Abstract
The specific barrier model (SBM) is a particular case of a composite earthquake source model where the seismic moment is distributed in a deterministic manner on a rectangular fault plane on the basis of moment and area constraints. It is assumed that the fault surface is composed of an aggregate of subevents of equal diameter, the ‘barrier interval’. Furthermore, the subevents are assumed to rupture randomly and statistically independent of one another as the rupture front sweeps the fault plane. In the formulation of the far-field source spectrum of the SBM the ‘arrival time’ of the seismic radiation emitted by each subevent is specified via a probability density function (PDF). In the SBM the subevents are assumed to be of equal sizes (an assumption relaxed in a companion paper, referred to as Part I) and the PDF of ‘arrival times’ is assumed to be uniform. In this study we investigate the effects of different PDFs of ‘arrival times’ on the far-field source spectrum of the SBM. Different PDFs of ‘arrival times’ affect the source spectra primarily at the intermediate frequency range (between the first and second corner frequencies). Such effects become more pronounced as the earthquake magnitude increases. The far-field spectrum of seismic energy observed/recorded at a site depends on the location of the site relative to the causative fault plane, the location of rupture initiation (hypocenter) and the onset times of the rupturing subevents. All the above factors are effectively taken into account by the ‘isochrons’, which vary with source-site geometry. We investigate the selection of the appropriate PDF of seismic energy arrival times at a given site by computing isochrons for a grid of stations surrounding the earthquake fault, represented by the SBM. We show that only for stations located in a direction normal to the fault plane is the assumption of uniform PDF of ‘arrival times’ valid. At other sites non-uniform PDFs of ‘arrival times’ are observed. We identify and categorize the prevalent types of PDFs by directivity (forward vs. backward vs. neutral) and source-site distance (near-fault vs. far-field), show examples in which we group the stations accordingly. We investigate the effects of the different PDF-groups on the SBM source spectrum. Selection of the appropriate PDF for a given source-site configuration when simulating strong ground motions using the SBM in the context of the stochastic method is expected to yield more self-consistent, and physically realistic simulations.
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References
Aki K (1967) Scaling Law of seismic spectrum. J Geophys Res 72(4): 1217–1231
Aki K, Papageorgiou AS (1988) Separation of source and site effects in acceleration power spectra of major California earthquakes. In: Proceedings of the 9th world conference on Earthquake Engingeering, pp 163–165
Aki K, Richards PG (1980) Quantitative seismology. Theory and methods. W. H. Freeman and Company, San Francisco
Davenport WB (1970) Probability and random processes: an introduction for applied scientists and engineers. McGraw-Hill, New York
Douglas J (2010) Consistency of ground-motion predictions from the past four decades. Bull Earthq Eng 8(6): 1515–1526
Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond Ser A Math Phys Sci 241(1226): 376–396
Foster KM, Halldorsson B, Green RA, Chapman MC (2012) Calibration of the specific barrier model to the NGA dataset. Seism Res Lett (in press)
Frankel A (1991) High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults. J Geophys Res 96(B4): 6291–6302
Gusev AA (1983) Descriptive statistical model of earthquake source radiation and its application to an estimation of short-period strong motion. Geophys J R Astron Soc 74(3): 787–808
Halldorsson B, Mavroeidis GP, Papageorgiou AS (2011) Near-fault and far-field strong ground motion simulation for earthquake engineering applications using the specific barrier model. J Struct Eng 137(3): 433–444
Halldorsson B, Ólafsson S, Sigbjörnsson R (2007) A fast and efficient simulation of the far-fault and near-fault earthquake ground motions associated with the june 17 and 21, 2000, earthquakes in South Iceland. J Earthquake Eng 11(3): 343
Halldorsson B, Papageorgiou AS (2005) Calibration of the specific barrier model to earthquakes of different tectonic regions. Bull Seismol Soc Am 95(4): 1276–1300
Halldorsson B, Papageorgiou AS (2012) Variations of the specific barrier model—part I: effect of subevent size distributions. Bull Earthq Eng. doi:10.1007/s10518-012-9344-0
Housner GW (1947) Characteristics of strong-motion earthquakes. Bull Seismol Soc Am 37(1): 19
Housner GW (1955) Properties of strong ground motion earthquakes. Bull Seismol Soc Am 45(3): 197–218
Joyner WB, Boore DM (1986) On simulating large earthquakes by Green’s function addition of smaller earthquakes. In: Das S (ed) Earthquake source mechanics. Maurice Ewing series. American Geophysical Union, Washington, pp 269–274
Keilis-Borok VI (1959) On the estimation of the displacement in an earthquake source and of source dimensions. Ann Geo 12: 205–214
Lin YK (1967) Probabilistic theory of structural dynamics. McGraw-Hill, New York
Lin YK, Cai G-Q (1995) Probabilistic structural dynamics: advanced theory and applications. McGraw-Hill Professional, New York
Mavroeidis GP, Papageorgiou AS (2003) A mathematical representation of near-fault ground motions. Bull Seismol Soc Am 93(3): 1099–1131
Middleton D (1960) An introduction to statistical communication theory 1987th edn. McGraw-Hill, New York
Papageorgiou AS (1988) On two characteristic frequencies of acceleration spectra: patch corner frequency and fmax. Bull Seismol Soc Am 78(2): 509–529
Papageorgiou AS (2003) The barrier model and strong ground motion. Pure App Geophy 160(3): 603–634
Papageorgiou AS, Aki K (1983a) A specific barrier model for the quantitative description of inhomogeneous faulting and the prediction of strong ground motion. I. Description of the model. Bull Seismol Soc Am 73(3): 693–722
Papageorgiou AS, Aki K (1983b) A specific barrier model for the quantitative description of inhomogeneous faulting and the prediction of strong ground motion. Part II. Applications of the model. Bull Seismol Soc Am 73(4): 953–978
Papageorgiou AS, Aki K (1985) Scaling law of far-field spectra based on observed parameters of the specific barrier model. Pure Appl Geophys 123(3): 353–374
Papoulis A (1965) Probability, random variables, and stochastic processes. McGraw-Hill, New York
Rice SO (1944) Mathematical analysis of random noise. Bell Syst Tech J 23: 282–332
Rice SO (1945) Mathematical analysis of random noise. Bell Syst Tech J 24: 46–156
Sato T, Hirasawa T (1973) Body wave spectra from propagating shear cracks. J Phys Earth 21: 415–431
Silver P (1983) Retrieval of source-extent parameters and the interpretation of corner frequency. Bull Seismol Soc Am 73(6A): 1499–1511
Spudich P, Frazer LN (1984) Use of ray theory to calculate high-frequency radiation from earthquake sources having spatially variable rupture velocity and stress drop. Bull Seismol Soc Am 74(6): 2061–2082
Trifunac MD, Brune JN (1970) Complexity of energy release during the Imperial Valley, California, earthquake of 1940. Bull Seismol Soc Am 60(1): 137–160
Vallée M, Bouchon M (2004) Imaging coseismic rupture in far field by slip patches. Geophys J Int 156(3): 615–630
Wennerberg L (1990) Stochastic summation of empirical Green’s functions. Bull Seismol Soc Am 80(6A): 1418–1432
Wyss M, Brune JN (1967) The Alaska earthquake of 28 March 1964: a complex multiple rupture. Bull Seismol Soc Am 57(5): 1017–1023
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Halldorsson, B., Papageorgiou, A.S. Variations of the specific barrier model—part II: effect of isochron distributions. Bull Earthquake Eng 10, 1321–1337 (2012). https://doi.org/10.1007/s10518-012-9345-z
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DOI: https://doi.org/10.1007/s10518-012-9345-z