A simplified method for simulation of strong ground motion using finite rupture model of the earthquake source

We present a simplified method to simulate strong ground motion for a realistic representation of a finite earthquake source burried in a layered earth. This method is based on the stochastic simulation method of Boore (Boore, D. M., 1983, Bull. Seism. Soc. Am. 73, 1865–1894) and the Empirical Greens Function (EFG) method of Irikura (Irikura, K., 1986, Proceedings of the 7th Japan Earthquake symposium, pp. 151–156). The rupture responsible for an earthquake is represented by several subfaults. The geometry of subfaults and their number is decided by the similarity relationships. For simulation of ground motion using the stochastic simulation technique we used the shapping window based on the kinetic source model of the rupture plane. The shaping window deepens on the geometry of the earthquake source and the propagation characteristics of the energy released by various subfaults. The division of large fault into small subfaults and the method for accounting their contribution at the surface is identical to the EGF. The shapping window has been modified to take into account the effect of the transmission of energy released form the finite fault at various boundaries of the layered earth model above the source. In the present method we have applied the correction factor to adjust slip time function of small and large earthquakes. The correction factor is used to simulate strong motion records having basic spectral shape of ² source model in broad frequency range. To test this method we have used the strong motion data of the Geiyo earthquake of 24th March 2001, Japan recorded by KiK network. The source of this earthquake is modelled by a simple rectangular rupture of size 24 × 15 km, burried at a depth of 31 km in a multilayered earth model. This rupture plane is divided into 16 rectangular subfaults of size 6.0 × 3.75 km each. Strong motion records at eight selected near-field stations were simulated and compared with the observed records in terms of the acceleration and velocity records and their response spectrum. The comparison confirms the suitability of proposed rupture model responsible for this earthquake and the efficacy of the approach in predicting the strong motion scenario of earthquakes in the subduction zone. Using the same rupture model of the Geiyo earthquake, we compared the simulated records from our and the EGF techniques at one near-field station. The comparison shows that this technique gives records which matches in a wide frequency range and that too from simple and easily accessible parameters of burried rupture.     

A Local Least-Squares Modification of Stokes’ Formula

The combination of Stokes formula and an Earth Gravity Model (EGM) for geoid determination has become a standard procedure. However, the way of modifying Stokes formula vary from author to author, and numerous methods of modification exist. Most methods are deterministic, with the primary goal of reducing the truncation bias committed by limiting the area of Stokes integration around the computation point, but there are also some stochastic methods with the explicit goal to reduce the global mean square error of the geoid height estimator stemming from the truncation bias as well as the random errors of the EGM and the gravity data. The latter estimators are thus, at least from a theoretical point of view, optimal in a global mean sense, but in a local sense they may be far from optimality.Here we take advantage of the error variance-covariance matrices of the EGM and the terrestrial gravity data to derive the modification parameters of Stokes kernel in a local least-squares sense. The solution is given for the unbiased type of modification of Stokes formula of Sjöberg (1991).     

Estimation of the Source Time Function Based on Blind Deconvolution with Gaussian Mixtures

It is demonstrated that the blind deconvolution method is fully capable of recovering the unknown Greens function and of estimating the source time functions from observed seismic data of small earthquakes. Based on the assumption of the Gaussian-mixture model of the Greens function, the newly-formulated algorithm is evaluated using synthetic seismic data along with those of the May 8, 1996 Mexico earthquake (M_c = 4.6). Since the estimated results closely match the theoretical input very well, the method is then employed to analyze the source time functions of the July 7, 1995 Pu-Li, Taiwan earthquake (M_L = 5.3). The stations triggered by this event were azimuthally well covered. Using the estimated source time functions, information pertaining to the directivity effect is readily obtained, and the actual fault plane of this event is identified, thus clearly indicating that this method provides a most efficient way to estimate the source time function of a small earthquake.Acknowledgment The authors would like to express their thanks to two anonymous reviewers for their valuable suggestions and Dr. I. Santamarias courteous assistance. They also appreciate the efforts of Drs. H.C. Chiu and R.J. Rau, who provided the seismic data and the fault plane solutions. The National Science Council, Taiwan, has supported this research (NSC 91-2119-M-194-011).     

Integral Equations for Kinematic Dynamo Models

A new technique for the treatment of the kinematic dynamo problem is presented. The method is applicable when the dynamo is surrounded by a medium of finite conductivity and is based on a reformulation of the induction equation and boundary conditions at infinity into an integral equation. We show that the integral operator involved here is compact in the case of homogeneous conductivity, which is important for both mathematical and numerical treatment. A lower bound for the norm of then yields a necessary condition for the generation of magnetic fields by kinematic dynamos. Numerical results are presented for some simple ²-dynamo models. The far-field asymptotics for stationary and time-dependent field modes are discussed.     

Cenozoic Intraplate Alkaline Volcanism of Western Bohemia

Three independent volcanic suites have been recognised in W Bohemia: (i) the old unimodal alkaline ol. nephelinite-tephrite (29-19 Ma) in the Ohe Rift, (ii) two contemporaneous weakly (trachybasalt/trachyandesite-trachyte/rhyolite; 13-11 Ma) and strongly (ol. nephelinite-tephrite/basanite; 12-8 Ma) alkaline series in the flank of the Cheb-Domalice Graben formed by the Teplá Highland and (iii) the young unimodal ol. melilitite/ol. nephelinite alkaline suite (2.0-0.12 Ma) at the intersection of the above mentioned structures in the Cheb Basin. The magmas of all the suites are mantle-derived and, in the case of the Cheb-Domalice Graben series, associated with the AFC process. Two main fault systems: (i) ENE-WSW and (ii) NNW-SSE are developed in W Bohemia, corresponding to the directions of the two prominent taphrogenic structures. The southwesterly continuation of the Ohe Rift across the Mariánské Lázn Fault is marked by volcanics only.     

Dispersion Measurements of <Emphasis Type="Italic">P</Emphasis> Waves and their Implications for Mantle <Emphasis Type="Italic">Q</Emphasis><Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

We analyze the anelasticity of the earth using group delays of P-body waves of deep (>200 km) events in the period range 4–32 s for epicentral distances of 5–85 degrees. We show that Time Frequency Analysis (TFA), which is usually applied to very dispersive surface waves, can be applied to the much less dispersive P-body waves to measure frequency-dependent group delays with respect to arrival times predicted from the CMT centroid location and PREM reference model. We find that the measured dispersion is due to: (1) anelasticity (described by the P-wave quality factor Q _p ), (2) ambient noise, which results in randomly distributed noise in the dispersion measurements, (3) interference with other phases (triplications, crustal reverberations, conversions at deep mantle boundaries), for which the total dispersion depends on the amplitude and time separation between the different phases, and (4) the source time function, which is dispersive when the wavelet is asymmetrical or contains subevents. These mechanisms yield dispersion ranging in the order of one to 10 seconds with anelasticity responsible for the more modest dispersion. We select 150 seismograms which all have small coda amplitudes extending to ten percent of the main arrival, minimizing the effect of interference. The main P waves have short durations, minimizing effects of the source. We construct a two-layer model of Q _p with an interface at 660 km depth and take Q _p constant with period. Our data set is too small to solve for a possible frequency dependence of Q _p . The upper mantle Q ₁ is 476 [299–1176] and the lower mantle Q ₂ is 794 [633–1064] (the bracketed numbers indicate the 68 percent confidence range of Q _p ^–1). These values are in-between the AK135 model (Kennett et al., 1995) and the PREM model (Dziewonski and Anderson, 1981) for the lower mantle and confirm results of Warren and Shearer (2000) that the upper mantle is less attenuating than PREM and AK135.     

On the consistency of the indirect lognormal correction

The indirect lognormal correction is a change-of-support model commonly used in geostatistical applications when dealing with additive variables, for which the upscaling amounts to arithmetic averaging. It was designed as a generalization of the lognormal correction that states the permanence of lognormality, but so far its internal consistency has not been proven in the general case. After a recall of the theoretical conditions that change-of-support models must honor, the concept of conventional income is introduced and used to establish the mathematical consistency of the indirect lognormal correction. However, the suitability of this model is questionable in many situations, in particular when the support effect is important or when the point-support distribution presents a zero effect, is not continuous or not positively skewed.Tel.: +56-2-672-3504, +56-2-678-4498     

A statistical study of the upstream intermediate ion boundary in the Earth’s foreshock

A statistical investigation of the location of onset of intermediate and gyrating ion populations in the Earths foreshock is presented based on Fixed Voltage Analyzer data from ISEE 1. This study reveals the existence of a spatial boundary for intermediate and gyrating ion populations that coincides with the reported ULF wave boundary. This boundary position in the Earths foreshock depends strongly upon the magnetic cone angle _BX and appears well defined for relatively large cone angles, though not for small cone angles. As reported in a previous study of the ULF wave boundary, the position of the intermediate-gyrating ion boundary is not compatible with a fixed growth rate of the waves resulting from the interaction between a uniform beam and the ambient plasma. The present work examines the momentum associated with protons which travel along this boundary, and we show that the variation of the boundary position (or equivalently, the associated particle momentum) with the cone angle is related to classical acceleration mechanisms at the bow shock surface. The same functional behavior as a function of the cone angle is obtained for the momentum predicted by an acceleration model and for the particle momentum associated with the boundary. However, the model predicts systematically larger values of the momentum than the observation related values by a constant amount; we suggest that this difference may be due to some momentum exchange between the incident solar-wind population and the backstreaming particles through a wave-particle interaction resulting from a beam plasma instability.     

Critical remarks on the use of medieval eclipse records for the determination of long-term changes in the Earth's rotation

The use of some Arabic medieval solar and lunar eclipse records for the determination of secular changes in the Earth's rotation is critically reviewed. The published results derived from these data suggest a non-uniform decrease in the Earth's rotation rate over the last 27 cy. There is, however, up to this day no sound physical explanation for the deduced non-tidal oscillations, with an apparent period of about 1500 yr and a semi-amplitude of some 4 ms in the l.o.d., which overlayed to a constant secular tidal change in the Earth's rotation rate produce a net non-uniform deceleration of the Earth's rotation. In this paper we discuss a set of observations, which were executed by professional Arabic astronomers. We show by our analysis the way in which the non-uniform deceleration of the Earth's rotation was constructed. A correct reading of the Arabic medieval observations shows that they do not contradict a secular constant decrease in the Earth's rotation rate of nearly -4.6 10-22 rad s-2. This value is in accordance with other similar ones derived from ancient eclipse records and from satellite tracking data.     

The gross features of the lithosphere-asthenosphere system in Europe from seismic surface waves and body waves

Long-period recordings of dispersive Rayleigh waves along numerous station lines, or profiles, in Europe have for the first time permitted a uniform inversion of these observations based on a new method of phase velocity regionalization.Regional dispersion relations obtained by this method have then been subjected to a complete inversion procedure commonly known as the hedgehog method. The results are presented in a map outlining the thickness of the lower lithosphere (lid) and the shear (S) velocities in both the lid and the asthenosphere channel.A comparison of these results with the minimum compressional (P) wave velocities in the asthenosphere and their corresponding depths provides an estimate of theV _p /V _s ratio for the asthenosphere in the European area.Contribution No. 314, Institute of Geophysics, ETH-Zürich, Switzerland.     

Further evidence for radial velocity anomalies in the lower mantle

Summary Wright andLyons (1981) used a least-squares matching technique (LMM) and an adaptive processing method (ADP) to study the behaviour of slowness and azimuth measurements made on two synthetic interfering wavelets having different arrival vectors and onset times. We have applied these results to the analysis of real array seismograms. Some of the effects generated synthetically are frequently observed on real seismograms of earthquakes recorded at Yellowknife at distances close to 50° and 90°. We have also processed sufficient data to illustrate how the interference phenomenon can be used to confirm the presence of radial velocity anomalies in the lower mantle. NumerousP arrivals from South American earthquakes at distances between 78° and 98° suggest the presence of two radial velocity anomalies at depths close to 2400 and 2730 km below the Caribbean region; these anomalies also appear to vary laterally.Contribution No. 864 from the Earth Physics Branch.     

Theory of Basin Scale Dynamics of a Stratified Rotating Fluid

The dynamics of a stratified fluid contained in a rotating rectangular box is described in terms of the evolution of the lowest moments of its density and momentum fields. The first moment of the density field also gives the position of the fluids centre-of-mass. The resulting low-order model allows for fast assessment both of adopted parameterisations, as well as of particular values of parameters. In the ideal fluid limit (neglect of viscous and diffusive effects), in the absence of wind, the equations have a Hamiltonian structure that is integrable (non-integrable) in the absence (presence) of differential heating. In a non-rotating convective regime, dynamically rich behaviour and strong dependence on the single (lumped) parameter are established. For small values of this parameter, in a self-similar regime, further reduction to an explicit map is discussed in an Appendix. Introducing rotation in a nearly geostrophic regime leads through a Hopf bifurcation to a limit cycle, and under the influence of wind and salt to multiple equilibria and chaos, respectively.     

Lagrangian Solution of Dynamo Equations and Path Integrals

We discuss an explicit solution of the Cauchy problem for induction equation and suggest its generalization for equations of ²-dynamo. These solutions are based on concepts of multiplicative, Wiener path, and stochastic integrals. Obtained explicit solution can be useful as a tool in investigations of a dynamo with fluctuating helicity.     

On strong ground motion synthesis with k −2 slip distributions

This study deals with the methodical aspects of k ^–2(Bernard et al., 1996) kinematic strong motions modelling: (1) it is shown how to incorporate the k-dependent rise time for 2D fault geometry in the strong motion synthesis according to the representation theorem, (2) it is suggested how to produce realistic k ^–2 slip models including asperity(ies), (3) modifications are introduced concerning the typeof used slip velocity function and the corner wave number in the slip distribution. High frequency effects of these generalized models are discussed.It is shown that, assuming the rise time proportional to the spatial slip wavelength at high wave numbers, the spectral decay of displacement at frequencies higher than the corner frequency is given just by the decay ofthe slip distribution spectrum, regardless of the type of slip velocity function. It is shown numerically that this model provides -squared source spectrum even in a vicinity of a 2D normal fault buried in 1D structure, which is an agreement with previous studies.     

Emplacement mechanisms of the South Kona slide complex,Hawaii Island: sampling and observations by remotely operated vehicle Kaiko

Emplacement of a giant submarine slide complex, offshore of South Kona, Hawaii Island, was investigated in 2001 by visual observation and in-situ sampling on the bench scarp and a megablock, during two dives utilizing the Remotely Operated Vehicle (ROV) Kaiko and its mother ship R/V Kairei. Topography of the bench scarp and megablocks were defined in 3-D perspective, using high-resolution digital bathymetric data acquired during the cruise. Compositions of 34 rock samples provide constraints on the landslide source regions and emplacement mechanisms. The bench scarp consists mainly of highly fractured, vesiculated, and oxidized aa lavas that slumped from the subaerial flank of ancestral Mauna Loa. The megablock contains three units: block facies, matrix facies, and draped sediment. The block facies contains hyaloclastite interbedded with massive lava, which slid from the shallow submarine flank of ancestral Mauna Loa, as indicated by glassy groundmass of the hyaloclastite, low oxidation state, and low sulfur content. The matrix facies, which directly overlies the block facies and is similar to a lahar deposit, is thought to have been deposited from the water column immediately after the South Kona slide event. The draped sediment is a thin high-density turbidite layer that may be a distal facies of the Alika-2 debris-avalanche deposit; its composition overlaps with rocks from subaerial Mauna Loa. The deposits generated by the South Kona slide vary from debris avalanche deposit to turbidite. Spatial distribution of the deposits is consistent with deposits related to large landslides adjacent to other Hawaiian volcanoes and the Canary Islands.     

Hawaiian magma-reservoir processes as inferred from the petrology of gabbro xenoliths in basalt,Kahoolawe Island

Gabbro xenoliths in a tholeiitic lava of Kahoolawe Island, Hawaii, a 1.3–1.4 Ma shield volcano, are 1–3 cm in size and comprised of plagioclase, clinopyroxene, and orthopyroxene. Gabbro textures — while intergranular and in part subophitic-are open due to 28–48 vol.% of vesicular basalt occupying xenolith space. Vesicles in and around the xenoliths are lined or filled with rhyolitic glass (segregation vesicles). The host is evolved tholeiite (MgO 6.1 wt%) with phenocrysts, microphenocrysts, and glomerocrysts of olivine, clinopyroxene, orthopyroxene, and plagioclase, and megacrysts (1 cm) of plagioclase. The Sr-isotope ratio of one xenolith is 0.70489; the host basalt ratio is 0.70460. Xenolith isotope composition, grain resorption, and clinopyroxene (Fs_12.5–15Wo_38–35.5), orthopyroxene (Fs_19.5–24Wo_4.1), and plagioclase (An_68–65Or_0.8–1.2) compositions suggest that these gabbros crystallized from Kahoolawe tholeiitic magma of essentially the same composition as the host basalt, but pre-dating the magma represented by the host. Based on the absence of intergranular Fe–Ti oxide phases from the pl+cpx+opx assemblages, and the open, vuggy textures, we envision crystallization on a reservoir roof at temperatures >1100°C. Entrainment of gabbro assemblages and plagioclase megacrysts from a roof mush/suspension zone occurred during convection associated with replenishment of the magma reservoir. These open-textured gabbro xenoliths are therefore not fragments of preexisting coarse-grained bodies such as sills or segregation veins. Rhyolitic glass in vesicles represents a gas-effervescence filtration process that forced fractionated residual liquids from the groundmass into voids associated with the xenoliths.Sirrine Environmental Consultants, Fremont, CA 94538     

A method of searching for radial velocity anomalies in the lower mantle using interfering signals

Radial velocity anomalies in the lower mantle that give rise to triplications in the travel-time curve for short-periodP waves will produce arrivals havingdT/d values that differe by roughly 0.2–0.5 s/deg. The first two arrivals associated with such triplications will be separated by less than one second over a distance range of 4°–10° they may not, therefore, be separable visually on single seismograms, so that their presence can only be inferred from some measurable property that depends on their mutual interference. If there are lateral variations in the regions of anomalous velocity gradients, the interfering signals will also have different azimuths of arrival. Using two synthetic wavelets we have investigated the effect of interference on bothdT/d and azimuth measurements at the Yellowknife Array. We found that if the interfering pulses have a dominant frequencyv, there is a range of time separations (0.30/v0.55/v) over which the measureddT/d and azimuth values may fluctuate by much more than the differences indT/d and azimuth between the interfering signals. We have evaluated the following empirically defined functions for three different primary signals, and for three different relative amplitudes of the interfering signals:f (t), the drift function, which expresses how the measured slownesses,p, and azimuths, , differ from the slownesses and azimuths of the primary wavelets; f(), the range function, which describes the behaviour of the upper and lower bounds ofp and as a function of the difference in arrival times of the signals, andf , studied the properties of these functions, and have outlined how these properties provide criteria based on the numerical and statistical characteristics of the arrival vectors, and on the waveform of the signal that will enable small radial velocity anomalies to be more clearly delineated.Contribution No. 863 from the Earth Physics Branch.     

Quasilinear heating of electrons in the earth's plasmasphere

In the framework of a quasilinear theory we examine the interaction between thermal electrons and ion-cyclotron waves (ICW) in the outer plasmasphere of the earth. For this type of wave-particle interaction, a simplification of the quasilinear diffusion integral in a magneto-active plasma under plasmaspheric conditions is given. Under the assumption of a Maxwellian distribution of electrons we have calculated the collision frequency and the heating source as the electrons are scattered by ICW. The obtained values of intrinsic parameters of the outer plasmasphere may exceed greatly, accordingly, the Coulomb frequency of collisions and the heating source due to suprathermal electrons. ICW-heating causes the ionosphereward thermal flux to increase, and this must lead to an increase in electron temperature in lower-lying plasmaspheric regions and in the subauroral ionosphere. A quantitative estimation of the electron temperature for the hot zone, made in this paper, is consistent with available experimental data.