Coda waves from small local earthquakes are interpreted as backscattering waves from numerous heterogeneities distributed uniformly in the earth's crust. Two extreme models of the wave medium that account for the observations on the coda are proposed. In the single backscattering model the scattering is considered to be a weak process, and the loss of seismic energy by scattering is neglected. In the diffusion model the seismic energy transfer is considered as a diffusion process. Both models lead to similar formulas that allow an accurate separation of the effect of earthquake source from the effects of scattering and attenuation on the coda spectra. A unique difference was found in the scaling law of earthquake source spectra between central California and western Japan, which may be attributed to the difference in inhomogeneity length of the earth's crust. The Q of coda waves in the two regions is strongly frequency dependent with values increasing from 50-200 at 1 Hz to about 1000-2000 at 20 Hz. This observation is interpreted as a combined effect of variation of Q with depth and frequency-dependent composition of coda waves described below. The turbidity coefficient of the lithosphere required at 1 Hz to explain the observed coda as body wave scattering is orders of magnitude greater than previously known values such as those obtained by Aki (1973) and Capon (1974) under the Montana Lasa from the amplitude and phase fluctuations of teleseismic P waves. From the high attenuation and turbidity obtained at this frequency we conclude that at around 1 Hz the coda is made of backscattering surface waves from heterogeneities in the shallow, low-Q lithosphere. The high Q observed for the coda at frequencies higher than 10 Hz, on the other hand, eliminates the possibility that these waves are backscattering surface waves. We conclude that at these high frequencies the coda must be made of backscattering body waves from heterogeneities in the deep lithosphere. The low turbidities found for deep earthquake sources under western Japan are consistent with this model of coda wave generation. tempts in recent years along this direction in •arthquake coda waves emerges from the quantitative analysis of the seismology [,4ki, 1969, 1973; Takano 1971; Haddon, 1972; Cleary and Haddon, 1972; King et al., 1973; Capon, 1974], and explosion seismology [Wesley, 1965; Nikolayet), 1968; Nikolayet) and Tregub, 1970; Let)in and Robinson, 1969; Dunkin, 1969; Greenfield, 1971], as well as lunar seismology [Nakamura et al., 1970; Dainty et al., 1974a].The longer the waves travel, the greater the variety of heterogeneities they encounter. The later portions of a seismogram therefore may be considered as a result of some kind of averaging over many samples of heterogeneities, thus scattering and attenuation properties. We shall conclude that at around 1 Hz they are backscattering surface waves from heterogeneities in the shallow, low-Q part of the earth's crust. On the other hand, for frequencies higher than 10 Hz they are primarily backscat...

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[1] Seismic data recorded in the 2-30 s band at Stromboli Volcano, Italy, are analyzed to quantify the source mechanisms of Strombolian explosions during September 1997. To determine the source-centroid location and source mechanism, we minimize the residual error between data and synthetics calculated by the finite difference method for a point source embedded in a homogeneous elastic medium that takes topography into account. Two source centroids are identified, each representative of the distinct event types associated with explosive eruptions from two different vents. The observed waveforms are well reproduced by our inversion, and the two source centroids that best fit the data are offset 220 and 260 m beneath and $160 m northwest of the active vents. The source mechanisms include both moment-tensor and single-force components. The principal axes of the moment tensor have amplitude ratios 1:1:2, which can be interpreted as representative of a crack, if one assumes the rock matrix at the source to have a Poisson ratio n = 1/3, a value appropriate for hot rock. Both imaged cracks dip $60°to the northwest and strike northeast-southwest along a direction parallel to the elongation of the volcanic edifice and a prominent zone of structural weakness, as expressed by lineaments, dikes, and brittle structures. For our data set, the volume changes estimated from the moments are $200 m 3 for the largest explosion from each vent. Together with the volumetric source is a dominantly vertical force with a magnitude of 10 8 N, consistent with the inferred movement of the magma column perched above the source centroid in response to the piston-like rise of a slug of gas in the conduit.

The finite difference method is applied to the study of the dynamics of a three-dimensional fluid-filled crack excited into resonance by the sudden failure of a small barrier of area AS on the crack surface. The impulse response of the crack is examined for various ratios of crack width to crack length and for several values of the crack stiffness C = (b/la)(L/d), where b is the bulk modulus of the fluid, /• is the rigidity of the solid, and L and d are the crack length and crack thickness, respectively. The motion of the crack is characterized by distinct time scales representing 'the duration of brittle failure and the periods of acoustic resonance in the lateral and longitudinal dimensions of the source. The rupture has a duration proportional to the area of crack expansion and is the trigger responsible for the excitation of the crack into resonance; the resonant periods are proportional to the crack stiffness and to the width and length of the crack. The crack wave sustaining the resonance is analogous to the tube wave propagating in a fluid-filled borehole. It is dispersive, showing a phase velocity that decreases with increasing wavelength. Its wave speed is always lower than the acoustic velocity of the fluid and shows a strong dependence on the crack stiffness, decreasing as the stiffness increases. The initial motion of the crack surface is an opening, and the radiated far-field compressional wave starts with a strong but brief compression which has a duration proportional to the crack stiffness and size of the rupture area; the amplitude of this pulse increases with the area of rupture but decreases with increasing stiffness. Flow into the newly created cavity triggers a pressure drop in the fluid, which produces a partial collapse of the wall propagated over the crack surface at the speed of the crack wave. The collapse of the crack surface generates a weak long-period component of dilatation following the compressional first motion in the far-field P wave train; the dilatational component is clearer in the signal from stiffer cracks when seen in the direction of the rupture. The energy loss by radiation is stronger for high frequencies, resulting in a progressive enrichment of the crack response in lower frequencies over the duration of resonance. These source characteristics translate into a far-field signature that is marked by a high-frequency content near its onset and dominated by a longer-period component in its coda. The source duration shows a strong dependence on the fluid viscosity and associated viscous damping at the crack wall. 1983; Spence and Turcotte, 1985; Sammis and Julian, 1986]. Aki et al. [1977] and Chouet and Julian [1985] studied the dynamics of propagating two-dimensional fluid-filled cracks using a stress-velocity finite difference method, and Chouet [1981, 1982] used the discrete wave number method [Bouchon, 1979] to study the elastic radiation in the near field of propagating fluid-filled and dry cracks with various geometries. The above studies underscore the need for furt...

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Abstract. We use data from broadband seismometers deployed around the summit of Kilauea Volcano to quantify the mechanism associated with a transient in the flow of magma feeding the east rift eruption of the volcano. The transient is marked by rapid inflation of the Kilauea summit peaking at 22 ttrad 4.5 hours after the event onset, followed by slow deflation over a period of 3 days. Superimposed on the summit inflation is a series of sawtooth displacement pulses, each characterized by a sudden drop in amplitude lasting 5-10 s followed by an exponential recovery lasting 1-3 min. The sawtooth waveforms display almost identical shapes, suggesting a process involving the repeated activation of a fixed source. The particle motion associated with each sawtooth is almost linear, and its major swing shows compressional motion at all stations. Analyses of semblance and particle motion are consistent with a point source located I km beneath the northeast edge of the Halemaumau pit crater. To estimate the source mechanism, we apply a moment tensor inversion to the waveform data, assuming a point source embedded in a homogeneous half-space with compressional and shear wave velocities representative of the average medium properties at shallow depth under Kilauea.

[1] The current eruption at Mount St. Helens is characterized by dome building and shallow, repetitive, long-period (LP) earthquakes. Waveform cross-correlation reveals remarkable similarity for a majority of the earthquakes over periods of several weeks. Stacked spectra of these events display multiple peaks between 0.5 and 2 Hz that are common to most stations. Lower-amplitude very-long-period (VLP) events commonly accompany the LP events. We model the source mechanisms of LP and VLP events in the 0.5-4 s and 8-40 s bands, respectively, using data recorded in July 2005 with a 19-station temporary broadband network. The source mechanism of the LP events includes: 1) a volumetric component modeled as resonance of a gently NNW-dipping, steam-filled crack located directly beneath the actively extruding part of the new dome and within 100 m of the crater floor and 2) a vertical single force attributed to movement of the overlying dome. The VLP source, which also includes volumetric and single-force components, is 250 m deeper and NNW of the LP source, at the SW edge of the 1980s lava dome. The volumetric component points to the compression and expansion of a shallow, magmafilled sill, which is subparallel to the hydrothermal crack imaged at the LP source, coupled with a smaller component of expansion and compression of a dike. The single-force components are due to mass advection in the magma conduit. The location, geometry and timing of the sources suggest the VLP and LP events are caused by perturbations of a common crack system.

) summit eruptive activity at Kilauea Volcano is characterized by explosive degassing bursts accompanied by very long period (VLP) seismic signals. We model the source mechanisms of VLP signals in the 10-50 s band using data recorded for 15 bursts with a 10-station broadband network deployed in the summit caldera. To determine the source centroid location and source mechanism, we minimize the residual error between data and synthetics calculated by the finite difference method for a point source embedded in a homogeneous medium that takes topography into account. The VLP signals associated with the bursts originate in a source region ∼1 km below the eastern perimeter of Halemaumau pit crater. The observed waveforms are well explained by the combination of a volumetric component and a vertical single force component. For the volumetric component, several source geometries are obtained which equally explain the observed waveforms. These geometries include (1) a pipe dipping 64°t o the northeast; (2) two intersecting cracks including an east striking crack (dike) dipping 80°to the north, intersecting a north striking crack (another dike) dipping 65°to the east; (3) a pipe dipping 58°to the northeast, intersecting a crack dipping 48°to the westsouthwest; and (4) a pipe dipping 57°to the northeast, intersecting a pipe dipping 58°to the west-southwest. Using the dual-crack model as reference, the largest volume change obtained among the 15 bursts is ∼24,400 m 3 , and the maximum amplitude (peak to peak) of the force is ∼20 GN. Each burst is marked by a similar sequence of deflation and inflation, trailed by decaying oscillations of the volumetric source. The vertical force is initially upward, synchronous with source deflation, then downward, synchronous with source reinflation, followed by oscillations with polarity opposite to the volumetric oscillations. This combination of force and volume change is attributed to pressure and momentum changes induced during a fluid dynamic source mechanism involving the ascent, expansion, and burst of a large slug of gas within the upper ∼150 m of the magma conduit. As the slug expands upon approach to the surface and more liquid becomes wall supported by viscous shear forces, the pressure below the slug decreases, inducing conduit deflation and an upward force on the Earth. The final rapid slug expansion and burst stimulate VLP and LP oscillations of the conduit system, which slowly decay due to viscous dissipation and elastic radiation. Consideration of the fluid dynamic arguments leads us to prefer the dual-crack VLP source model as it is the only candidate model capable of producing plausible values of length scales and pressure changes. The magnitudes of the vertical forces observed in the 15 bursts appear consistent with slug masses of 10 4 to 10 6 kg.Citation: Chouet, B. A., P. B. Dawson, M. R. James, and S. J. Lane (2010), Seismic source mechanism of degassing bursts at Kilauea Volcano, Hawaii: Results from waveform inversion in the 10-50 s band,