Apostolos S. Papageorgiou

Sealing law of far-field spectra based on observed parameters of the specific barrier model

A set of acceleration source spectra is constructed using the observed parameters of the specific barrier model of Papageorgiou and Aki. The spectra show a significant departure from the ‘ω2-model’ at the high frequency range. Specifically, the high frequency spectral amplitudes of seismic excitation are higher as compared to the level predicted by the ‘ω2-model’. This is also supported by other observational evidence. The high frequency amplitudes of acceleration scale proportionally to the square root of the rupture areaS, to the rupture spreading velocityv, and to the local strain drop (Δσ/μ) (=strain drop in between barriers). The local strain drop in between barriers is not related in a simple way to the global strain drop, which is the strain drop estimated by assuming that it is uniform over the entire rupture area. Consequently, the similarity law does not apply. Using the source spectra which we constructed, we derive expressions for high frequency amplitudes of acceleration such asarms andamax. Close to the fault both are independent of fault dimensions and scale as (Δσ/µ)(Δf)1/2, while away from the fault plane they scale asW1/2(Δσ/µ)(Δf)1/2, whereW is the width of the fault and Δf is the effective bandwidth of the spectra.

A Discrete Wavenumber Boundary Element Method for study of the 3-D response 2-D scatterers

A mathematical formulation of the 2·5D elastodynamic scattering problem is presented and validated. The formulation is a straightforward extension of the Discrete Wave number Boundary Integral Equation Method (DWBIEM) originally proposed by Kawase1 for 2D scattering problems and subsequently extended to the 3D problem by Kim and Papageorgiou.2 It is demonstrated that the Greens function which is appropriate for a boundary formulation of the 2·5D elastodynamic scattering problem is the one corresponding to a unit force moving on a straight line with constant velocity. Such a Greens function is derived in the present study. The formulation may be used to study the wavefields in models of sedimentary deposits (e.g. valleys) or topography (e.g. canyons or ridges) with a 2D variation in structure but obliquely incident plane waves. The advantage of a 2·5D formulation is that it provides the means for calculations of 3D wavefields in scattering problems by requiring a storage comparable to that of the corresponding 2D calculations.

The Barrier Model and Strong Ground Motion

An overview of the most important developments in Engineering (or Strong Motion) Seismology is presented alongside Professor Keiiti Aki’s contributions, who is one of the founders of this field. The mechanics of earthquake rupture are discussed with due emphasis on the various physical phenomena. The presentation is made in a tutorial manner, borrowing freely from Keiiti Aki’s papers, and endeavoring to emulate his unique style of clarity, simplicity and synthetic ability.

Modeling, synthetics and engineering applications of strong earthquake wave motion

State of the art in modeling, synthetics, statistical estimation, and engineering applications of strong ground motion is reported in this paper. In particular, models for earthquake wave motion are presented, in which uncertainties both in the earth medium and the seismic source are taken into consideration. These models can be used to synthesize realistic strong earthquake ground motion, specifically near-field ground motion which is quite often not well recorded in real earthquakes. Statistical estimation techniques are also presented so that the characteristics of spatially-correlated earthquake motion can be captured and consequently used in investigating the seismic response of such large scale structures as pipelines and long-span bridges. Finally, applications of synthesized strong ground motion in a variety of engineering fields are provided. Numerical examples are shown for illustration.

Analysis of recorded earthquake response and identification of a multi-story structure accounting for foundation interaction effects

Abstract Analysis of recorded earthquake response and identification, of the 14-story, reinforced concrete Hollywood Storage building shaken during the 1987 Whittier Narrows earthquake, are presented. Since only the translational components of motion of the foundation were recorded and considered as input motions in the identification analysis, the inferred parameters reflect not only the characteristics of the superstructure but also the characteristics of the foundation and of the underlying soil, and as such are referred to as apparent system parameters. Further processing of the apparent system parameters is performed in order to extract the modal parameters of the superstructure. The pronounced interaction of the superstructure with the soil in the longitudinal direction reduced considerably (25%) the base shear which the building would have experienced if the superstructure were supported in a rigid half-space. On the other hand, the weak soil-structure interaction in the transverse direction reduced the base shear only by a very small amount ( ∼1.2% ).

Variations of the specific barrier model—part I: effect of subevent size distributions

The specific barrier model (SBM), introduced and developed by Papageorgiou and Aki (1983a; 1983b; 1985) and recently re-calibrated by Halldorsson and Papageorgiou (2005) for earthquakes of different tectonic regions, is a particular case of a composite seismic source model according to which the seismic moment is distributed in a deterministic manner on the fault plane on the basis of moment and area constraints. Namely, it assumes that a rectangular fault surface is filled with an aggregate of non-overlapping subevents modeled as circular cracks of equal diameter, the ‘barrier interval’, on which a ‘local stress drop’ takes place. In the present work, we relax the basic assumption regarding subevent size of the SBM. Subevents, still modeled as circular cracks, are allowed to vary in size according to various prescribed probability density functions controlling the frequency of occurrence of subevent sizes. Closed form expressions of the ‘far-field’ spectra of the composite source are derived using an approach proposed by Joyner and Boore (1986). The seismic energy radiated by individual subevents arrives at a site in a time window the duration of which is related to the duration of rupture and the source-site geometry. The effect of the distribution of ‘arrival times’ on the spectral amplitudes of the composite source is investigated in a companion paper, referred to as Part II. The type of subevent size distribution and its allowed size range directly affects the number of subevents required to satisfy the moment constraint. A larger number of subevents leads to increased ‘complexity’ of the earthquake which generally results in relatively higher source acceleration spectral levels at high-frequencies. The level of the plateau of the high-frequency acceleration spectral amplitudes, corresponding to different size-distributions, does not differ significantly from that of the far-field spectrum of the SBM, for a constant local stress drop. Furthermore, the differences observed in the spectral amplitudes of the SBM and its variants are likely to be less than the expected uncertainty associated with local stress drop values determined from strong-motion data. Thus, despite its simplifying assumptions, the SBM appears to provide the most simple, yet effective, description that captures the essential characteristics of a composite seismic source. This is especially advantageous for consistent strong-motion modeling in the ‘near-fault’, as well as in the ‘far-field’ region for earthquake engineering applications.

LOCALLY GENERATED SURFACE WAVES IN SANTA CLARA VALLEY: ANALYSIS OF OBSERVATIONS AND NUMERICAL SIMULATION

The motions recorded by the Gilroy array of instruments on the surface of the Santa Clara Valley, California, during the 1989 Loma Prieta and 1984 Morgan Hill earthquakes are analysed for evidence of valley induced surface waves. The Santa Clara Valley extends in a NW–SE direction, south of the San Francisco Bay. The Gilroy linear array of instruments is an east–west alignment of stations crossing the Santa Clara Valley. Seismic refraction studies in the vicinity of the array indicate that the valley is wedge-shaped in cross-section with maximum thickness of the order of 1 km. Analysis of the recorded motions of the 1989 Loma Prieta earthquake reveal clear evidence of the fundamental and first and second higher modes of Rayleigh waves, while analysis of the recorded motions of the 1984 Morgan Hill earthquake shows, in addition to the above surface wave modes, the presence of the fundamental Love mode. Motions generated by the latter event were more complicated due to the presence of the low-velocity zone of the Calaveras fault, which traps and focuses seismic energy generated by slip on the fault, and leaks it to the surrounding medium in a rather complicated manner. The observed valley-induced surface waves are simulated using a hybrid numerical technique which combines the Boundary Integral Equation Method with the Finite Element Method. The mathematical formulation that we use has been developed for a class of cylindrical inclusions of infinite length, having an arbitrary cross-section, embedded in a homogeneous (or layered) half-space, subjected to plane waves impinging at an oblique angle with respect to the axis of the inclusion. Even though the model of the valley is two-dimensional, the response is three-dimensional and has the particular feature of repeating itself with a certain delay for different observers along the axis of the valley. This feature leads to a considerably simpler solution than that for a valley with a 3-D geometry.

Earthquake response of two repaired buildings damaged in past seismic shaking

Abstract Two reinforced concrete buildings which suffered architectural and minor structural damage during the 1971 San Fernando earthquake, were shaken again by the 1987 Whittier Narrows earthquake. Their well recorded responses are analyzed employing a system identification technique. Comparison of the vibration parameters inferred from analyses of the Whittier earthquake response to the corresponding parameters inferred from dynamic response data before, during and after the San Fernando earthquake verify the adequacy of the repairs made on the structures. Also, comparison of the recorded dynamic responses with the design code requirements provides supporting evidence for the adequacy of current design practices.