Keiiti Aki’s research while affiliated with California Institute of Technology and other places

RIASSUNTO. - Questa nota descrive un nuovo metodo per calcolare le registrazioniaccelerografìehe per una data regione sismica in base alle leggi fisicheusando le informazioni relative alla tettonica ed alle proprietà fisiche della fagliasismica.Il metodo si basa su di un nuovo modello sismico, chiamato « modellob a r r i e r a » , caratterizzato da cinque parametri focali: lunghezza della faglia,larghezza, scorrimento massimo, velocità di rottura ed intervallo di barriera.I primi tre parametri possono essere vincolati dalla tettonica a placche, ilquarto parametro è approssimativamente una costante. Il parametro più importante,che controlla l'accelerazione del terremoto, è l'ultimo, l'intervallo « barriera ».Vi sono tre metodi per valutare 1' « intervallo barriera » per una dataregione sismica: 1) misurazione in superficie dello scorrimento attraverso fratturedi faglia; 2) creazione di un modello che si adatti all'osservazione dicampi vicini e lontani; 5) una legge che regoli i dati per i piccoli terremoti nellaregione.Gli intervalli barriera sono stati valutati per una dozzina di terremoti eper quattro regioni sismiche, per mezzo dei tre metodi suindicati. I risultatipreliminari ottenuti per la California suggeriscono che l'intervallo barrierapossa essere determinato quando sia dato il massimo scorrimento. La relazionetra l'intervallo barriera ed il massimo scorrimento varia da una regione sismicaall'altra. Ad esempio, l'intervallo appare insolitamente lungo per Kilanea (Hawaii),il che può spiegare perché traccia di forte scorrimento del terreno sia stataosservata soltanto nell'area epicentrale del terremoto delle Isole Hawaii del 29novembre 1975.

Using the indirect boundary integral scheme for multiple scattering of seismic waves developed by Benites, Aki & Yomogida (1992), we compute SH-wave seismograms and measure frequency-dependent characters of coda Q in 2-D random media with a flat layer over a half-space. Many circular cavities are randomly distributed in both the upper layer and the half-space, down to a certain depth (called the lower layer), simulating the upper and lower crusts. The scattering strength and the intrinsic attenuation, Qi, are varied for each layer, and the S-wave velocity is prescribed to be constant throughout the medium so that the computation of Green's functions for the boundary integral is simple. Considering two basic parameters of our random media, scattering strength and intrinsic attenuation Qi, we represent the shallow-earth structure by an upper crust with large intrinsic attenuation and a lower crust with effective scatterers. Computations of coda Q for several values of those parameters show that when the scattering is relatively strong, coda Q-1 is roughly independent of frequency. This result differs from the case of a uniformly random model where coda Q-1 peaks around kd= 2, where k is the wavenumber and d is the cavity diameter. If the scattering strength in the lower layer is large enough for multiple scattering to dominate over single scattering, coda Q-1 strongly depends on the intrinsic attenuation in the lower layer, Q-1i2, and these two values (coda Q-1 and Q-1i2) become similar. We explain this feature as follows. Waves scattered in the upper layer attenuate quickly due to high intrinsic attenuation and contribute little to the coda envelope in a time window starting at twice the traveltime of the direct wave. Multiply scattered waves in the lower layer eventually arrive at the surface, dominating the coda envelope, which decays at a rate determined by the intrinsic attenuation in the lower layer, Q-1i2. The hypothesis that the temporal decay of coda is controlled not by the scattering but by the energy leakage into a ‘transparent’ underlying mantle is ruled out in general by our numerical simulations, except at low frequencies. Although our model may be too simple to simulate the details of observed coda Q, coda Q is likely to reflect the intrinsic attenuation in the Earth's lower crust

We investigate the effects of various sources of error on the estimation of the seismic moment tensor using a linear least squares inversion on surface wave complex spectra. A series of numerical experiments involving synthetic data subjected to controlled error contamination are used to demonstrate the effects. Random errors are seen to enter additively or multiplicitively into the complex spectra. We show that random additive errors due to background recording noise do not pose difficulties for recovering reliable estimates of the moment tensor. On the other hand, multiplicative errors from a variety of sources, such as focusing, multipathing, or epicentre mislocation, may lead to significant overestimation or underestimation of the tensor elements and in general cause the estimates to be less reliable.

The method proposed by Mendiguren to determine the source parameters from free oscillation data is applied to the 1970 July 31 deep Colombian earthquake. The results indicate a source propagating horizontally for about 150 km along the lithosphere and cutting across its width. The slab behaves as a guide for source propagation. The horizontal propagation velocity is determined as 3.8 km/s. The intensity of the source grew proportionately to the second power of the propagation distance. This rate of source intensity growth may be interpreted either by a fan-shaped fault model or by a cone-shaped volume source. The average slip and stress drop are estimated as 360 cm and 300 bar for the fault model. For the volume source model the transformational shear strain and stress are estimated as 11 × 10−5 and 160 bar. There is no evidence of a double couple radiation preceding the P origin time. It is shown that the isotropic and deviatoric components of the moment tensor cannot be uniquely resolved when only observations of a single mode are available. It is observed that, from a statistical basis, the available 0Sn data for Colombian shock can be equally well explained by a pure deviatoric source model or by a source model including an isotropic component. Numerical experiments indicate that the inclusion of higher mode data does not change this situation. But, on the other hand, numerical experiments show that the available data and the scheme used for the inversion would not result in a solution including an artificial implosive component if the actual source were pure deviatoric. If the departure from a pure deviatoric source is produced by noise, it has to be non-random, as it could be produced by lateral heterogeneities not included in the inversion scheme.

About 1500 readings of teleseismic P-time residuals obtained from the US Geological Survey seismograph network in central California have been used to obtain a three-dimensional image of seismic velocity anomalies for this area by the method of Aki, Christoffersson & Husebye We found that the California network is less suitable than the LASA and NORSAR arrays for this kind of studies because of its greater proportion of peripheral blocks in which the resolution is very poor for the stochastic inverse solution and the random error effect is severe for the generalized inverse solution. Nevertheless, the resultant velocity anomalies show a remarkable correlation with the San Andreas fault zone to a depth of 75 km. The anomaly pattern changes drastically as the depth exceeds 75 km, suggesting that the asthenosphere has been reached.

Further evidences support the scaling law of far-field seismic spectrum based upon the ω-square model (Aki) for earthquakes with MS > 6 and for periods T > 10s. Recent observations, however, unequivocally require the modification of the above law for periods T < 10s. Unfortunately, the presently available data are not sufficient for a unique revision of the scaling law. We propose two alternatives and discuss their implications and consequences. In either case, we have to conclude that a large earthquake and a small one are substantially different. One interesting feature of the ω-square model appears to be unaffected by the required revision; that is, the spectral density of the fault-slip time-function for periods T < 5s takes the same absolute value, independent of magnitude, for earthquakes greater than Ms= 65. This result has important consequences in earthquake engineering because the seismic motion in the vicinity of an earthquake fault will scale as the fault-slip motion.

Rayleigh wave phase velocities at periods 30-80 s in the Pacific Ocean are calculated by inverting phase and amplitude anomaly data using the paraxial ray approximation and the Gaussian beam method. The region is divided into 5o X 5o blocks, and approx 200 source-receiver pairs from 18 well-studied events around the Pacific Ocean are used. The resulting model displays some interesting deviations from the lithospheric age-dependent model. For example, low velocity regions are correlated with the Hawaii, Samoa, French Polynesia and Gilbert Islands hotspots.-from Author

The boundary integral-Gaussian beam method (Benites & Aki 1989) is applied to study the ground motion in 2-D structures that exhibit irregular topography and interface, and whose shear wave velocity varies linearly with depth, for incident plane SH waves. In our first example of application the model is a half-space whose free-surface topography is a ridge of cosine shape, with vertical shear wave velocity gradient. In the second, the model is a semi-cylindrical sedimentary basin in a homogeneous half-space, in which the shear wave velocity of the sediments increases with depth. Our results for the case of the mountain show that the amplification on its top, predicted by the 2-D modelling when the velocity is constant, is enhanced when the velocity gradient is present, for all frequencies and by a factor up to 3. In the case of the basin, results show that the velocity gradient; (1) enhances the amplification at the edges of the valley, (2) makes the reverberations due to 2-D resonance have larger amplitudes and shorter intervals between arrivals, (3) shortens the total duration of the seismograms at all stations within the basin.

In this paper, velocity inversion using waveform data is investigated. A linearized approach is used in which a linear sensitivity operator must be derived. This operator can be computed economically using reciprocity of the Green's function. In order to avoid a large matrix inversion, several descent algorithms are described. Data errors and a priori model information are incorporated using covariance operators. A fast and reasonably accurate forward modelling scheme is required and here the Gaussian beam method for a slowly varying heterogeneous medium is used. Several types of linearizations can be done including the Born approximation, a linearization in terms of the field, and the Rytov approximation, a linearization in terms of the log field. Field linearizations are expected to be useful for small-scale heterogeneities which result in scattering effects that are additive in the field. For small perturbations from a homogeneous background, a linearized inversion in terms of the field is equivalent to a sequence of Kirchhoff migrations. Log field linearizations may be more robust for large-scale heterogeneities where forward scattering predominates, but phase unwrapping may be difficult numerically. Several numerical examples using a field linearization are performed in which transmitted body waves through a model with small velocity variations are used. The results using the waveform data identify the trial structures and are comparable or slightly better than the travel-time inversion results.

We present a study of the tremor that accompanied several eruptions of the Piton de la Fournaise volcano. We locate tremor sources in several frequency bands with a method based on the use of seismic amplitudes corrected for the recording site effect. The location of the sources is obtained by approximating the decay of the amplitude as a function of the hypocentral distance using the body wave amplitude decay. For frequencies above 1.5 Hz, sources are generally found at hallow depth and close to the location of the eruptive vents or fissures. The best correlation between the position of the vents and tremor sources is obtained for the 5–10 Hz frequency band suggesting the tremor in that band is directly generated at the eruption sites. Lower frequencies seem to be related to deeper processes than the eruption process observed at the surface. As sources are found at shallow depth, locating the tremor origin does not appear to be efficient for mapping the underground plumbing system of the volcano. On the other hand, during some eruptions, it appears as an efficient tool for monitoring the evolution of the eruption such as the opening of new eruptive fissures.