J. A. Snoke, Chairman

Transcription

1 Source Studies over a Wide Range in Earthquake Magnitude by David W. A. Taylor, Jr. Dissertation submitted to the Faculty of the Virginia Polytechnic nstitute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy '' ' m Geophysics APPROVED: V' J. A. Snoke, Chairman G. A. Bollinger J E. S. Robinsoy 1.-S: Sacks May 12, 1988 Blacksburg, Virginia

2 Source Studies over a Wide Range in Earthquake Magnitude by David W. A. Taylor, Jr. J. A. Snoke, Chairman Geophysics (ABSTRACT) The concept of similarity (that earthquake source parameters obey scaling relations) and the empirical linear relation between magnitude and the log 10 of the number of events (the Gutenberg-Richter relation) describe well the behavior and recurrence of many earthquake data sets. The universality of these relations are tested herein using a suite of earthquakes from the. southeast comer of Hokkaido sland, Japan. Within this active seismic region, over 11, 100 events ranging in magnitude from 0 to 7.1 were cataloged by the Hokkaido University network in the period with epicentral distances of less than 50 km from the Carnegie broadband station KMU. Two subsets of the events are examined herein: crustal earthquakes, those with locations shallower than 45 km and above the top of the subducting Pacific plate, and subduction earthquakes, those with locations below 60 km within the subducting plate. The frequency of occurrence versus magnitude relations for both the crustal and subduction events are nonlinear with a definite decrease in the number of detected events for lower magnitudes, but the subduction events have proportionally more large earthquakes and fewer small earthquakes than ihe crustal data suite. A completeness analysis indicates that the catalogs are complete to less than magnitude 2, which is clearly in the nonlinear region, suggesting that the observed curvature of the frequency-magnitude curves is not due to incompleteness of the catalogs. Hence, a single, linear Gutenberg-Richter relation is inadequate for describing the frequency of occurrence of these events. The ratio of the frequency-magnitude curves gives a remarkably linear relation from magnitude l to magnitude 5, indicating that in terms of fitting these frequency-magnitude curves to higher order polynomials, the crustal and subduction data sets have identical higher order coefficients, and their curvature difference is caused by only the constant and linear coefficients.

3 A possible cause for the difference in the recurrence relations is the increased lithostatic load with depth. n an attempt to gain insight into the frequency of occurrence characteristics of the data, the seismic energy release of the crustal and subduction regions was calculated as a function of time. Evaluation of the energy release versus time indicates that there was a precursory energy decrease prior to the ml = 7.1 event in Analysis of energy release appears to be a potentially useful and relatively objective technique for studying precursory quiescence. Using dat~ from the Carnegie broadband station KMU, seismic source scaling relations were derived for 21 crustal and 24 subduction events. Using Q-corrected SV and SH amplitude spectra and assuming an average focal mechanism, spectral parameters (zero frequency level and comer frequency) were estimated using the objective technique of Snoke ( 1987). Cepstral filtering was employed both to remove the effect of multiple arrivals, as well as to increase the objectivity with which parameters were determined. The resulting moment versus magnitude relations indicate a significant change in slope around magnitude 3.5 and moment 2 x 1020 dyne-cm. Brune radii average 0.3 km over the range 1018 to dyne-cm, and increase from 0.6 to 2 km over the range 1022 to 1025 dyne-cm. Log Brune stress drop was found to be linearly correlated with log moment with a slope of approximately unity below 1021 dyne-cm, and highly correlated but with a slightly smaller slope above that point. For lower moments, stress drops increase with moment from bar to 10 bar, and for higher moments, stress drops range from bar, with most values near 100 bar. These variations of radius and stress drop with moment for moments below 1021 dyne-cm is inconsistent with the similarity hypothesis. Stress drop versus moment relations were compared with those from a study for the Matsushiro region, Japan, which is characterized by a shallow, localized crustal seismicity. No significant difference is found between the scaling relations for the crustal earthquakes, subduction earthquakes, and Matsushiro earthquakes taken separately, even though the tectonic stress is expected to be quite different in the three regions. We conclude that the calculated scaling relations are not directly determined by the tectonic stress.

4 Acknowledgements Support for this study has been provided by the Carnegie nstitution of Washington, Department of Terrestrial Magnetism. Financial support in the form of assistantships and fellowships have been provided by Arco Exploration Company, Chevron, U.S.A., and the Department of Geological Sciences, Virginia Polytechnic nstitute and State University. would like to thank my committee chairman, Arthur Snoke, and Selwyn Sacks for their continued involvement in this project. would also like to thank G. A. Bollinger and Alan Linde for many helpful comments and suggestions during the course of this study. Grateful appreciation is expressed to Tetsuo Takanami of Hokkaido University for providing the catalog of events and his interest in and support of the analysis. thank all of my committee members for their critical reviews of the manuscript. Most of all, would like to express my appreciation to my wife for her continuing support which made this work possible. Acknowledgements iv

5 Table of Contents ntroduction Statement of problem.... Tectonic and Geologic setting Velocity structure Seisrnicity Plan of study Frequency of Occurrence Relations Previous work Recurrence relations Completeness analysis Discussion Energy release Scaling Relations Previous work Table of Contents v

6 Source parameters - Theory Data Magnitude 7.1 event of 21 March nitial data processing Radiation, propagation and site effects Spectral measurements Moment versus magnitude relations Radius and stress drop versus moment relations Comparisons between the Hokkaido and Matsushiro data sets Discussion Conclusions Bibliography Appendix A S- and SV waveforms Appendix B Crustal event information Subduction event information Appendix C Crustal event spectral and source parameters Subduction event spectral and source parameters Vita Table of Contents vi

7 List of llustrations Figure 1. Map of the Japanese slands Figure 2. Vertical cross sections of events beneath KMU... 8 Figure 3. Epicenter map of study area Figure 4. Hokkaido University Network stations near KMU Figure 5. Recurrence relationship for crustal and subduction events Figure 6. Ratio of crustal and subduction recurrence relations Figure 7. Recurrence relations with best straight line fits Figure 8. Small events recorded at KMU Figure 9. Stepp test for crustal events Figure 10. Stepp test for the subduction events Figure 11. Energy release versus time for the crustal events Figure 12. Energy release versus time for the subduction events Figure 13. Radiated energy for both the crustal and subduction data sets Figure 14. Time series for event Figure 15. Time series for magnitude 7.1 earthquake Figure 16. Free surface corrections Figure 17. Example of determination of spectral parameters Figure 18. Example of cepstral filtering Figure 19. Example of P amplitude spectrum Figure 20. Moment versus magnitude Figure 21. Moment versus magnitude with best fit lines List of llustrations vii

8 Figure 22. Relationships between SV and SH corner frequencies Figure 23. Moment versus Brune radius Figure 24. Comparison between two different amplitude spectra Figure 25. Brune stress drop versus moment Figure 26. Stress drop versus moment for all events with least squares fit Figure 27. Brune stress drop and radius versus moment for Matsushiro region events 74 Figure 28. Brune stress drop versus moment for KMU and Matsushiro events Figure 29. Earthquake stress drops compiled by Hanks ( 1977) and this study Figure 30. Crustal SH waveforms Figure 31. Crustal SV waveforms Figure 32. Subduction SH waveforms Figure 33. Subduction SV waveforms List of llustrations viii

9 ntroduction Statement of problem Earthquake source scaling relations relate source properties such as change in stress, rupture zone size, and seismic moment or magnitude (measures of earthquake size) for a suite of earthquakes. A fundamental question in earthquake seismology is the degree of similarity of large and small earthquakes. f large and small earthquakes are truly similar, then such scaling relations should hold for all sizes so that studying the more numerous small earthquakes could provide useful information about the more damaging large earthquakes. t is the objective of this project to quantify and interpret the size-dependent properties of a suite of earthquakes. Specifically, the degree of similarity between "small" and '1arge" earthquakes will be quantified. Earthquakes from a restricted epicentral area will be used so that path effects, local geologic and tectonic effects will be consistent throughout the data suite, allowing meaningful observations of size-dependent phenomena to be made. A consistent analysis procedure will be used over the entire data set and all earthquakes were recorded on the same instrument. n addition to the analysis of scaling relations, the frequency of occurrence versus magnitude relations will be studied, and the variation in energy release with time. Use of a small hypocentral volume allows the frequency of occurrence analysis to be carried to smaller magnitudes than is usually possible. ntroduction

10 Our data suite is from over 11,000 events located within 50 km of a Department of Terrestrial Magnetism, Carnegie nstitution of Washington (DTM/CW) broad-band, wide dynamic range seismograph installed at Kamikeineusu (KMU) in southeastern Hokkaido, Japan. The 50 km radius was chosen to ensure a uniform data set for which reliable locations could be obtained and was not based on any geologic consideration. These events range in magnitude from less than zero to greater than seven and include shallow crustal earthquakes as well as deeper earthquakes caused by the subduction of the Pacific plate beneath Japan. By analyzing both crustal and subduction related earthquakes within the same geologic environment and using the same seismograph and processing techniques, differences and similarities between these two subsets can also be obtained. n addition, comparisons will be made with a study from the Matsushiro region, Japan, which employed an identical seismograph and similar processing techniques, yet is in a very different tectonic environment. Tectonic and Geologic setting Hokkaido, the second largest of the Japanese islands, is located directly to the north of the main island of Honshu (Figure 1). The Japan trench trends to the north along Honshu where it meets the Kurile trench near the northern edge of Honshu and the southern edge of Hokkaido. The Pacific plate subducts beneath Hokkaido, the top of the slab reaching depths of 300 km toward the northwestern edge of the island (Figure 1). The volcanic front runs through the middle of the island, but is well to the northwest of the study region (e.g., Nakanishi, et al., 1981). A bend of about 120 in the trench system is located just offshore of the southeast corner of Hokkaido. With its location near the trench, Hokkaido has had a very complex geologic development. Chronostratigraphic and lithostratigraphic correlations between different regions are difficult to obtain due to the numerous orogenic episodes. The Hidaka mountains run from the Hokkaido comer (the southeast comer of the island) to the northwest and are characterized by three zones of metamorphism ranging from amphibolite, meta-gabbro, and peridotite complexes on the west, ntroduction 2

11 g A -- / 07 ~, _, '..... / s, ifp.,,,,..,,,,. --.re ca,, WJ1''1>1 '.~.,o ~,,. / / ~.. ~,1 /. "' ~- -" "' v... 8 l)t...,., ,... Figure. Map of the Japanese slands: The Japanese slands (shaded in the left hand figure) are bounded by the Pacific Ocean to the east and the Japan Sea to the west. Hokkaido, the large northern island, is shown in the right hand figure. The small circular area on the southeast corner of Hokkaido is the 50 km radius study area centered on station KMU. The other stations shown on Hokkaido are operated by JMA. A more dense coverage of Hokkaido is provided by the Hokkaido University Network. Dashed lines are approximate depths to the subducting slab in kilometers, while the solid line indicates the volcanic front. ntroduction 3

12 to high temperature metamorphism along the axis of the mountain range, to more recent metamorphic rocks to the east (Takanami, 1982). KMU is located in the axial region, and the circular study area encloses parts of all three regions. To the west of the Hidaka mountains, extending to the city of Sapporo, is the shikari Depression, a thick sedimentary zone which generates a low gravity anomaly (Shimamura, 1981). This highly attenuative region does not extend to the study area. The primary stress in the crust of the Japan arc is horizontal compression (Hashimoto, 1984; Ando, 1979; Shimazaki and Sommerville, 1979; Aki, 1966; and chikawa, 1971). n the Hokkaido region, the stress field is more complicated, with many focal mechanisms showing P-axes in an east-west direction, while the slip vector of the Pacific plate is more northwesterly (Takanami, 1982). Hashimoto (1984), Takanami (1982), and Aki (1966) all agree that the stress direction is primarily east-west, but also note that a northeast-southwest compression axis is found for many of the events. Focal mechanisms show primarily reverse faulting in the southern Hidaka range, with some strike-slip faulting to the north and east (chikawa, 1971; Takanami, 1982; Hashimoto, 1984). Hashimoto uses a finite element modeling scheme to attempt to explain why the direction of the principal stress (NE-SW for many events) could be parallel to the strike of the subducting slab, and he concludes that negative buoyancy of the subducting slab could yield the complex stress field. This interpretation, however, does not explain the prevalence of thrust faulting in the vicinity of the southern Hidaka mountains (Hashimoto, 1984) because it predicts a prevalence of normal faulting. Den and Hotta ( 1973) suggest that eastern and western Hokkaido were once separated, and that the Hidaka range is the collisional boundary between the Eurasian and Okhotsk plates. the direction of many null vectors of focal mechanisms being parallel to the strike of the Hidaka range (Takanami, 1982) supports the plausibility of this argument. ntroduction 4

13 Velocity structure The velocity structure in the southeast comer of Hokkaido is extremely complicated. Studies by Shimamura (1981) using Usu swarm events, Fujii and Moriya (1983) using quarry blasts, and Takanarni (1982) and Miyamachi and Moriya (1984) using three dimensional inversion with P arrivals from local earthquakes all found strong lateral and vertical velocity variations beneath the Hidaka mountains. Shimamura (1981) used events from the Usu volcanic swarm as a Hsource" for a refraction experiment. The earthquakes from this swarm were concentrated within a source region of diameter 1 km, allowing travel time errors in the refraction study to be reduced to the corresponding level in explosion studies. A crude velocity structure was determined with a P velocity of 5.8 km/sec in the top layer of thickness 20 km, P velocity of 6.6 km/sec and thickness of 20 km in the lower crustal layer, and a mantle P velocity of 7.8 km/sec. This 40 km crust is thick compared to other regions in Japan. Takanarni (1982) concentrated on the velocity structure in southern Hokkaido. Using the three-dimensional inversion method of Aki and Lee (1976), Takanarni was able to determine velocity variations to a depth of 120 km. He found significant horizontal velocity variations down to at least 90 km and, significantly, that there was a correlation of the velocity variations with the surface geology. He finds the western flank of the Hidaka Mountains to be characterized by lower velocity rocks, and the eastern region by higher velocity rocks, and that these trends continue at depth. nterestingly, this low velocity region is associated with higher levels of seisrnicity than the high velocity region, in contrast to the usual assumption of higher seismicity in colder, more brittle, high velocity rocks, and lower seismicity in hotter, more ductile, low velocity rocks. Takanarni proposes that the low velocity zone may represent a weak spot where a concentration of stress had occurred in an otherwise rigid lithosphere. While Takanarni used a low density array, Miyamachi and Moriya (1984) used a high density array and many more earthquakes over two separate smaller areas in the three dimensional ntroduction 5

14 mvers10n. The first region, with KMU approximately in the center, was 120 km by 120 km in dimension, and the second region was 80 km by 40 km centered on the epicenter of the magnitude 7.1, 21 March 1982 Urakawa-Oki event, containing the majority of its aftershock area, and including station KMU. nitially, a one dimensional inversion was computed to provide initial estimates of P-wave velocities for the three-dimensional inversion and to better identify horizontal boundaries. Results of this inversion are that the Moho is at 45 ± 5 km, and as with Shimamura (1981), the crust can be approximated by two 20 km thick layers. The three-dimensional inversion shows dramatic horizontal velocity variations of up to 20% in the upper 20 km. As with Takanami ( 1982), lower velocities were found to the west of the mountains, and higher velocities to the east. Miyamachi and Mariya report that a low velocity zone approximately km thick dips 60 from the horizontal, striking along the axis of the mountains and extending continuously to a depth of at least 65 km. n the second region studied, Miy~achi and Mariya found that the hypocentral region of the magnitude 7.1 event is dominated by the low velocity zone, and that again, horizontal velocity variations of 20% in the upper 20 km are common. They suggest that this low velocity zone is a result of the subduction of the northeast Japanese arc under the Kurile arc in a northeasterly direction, and that the subduction of the Pacific plate, in a northwesterly direction, is not simple, but instead results in deformation and bending of the Pacific plate due to the low velocity zone. They note that this complicated pattern of subduction would be inconsistent with the presence of undeformed double seismic zones such as are observed beneath Honshu (Hasegawa, et al., 1978a, 1978b, 1979). Nakanishi ( 1985) used an approximate inversion technique known as ART (Algebraic Reconstruction Technique) to model the three dimensional structure beneath Hokkaido and Tohoku (northern Honshu). The low velocity structure near KMU was observed, but not with as high a spatial resolution as the previously mentioned studies. Nakanishi particularly looked for velocity variations before and after the magnitude 7.1 event, but was unable to detect any differences. ntroduction 6

15 Seismicity The southeastern corner of Hokkaido is a particularly active seismic region. Both crustal and subduction events are observed. A cylindrical volume with radius 50 km centered on station KMU was chosen for the study region because station coverage would ensure reliable detection and accurate locations for events within the region. Based on the seismicity, the subducting Pacific plate enters the region at about 30 km depth has extended to 100 km depth on the northwestern edge of the area, with the lower seismic plane within the subducting slab just beginning to develop at 100 km depth (Hasegawa, et al., 1983 and Faculty of Science, Hokkaido University, 1987), (Figure 2). Fujita and Kanamori (1981) suggest that the stresses in double seismic zones are in-plate compression in the upper plane, and in-plate tension in the lower plane, though the stresses are not necessarily aligned in the down-dip direction. The data set for this study is from among 11, 103 events detected and cataloged by the Hokkaido University Network in the period June, 1976 through January, 1987 within the 50 km epicentral radius from station KMU (Figure 3). The events range in magnitude from less than zero to 7.1 (for the Urakawa-Oki event of 21 March, 1982). Approximately half of the events, 5400, were recorded in 1982, the majority of which can be considered aftershocks of the ml = 7.1 event. The crustal data set comprises those events that are above the subducting slab and above 45 km. The subduction events are those earthquakes that occurred within the slab, below 60 km, and above 125 km. A total of 3342 earthquakes are classified as crustal and 576 as subduction. Plan of study The difference in the behavior of large and small earthquakes will first be analyzed using the catalog of events detected within the study region by the Hokkaido University Network. The frequency of occurrence of earthquakes will be determined, and comparisons will be made between ntroduction 7

16 : April U~ - Jaa.. r7 Ul Ml 2 l 4 S 6 7 & 0 <40... E ~ 60..._,.c eo ~ a. ~ :.a , < Distance from KMU (km) Figure 2. Vertical cross sections of events beneath KMU: Top is a vertical cross section along dip of the slab showing all events detected by the Hokkaido University Network, after the Faculty of Science, Hokkaido University (1987). Below are the events detected by the Hokkaido University Network with magnitude greater than 3 located within the study region. KMU is located above the center of lhe lower figure. The division between crustal and subduction events is indicated, wilh crustal events defined as being located above 45 km and above lhe slab, while subduction events are found below 60 km and below lhe top of the slab. Both cross sections are projections on a plane striking N 31 W. ntroduction 8

17 O.U KUU excluding ~42.4 ~42.l -g :;:; C J ~ Longitude (deg) Longitude (deg) Figure 3. Epicenter map of study area: Left are all events. Station KMU is located in the center. Right are the same events, excluding events from ntroduction 9

18 the crustal and subduction data sets. Additionally, an analysis of the energy release versus time will also be made. Next, individual digitized earthquakes will be studied to estimate the source parameters of moment, radius, and stress drop. Data processing will correct for the effects of radiation, propagation, and site effects. The variation of these source parameters with earthquake size will indicate the degree to which these earthquakes can be considered similar. Comparisons will be drawn between the crustal and subduction data sets, as well as with a study from the Matsushiro region, Japan. ntroduction 10

19 Frequency of Occurrence Relations Previous work Within a given geographic region, the frequency of occurrence of an earthquake is known to be dependent upon the size of the earthquake. The frequency of occurrence versus magnitude relation of the form logn= a-bm [l] where N is the cumulative number of events larger than M, or, N is the number of events in a magnitude interval M ± M, t1m being the magnitude interval, and a and b are constants, is attributed to Richter (1958), and has found a prominent place in the analysis of seismicity. The constant a, or a value, is a measure of the level of seismicity in a region and is sometimes referred to as the nactivity parameter". The constant b, orb value, is typically near 1 in value. This linear relation between the logarithm of the number of events and magnitude is very well established observationally, and Kanamori and Anderson (1975) present a possible a geometrical explanation for the relationship. Frequency of Occurrence Relations ti

20 Determination of the a and b values in a region is a basic description of the seismicity. The procedure typically employed, such as Bollinger et al., ( 1988), is to identify a catalog of earthquakes within some geographic region and within some time interval, and then to construct a histogram of the logarithm of either Ni, the number of events within a magnitude interval, or Nc, the cumulative number of events with magnitude greater than each histogram interval, versus magnitude. These data points can then be fit with a least squares regression line, or the a and b values can be found from a maximum likelihood estimate of the best straight line. Most of the earlier studies analyzed Nc, the cumulative number of events, following the technique of Richter. Several recent studies, such as Bender (1983), have shown that the interval number of events, Ni, is a more appropriate parameter to analyze because, in contrast with Nc, each data point in an Ni distribution is statistically independent of the other data points. Also, since the repeat time of very large earthquakes is very long and poorly determined, the cumulative number of events for smaller magnitudes will be ~iased by errors in determining the repeat time for larger magnitudes. A difficulty in the determination of the a and b values is the estimation of the smallest magnitude to which the catalog is complete, that is, the determination of the smallest magnitude for which all events of that magnitude were detected and cataloged. Many older studies detected this low magnitude limit simply by looking for curvature in the log N versus M relation. Whenever the value of log N at some magnitude M would fall below the best fit straight line determined for the larger events, the catalog would be considered incomplete at that magnitude and below. Other studies, such as Stepp (1972) and Veneziano and Van Dyck (1985), have applied more rigorous statistical tests to evaluate completeness. Aki ( 1987) suggested that curvature of the frequency of occurrence versus magnitude relation for some suites of events might not be related to incompleteness in the catalog, but instead might be related to the change in spectral scaling that is observed around magnitude 3. Using a high sensitivity seismometer located in a borehole adjacent to the Newport-nglewood fault, California, Aki claims to detect a change in curvature of Nc at a magnitude of 3. Frequency of occurrence Frequency of Occurrence Relations 12

21 versus magnitude for the KMU data sets are analyzed herein to look for curvature in this magnitude range. Recurrence relations The small, well instrumented epicentral area considered in this study provides an excellent opportunity to analyze the frequency of occurrence relationships for the crustal and subduction data suites. The time period under consideration is July, 1976 through January, As stated previously, the epicentral area is defined by a 50 km radius circle centered at station KM U. The crustal data set comprises those events that are above the subducting slab and above 45 km. The subduction events are those earthquakes that occurred within the slab and below 60 km (Figure 2). A cutoff depth of 125 km was chosen to limit the source volume. The top of the slab dips 37 toward N 31 W, enters the study region at approximately 30 km and extends to approximately 100 km on the northwestern edge of the region (Faculty of Science, Hokkaido University, 1987). Magnitudes were determined by the Hokkaido University staff using the standard Japan Meteorological Agency (JMA) technique: the total signal duration time in seconds was determined and then ml = 3.l5T duration , [2] is evaluated where T <hlrot1on is the signal duration in seconds. Hypocentral locations and origin times were determined by a least squares fit to chikawa and Mochizuki's (1971) travel-time curves for P waves. Location errors are estimated as less than a few kilometers and not beyond several kilometers in depth (Tetsuo Takanami, personal communication, 1987). The Hokkaido University Network consists of many stations located throughout Hokkaido. Within the small, circular area used in this study, five network stations were in operation since July, 1976, of which broad band station KMU is one, with one more permanent station added in 1984 Frequency of Occurrence Relations 13

22 c;,43.0 Q) -0 '-" 42.5 Q) -0 ::J _,_, ' c: 0...J Latitude (deg) Figure 4. Hokkaido University Network stations near KMU: Hokkaido University network stations located in and around the study area. All stations shown were in place during the entire study period. The star represents station KMU and the triangles are other Hokkaido Network stations. The circle is the 50 km radius study area. Frequency of Occurrence Relations 14

23 (Figure 4). An additional four stations were located on the perimeter of the area during the entire study period, with various other permanent and temporary stations added within and around the area since This relatively dense instrumentation of a small area provides excellent data for accurate locations, detection of smaller events, and magnitude estimations. The most prominent seismic event of this 10.5 year period was the Urakawa-Oki event of 21 March, This magnitude 7.1 event, located at a depth of 34 km, generated numerous aftershocks. Of the 11, 00 earthquakes, a total of 5,400 events were cataloged by the Hokkaido University network in 1982 alone. So as not to unduly bias the recurrence relations with the aftershock series, all events from the year 1982 were excluded, consistent with a study by the Faculty of Science, Hokkaido University ( 1983) which indicates the rate of occurrence of events with ml ;;::: 2 returned to normal within approximately 200 days after the mainshock. A total of 3342 events are classified as crustal and 576 as subduction. The recurrence relations versus magnitude are shown in Figure 5 for both the crustal and subduction data sets. A magnitude interval of 0.5 is used. The crustal events appear show a relatively linear relation between the logarithm of the number of events and the magnitude from about ml = 2.5 to ml = 4.5, the slope of which is approximately. The subduction events, however, appear to show a continuous curvature from ml = 1 to ml = 6, in contrast to the expected linear relation. Figure 6 shows the ratio of the logarithm of the number of crustal events to the number of subduction events versus magnitude. The result is a remarkably linear relationship from ml = to ml = 5; a least squares fit to the data is shown on the plot. The line, with a slope of -0.59, has a correlation coefficient of 0.998, indicating the high quality of the straight line fit. The linearity of this relationship indicates that if the ratio of the the log N, versus magnitude curves can be expressed as a polynomial with only a zeroth order term and a linear term, then the coefficients of the higher order terms in a polynomial expansion of the individual log N; versus magnitude relations must be identical. n terms of a polynomial fit from ml = 1 to ml = 5, only the zeroth order term (a vertical offset) and a linear term (slope) are different, with the coefficients of all the higher order Frequency of Occurrence Relations 15

24 crustal (!) subduction ' Q) + ~ + '- + Q) a. 10 (!) (!) (!) '- Q) + (!) (!)..a + (!) E + ::s (!) (!) + z 1 ~ (!) Magnitude + Figure S. Recurrence relationship for crustal and subduction events: The mean number of earthquakes per year for the crustal and subduction data sets. Frequency of Occurrence Relations 16

25 0 - +J 0 s... c: J 0 ::J "O..0 ::J Cl) ' J rn ::J s... () * Magnitude * Figure 6. Ratio of crustal and subduction recurrence relations: The ratio of the number of crustal events per year to the number of subduction earthquakes per year. This is the ratio of the two curves in Figure 5. Frequency of Occurrence Relations 17

26 terms having the same value. This was verified using a fourth order polynomial fit to the two data sets, and all coefficients of polynomial terms of order two and higher were found to be identical. As an alternative to analysis of the crustal and subduction data suites, the recurrence relations and their ratio were determined for separation of the catalog into "shallow" and "deep" subsets with a plane, horizontal boundary at 40, 50, 60 and 70 km depth. n each case, the logarithm of the ratio of the "shallow" to the "deep" recurrence relations was approximately linear from magnitude 1 through 5, suggesting that this linear relation might be somehow attributed to the effect of the lithostatic load at depth rather than the tectonic regime. The slope of the line decreased in magnitude as the separation depth became more shallow. To compare with Aki (1987), a least squares line was fit to the logarithm of the four largest magnitude intervals with a recurrence of at least 1 per year. The recurrence relation with the least square fit lines for the crustal and subduction events is shown in Figure 7. Both curves show fewer events detected than inferred from the straight lines starting at about ml = 3, which is consistent with Aki's suggestion that fewer small events would be observed than are predicted by a linear relation determined from the larger events. t is concluded, therefore, that the frequency of occurrence relations for both the crustal and subduction events exhibit a continuous curvature over the entire magnitude range, and, that, in particular, fewer events are detected below ml of about 3.5 than are predicted by a straight line determined from the larger events. Because of the lack of linearity, comparisons of b values for crustal and subduction events have limited meaning. However, the ratio of large events to small events is considerably larger for subduction events than for crustal events. Completeness analysis Determination of the minimum magnitude at which the event catalog is complete is crucial to the preceding analysis. The interpretation made in the preceding section that there is a change Frequency of Occurrence Relations 18

27 crustal (!) subduction L G> + ~ L. G> a L. G> (!).0 E + ::J z 1 (!) (!) Magnitude + Figure 7. Recurrence relations with best straight line tits: Least squares fits determined from the four largest magnitude intervals with recurrence rates of more than l per year. Frequency of Occurrence Relations 19

28 in curvature of the frequency of occurrence relations which is correlated with the spectral scaling relations requires that the recurrence relations be complete at least down to magnitude 2.5. Figure 8 shows four small events recorded on the vertical component of station KMU. All four events are well recorded with readily apparent P and S arrivals. The clarity with which these events were recorded, particularly the more distant events, indicates that the catalog should be essentially complete down to magnitude 1.0. Excluding the year 1982, an average of less than 2 events per day were detected and cataloged by the Hokkaido University staff, which suggests that even though the catalog is very large, there would not be a problem with overprinting of events on the seismic records. Cultural noise would not be expected to cause difficulty with discrimination of earthquakes from other seismic sources due both to the remoteness of the study area and the fact that travel paths from earthquakes within our selected source volume to the network stations are essentially vertical, making the identification less ambiguous. Stepp ( 1972) described a technique to estimate the consistency of a catalog based upon the assumption that recent catalogs are more complete than older catalogs. Assuming that the variance of the estimate of the mean number of events per unit time interval is proportional to the number of time intervals considered, Stepp shows that the standard deviation of the mean number of events within a magnitude interval, sda, should be inversely proportional to the square root of the number of time intervals and proportional to the square root of the mean number of events, JT sd =---.t.jn6.t [3] where A. is the mean number of events, N is the number of time intervals, and 6. T is the time interval. So, starting at the most recent time intervals and expanding the window from which the mean number of earthquakes is calculated going back in time, the standard deviation of the mean should decrease inversely proportional to the square root of the number of time intervals. f, however, the catalog becomes incomplete going back in time, then the standard deviation will fall off faster then _k due to the underestimate of A.. Therefore, since the amount of NtiT instrumentation at KMU increased after 1976, and since the network seismologists became more Frequency of Occurrence Relations 20

29 z - 41 km :: 19 km z = 88 km Distance = 44 km z :: 98 km Distance =- 49 km ~ 20 JO Time (sec) Figure 8. Small events recorded at KMU: Four small events recorded on the vertical component of KMU. Depths and epicentral distances are given. Frequency of Occurrence Relations 21

30 experienced with time, Stepp's test can evaluate the overall stability of observations of small events with time. Stepp's test is applied to the crustal events in Figure 9 for magnitude intervals 0.5 unit wide, centered on ml = 1, 2, and 3 respectively, and time intervals of 1 year. The year 1982 is excluded since it was an anomalous year. The straight lines represent a falloff of k. The curvature NilT of these standard deviation curves is due to additional aftershocks in the years following Therefore, the curvature to slopes steeper than the straight lines does not necessarily indicate incompleteness. To estimate the completeness of the catalog for small events, we must consider how the standard deviation of the mean number of smaller events events varies as compared to the larger events. Since magnitude 3 events are relatively numerous and are certain to be completely detected and cataloged, the change in the standard deviation of the smaller events, magnitude 1 and 2, can be compared to that of the magnitude 3 events. t is seen in Figure 9 that the change in the standard deviation of the mean number of events in each magnitude range are parallel. Therefore, the magnitude 1 and 2 events appear to be complete to the same degree as the magnitude 3 events. Since the magnitude 3 events are assumed to be entirely complete, then the magnitude 1 and 2 events should also be complete. The subduction earthquakes, Figure 10, show a similar relationship with the standard deviation of the mean number of magnitude 2 events being parallel to that of the magnitude 3 events. The fluctuations in the ml = 1 curve suggests instability in the observation of the ml = 1 events. However, since an average of only one ml = 1 event is detected per year, and since the curve fluctuates but does not clearly decrease, it is not clear whether all of the ml = earthquakes have been detected. t is worth noting that the ml = 2 and ml = 3 events show no influence from the ml = 7. mainshock. t is not clear whether the ml = earthquakes show any such influence. f the linear relation between magnitude and the logarithm of the number of earthquakes is, for some reason, physically valid, and then the curvature of the frequency of occurrence relation is due to incompleteness of the catalog, we can estimate the proportion of the small events that were detected and cataloged by the Hokkaido network staff. The least squares line through the larger events in the recurrence relation for the crustal events can is Frequency of Occurrence Relations 22

31 crustal "O A q> A AA (!) A + (!) (!) AA ++<!>~ ml == 2 ++ ml == 1 +-q. ml == Time (year) Figure 9. Stepp test for crustal events: Standard deviation (sd) of the estimate of the mean number of earthquakes per year at magnitude intervals centered on l, 2, and 3, 0.5 magnitude unit wide. Straight lines fall off as ~. N~T Frequency of Occurrence Relations 23

32 subduction Time (year) Figure 0. Stepp test for the subduction events: Standard deviation (sd) of the estimate of the mean number of earthquakes per year at magnitude intervals centered on l, 2, and 3, 0.5 magnitude unit wide. Straight lines fall of as ~. NdT Frequency of Occurrence Relations 24

33 [4] and for the subduction events as log N 1 = mL [5] (Figure 7). f all of the curvature in the frequency of occurrence relation is due to incompleteness of the catalog, then only 0.5% of the ml = 1 events and 16.8 % of the ml = 2 in the crustal data set would have been cataloged and detected. For the subduction earthquakes, only 0.73% of the ml = 1 events and 24. 7% of the mi = 2 events would have been cataloged and detected. Since the mi = l events are well recorded at KMU (Figure 8), which is a station in the Hokkaido network, and since the ml = 2 events should, therefore, be very well recorded, it is improbable that such a small percentage of the ml = l and 2 events should be detected. Additionally, if only one third of the mi = 2 events are detected, it seems unlikely that any of the ml = l events would be detected. t could be suggested that the linear decrease of the logarithm of the ratio of the number of crustal earthquakes to the number of subduction earthquakes as a function of magnitude could be related to an increasing incompleteness in the subduction catalog with decreasing magnitude. This is not considered plausible due to the linear nature of the ratio remaining constant out to at least magnitude 5 and the clarity with which the subduction events are recorded. As a final test of the completeness of the catalog, epicenter maps at varying depth ranges and various magnitude ranges, as well as cross sections at various magnitude ranges, were studied to look for patterns in the locations of the small events. A preference for earthquakes to be located near network stations or for events to be be located only above a certain depth would indicate possible incompleteness. No such patterns were detected for the mi = 1 and 2 events, though a marked decrease was detected in the mi = 0 events below 70 km depth. For earthquakes with magnitudes greater than 4, however, clusters were seen where the larger events were grouped together to the exclusion of other locations. This suggests that only certain faults, or fault systems, Frequency of Occurrence Relations 25

34 can support larger events, while many more faults, or fault systems, can support smaller earthquakes. t is concluded, therefore, that the catalog is essentially complete down to ml = 2 and that the catalog is probably complete down to ml = l, and hence the curvature of the frequency of occurrence versus magnitude relations is real. Discussion The frequency of occurrence relations show a significant decrease in the number of observed small events from the number predicted by a linear relation determined at higher magnitudes. This lack of small events cannot be explained by incompleteness of the event catalog. Though Aki ( 1987) predicted and observed this decrease in the number of small events, he provided no basis for the prediction. Other studies, such as Schneider et al., ( 1988), have observed a lack of small events at depth, but no clear explanation has emerged for the observations. Since a relative lack of small events at depth was found when dividing the catalog at differing depths, it is interpreted that the the relatively fewer numbers of small earthquakes at depth and the relatively many large events at depth is due to the effect of the lithostatic load. The deeper events will be in a higher compressive stress regime due to the lithostatic load, and hence the shear stress will have to reach a higher level to initiate slip than would be necessary at a more shallow location. Therefore, the additional compressive stress due to depth will inhibit the occurrence of small events, in favor of large events. The extremely linear relationship of the log ratio of the number of crustal events to the number of subduction events plotted versus magnitude remains to be explained. Frequency of Occurrence Relations 26

35 Energy release Separate from the preceding analysis, the catalog of earthquakes can be used to calculate the total seismic energy release for the crustal and subduction data sets. Variation of the energy release with time might indicate changes in the seismicity or precursory phenomena prior to large earthquakes. Gutenberg and Richter (1956) proposed the relation between radiated energy and magnitude, log Es = l.5ms , [6] where E, is the radiated seismic energy and Ms is the surface wave magnitude. Kanamori (1977) estimated radiated energy using the relation um 0 Es=--, 2µ. [7] where u is the earthquake stress drop, µ. is the shear modulus, and M 0 is the scalar moment. The Gutenberg-Richter relation, Equation 6, implicitly assumes a constant stress drop for all events and a linear relation between surface wave magnitude and log M 0 Since Hanks and Kanamori ( 1979) show that, in many studies for magnitudes greater than 3, the moment-magnitude relations are identical for surface wave magnitude and local magnitude, the surface wave magnitude, M,, can be Energy release 27

36 replaced with the local magnitude, mv in Equation 6. As is apparent from Equation 6, the total radiated energy over a given length of time will be dominated by the radiated energy of the few largest events, and will be influenced to a much lesser degree by the more numerous smaller events, even though Equation 6 may overestimate the stress drop, and hence the energy release, of the smaller events by assuming a constant stress drop for all events. Figure 11 shows the calculated energy release versus time for the crustal events, calculated on a monthly basis in the lower figure and in 7 month intervals in the upper figure. The highest point is March, 1982, the month of the ml = 7.1 mainshock. t is apparent that in the period preceding this large event, a precursory decrease in radiated energy is seen. The net radiated energy began to decrease approximately 2.5 years prior to the mainshock. An increasing trend appears to begin approximately 10 months prior to the mainshock. The large energy release 7 months prior to the mainshock, log E, = 19, is primarily due to a large foreshock, ml = 4, located directly above the hypocenter of the upcoming mainshock. Approximately one year after the mainshock, the energy release has returned to the apparent "ambient" level of 1018 erg. The subduction events, Figure 12, do not show a similar relation. The radiated energy per month is typically higher for the subduction events, 1019 ergs versus 1018 ergs for the crustal events, as would be expected from the frequency of occurrence relations, Figure 5, where the crustal region was found to have more numerous small events, while the subduction region contained more larger events. The subduction events do not show any prominent patterns in energy release, and specifically do not show a long term energy release decrease prior to the largest events, such as the ml= 6.9 event of January, The energy release in 7 month intervals for the crustal and subduction events are shown together in Figure 13. The net energy release per month in the crustal data set appears to show a precursory decrease prior to the ml = 7.1 event that could have been useful in the prediction of the upcoming mainshock. t is interesting that the year before the mainshock, Nishenko and McCain ( 1981) predicted that, on a scale of 1 to 6, with 1 being the highest probability of an earthquake with magnitude greater than 7 occurring within the next few decades, and 6 being the lowest probability, Energy release 28