distribution and the mechanics of faulting. J. Geophys. Res.88, 9331–9340.
About this article
Cite this article
Tinti, S., Rimondi, R. & Mulargia, F. On estimating frequency-magnitude relations from heterogeneous catalogs. PAGEOPH 125, 1–18 (1987). https://doi.org/10.1007/BF00878611
- Apparent magnitude
- heterogeneous catalog
- magnitude errors
- frequency-magnitude law