Anomalously high b-values in the South Flank of Kilauea volcano, Hawaii: evidence for the distribution of magma below Kilauea's East rift zone
Introduction
The island of Hawaii is built upon the ocean floor by magmatic intrusive and extrusive material (Hill and Zucca, 1987). As the ocean floor moves over the hot spot, older volcanoes (Mauna Kea) are disconnected from the magma supply and new volcanoes (Loihi) are created. For this reason, the magma plumbing system under Hawaii may be expected to be more complex (Ryan, 1988) than under single volcanoes that remain above their magma supply for long periods. In such a case of strong complexity it is of special interest, but perhaps also more difficult than usual, to map the conduits and chambers containing magma. In this paper, we use the frequency magnitude distribution (FMD) of earthquakes to infer the presence of magma, concentrating on Kilauea's South Flank and in the Kaoiki-Hilea region between Mauna Loa and Kilauea. Because our method is based on seismicity, we can extract information only from parts of the crust and upper mantle that produce numerous earthquakes. In Hawaii, most seismic activity is concentrated in the volcanic edifice that rests on the depressed oceanic sea floor.
The crustal volumes beneath the South Flank and Kaoiki produce abundant earthquakes (Fig. 1), mostly at depths between 4 and 10 km within the volcanic edifice (Fig. 2). The earthquakes in these volumes are thought to be volcano-tectonic in the sense that they are generated by stresses exerted by the volcanoes and their rifts, but not directly related to opening of magmatic conduits or the flow of magma. The distances of the epicenters from the rift zones and the calderas range from about 1–10 km. The largest recent earthquakes were an M6.6 in 1983 and an M6.1 in 1989 in the Kaoiki and South Flank areas, respectively. However, both areas are underlain by a near horizontal decollement plane, the surface of the old sea floor, which can generate large to great earthquakes (Wyss, 1988). In 1975, an M7.2 earthquake ruptured most of the decollement plane under the South Flank (Swanson et al., 1976b), and in 1868, a M7.9 earthquake probably ruptured all of the South Flank, Kaoiki, Hilea and adjacent areas (Wyss, 1988).
Along Kilauea's east- and southwest rift zones, large numbers of small earthquakes occur during magmatic intrusions (Dvorak et al., 1986). These intrusions often initiate under Kilauea's caldera (Dzurisin et al., 1984, Klein et al., 1987), propagate down the rift zones, generate varying degrees of seismicity, and in many cases end up in eruptions from a subsidiary cone in the rift zone (Hardee, 1987). The seismic activity during rift intrusions occurs primarily between 2 and 4 km depth and follows closely the surface trace of the rift. Because of this, most early models of the east rift zone envisioned the active zone to exist down to 4 or 6 km. However, a model with magma bodies down to 10 km depth beneath the rift zones (Crosson and Endo, 1982, Ryan, 1988) received support from geodetic data (Delaney et al., 1990), which required an expanding magma body at 3–9 km depth to satisfactorily explain the surface deformations. In this paper we present data from the frequency–magnitude relation of earthquakes beneath the South Flank that support the model of magma bodies beneath the East Rift zone that may reach depths of 8 km. The data also suggest that the greatest effect on the South Flank earthquake magnitude distribution occurs at intermediate depths (4–7 km) adjacent to shallow (2–4 km) magma bodies under the rift that have been proposed based on analysis of deformation, lava chemistry and seismicity patterns. We do not analyze the seismicity of the rift zone itself because the earthquakes in it occur primarily during intrusions of magma, have a complicated time–space history and carry no information about crustal conditions in the South Flank.
The relative abundance of small earthquakes compared to large ones is measured by the b-value in the FMD (Ishimoto and Iida, 1939, Gutenberg and Richter, 1944)where N is the cumulative number of earthquakes with magnitude M and larger.
A number of recent papers demonstrated that the constants a and b vary strongly over a few kilometers distance in seismogenic volumes (Ogata et al., 1995, Wiemer and Benoit, 1996, Wiemer and McNutt, 1997, Wiemer and Wyss, 1997, Wyss et al., 1997, Wiemer et al., 1998, Power et al., 1998, Murru et al., 1999, Wiemer and Katsumata, 1999). This means that the mean magnitude, m, varies as a function of space because the b-value is inversely proportional to the mean magnitude (Aki, 1965, Utsu, 1965)In this paper, we map m. We do not assume that the FMD is approximated well by a power law, nor do we make any extrapolations based on a straight line fit. Therefore, it is inconsequential if the straight line fit may not be a good approximation in some volumes, because we are simply comparing the mean magnitude in different volumes by mapping the b-value.
Along the San Andreas fault system, creeping segments show anomalously high values (b>1.3) (Amelung and King, 1997, Wiemer and Wyss, 1997), whereas asperities correlate with anomalously low values (b<0.6) (Wiemer and Wyss, 1997, Wyss et al., 1999). In general, the b-values decrease with depth in California (Mori and Abercrombie, 1997, Wiemer and Wyss, 1997, Wiemer et al., 1998, Gerstenberger et al., 2000). In aftershock sequences, great variability of b-values is possibly related to the amount of slip during the main shock (Wiemer and Katsumata, 1999). Beneath volcanoes, the volumes surrounding active magma chambers and conduits exhibit anomalously high b-values (Wiemer and McNutt, 1997, Wyss et al., 1997, Wiemer et al., 1998, Murru et al., 1999).
We know from laboratory experiments, observations in underground mines and near wells that the b-value increases with decreasing effective stress, and with increasing heterogeneity of the material (Mogi, 1962, Scholz, 1968, Wyss, 1973, Urbancic et al., 1992), and that it may also be sensitive to the temperature gradient (Warren and Latham, 1970). A recent study by Lahaie and Grasso (1999) showed a correlation between the loading rate and the b-value at the Lacq gas field in France: When the loading rate was reduced, the b-value increased by almost a factor of two.
We interpreted the low b-values in asperities as expressions of elevated stress levels. The anomalously high b-values near magma chambers can be explained as due to larger-than-normal heterogeneity, or, alternatively, as due to high pore pressure. The purpose of this paper is to map the distribution of b-values in Kilauea's South Flank and in the Kaoiki-Hilea area, and to construct a model for the generation of the related earthquakes.
Section snippets
Data
The newest version of the Hawaiian Volcano Observatory's earthquake catalog was used to estimate the mean magnitude (b-value). Among the several magnitudes available, we have most confidence in the homogeneity of the ‘preferred magnitude’ (Mp) because this magnitude furnishes stable b-value estimates and it is available for the largest number of earthquakes. Mp is selected by a hierarchical scheme defined in the data description prepared by F. Klein for distribution of the Hawaiian earthquake
Method
We estimate the mean magnitude, or b-value, by both the maximum likelihood and the least squares method at every node of grids with spacing of 1 km or less (Wiemer, 1996). At each node, we extract the nearest N events (50<N<300, but typically N=100) to estimate b. The radii of the cylindrical volumes that contain 100 events are typically r=1, 1.5 and 3 km on the South Flank, in Kaoiki and in Hilea, respectively, but they vary inversely proportional to the local seismicity rate. From the resulting
Average b-value as a function of depth
The average b-value is estimated as a function of depth by a moving sample window of N=300 events, starting with the 300 shallowest earthquakes and moving the window deeper in steps of 10 events (Fig. 3). In the Kaoiki-Hilea area, the b-value remains approximately constant (b=0.8) down to about 10 km depth, below which it decreases slightly (Fig. 3b). This is similar to the pattern observed along parts of the San Andreas fault (Eaton et al., 1970, Wyss, 1973, Mori and Abercrombie, 1997, Wiemer
Discussion and conclusions
A normal pattern of b-value as a function of depth (Eaton et al., 1970, Wyss, 1973, Mori and Abercrombie, 1997, Wiemer and Wyss, 1997, Gerstenberger et al., 2000) is exhibited by the crust beneath Kaoiki-Hilea (Fig. 3, Fig. 4). We interpret this to mean that there is nothing special about the distribution of cracks, or the state of stress, in Hawaiian crust, in general. However, the anomalously high b-values beneath Kilauea's South Flank (Fig. 3, Fig. 4, Fig. 5, Fig. 6) show that there the
Acknowledgements
We thank M. R. Ryan and G. Saccorotti for suggestions and rewording in reviews that led to many improvements and T. Wright for helpful comments. This work was supported by NSF under grant number EAR-9614783, the Wadati endowment at the Geophysical Institute of the University of Alaska, Fairbanks, and a fellowship from the overseas research scholarship fund number 8-waka-190 by the Ministry of Education, Science, Sports and Culture, Japan for K. N. This paper is contribution number 1133 of the
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