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2nd International Symposium on Strong-motion Earthquake Effects
100 year Anniversary Symposium of the University of Iceland
ISSEE 2011
29 April 2011
University of Iceland – Askja – Auditorium 132
Reykjavik, Iceland – 9:00-17:00
www.eerc.hi.is/ISSEE2011
ISSEE 2011 Committees International Scientific Committee
Prof. Apostolos S. Papageorgiou, University of Patras, Patras, Greece (Chairman)
Prof. Atilla Ansal, Bogazici University, KOERI, Istanbul, Turkey
Dr. Hamish Avery, Canterbury Seismic Instruments, Christchurch, New Zealand
Prof. Bjarni Bessason, University of Iceland, Reykjavik, Iceland
Prof. Athol Carr, University of Canterbury, Christchurch, New Zealand
Dr. Andrew A. Chanerley, University of East London, London, United Kingdom
Dr. John Douglas, BRGM, Orleans, France
Prof. Amr S. Elnashai, University of Illinois, Illinois, USA
Prof. Russell Green, Department of Civil Engineering, Virginia Tech, Blacksburg, USA
Assoc. Prof. Radan Ivanov, VSU, Sofia, Bulgaria
Dr. Ioannis Kalogeras, National Observatory of Athens, Athens, Greece
Dr. Dmytro Malytskyy, Branch of Subbotin Institute of Geophysics, Lviv, Ukraine
Prof. Carlos S. Oliveira, Instituto Superior Técnico, Lisbon, Portugal
Prof. Svein N. Remseth, NTNU, Trondheim, Norway
Prof. Jonas T. Snæbjörnsson, University of Stavanger, Stavanger, Norway
Prof. Hirokazu Tatano, DPRI, Kyoto University, Kyoto, Japan
Prof. Colin A. Taylor, University of Bristol, Bristol, United Kingdom
Assist. Prof. Eythor Thorhallsson, Reykjavik University, Reykjavik, Iceland
Dr. Hjortur Thrainsson, Munich Reinsurance Company, Munich, Germany
Dr. Kristín Vogfjörð, Icelandic Meteorological Office, Reykjavik, Iceland
Local Scientific Committee Prof. Ragnar Sigbjörnsson, EERC Director, University of Iceland (Chairman)
Res. Prof. Símon Ólafsson, EERC, University of Iceland
Assist. Res. Prof. Benedikt Halldórsson, EERC, University of Iceland
Adj. Prof. Rajesh Rupakhety, EERC, University of Iceland
Res. Prof. Jónas Elíasson, EERC, University of Iceland
Local Organizing Committee Prof. Ragnar Sigbjörnsson, EERC Director, University of Iceland (Chairman)
Assist. Res. Prof. Benedikt Halldorsson
Elinborg Gunnarsdottir, Manager
29 April 2011 Askja - 132
ISSEE attendance is free and open for everyone. www.eerc.hi.is/ISSEE2011
INTERNATIONAL SYMPOSIUM ON STRONG-MOTION EARTHQUAKE EFFECTS 9:00-9:05 ISSEE-2011 Opening Remarks: Professor Ragnar Sigbjörnsson, EERC Director, University of Iceland
SESSION 1 – RECENT EARTHQUAKE DISASTERS Chair: Ragnar Sigbjörnsson
KEYNOTE The M7.0 and M6.3 New Zealand Earthquakes
9:05-9:55 Athol Carr, University of Canterbury, New Zealand Coffee break (10 min)
SESSION 2 – EARTHQUAKE STRONG MOTION Chair: Attilla Ansal 10:05-10:25 The Hellenic Strong Seismic Motion Network: Present and near future situation and perspectives
Ioannis Kalogeras, Christos Evangelidis, Stylianos Koutrakis and Nikolaos Melis
10:25-10:45 Attenuation of ground motion in shallow strike-slip earthquakes
Símon Ólafsson and Ragnar Sigbjörnsson
10:45-11:05 Baseline correction – an alternative to high-pass filtering
Sigurður U. Sigurðsson, Rajesh Rupakhety and Ragnar Sigbjörnsson
11:05-11:25 The ICEARRAY and the M6.3 Ölfus Earthquake of 29 May 2008
Benedikt Halldórsson and Ragnar Sigbjörnsson
11:25-11:45 On the incoherence of strong ground motion
Ragnar Sigbjörnsson, Benedikt Halldórsson, Rajesh Rupakhety, Jónas Thór Snaebjörnsson, Símon Ólafsson
Lunch (45 min)
SESSION 3 – RECENT EARTHQUAKE DISASTERS Chair: Athol Carr
KEYNOTE The M9.0 Japan Earthquake of 11 March 2011 12:30-13:20 Radan Ivanov, VSU, Bulgaria
Coffee break (10 min)
SESSION 4 – EARTHQUAKE STRONG MOTION Chair: Radan Ivanov
13:30-13:50 Site Response from Istanbul Vertical Arrays and Strong Motion Network
Atilla Ansal, Asli Kurtulus and Gokce Tonuk
13:50-14:10 Quantifying the Characteristic Period of Earthquake Ground Motions
Russell A. Green and J. Lee
14:10-14-30 Seismic Site Categories and Site Coefficients Suggested Based on Geotechnical Earthquake Characterization in Korea
Chang-Guk Sun
14:30-14:50 Modelling the difference in ground-motion magnitude-scaling in small and large earthquakes
John Douglas and Philippe Jousset
Coffee break (10 min)
SESSION 5 – EARTHQUAKE STRUCTURAL RESPONSE Chair: Russell Green 15:00-15:20 Near-fault ground motion: Characterization of amplitude, frequency content and earthquake response spectra
Rajesh Rupakhety, Sigurður U. Sigurðsson and Ragnar Sigbjörnsson
15:20-15:40 Assessment of Aftershock Effects on Peak Ductility Demand Using Ground Motion Records from Shallow Crustal Earthquakes
Katsuichiro Goda, Zhi-Ming Liu and Colin Taylor
15:40-16:00 Analysis Model and Influence of the Soil-Structure Interaction on the Seismic Response of Large Panel RC Buildings
Radan Ivanov
SESSION 6 – RECENT EARTHQUAKE DISASTERS Chair: Ioannis Kalogeras
KEYNOTE The M7.0 Haiti Earthquake of 12 January 2010 16:00-16:50 Russell A. Green, Virginia Tech, USA
16:50-17:00 ISSEE-2011 – Closing Remarks
ISSEE 2011 Contributions and Contacts Keynote Presentations ----------------------------------------------------------------- Contact: Prof. Athol Carr EMAIL: [email protected] Title: The Darfield and Christchurch Earthquakes in New Zealand Authors: Athol Carr ----------------------------------------------------------------- Contact: Dr. Radan Ivanov EMAIL: [email protected] Title: The M 9.0 Japan Earthquake of 11 March 2011 Authors: Radan Ivanov ----------------------------------------------------------------- Contact: Prof. Russell Green EMAIL: [email protected] Title: The M7.0 Haiti Earthquake of 12 January 2010 Authors: Russell Green, Scott Olson, Brady Cox and Ellen Rathje -----------------------------------------------------------------
Presentations ----------------------------------------------------------------- Contact: Dr. Radan Ivanov EMAIL: [email protected] Title: Analysis Model and Influence of the Soil-Structure Interaction on the Seismic
Response of Large Panel RC Buildings Authors: Radan Ivanov ----------------------------------------------------------------- Contact: Dr. Katsuichiro Goda EMAIL: [email protected] Title: Assessment of Aftershock Effects on Peak Ductility Demand Using Ground Motion
Records from Shallow Crustal Earthquakes Authors: Katsuichiro Goda, Zhi-Ming Liu and Colin Taylor ----------------------------------------------------------------- Contact: Dr. Símon Ólafsson EMAIL: [email protected] Title: Attenuation of ground motion in shallow strike-slip earthquakes Authors: Símon Ólafsson ----------------------------------------------------------------- Contact: Mr. Sigurður U. Sigurðsson EMAIL: [email protected] Title: Baseline correction – an alternative to high-pass filtering Authors: Sigurður Unnar Sigurðsson, Rajesh Rupakhety and Ragnar Sigbjörnsson ----------------------------------------------------------------- Contact: Dr. John Douglas EMAIL: [email protected] Title: Modelling the difference in ground-motion magnitude-scaling in small and large
earthquakes Authors: John Douglas and Philippe Jousset ----------------------------------------------------------------- Contact: Dr. Rajesh Rupakhety EMAIL: [email protected] Title: Near-fault ground motion: characterization of amplitude, frequency content, and
earthquake response spectra Authors: Rajesh Rupakhety, Sigurður U. Sigurðsson and Ragnar Sigbjörnsson -----------------------------------------------------------------
----------------------------------------------------------------- Contact: Prof. Ragnar Sigbjornsson EMAIL: [email protected] Title: On the incoherence of strong ground motion Authors: Ragnar Sigbjornsson, Benedikt Halldorsson, Rajesh Rupakhety, Jonas Th.
Snaebjornsson and Simon Olafsson ----------------------------------------------------------------- Contact: Prof. Russell Green EMAIL: [email protected] Title: Quantifying the Characteristic Period of Earthquake Ground Motions Authors: Russell Green ----------------------------------------------------------------- Contact: Dr. Chang-Guk Sun EMAIL: [email protected] Title: Seismic Site Categories and Site Coefficients Suggested Based on Geotechnical
Earthquake Characterization in Korea Authors: Chang-Guk Sun ----------------------------------------------------------------- Contact: Prof. Atilla Ansal EMAIL: [email protected] Title: Site Response from Istanbul Vertical Arrays and Strong Motion Network Authors: Atilla Ansal, Asli Kurtulus and Gokce Tonuk ----------------------------------------------------------------- Contact: Dr. Ioannis Kalogeras EMAIL: [email protected] Title: The Hellenic Strong Seismic Motion Network: Present and near future situation
and perspectives Authors: Ioannis Kalogeras, Christos Evangelidis, Stylianos Koutrakis and Nikolaos Melis ----------------------------------------------------------------- Contact: Dr. Benedikt Halldorsson EMAIL: [email protected] Title: The ICEARRAY and the M6.3 Ölfus Earthquake of 29 May 2008 Authors: Benedikt Halldorsson and Ragnar Sigbjörnsson -----------------------------------------------------------------
Other Contributions ----------------------------------------------------------------- Contact: Prof. Svein Remseth EMAIL: [email protected] Title: Earthquake design practice of traditional Norwegian buildings according to
Eurocode 8 Authors: Anders Rønnquist, Tommy Karlson and Svein Remseth ----------------------------------------------------------------- Contact: Dr. Dmytro Malytskyy EMAIL: [email protected] Title: Modeling of seismic waves in layered media and the inversion of source
parameters Authors: Dmytro Malytskyy -----------------------------------------------------------------
The Darfield and Christchurch Earthquakes in New Zealand
A. Carr*
1) Professor Emeritus of Civil Engineering, Department of Civil and Natural Resources Engineering, University
of Canterbury, Christchurch, New Zealand.
2) Visiting Professor, Earthquake Engineering Research Centre, University of Iceland, Iceland
The tectonic structure of New Zealand and the structure of the Canterbury plains under
Christchurch are presented and the seismic risk factors for the Canterbury region put in
perspective. An overview of historical earthquakes that have occurrred during the past 160
years is given and how these have affected the perception of the expected seismic events in
the Christchurch area.
The Magnitude 7.1 Darfield earthquake of the 4th September 2010 will be described. This
will cover the level of shaking, the fault movements, the damage to structures in the
Christchurch area and liquefaction damage in both Christchurch and the surrounding regions
of Kaiapoi and Halswell. The aftershock of the 26th December 2010 led to further significant
damage in the city, particularly to un-reinforced masonry structures.
The Magnitude 6.3 earthquake of the 22nd February 2011 is officially described as an
aftershock of the September earthquake but because the epicentre was so close to the surface
and so near to the centre of Christchurch the damage seen in the city was very severe. There
was very extensive damage to un-reinforced masorny structures, many of which had been
damaged in the earlier earthquake but also significant damge to reinforced concrete structures
built in more recent times. Liquefaction damage was again very evident but this time over a
much greater area of the city. Whereas after the September earthquake there were parts of the
city that would need to be rebuilt, after the February earthquake virtually the whole of the
Central Business District will need reconstruction. The majority of the heritage structures in
the city were also destroyed and only a very small fraction of these are likely to be rebuilt,
possibly with a very different structural system from that of the original structure.
There has also been significant damage to buildings built since the 1960s. The earlier
buildings did not have the advantage of the Capacity Design philosophy which did not come
into practice until the early 1980s. Four buildings have collapsed, resulting in a considerable
loss of life and many others, maybe up to 16 may be required to be demolished. Those
collapses have lead to investigations sponsored by the Department of Building and Housing
as to why the failures occurred and they will also be considered by a Royal Commission of
Inquiry. Though, when compared with many earthquakes in other countries, the estimated
182 deaths seems a small number, there are questions as to why they should have occurred at
all.
* e-mail: [email protected]
The M 9.0 Japan Earthquake of 11 March 2011
R. Ivanov* Higher School of Civil Engineering (VSU) “L. Karavelov”, 175 Suhodolska St, 1373 Sofia, Bulgaria
This earthquake which occurred on March 11, 2011, had a magnitude of 9.0, which places it as the fourth largest in the world since 1900, and the largest in Japan since modern instrumental recordings began 130 years ago. It will surely become a landmark earthquake, and one which will shape future research in seismology, earthquake engineering and all related fields, just as the 1995 Kobe earthquake did. Three things will surely be remembered about this earthquake - the gigantic ground shaking, the devastating tsunami, and the nuclear accident at the Fukushima NPP. The main shock recorded a magnitude of 9.0, with peak ground accelerations reaching almost 3000 gal at one station and exceeding 1000 gal in substantial areas [1]. The largest intensity of the Japanese scale (JMA) 7 was reached just north of the city of Sendai, and large areas along the coastline to the south of Sendai registered intensities of 6. The earthquake was a typical inter-plate one, caused by the rebound of the North American plate against the subducting Pacific plate, with a hypocenter located 130km ESE off the Sanriku coast, and a focal depth of 24km. The largest slip along the plate boundary was estimated at 23 m, and huge horizontal and vertical permanent displacement were recorded by the GPS network, with maxima of 530 cm and 120 cm respectively, at the area nearest to the hypocentre - Oshika peninsula. Two days before the main shock a M7.3 earthquake occurred, and the previous day a M6.8 earthquake occurred, which nobody expected to be foreshocks, as those were potent quakes themselves. A multitude of aftershocks, some of them M7 and M6 events were recorded during the first month after the quake. Most events including the main, occurred on a focal region of 200km (EW) by 500km (NS) [2]. Early analysis of pre- and post- earthquake imagery indicates that the damage to buildings due to ground shaking was relatively small, with most of the damage caused by the tsunami which swept the lowlands along the coastline. The highest tsunami was about 10 m, with extensive stretches of shoreline recording heights of more than 5 m. The permanent subsidence of the terrain further reduced the effectiveness of sea walls. Human loss is estimated at about 30000 dead or missing people. It is believed that most of the fatalities were caused by the tsunami. The most tragic event was arguably the accident at the Fukushima NPP, where the tsunami disabled the cooling system, resulting in an explosion, uncontrolled release of radioactive material, and ultimately nationwide and indeed worldwide distress. The accident is a clear example of disproportionate damage, and will surely lead to rethinking of the way NPPs are designed, maintained and managed, including the degree of involvement of the private sector in the nuclear power business. This earthquake was not unexpected, given the milenia old record of destructive earthquakes along the Japanese Pacific coast. Regardless of the damage it caused, it will likely not have long lasting adverse effect on the Japanese economy, provided the nuclear accident is contained.
References: [1] NIED, 2011 Off the Pacific Coast of Tohoku earthquake, Strong Ground Motion, (2011) http://www.k-net.bosai.go.jp/k-net/topics/TohokuTaiheiyo_20110311/nied_kyoshin2e.pdf [2] NIED, Preliminary report of the 2011 off the Pacific coast of Tohoku Earthquake,
http://www.bosai.go.jp/e/international/Preliminary_report110328.pdf, (2011) * e-mail: [email protected]
The M7.0 Haiti Earthquake of 12 January 2010
R. A. Green*, S. M. Olson
1, B. R. Cox
2, and E. Rathje
3
The 2010 M7.0 Haiti earthquake was one of the most devastating in history, resulting in
approximately 300,000 deaths and widespread damage to buildings and infrastructure.
Presented herein are the results of two post-earthquake reconnaissance missions, and
subsequent laboratory and data analyses, of areas affected by the earthquake. Particular focus
is given to: (1) performance of the Port-au-Prince seaport [1]; (2) liquefaction and lateral
spreading [2]; (3) the influence of geology, site shear wave velocities, and topography on
observed damage patterns [3]; and (4) a proposed seismic site classification microzonation of
the city of Port-au-Prince [4].
The earthquake caused catastrophic ground failures in calcareous-sand artificial fills at the
Port-au-Prince seaport, including liquefaction, lateral spreads, differential settlements, and
collapse of the pile-supported wharf and pier. Although the soil profiles at the port were
artificial calcareous sand fills, case histories for which are relatively lacking in liquefaction
databases, the overall response of the fills is consistent with predictions made using semi-
empirical relations developed primarily from field data of silica sands.
In addition to the seaport, the earthquake caused severe liquefaction and lateral spreading
along the Gulf of Gonave coast, along rivers draining into the Gulf to the north of Port-au-
Prince, and a liquefaction-induced structural/bearing capacity failure of a three-story concrete
hotel along the southern coast of Gulf of Gonave. The authors estimated median peak ground
accelerations (PGAs) of approximately 0.14g to 0.28g at these sites using the Next Generation
Attenuation (NGA) relations [5].
Damage to structures was widespread across the city of Port-au-Prince, but its intensity
varied considerably from neighborhood to neighborhood. The most heavily damaged areas in
downtown Port-au-Prince were underlain by Holocene alluvium with shear wave velocities
that average about 350 m/s over the top 30 m. The remainder of Port-au-Prince is underlain
mostly by older geologic units with higher shear wave velocities. Damage was also
concentrated on hillsides around Port-au-Prince. These pockets of damage appear to be caused
by a combination of factors including topographic amplification, soil amplification and failure
of weakly-cemented, steep hillsides.
The authors performed a seismic site classification microzonation for the city of Port-au-
Prince, based on 35 shear wave velocity (Vs) profiles that they collected throughout the city
and a new geologic map that they developed for the region. The Vs profiles were obtained
using the Multi-channel Analysis of Surface Waves (MASW) method, while the geologic
map was developed from a combination of field mapping and geomorphic interpretation of a
digital elevation model (DEM). Relationships between mean shear wave velocity over the
upper 30m of the subsurface (Vs,30m) and surficial geologic unit were developed, permitting
NEHRP/IBC seismic site classifications to be determined throughout the city. Much of the
city is founded on deposits that classify as either NEHRP Site Class C or D, based on Vs,30m.
However, some areas within mapped Holocene alluvial deposits and coastal artificial fills may
classify as Site Class E or F, depending on local subsurface conditions (e.g., presence of soft
clay or liquefiable soil).4
* Charles E. Via, Jr., Department of Civil and Environmental Engineering, 120B Patton Hall, Virginia Tech,
Blacksburg, VA 24061, USA. Email: [email protected] 1 University of Illinois at Urbana-Champaign, Dept. of Civil and Environmental Engineering, Urbana, IL, USA.
2 University of Arkansas, Department of Civil Engineering, Fayetteville, AR, USA.
3 University of Texas at Austin, Dept. of Civil, Architectural and Environmental Engineering, Austin, TX, USA.
4 References: [1] Green, R.A. et al., Earthquake Spectra, in press (2011); [2] Olson, S.M. et al., Earthquake
Spectra, in press (2011); [3] Rathje et al. et al., Earthquake Spectra, in press (2011); [4] Cox, B.R. et al.,
Earthquake Spectra, in press (2011); [5] Power, M. et al., Earthquake Spectra, 24, 1 (2008)
Analysis Model and Influence of the Soil-Structure Interaction on the Seismic Response of Large Panel RC Buildings
R. Ivanov*
Higher School of Civil Engineering (VSU) “L. Karavelov”, 175 Suhodolska St, 1373 Sofia, Bulgaria The era of precast RC buildings in Bulgaria ended in 1989. With most of these buildings designed before 1987, when the current values of the seismic coefficients were adopted, the knowledge of their true resistance to ground shaking is of great importance to their future use and maintenance. Further, since the design of most large panel (LP) buildings was done before the use of computers became commonplace, the calculation of seismic forces was done either by empirical formulae, by approximate methods for hand calculation, or by simple computer programs. The principle objective of this study is to establish an appropriate model for analysis, and to clarify the degree to which soil-structure interaction influences the dynamic response of LP buildings. The computation is done by the software SAP2000.
A building like the one in Fig. 1 (a), with floor plan (shear walls) shown in Fig. 1 (b) and material properties as described in [1] is investigated, in order to arrive at an appropriate analysis model. Two types of models are considered – one using only shell elements, and another one in which the shear walls are modelled by frame elements. Three variants of the frame model, differing in the way floor slabs interact with shear walls are compared. It is found that the model for which the nodes common to a shear wall and the slab at each floor level are constrained as a rigid body, Fig. 1 (c), behaves almost identically to the reference shell model, and is therefore chosen for further use.
5.76
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(a) typical building (b) typical floor plan (c) analysis model Fig. 1. Overview of the analysed building
A parametric study is carried out, in which the height of the building is varied between 5
and 8 stories, and the soil stiffness between 0.2x105 and 1.0x105 kN/m3, which are the practicable lower and upper bounds of the parameters. The stress in the shear walls is consistently higher when SSI was considered; however the difference is negligibly small for the most heavily loaded walls. The first and second translational modes are significantly altered due to the rocking induced by SSI, while the third torsional mode remained practically unchanged. The horizontal displacements can be as much as five times larger when SSI is considered. Most of the increase is due to the rigid body motion from rocking. References: [1] I. Mitev, Large panel buildings, Tehnika, (1985) * e-mail: [email protected]
Assessment of Aftershock Effects on Peak Ductility Demand Using Ground Motion Records from Shallow Crustal Earthquakes
K. Goda*, Z.M. Liu, and C.A. Taylor
Department of Civil Engineering, University of Bristol, University Walk, Bristol, United Kingdom.
A large mainshock triggers numerous aftershocks. The occurrence rate of aftershocks decays gradually over time, and the temporal features can be described by the modified Omori’s law [1,2]. From post-earthquake decision-making viewpoint (e.g. evacuation and building tagging), quantitative assessment of aftershock effects on buildings and infrastructure, which might have already sustained some damage due to a mainshock, is of critical importance. The current performance-based earthquake engineering methodology can be further extended by taking into account additional damage potential due to aftershocks in seismic vulnerability assessment.
Aiming at characterizing nonlinear damage potential due to aftershocks, several studies have been conducted by using real and artificial mainshock-aftershock sequences (see references cited in [3,4]). The artificial mainshock-aftershock sequences are often generated by repeating a scaled mainshock record multiple times as aftershocks [3]. The investigation by [4], using several real sequences, showed that frequency content of mainshocks and aftershocks is not significantly correlated and thus repetition of (scaled) mainshocks as aftershocks might result in biased assessment of the aftershock effects. Moreover, there is a noticeable discrepancy between [3] and [4] in the aftershock impact assessment for nonlinear damage potential; this may be caused by the use of a simplified approach for generating mainshcok-aftershock sequences (as in [3]) and by the scarcity of real mainshock-aftershock sequences (as in [4]).
This study is focused on the probabilistic assessment of aftershock effects on peak ductility demand of inelastic single-degree-of-freedom (SDOF) systems with known strength, whose hysteretic characteristics are represented by the Bouc-Wen model [5]. The use of inelastic SDOF systems facilitates extensive statistical analysis of the aftershock effects on peak ductility demand, and thus is of advantage to draw a generic conclusion. The objectives of this research are twofold: (i) to establish a benchmark by using real mainshock-aftershock sequences from the PEER-NGA database, and (ii) to devise a method for generating artificial mainshock-aftershock sequences based on the generalized Omori’s law [2]. For a simulated mainshock-aftershock sequence, records with similar key seismic parameters (i.e. magnitude, distance, and local soil condition) to the target scenario are selected from a large ground motion record pool. Using the constructed real and artificial mainshock-aftershock sequences, numerous nonlinear dynamic analyses are carried out to evaluate the impact of aftershocks in terms of peak ductility demand quantitatively. The analysis results indicate that the aftershock effects increase the peak ductility demand (as expeted) and lead to greater variability of the peak ductility demand. Finally, implication of the obtained results, in comparison with existing studies [3,4], is discussed.
References: [1] P.A. Reasenberg, & L.M. Jones, Science 243, 1173 (1989) [2] R. Shcherbakov, D.L. Turcotte, & J.B. Rundle, Pure & Applied Geophysics 162, 1051 (2005). [3] G.D. Hatzigeorgiou, & D.E. Beskos, Engineering Structures 31, 2744 (2009). [4] J. Ruiz-Garcia, & J.C. Negrete-Manriquez, Engineering Structures 33, 621, (2011). [5] K. Goda, H.P. Hong, & C.S. Lee, Journal of Earthquake Engineering 13, 600, (2009).
* e-mail: [email protected]
Attenuation of ground motion in shallow strike-slip earthquakes
S. Ólafsson* and R. Sigbjörnsson
Earthquake Engineering Research Centre, University of Iceland, Austurvegur 2a, 800 Selfoss, Iceland.
A theoretical ground motion model based on seismic source models has been applied to the
available ground motion recordings in Iceland. The source parameters have been estimated
from the acceleration records and different estimation methods are studied. The applied model
is used to study the characteristics of strong ground motion with the main objective
of improving models for seismic hazard studies. The applied ground motion model is useful
for describing the attenuation of ground motion parameters such as peak ground acceleration,
root mean squared acceleration and spectral acceleration. The model can also be used
for simulating realistic input records for computational structural models using a stochastic
approach. An advantage of the modelling approach used in this study is that the model
parameters have direct physical meaning.
Based on source parameters that are estimated from the available strong motion
acceleration records from Icelandic earthquakes, a ground motion prediction equation
(GMPE) is presented that is representative for Icelandic earthquakes in the magnitude range
M4 – M6.6. A study of M7 earthquakes from other regions is used for estimating probable
strong ground motion of earthquakes in Iceland with similar magnitudes.
A comparison of the results for the attenuation of the ground motion parameters obtained
from the Icelandic data is compared with results data and GMPEs from the NGA-project. The
models are applied to specific earthquakes from the NGA dataset from shallow strike-
slip earthquakes. Special consideration is given to near field acceleration as well as rate of
attenuation.
* e-mail: [email protected]
Baseline correction – an alternative to high-pass filtering
S. U. Sigurðsson*
Earthquake Engineering Research Centre, University of Iceland, Austurvegur 2a, 800 Selfoss, Iceland. , R. Rupakhety and R. Sigbjörnsson
Processing of strong-motion data recorded by accelerometers is essential to remove
artificial noise that infects the recorded earthquake signal. The effects of the noise are mostly limited to disturbances at long-periods and affect the velocity and displacement traces obtained by cumulatively integrating the recorded acceleration time-histories as well as their spectral counterparts.
Filtering is an effective and well established tool to remove noise at both ends of the
frequency band earthquake signals produce. The main subjectivity involved is the choice of the high-pass cut-off frequency which has a dominating effect on the integrated velocity and displacement traces and the usable range of periods for response spectra.
In this work, a baseline correction scheme is proposed as an alternative to high-pass filtering. This correction scheme is an extension of a method introduced by [1] for the near-fault zone but generalised to capture a realistic baseline for far-field records. The criteria adopted is the shape of the far-field source spectra at low frequencies introduced by [2]. The procedure described seams to be robust and non-sensitive for subjective choice of the parameters involved.
References: [1] R. Rupakhety, B. Halldorsson, and R. Sigbjörnsson, “Estimating coseismic deformations
from near source strong motion records: methods and case studies,” Bulletin of Earthquake Engineering, 2010, pp. 1–25.
[2] J.N. Brune, “Tectonic Stress and the Spectra of Seismic Shear Waves from Earthquakes,” Journal of Geophysical Research, vol. 75, pp. PP. 4997-5009.
* e-mail: [email protected]
Modelling the difference in ground-motion magnitude-scaling
in small and large earthquakes
J. Douglas* and P. Jousset
BRGM – RNSC, 3 avenue C. Guillemin, BP 36009, 45060 ORLEANS Cedex 2, France.
It is often case that ground-motion records for a given area of interest are available in relative
abundance for small (Mw<5) earthquakes but are practically non-existent for larger
earthquakes, which have the potential to cause damage to structures. This is a direct
consequence of the almost universally observed Gutenberg-Richter relation that a unit
increase in magnitude decreases the number of earthquakes observed by a factor of ten. The
productive use of data from small earthquakes for seismic hazard assessments relies on
knowledge of how earthquake ground motions scale with magnitude. The majority of ground-
motion prediction equations (GMPEs) are derived, usually by regression analysis, for the
prediction of shaking from earthquakes with Mw≥5 but there is often little consideration given
to how they extrapolate to small magnitudes, which are sometimes considered within the
hazard integral of probabilistic seismic hazard assessments (PSHAs) or for the testing of
GMPEs against observations, especially for regions of low-to-moderate seismicity. These
reasons for needing to extrapolate GMPEs pose a significant challenge because the use of
GMPEs beyond (or even close to the edges of) the magnitude range for which they were
derived can lead to significant under- or over-estimation of ground motions, even if the
functional form includes nonlinear magnitude-scaling terms.
Here we show that simple stochastic models comprised of a Brune source spectrum and a
constant stress (drop) parameter ∆σ coupled with a site attenuation modeled by κ leads to a
nonlinear magnitude scaling of peak ground acceleration (PGA) and response pseudo-spectral
acceleration (PSA) at 1s that matches the observed dependency over the whole range of
magnitudes from Mw 1 to 7. Higher magnitude dependency for models derived using only
data from small earthquakes compared to that found using data from large earthquakes is
physically-realistic. Assuming a linear magnitude dependence of the logarithm of PGA and
PSA is reasonable for Mw≥5, especially at high frequencies, but the magnitude-scaling of
PGA and PSA is nonlinear when a broader magnitude range is considered (a cubic function
fits quite well). This shows why extrapolation of GMPEs beyond their range of applicability
is likely to lead to under- or over-prediction unless constraints are applied to the magnitude
scaling. Simple stochastic models are a good basis for such constraints. Finally, we
demonstrate that variations in κ are much more important for small shocks than at large
magnitudes and could be a contributing factor to the often observed magnitude-dependency of
the standard deviations of GMPEs.
* e-mail: [email protected]
�ear-fault ground motions: characterization of amplitude, frequency
content, and earthquake response spectra
R. Rupakhety*, S. U. Sigurðsson and R. Sigbjörnsson
Earthquake Engineering Research Centre, University of Iceland, Austurvegur 2a, 800 Selfoss, Iceland.
This study focuses on the characteristics of near-fault ground motions in the forward-direction
and structural response associated with them. These ground motions are narrow-banded in
nature and are characterized by a predominant period at which structures excited by them are
severely affected. In this work, the frequency content of near-fault ground motions is
quantified by its predominant period which is defined as the undamped natural period of a
single-degree-of-freedom (SDOF) oscillator at which its 5% damped linear elastic pseudo-
spectral velocity (PSV) contains a clear and dominant peak. It is found that a linear
relationship exists between the predominant period and seismic moment. An empirical
equation describing this relationship is presented by using a large set of accelerograms. The
calibrated model is found to be consistent with self-similar scaling of ground-motion
parameters.
The amplitude or the intensity of ground-motion is characterized in this work by the peak
ground velocity (PGV). Attenuation equations are developed to estimate PGV as a function of
earthquake magnitude and source-to-site distance. The proposed attenuation model is
compared to published models from the literature, and found to be a better representation of
data available up to date. A potentially useful parameter, in the form of average isochrone
velocity ratio, is investigated considering its capacity in predicting the spatial variation of
PGV due to rupture directivity effects. It was found that accurate prediction of directivity
effects can not be accomplished by average isochrone velocity ratio alone.
In addition, a predictive equation for spectral shapes of PSV (i.e., PSV normalized by PGV) is
presented as a continuous function of the undamped natural period of SDOF oscillators. The
model is independent of PGV, and can be used in conjunction with any available PGV
attenuation relation applicable to near-fault ground motion exhibiting forward-directivity
effects. The proposed model incorporates the effects of earthquake size on response spectral
shapes in a simple and effective manner. Furthermore, viscous damping of the SDOF is
included in the model as a continuous parameter, eliminating the use of so-called damping
correction factors. Finally, simple equations relating force reduction factors and displacement
ductility of elasto-plastic SDOF systems are presented.
* e-mail: [email protected]
On the incoherence of strong ground motion
R. Sigbjörnsson*, B. Halldórsson, R. Rupakhety, J. Th. Snæbjörnsson and S. Ólafsson
Earthquake Engineering Research Centre, University of Iceland, Austurvegur 2a, 800 Selfoss, Iceland
Strong-motion recordings have revealed significant incoherence in earthquake ground
motions at different locations within the spatial dimensions of large horizontally expanded
structures. In the Eurocode 8, the effects of incoherent ground motions are addressed,
however, without the sufficient detailing needed for practical applications in engineering
design. The objective of this paper is to present a simplified model for design purposes that
takes the spatial variability into consideration.
Strong-motion effects measured at different locations within the dimensions of an
engineered structure are typically different, even for structures of moderate size. However, the
current engineering practice assumes routinely: (a) excitations at all support points are the
same; or (b) excitations are different by only a wave propagation time delay, i.e., excitations
at all locations are assumed to be fully coherent. The first approximation, (a), is valid for
structures with small horizontal dimensions at the structure-ground interface. The second
approximation, (b), is considered acceptable for horizontal structures with large dimensions.
However, these assumptions ignore the natural incoherence in the ground motion, which may
lead to incorrect or inaccurate results.
An improved model should include the main effects governing the spatial structure of
strong ground motion, i.e.: (a) wave passage effects, (b) incoherence effects, and (c) local site
effects. If local site effects are neglected, the spatial variability of the strong ground shaking
phase can be modelled as a locally homogeneous and stationary random field with a specified
cross-spectral density.
This study emphasises the horizontal incoherence of ground motion. Selected records
from shallow strike-slip earthquakes obtained at rock sites in events with moderate sized
magnitude, about 6.5, are used to facilitate the study. It is seen that the loss in coherence,
notably for far-fault records, increases on the average with increasing frequency and
increasing separation distance, which is in accordance with results reported in the literature.
The near-fault records reveal more complex behaviour. The presented model is found useful
in response calculations of horizontal structures.
____________________
* e-mail: [email protected]
Quantifying the Characteristic Period of Earthquake Ground Motions
R.A. Green* Charles E. Via, Jr., Departmen of Civil and Environmental Engineering, 120B Patton Hall, Virginia Tech,
Blacksburg, VA 24061, USA.
J. Lee Paul C. Rizzo Associates, Inc., 500 Penn Center Blvd., Suite 100, Pittsburgh, PA 15235, USA.
The objective of this study is to evaluate various definitions of "characteristic" period of earthquake ground motions. The Fourier decomposition of earthquake ground motions shows that they are comprised of a range of frequencies, each having an associated amplitude and phase. However, engineering analysis/design procedures sometime call for the frequency content of earthquake ground motions to be characterized by a single period [1]. Also, the quantification of the frequency content by a single characteristic period often facilitates the selection of ground motion time histories for various types of engineering analyses [2].
The authors found twenty eight different definitions of characteristic period in literature. Five of the more commonly used definitions were examined in this study. These include the mean period (Tm), the average spectral period (Tavg), the smoothed spectral period (To), the median spectral velocity-acceleration period (TV/A50), and the peak ground velocity-acceleration period (Tv/a). Recent ground motion predictive relationships that express these periods as functions of earthquake magnitude (M), site-to-source distance (R), site conditions, etc. are given in Rathje et al. [3] and Lee [4].
The five definitions of characteristic period were assessed by computing the amplification of earthquake ground motions propagated up through shallow soil profiles (e.g., backfill of retaining walls) and deeper soil profiles. For these analyses, eleven time histories (ten earthquake time histories and one windowed sine wave) and nineteen soil profiles were used, for a total of 209 site response analyses. These results were compared to the analytical solution of infinite duration, sinusoidal motions propagated up through the same soil profiles. For these latter set of computations, the periods of the sinusoidal motions were set equal to the various characteristic periods of the earthquake ground motions. A "validation metric" was then used to determine which characteristic period definition is most suitable for site response and retaining wall analyses. The validation metric is a single number ranging from 0 to 1, indicating that the characteristic period definition is very poor and very good, respectively. The validation metric equation used in this study is a modification of one proposed by Oberkampf and Trucano [5] for validating numerical models used in computational fluid dynamics, whereby numerical predictions are compared to experimental data, hence the name "validation metric".
The results showed that characterizing an earthquake ground motion by a single period, regardless of how quantified, is tenuous. However, of the definitions examined, To is the most suitable definition for motions used in the dynamic response of both soil profiles and retaining wall.
References: [1] Stewart, J.P. et al., Earthquake Spectra 19, 697 (2003) [2] Stewart et al., PEER-2001/09, Pacific Earthquake Engineering Research Center (2001) [3] Rathje et al., Earthquake Spectra 20, 119 (2004) [4] Lee, J., Ph.D. Dissertation, CEE, University of Michigan, Ann Arbor, MI, USA, (2009) [5] Oberkampf and Trucano, Progress in Aerospace Sciences 38, 209 (2002) * e-mail: [email protected]
The Hellenic Strong Seismic Motion Network: Present and near future situation and perspectives
I. Kalogeras*, C. Evangelidis, S. Koutrakis and N. MelisInstitute of Geodynamics, National Observatory of Athens, P.O.Box 20048, 11810 Athens, Hellas.
Since 2009 the Hellenic Strong Seismic Motion Network is being under a major upgrade not only in the number of new stations but also in the quality of the instrumentation and the records and the abilities derived from them. The two partners of the network, namely National Observatory of Athens - Institute of Geodynamics (NOAIG) and ITSAK, are in cooperation after the support of the Hellenic State (EPPO) aiming to increase the number of the installed instruments up to a number of 300 (and more), resulting to a dense network covering the entire territory of the country. The strong motion records will be available for any potential user and for any purpose (education, seismological and engineering studies, State and public informing etc).While the new installations are in progress after purchasing the majority of the instruments, both Institutions take already advantage of the enhanced abilities of the instruments. Since NOAIG runs also a seismological network (being the coordinator of the Hellenic Unified Seismological Network), its efforts are concentrated to incorporate the strong motion instruments to a 24/7 routine analysis, not only for the earthquake source estimation, but also for the strong seismic motion values calculation, concluding in such a way to a final set of information for response and relief purposes in case of a strong earthquake (shake map).
Fig. 1. The recent Tohoku, Japan Mw9.0 earthquake as recorded in the transverse component by an STS-2 seismometer (top) and a CMG-5TD accelerograph (bottom) installed at the same station, after the deconvolution
of both records to velocity . The two records seem to be identical.
Strong motion stations that are located in geographic areas where the broadband seismic network coverage is sparse, will improve considerably the earthquake detection threshold and location accuracy. Stations with high signal to noise ratio will also be used in the SeisComp3 automatic processing suite, since strong motion waveforms have clear recordings of weak local and strong teleseismic events (Fig. 1). Additionally, daily ambient noise monitoring of all stations, is performed not only for network performance purposes but also for monitoring building's response to strong motions.__________________* e-mail: [email protected]
Seismic Site Categories and Site Coefficients Suggested Based on Geotechnical Earthquake Characterization in Korea
C.-G. Sun*
Earthquake Research Center, Korea Institute of Geoscience and Mineral Resources, 92 Gwahang-ro, Yuseong-gu, Daejeon 305-350, Korea
The site categorization and corresponding site coefficients in the current Korean seismic design guideline are based on provisions for the western United States (US), although the site effects resulting in the amplification of earthquake ground motions are directly dependent on the regional and local site characteristic conditions [1]. In these seismic codes, two amplification factors called site coefficients, Fa and Fv, for the short-period band and mid-period band, respectively, are listed according to a criterion, mean shear wave velocity (VS) to a depth of 30 m, into five classes composed of A to E [2].
To suggest a site classification system reflecting Korean site conditions, in this study, systematic site characterization was carried out at four regional areas, Gyeongju, Hongsung, Haemi and Sacheon, to obtain the VS profiles from surface to bedrock in field and the non-linear soil properties in laboratory. The soil deposits in Korea, which were shallower and stiffer than those in the western US [1], were examined, and thus the site period in Korea was distributed in the low and narrow band comparing with those in western US. Based on the geotechnical characteristic properties obtained in the field and laboratory, various site-specific seismic response analyses were conducted for total 75 sites by adopting both equivalent-linear and non-linear methods.
The analysis results, as depicted in Fig. 1, showed that the site coefficients specified in the current Korean provision underestimate the ground motion in the short-period range and overestimate in the mid-period range. These differences can be explained by the differences in the local site characteristics including the depth to bedrock between Korea and western US. Based on the analysis results in this study and the prior research results for the Korean peninsula, new site classification system was developed by introducing the site period as representative criterion and the mean VS to a depth of shallower than 30 m as additional criterion, to reliably determine the ground motions and the corresponding design spectra taking into account the regional site characteristics in Korea.
0.0
1.0
2.0
3.0
4.0
0.0 0.5 1.0 1.5 2.0
Ra
tio
of
Re
sp
on
se
Sp
ec
tra
, R
RS
Period (s)
Average (CLE)
Avergae + Standard Dev. (CLE)
Average -Standard Dev. (CLE)
Fa on code (CLE; 0.14g)
Fv on code (CLE; 0.14g)
Average (OLE)
Site Class C
0.0
1.0
2.0
3.0
4.0
0.0 0.5 1.0 1.5 2.0
Ra
tio
of
Re
sp
on
se
Sp
ec
tra
, R
RS
Period (s)
Average (CLE)
Average + Standard Dev. (CLE)
Average -Standard Dev. (CLE)
Fa on code (CLE; 0.14g)
Fv on code (CLE; 0.14g)
Average (OLE)
Site Class D
Fig. 1. Ratio of response spectra from site response analyses and site coefficients in the current codes.
References: [1] C.-G. Sun, et al., Engineering Geology 81, 446 (2005) [2] R. Dobry, et al., Earthquake Spectra 16, 41 (2000)
* e-mail: [email protected]
Site Response from Istanbul Vertical Arrays and Strong Motion Network
A. Ansal*, A. Kurtuluş, and G. Tönük
Boğaziçi University, Kandilli Observatory and Earthquake Research Institute
An extensive site investigation study was carried out on the European side of Istanbul as
part of a large-scale microzonation project financed by Istanbul Metropolitan
Municipality. 2912 borings (mostly down to 30m depth with approximately 250m spacing)
were conducted within an area of about 182 km2 to investigate local soil conditions. Standard
Penetration Test (SPT), Cone Penetration Test (CPT), PS-Logging, Refraction Microtremor
(ReMi), seismic reflection, refraction and resistivity measurements were carried out at each
borehole location. Samples collected in the field were tested in the laboratory to determine
index and engineering properties of local soil within the investigated area.
Out of 100 Istanbul Rapid Response Network strong motion stations 55 stations and
Ataköy, Zeytinburnu and Fatih vertical arrays which are composed of downhole triaxial
accelerometers located at the various depths and on the ground surface are located within the
area where detailed microzonation study was conducted.
There have been few small earthquakes in the recent years with local magnitude slightly
over M=4. Vertical array stations at 4 levels and some of the 55 Istanbul Rapid Response
Network stations recorded these earthquakes. The acceleration time histories recorded by the
Rapid Response stations as well by the vertical array stations were used to model the recorded
motion characteristics in terms of peak ground accelerations and acceleration response
spectra using the recorded acceleration time histories on the engineering bedrock. The
recorded acceleration time histories are also modelled based on empirical site amplification
relationships proposed by Borcherdt based on average hsear wave velocity Vs30 and based on
a modified version of Shake91. The results indicate the suitability of the site response
analyses in modelling the observed variation with respect to peak ground acceleration.
An attempt is also made to model the recorded acceleration time histories during the
Mw=7.4, 1999 Kocaeli Earthquake recorded at Ataköy, Fatih and Zeytinburnu strong motion
stations located in the same area. Preliminary modelling at vertical array stations were rather
successful indicating the suitability of the vertical arrays in fine tuning the measured shear
wave velocity profiles for modelling and prediction at higher ground shaking levels.
* e-mail: [email protected]
The ICEARRAY and the M6.3 Ölfus Earthquake of 29 May 2008
B. Halldórsson* and R. Sigbjörnsson
Earthquake Engineering Research Centre, University of Iceland, Austurvegur 2a, 800 Selfoss, Iceland.
The Mw6.3 Ölfus earthquake of 29 May 2008 in Iceland occurred in the District of Ölfus in
the western part of the South Iceland Seismic Zone. The town of Hveragerdi, being in the
extreme near-fault region of the earthquake, suffered the heaviest damage [1].
The earthquake rupture took place on two parallel and vertical right-lateral strike slip
faults, separated by ~4 km, with the second fault rupturing shortly after the first. The
earthquake strong-motion was recorded on 11 stations of the ICEARRAY, the first small-
aperture strong-motion array in Iceland [2]. The array has an aperture of ~1.9 km, minimum
interstation distance of ~50 m and consists of CUSP-3Clp three-component accelerographs of
Canterbury Seismic Instruments [3,7].
The ICEARRAY data, recorded in the extreme near-fault region of one of the causative
faults (rJB~1-2 km), exhibit high-intensity ground motion of short duration (4-5 s), large
horizontal peak ground accelerations (38-88%g) and large amplitude, long-period velocity
components, characteristics of near-fault motions, both on the strike-normal and strike-
parallel components. The linear response spectra indicate that the long-period energy of the
velocity pulse seen along the strike-normal direction is not present in the strike-parallel
direction. Furthermore, the period of the pulse is shorter along the strike-parallel and it is
more narrow-banded in the elastic response spectrum than the pulse seen on the strike-normal
component. Additionally, along the strike-normal direction, the Eurocode 8 “Type 2” design
spectrum combined with a design spectrum for near-fault pulses appears to capture well the
overall spectral composition of the ICEARRAY response spectra [2].
The acceleration time histories have been baseline corrected using a novel and robust
method and integrated to velocity and displacement [4]. The correctio`ns confirm that both
the strike-normal and strike-parallel components are associated with considerable permanent
tectonic displacement. The results of tectonic translation using this method agree with
geodetic measurements near Hveragerdi, but the displacement estimates show some
variability across the array [5]. The salient features of the near-fault ground displacement can
be captured through kinematic modeling when adopting static slip distributions for the
causative faults, and assuming uniform rise times and spreading rupture fronts. The results
indicate that rupture on the second fault initiated ~2 s after the initial rupture on the first fault
[6].
Current analysis efforts include e.g. full scale source inversion, applying array processing
methods on and quantification of local site effects evident in the main-shock and aftershocks
recordings, spatial coherence, and differential motions across the array during the main-shock.
References:
[1] Sigbjörnsson, R., et al. (2009), Bull. Eq. Eng., 7(1), 113-126.
[2] Halldórsson, B., and R. Sigbjörnsson (2009), Soil Dyn. Eq. Eng., 29(6), 1073-1083.
[3] Halldórsson, B., et al (2009), Journal of Seismology, 13(1), 173–178.
[4] Rupakhety, R., et al. (2010), Bull. Eq. Eng., 8(4), 787-811.
[5] Halldórsson, B., et al. (2010), 9USN/10CCEE Proceedings, Paper no. 1157.
[6] Halldórsson, B., et al. (2010), 14ECEE Proceedings, Paper no. 1640.
[7] Halldórsson, B. and H. Avery (2009). Seism. Res. Lett., 80(4), 572-578.
* e-mail: [email protected]
Earthquake design practice of traditional Norwegian buildings
according to Eurocode 8
A. Rønnquist Norwegian University of Science and Technology, Trondheim, Norway
T. Karlson Norconsult AS, Norway
S. Remseth*
Norwegian University of Science and Technology, Trondheim, Norway
Earthquake design was introduced in Norway when the new design requirement was launched
in the beginning of this millennium. The new design code also requiring a control of
earthquake load effects came with the new and updated design code series, NS 3491-12
Design of structures – Design actions – Part 12: Seismic actions, 1st issue December 2004.
These new codes were meant to be a transition of the national codes to the new European
codes later implemented in Norway in 2010. Today is seismic actions in Norway completely
covered by the Eurocode 8 available with the relevant national box values.
Common practice in Norway seems to be dominated mainly by the elastic design approach
where available ductile design potential is little explored or utilized, e.g. increase confinement
of concrete elements or necking flanges to control plastic deformation in steel members.
Earlier Norwegian designs were based on dominating horizontal forces originating from wind
induced loads. This design requirement has over a long time also shaped the common practice
in design of traditional Norwegian building systems and foundation solutions. Applying the
recommended response spectrum analysis give in EC 8 may render horizontal design forces
largely above those corresponding to wind loading. This may become a challenge for new
buildings and even more so for retrofit of existing buildings, e.g. to extend a building with
additional floors.
The consequences for three representative Norwegian buildings where the new
requirements of EC 8 renders large design forces, initially established by response spectrum
analysis, are evaluated. The cases represent common office type buildings with different
foundation solution. The initial design forces are also compared with time series analysis in
accordance with EC 8, using a minimum of three time series, designing for the most
unfavorable. It is intentionally chosen to use time series with different characteristics to
highlight the importance of having ground acceleration series that represent the Norwegian
hazard levels. These are mainly influenced by the long distances to major faults but with low
distance damping due to the characteristics of the regional bedrock.
* E-mail: [email protected]
Modeling of seismic waves in layered media and the inversion of source parameters Dmytro Malytskyy
CB IGPH, Lviv, Ukraine e-mail: [email protected]
This paper is organized as follows. After a discussion of the differential equations for wave
propagation in the horizontally stratified medium and of the initial and boundary conditions, we derive the displacements on the free surface of the layered medium for plane waves when a point source is located on the s−th imaginary boundary at the depth sz (physical parameters of the layers s and (s+1) are put to be identical). Then, the source will be represented as a single force of arbitrary orientation and a general moment tensor point source. Further, “a primary field” for a point source will be introduced. Method for the solution of the direct seismic problem is considered based on the matrix method of Thomson-Haskell. The tensor represents a superposition of three single couples without moment along the x, y, z-axes and three double couples in xy, xz, yz-planes. Further, we give the results for the field of displacements on the free surface. The far-field displacements are:
[ ]dkgMLIkuu
iiiir
z 13
1 0
2)0(
)0(−
=
∞
∑∫=
, [ ]dkgMLJku iii
iϕϕ
16
5 0
2)0( −
=
∞
∑∫= (1)
=
0
11 0
0J
JI ,
=
1
02 0
0J
JI , 23 II = .
=
ir
iz
gg
ig , 05 JJ = , 16 JJ = .
The near- field displacements are:
( ) ( ) +
+⋅
−
⋅⋅⋅=
−∞
∫ dkggM
MLkrJk
ruu
51rr
ϕϕ
215
111
0)0(
)0(
( ) ( ) ( )
+⋅
−⋅⋅
−+ ∫
∞− dk gg
MM
LrkrJkrkJ 63r
0 6
4110 22
ϕ (2)
( ) [ ]dk gMLkrkJr
u 3zz ∫∞
− ⋅⋅⋅⋅=0
41
1)0( 1 ,
where ϕϕ sincos1 yzxz MMM += ,
zzMM =2 ,
xyyyxx MMMM ⋅+⋅+⋅= ϕϕϕ 2sinsincos 223 ,
xyyyxx MMMM ⋅−⋅+⋅−= ϕϕϕ 2sin22cos2cos4 , (3) ϕϕ sincos5 xzyz MMM −= ,
xyyyxx MMMM ⋅−⋅−⋅= ϕϕϕ 2cos22sin2sin6 The results of this direct problem (1-3) we use in the inversion of source parameters. The inverse
method relies on inverting for components of the moment tensor and a determination of an earthquake source-time function.
