Keiiti Aki

Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz

Abstract Q for shear-waves in the crust and upper mantle was determined as a function of frequency in the range 1–25 Hz, using band-pass filtered records of about 900 earthquakes occurring in the central Japan area with focal depths from 0 to 150 km. The data were supplied from two stations in the Kanto region, operated by the Earthquake Research Institute, University of Tokyo. The method is taken from Aki and Chouet (1975) and Rautian and Khalturin (1978), and is based on elimination of the source effect from observed spectra of shear-waves, by taking the ratio of their amplitudes to those of coda-waves (measured at a fixed lapse time). The effect of radiation patterns is removed by averaging the ratio over many events. The experimental procedure uses basically a single-station method, and its validity was confirmed by the agreement between results obtained from station Tsukuba and those from Dodaira. We found that Q shows a strong dependence on frequency: Q increases with frequency f proportionally to f n , where n was found to be 0.8 in the northeastern part of Kanto (area A), and 0.6 in the rest of the region (areas B + C). Previously, a value for n of 0.5 had been determined for the Garm area in central Asia by Rautian and Khalturin. In general, our results agree with those of Fedotov and Boldyrev (1969), who obtained values of n around 0.6 for the Kuril-Islands, using a single-station method based on assumptions more restrictive than those adopted here. Q values for the lithosphere have been estimated by various workers using surface-waves with periods greater than 15 s. If we combine the results from surface-waves with those obtained from the S- to coda-amplitude ratio, we find that the frequency-dependence of Q −1 is similar to that obtained from a simple relaxation model, with the peak somewhere around 0.5 Hz.

Source mechanism of volcanic tremor: fluid-driven crack models and their application to the 1963 kilauea eruption

Abstract We propose a model for the mechanism of magma transport based on a fluid-filled tensile crack driven by the excess pressure of fluid. Such a transport mechanism can generate seismic waves by a succession of jerky crack extensions, if the fracture strength of rock varies in space, or if there is a difference between the dynamic and static values of the critical stress intensity factor. We also find that the opening and closing of a narrow channel connecting two fluid-filled cracks may be a source of seismic waves. Using the finite-difference method, we calculated the vibration of dry and fluid-filled cracks generated by: (1) a jerky extension at one end or at both ends and (2) a jerky opening of a narrow channel connecting two cracks. We then calculated the far-field and near-field radiation from these vibrating cracks. The spectra show peaked structures, but interestingly, most high-frequency peaks are only present in the near-field and cannot be transmitted to the far-field. The spectral features described above are often observed for volcanic tremors and in some cases for seismic signals associated with hydraulic fracturing experiments. We first consider as a model of volcanic tremor randomly occurring jerky crack extensions, and derive a formula relating the tremor amplitude to the excess pressure in the magma, the incremental area in each extension, and the frequency of extensions. These parameters are also constrained by other observations, such as the rate of magma flow. Our model was tested quantitatively against observations made in one of the best-described case histories of volcanic tremor: the October 5–6, 1963 Kilauea flank eruption. We found that a single, long crack extending from the summit to the eruptive site cannot explain the observations. The model of a steadily expanding crack ran into difficulties when quantitative comparisons were made with observations. The extension of crack area needed to explain the amplitude of volcanic tremor should accompany a large increase in tremor period which was not observed. Our second model is a chain of cracks connected by narrow channels which open and close. The length of each crack is around 1 km, the channel area connecting neighboring cracks is about 103m2, and the channel opens jerkily with the magmatic excess pressure of about 20 bars. The frequency of jerky opening of each channel is about once in 15 seconds. The channel is closed after each jerky opening, as soon as magma is moved through the channel.

Scattering characteristics of elastic waves by an elastic heterogeneity

Elastic wave scattering by a general elastic heterogeneity having slightly different density and elastic constants from the surrounding medium is formulated using the equivalent source method and Born approximation. In the low‐frequency range (Rayleigh scattering) the scattered field by an arbitrary heterogeneity having an arbitrary variation of density and elastic constants can be equated to a radiation field from a point source composed of a unidirectional force proportional to the density contrast between the heterogeneity and the medium, and a force moment tensor proportional to the contrasts of elastic constant. It is also shown that the scattered field can be decomposed into an “impedance‐type” field, which has a main lobe in the backscattering direction and no scattering in the exact forward direction, and a “velocity type” scattered field, which has a main lobe in the forward scattering direction and no scattering in the exact backward direction. For Mie scattering we show that the scattered far f...

Scattering wave energy propagation in a random isotropic scattering medium: 1. Theory

In this paper we provide a complete formulation of scattered wave energy propagation in a random isotropic scattering medium. First, we formulate the scattered wave energy equation by extending the stationary energy transport theory studied by Wu (1985) to the time dependent case. The iterative solution of this equation gives us a general expression of temporal variation of scattered energy density at arbitrary source and receiver locations as a Neumann series expansion characterized by powers of the scattering coefficient. The first term of this series leads to the first-order scattering formula obtained by Sato (1977). For the source and receiver coincident case, our solution gives the corrected version of high-order formulas obtained by Gao et al. (1983b). Solving the scattered wave energy equation using a Fourier transform technique, we obtain a compact integral solution for the temporal decay of scattered wave energy which includes all multiple scattering contributions and can be easily computed numerically. Examples of this solution are presented and compared with that of the single scattering, energy flux, and diffusion models. We then discuss the energy conservation for our system by starting with our fundamental scattered wave energy equation and then demonstrating that our formulas satisfy the energy conservation when the contributions from all orders of scattering are summed up. We also generalize our scattered wave energy equations to the case of nonuniformly distributed isotropic scattering and absorption coefficients. To solve these equations, feasible numerical procedures, such as a Monte Carlo simulation scheme, are suggested. Our Monte Carlo approach to solve the wave energy equation is different from previous works (Gusev and Abubakirov, 1987; Hoshiba, 1990) based on the ray theoretical approach.

A comparative study of scattering, intrinsic, and coda Q−1 for Hawaii, Long Valley, and central California between 1.5 and 15.0 Hz

A new method recently developed by Hoshiba et al. (1991) was used to separate the effects of scattering Q−1 and intrinsic Q−1 from an analysis of the S wave and its coda in Hawaii, Long Valley, and central California. Unlike the method of Wu [1985], which involves integration of the entire S wave energy, the new method relies on the integration of the S wave energy for three successive time windows as a function of hypocentral distance. Using the fundamental separability of source, site, and path effects for coda waves, we normalized the energy in each window for many events recorded at many stations to a common site and source. We plotted the geometric spreading-corrected normalized energy as a function of hypocentral distance. The data for all three time windows were then simultaneously fit to Monte Carlo simulations assuming isotropic body wave scattering in a medium of randomly and uniformly distributed scatterers and uniform intrinsic Q−1. In general, for frequencies less than or equal to 6.0 Hz, scattering Q−1 was greater than intrinsic Q−1, whereas above 6.0 Hz the opposite was true. Model fitting was quite good for frequencies greater than or equal to 6.0 Hz at all distances, despite the models simplicity. The small range in energy values for any particular time window demonstrates that the site effect can be effectively stripped away using the coda method. Though the model fitting generally worked for 1.5 and 3.0 Hz, the model has difficulty in fitting the whole distance range simultaneously, especially at short distances. Despite the poor fit at low frequency, the results generally support that in all three regions the scattering Q−1 is strongly frequency dependent, decreasing proportional to frequency or faster, whereas intrinsic Q−1 is considerably less frequency dependent. This suggests that the scale length of heterogeneity responsible for scattering is at least comparable to the wavelength for the lowest frequencies studied, of the order of a few kilometers. The lithosphere studied in all three regions can be characterized as a random medium with velocity fluctuation characterized by exponential or Gaussian autocorrelation functions which predict scattering. Q−1 decreasing proportional to frequency or faster. For all frequencies the observed coda Q−1 is intermediate between the total Q−1 and expected coda Q−1 in contrast with theoretical results for an idealized case of uniform distribution of scatterers and homogeneous absorption which predict that coda Q−1 should be close to the intrinsic Q−1. We will discuss possible causes for this discrepancy.

Seismic guided waves trapped in the fault zone of the Landers, California, earthquake of 1992

A time assignment speech interpolation system is disclosed utilizing time-shared common control processing circuits. Speech signals from a plurality of trunks are interpolated on a lesser plurality of transmission channels by connecting trunks only during active periods. In order to accommodate transmission channels of varying delay times (e.g., cable and satellite channels), receiving terminal switching operations are delayed for a time corresponding to the transmission delay of the corresponding channel. This is implemented by common control digital delay time-out for each new connection.

Seismic trapped modes in the Oroville and San Andreas Fault zones

Three-component borehole seismic profiling of the recently active Oroville, California, normal fault and microearthquake event recording with a near-fault three-component borehole seismometer on the San Andreas fault at Parkfield, California, have shown numerous instances of pronounced dispersive wave trains following the shear wave arrivals. These wave trains are interpreted as fault zone-trapped seismic modes. Parkfield earthquakes exciting trapped modes have been located as deep as 10 kilometers, as shallow as 4 kilometers, and extend 12 kilometers along the fault on either side of the recording station. Selected Oroville and Parkfield wave forms are modeled as the fundamental and first higher trapped SH modes of a narrow low-velocity layer at the fault. Modeling results suggest that the Oroville fault zone is 18 meters wide at depth and has a shear wave velocity of 1 kilometer per second, whereas at Parkfield, the fault gouge is 100 to 150 meters wide and has a shear wave velocity of 1.1 to 1.8 kilometers per second. These low-velocity layers are probably the rupture planes on which earthquakes occur.

3-D inhomogeneities in the upper mantle

Abstract The method developed by Aki, Christofferson and Husebye for determining a 3-D seismic image of the earths interior from the travel-time data obtained at a 2-D array has been applied to seventeen arrays around the world by various authors. The most outstanding results from these works are that small-scale lateral velocity anomalies exist in the lower crust and upper mantle everywhere studied. The reality of these deep-seated anomalies is supported by: 1. (1) significant reduction of residual variance; 2. (2) resolution analysis for decoupling from shallower anomalies; and 3. (3) error analysis for the significance of anomalies. In this paper, we try to strengthen the credibility of these deep-seated anomalies by drawing attention to those found where they were expected; namely, low-velocity bodies under several geothermal areas and high-velocity anomalies associated with the subducting plate.

Characteristics of seismic waves composing Hawaiian volcanic tremor and gas‐piston events observed by a near‐source array

A correlation method, specifically designed for describing the characteristics of a complex wave field, is applied to volcanic tremor and gas-piston events recorded by a semicircular array of GEOS instruments set at the foot of the Puu Oo crater on the east rift of Kilauea volcano, Hawaii. The spatial patterns of correlation coefficients obtained as functions of frequency for the three components of motion over the entire array are similar for gas-piston events and tremor, and clearly depict dispersive waves propagating across the array from the direction of Puu Oo. The wave fields are composed of comparable amounts of Rayleigh and Love waves propagating with similar and extremely slow phase velocities ranging from 700 m/s at 2 Hz to 300 m/s at 8 Hz. The highly cracked solidified lava flow on which the array was deployed, and subjacent structure of alternating lava and ash layers formed during repeated eruptions of Puu Oo since 1983, appear to be responsible for the low velocities observed. The results from Puu Oo stand in sharp contrast to those obtained in an experiment conducted in 1976 on the partially solidified lava lake of Kilauea Iki. Rayleigh waves were not observed in Kilauea Iki, but well-developed trains of Love waves were seen to propagate there with velocities twice as high as those observed near Puu Oo. These differences in the propagation characteristics of surface waves at the two sites may be attributed to the presence of a soft horizontal layer of molten rock in Kilauea Iki, which may have lowered the phase velocity of Rayleigh waves more drastically than that of Love waves, resulting in severe scattering of the Rayleigh wave mode. On the other hand, the thin superficial pahoehoe flow under our array at Puu Oo may have favored the development of vertical columnar joints more extensively at this location than at Kilauea Iki, which may have reduced the shear moduli controlling the Love wave mode. The average phase velocities in the frequency band from 2 to 5 Hz found at Puu Oo are roughly similar to those determined for tremor at Klyuchevskoy volcano, Kamchatka, but the frequency dependence appears much stronger at Puu Oo.

Multiple scattering and energy transfer of seismic waves—Separation of scattering effect from intrinsic attenuation II. Application of the theory to Hindu Kush region

In order to separate the scattering effect from intrinsic attenuation, we need a multiple scattering model for seismic wave propagation in random heterogeneous media. In paper I (Wu, 1985), radiative transfer theory is applied to seismic wave propagation and the energy density distribution (or the average intensity) in space for a point source is formulated in the frequency domain. It is possible to separate the scattering effect and the absorption based on the measured energy density distribution curves. In this paper, the data from digital recordings in the Hindu Kush region are used as an example of application of the theory. We also discuss two approximate solutions of coda envelope in the time domain: the single scattering approximation and the diffusion approximation and discuss the relation with the frequency domain solution. We point out that in only two cases can the apparent attenuation be expressed as an exponential decay form. One is thedark medium case, i.e., whenB0≪0.5, whereB0 =ηs/(ηs +ηa) is the seismic albedo,ηs is the scattering coefficient,ηa is the absorption coefficient. In this case the absorption is dominant, the apparent attenuationb can be approximated by the coherent wave attenuationb =ηs +ηa. The other case is thediffuse scattering regime, i.e., whenB0≫0.5 (bright medium) andR≫Ls,t ≪ τs, whereR andt are the propagation distance and lapse time,Ls and τs are the scattering lengths (mean free path) and scattering time (mean free time), respectively. However, in this case the envelope decays with a rate close to the intrinsic attenuation, while the intensity decreases with distance with a coefficientb ≈d0(ηs +ηa) ≈dsηs, whered0 andds are the diffusion multipliers (0<d0,ds<1).For the Hindu Kush region, by comparing the theory with data from two digital stations of 53 events distributed up to depths of 350 km, we find that the scattering is not the dominant factor for the measured apparent attenuation ofS waves in the frequency range 2–20 Hz. From the observation on high frequency (f>20 Hz) seismograms, we suggest the existence of a stron-scattering surface layer with fine scale heterogeneities in the crust, at least for this region.