ΑΝΩΤΑΤΗ ΣΧΟΛΗ ΠΑΙ ΑΓΩΓΙΚΗΣ ΚΑΙ ΤΕΧΝΟΛΟΓΙΚΗΣ ΕΚΠΑΙ ΕΥΣΗΣ (Α.Σ.ΠΑΙ.Τ.Ε.) Υποέργο: 5 Τίτλος: «Αρχιμήδης ΙΙΙ Ενίσχυση Ερευνητικών ομάδων στην Α.Σ.ΠΑΙ.Τ.Ε.» «ΣΥΓΚΡΙΤΙΚΗ ΑΞΙΟΛΟΓΗΣΗ ΑΠΟΤΕΛΕΣΜΑΤΩΝ ΕΠΙΦΑΝΕΙΑΚΩΝ ΜΕΘΟ ΩΝ ΕΠΙ ΤΟΠΟΥ ΠΡΟΣ ΙΟΡΙΣΜΟΥ ΥΝΑΜΙΚΩΝ Ι ΙΟΤΗΤΩΝ Ε ΑΦΙΚΩΝ ΣΧΗΜΑΤΙΣΜΩΝ ΣΕ ΘΕΣΕΙΣ ΚΑΤΑΓΡΑΦΗΣ ΣΕΙΣΜΙΚΩΝ ΓΕΓΟΝΟΤΩΝ ΚΑΙ ΑΞΙΟΠΟΙΗΣΗ ΑΥΤΩΝ ΣΤΟΝ ΠΡΟΣ ΙΟΡΙΣΜΟ ΣΧΕΣΕΩΝ ΕΞΑΣΘΕΝΙΣΗΣ» Επιστημονικός Υπεύθυνος: Π. Κ. ΠΕΛΕΚΗΣ ΠΑΡΑΔΟΤΕΟ ΕΠΙΣΤΗΜΟΝΙΚΗ ΕΡΓΑΣΙΑ ΣΕ ΔΙΕΘΝΕΣ ΕΠΙΣΤΗΜΟΝΙΚΟ ΣΥΝΕΔΡΙΟ «Symposium on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP)» Τίτλος Παραδοτέου: «Π5» Τίτλος επιστημονικής εργασίας : «A COMPARATIVE STUDY OF SURFACE WAVES INVERSION TECHNIQUES AT STRONG MOTION RECORDING SITES IN GREECE» στο Πλαίσιο της Δράσης: 2, 3, 4. Συντάκτες:. Panagiotis C. Pelekis, ASPETE, Civil Engineering Dept., N. Heraklion, Greece 2. Alexandros Savvaidis, Institute of Engineering Seismology and Earthquake Engineering, Greece 3. Robert Kayen, USGS & UCLA, Dep. of Civil & Environmental Engineering (χωρίς αμοιβή) 4. Vasileios S. Vlachakis, University of Patras, Civil Engineering Dept., Greece 5. George A. Athanasopoulos, University of Patras, Civil Engineering Dept., Greece
Πίνακας περιεχομένων Σύντομη παρουσίαση της επιστημονικής εργασίας που παρουσιάστηκε στο συνέδριο... 2 Απόσπασμα προγράμματος συνεδρίου... 3 Η επιστημονική εργασία όπως δημοσιεύτηκε στα πρακτικά του συνεδρίου... 4 Διαφάνειες παρουσίασης...
Σύντομη παρουσίαση της επιστημονικής εργασίας που παρουσιάστηκε στο συνέδριο Η παρούσα εργασία παρουσιάσθηκε στο Symposium on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP) in Austin, Texas March 22-26, 5. Τίτλος εργασίας: A COMPARATIVE STUDY OF SURFACE WAVES INVERSION TECHNIQUES AT STRONG MOTION RECORDING SITES IN GREECE ΠΕΡΙΛΗΨΗ Χρησιμοποιήθηκε η μέθοδος των επιφανειακών κυμάτων για τον προσδιορισμό του προφίλ Vs-βάθος στη θέση σταθμών καταγραφής ισχυρής κίνησης του εθνικού δικτύου επιταχυνσιογράφων. Η πειραματική καμπύλη διασποράς προσδιορίστηκε κάνοντας χρήση της μεθόδου επιφανειακών κυμάτων και συγκεκριμένα της μεθόδου SASW, χρησιμοποιώντας ζεύγος ηλεκτρομηχανικών δονητών ή πίπτων βάρος 25kg. Στα πλαίσια της παρούσας εργασίας, χρησιμοποιήθηκαν τρεις μέθοδοι αντιστροφής της καμπύλης διασποράς: α) μία πρόσφατα προταθείσα απλοποιημένη μέθοδος αντιστροφής - SIM, β) μία τεχνική αντιστροφής βασισμένη στον αλγόριθμο "neighbour algorithm (ΝΑ)", η οποία προυποθέτει την χρήση αρχικών τιμών για τις παραμέτρους του υπεδάφους, και γ) τον αλγόριθμο αντιστροφής "Occam". Για τον προσδιορισμό του προφίλ Vs-βάθος σε όλες τις εξεταζόμενες περιπτώσεις, χρησιμοποιήθηκε σταθερή τιμή του λόγου του Poisson (θεωρήθηκε ν =,4), δεδομένου ότι ο στόχος της παρούσας μελέτης είναι η σύγκριση των τριών μεθόδων αντιστροφής, ανεξάρτητα από άλλες αβεβαιότητες που προκύπτουν λόγω έλλειψης γεωτεχνικών δεδομένων για τις εδαφικές στρώσεις. Για τη σύγκριση των προφίλ Vs-βάθος που προέκυψαν με κάθε μέθοδο αντιστροφής και την ποσοτικοποίηση των αποκλίσεων, χρησιμοποιήθηκε μια συνάρτηση ποινής (penalty function). Τα προφίλ Vs-βάθος, συγκρίνονται ως προς τις απόλυτες τιμές ταχυτήτων συναρτήσει του βάθους, την προκύπτουσα τιμή Vs,3 και την προκύπτουσα κατηγορία εδάφους σύμφωνα με τον Ευρωκώδικα 8, ώστε να φανεί η ασημαντότητα των διαφοροποιήσεων που προκύπτουν. Τα αποτελέσματα της σύγκρισης έδειξαν ότι η μέση διαφοροποίηση του προφίλ ταχύτητας που προέκυψε από τη μέθοδο SIM είναι 9% και 4,9% σε σύγκριση με τα προφίλ που προέκυψαν από τη μέθοδο ΝΑ και τη μέθοδο που χρησιμοποιεί τον αλγόριθμο του Occam, αντίστοιχα, ενώ η μέση διαφορά των τιμών Vs,3 που προέκυψαν από τη μέθοδο αντιστροφής SIM είναι 7,4% και 5,% σε σύγκριση με τις τιμές που προέκυψαν από τις μεθόδους ΝΑ και Occam. 2
Απόσπασμα προγράμματος συνεδρίου 3
Η επιστημονική εργασία όπως δημοσιεύτηκε στα πρακτικά του συνεδρίου A COMPARATIVE STUDY OF SURFACE WAVES INVERSION TECHNIQUES AT STRONG MOTION RECORDING SITES IN GREECE Panagiotis C. Pelekis, ASPETE, Civil Engineering Dept., N. Heraklion, Greece Alexandros Savvaidis, Institute of Engineering Seismology and Earthquake Engineering, Greece Robert Kayen, USGS & UCLA, Dep. of Civil & Environmental Engineering Vasileios S. Vlachakis, University of Patras, Civil Engineering Dept., Greece George A. Athanasopoulos, University of Patras, Civil Engineering Dept., Greece Abstract Surface wave method was used for the estimation of Vs vs depth profile at strong motion stations in Greece. The dispersion data were obtained by SASW method, utilizing a pair of electromechanical harmonic-wave source (shakers) or a random source (drop weight). In this study, three inversion techniques were used a) a recently proposed Simplified Inversion Method (SIM), b) an inversion technique based on a neighborhood algorithm (NA) which allows the incorporation of a priori information regarding the subsurface structure parameters, and c) Occam's inversion algorithm. For each site constant value of Poisson s ratio was assumed (ν=.4) since the objective of the current study is the comparison of the three inversion schemes regardless the uncertainties resulting due to the lack of geotechnical data. A penalty function was introduced to quantify the deviations of the derived Vs profiles. The Vs models are compared as of Vs(z), Vs3 and EC8 soil category, in order to show the insignificance of the existing variations. The comparison results showed that the average variation of SIM profiles is 9% and 4.9% comparing with NA and Occam's profiles respectively whilst the average difference of Vs3 values obtained from SIM is 7.4% and 5.% compared with NA and Occam's. Introduction The inversion of a dispersion curve i.e. the estimation of the Vs vs. depth profile is probably the most critical step since the problem cannot be solved directly (i.e. in terms of a unique solution) and requires an optimization technique to find the most probable solution(s) among an infinite number of candidates. The aim of this study is the further confirmation of the SIM against other advanced inversion techniques. Simplified Inversion Method (SIM) SIM is an inversion technique recently proposed by Pelekis and Athanasopoulos (, 2). The SIM method is a direct straightforward scheme which takes into consideration the slope of dispersion curve. The SIM method can handle both normally and inversely dispersive soil profiles without using the concept of the elastic Half Space. The 4
critical parameter of the SIM is the wavelength to depth converter which is highly affected by the shape of the dispersion curve and the Poisson's ratio, (Pelekis and Athanasopoulos, 2). Occam's Algorithm The algorithm solves the nonlinear inverse problem of estimating the shear wave velocity profile given a surface wave dispersion curve (i.e., phase velocity vs. frequency) and associated uncertainties, which are assumed to represent the fundamental mode of propagation (Constable et al., 987). The algorithm for an experimental dispersion curve finds the smoothest shear wave velocity profile subject to the constraint of a specified misfit between experimental and theoretical data. Convergence is defined as achieving a root-meansquare (rms) error of. or less (i.e., the specified misfit) (Lai and Rix, 998). The forward algorithm used to calculate theoretical dispersion curves and partial derivatives of the phase velocity with respect to the shear wave velocity of each layer is based on Hisada, 994. Neighborhood Algorithm Inversion Method (NA) The inversion of the surface waves dispersion curve is based on the Neighborhood Aalgorithm (NA) which allows the incorporation of a priori information about the subsurface structure parameters (Wathelet, et al., 4; Wathelet, 5). The neighborhood algorithm is a stochastic direct search method for finding models of acceptable data fit inside a multidimensional parameter space. The inverted structure parameters (parameter space) are the P and S wave velocities, Poisson ratio, density and thickness of each layer. The algorithm generates theoretical ground models with a random seed from the parameter space and the dispersion curves are computed (forward problem) for all these models. Furthermore, due to data uncertainties and the non-linearity of the problem itself, the solution of the dispersion curve inversion is generally non-unique. Comparison of the computational results with the experimental dispersion curve provides misfit values that quantify the quality of the modelgenerated curves (Wathelet, et al., 4). 5
Comparison of Surface Waves Inversion Techniques Ten dispersion curves of surface wave data were obtained using SASW method at strong motion recording station of National Hellenic Network, Figure. The dispersion curves are presented at Figure 2, and as it can be seen, at least 4 curves having a portion characterized as inversely dispersive. The Vs profiles obtained from each inversion method are presented in Figure 3. A penalty function (Weighted Average Deviation, wad, Pelekis and Athanasopoulos, ), was introduced for the comparison of the computed profiles, in the entire depth. Table summarizes the comparison results in terms of wad, Vs3 and Ground Type according to EC-8. It can be seen that the SIM profiles variation ranges between 3.75%- 4.5% and.75%-.3% comparing with the NA and Occam's profiles respectively. Site Accelegraphic Station Figure : Locations and coordinates of strong motion recording stations. Lat ( ) Lon ALM 39.872 22.7673 2 DMKB 37.99896 23.883 3 KYT 36.29859 22.964295 4 KYP2 37.24949 2.66754 5 SFIR 36.42623 25.428652 6 VA 38.232539 2.793 7 VLSA 38.76866.588644 8 VAR2 37.863995 2.769 9 UP4 38.2778 2.7855 PYR 37.6736 2.44582 ( ) 6
Phase Velocity, Vr (m/sec) Wavelenght, Lr (m) 6 3 5 6 7 8 9 6 8 6 8 6 8 6 8 6 8 6 8 6 2 3 4 5 3 3 3 5 6 7 8 5 25 6 8 5 6 7 8 9 6 7 8 9 5 3 3 3 5 6 7 8 9 3 3 5 6 5 6 7 3 5 6 7 8 9 5 6 6 3 Figure 2: The dispersion curves used in the present study. 8 7 Shear Wave Velocity, Vs (m/sec) 6 8 SIM NA OCCAM 3 8 6 SIM NA 5 OCCAM 5 8 6 SIM NA OCCAM 5 8 6 5 4 6 8 SIM 5 NA OCCAM 5 3 25 Depth, m 5 6 7 8 6 8 SIM NA OCCAM 25 3 35 2 5 5 25 SIM NA OCCAM 5 6 3 6 8 25 3 35 5 SIM NA OCCAM 3 5 6 SIM NA OCCAM 3 35 45 5 5 5 6 8 SIM NA OCCAM 5 5 5 6 3 25 25 3 3 8 35 35 6 5 7 5 6 SIM NA OCCAM Figure 3: The Vs profiles obtained from the three inversion techniques. 45 5 9 45 5 7
Table : Summary of comparison results between the three inversion techniques. Wad (%) Vs,3 (m/sec) Site NA Occam's difference, difference, vs. vs. SIM NA Occam's % % SIM SIM GROUND TYPE (EC-8) 8.7.75 4 456 2.9 395 2.2 B 2 7.59 4.76 796 735 7.7 785.4 B 3 6.92.65 66 599 9.2 633 4. B 4 4.5.27 627 653 4. 677 8. B 5 5.2 2.84 47 427 9. 444 5.5 B 6.4 2.43 32 284 6. 296 2. C 7 3.4 7.38 929 874 5.9 84 2.4 A 8 3.75 5.73 25 252.8 23 7.6 C 9 2. 8.58 7 92 7.2 7. C 7.95 3.92 466 45.9 434 6.9 C Mean 9. 4.9 7.4 5. Conclusions Ten dispersion curves of surface wave data were inverted using a) Simplified Inversion Method (SIM) b) neighborhood algorithm method (NA) and c) Occam's algorithm. In all cases, including both normally and inversely dispersive soil profiles, the results obtained by using the SIM, were found to be in remarkable agreement with the results of the two other advanced methods of inversion (average deviation for the entire soil profiles less than %) having no significant influence on estimation of Vs3, and Ground Type based on EC-8 for site characterization. ACKNOWLEDGEMENTS This research has been co-financed by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) - Research Funding Program: ARCHIMIDIS III: Research Teams Reinforcement in ASPETE (MIS:383576) of the Operational Program "Education and Lifelong Learning. References Constable, S. C., Parker, R. L., and Constable, G. G. (987). "Occam's Inversion: A Practical Algorithm for Generating Smooth Models from Electromagnetic Sounding Data." Geophysics, 52, 289-3. Hisada, Y., (994). "An Efficient Method for Computing Green's Functions for a Layered Half-Space with Sources and Receivers at Close Depths," Bulletin of the Seismological Society of America, 84(5), 456-472. Lai, C. G. and Rix, G. J. (998). "Simultaneous Inversion of Rayleigh Phase Velocity and Attenuation for Near-Surface Site Characterization", Report No. GIT-CEE/GEO-98-2, School of Civil and Environmental Engineering, Georgia Institute of Technology, 258 pp. 8
Pelekis P.C. and Athanasopoulos G.A., (), An Overview of Surface Wave Methods and a Reliability Study of a New Simplified Inversion Technique, Soil Dynamics and Earthquake Engineering, Volume 3, Issue 2, December, Pages 654-668. Pelekis P.C. and Athanasopoulos G.A., (2), Application of a Simplified Inversion Technique to Published Surface Wave Dispersion Data Comparisons with Advanced Methods of Inversion, Proceedings of Geo-Congress 2, Geotechnical Special Publication 225, ASCE, Oakland March 2, pp. 276-2725. Wathelet, M., (5), Array Recordings of Ambient Vibrations: Surface-Wave Inversion, PhD Thesis, University of Liège (Belgium), 77p, 5. Wathelet, M., Jongmans, D. and Ohrnbereger, M. (4), Surface-Wave Inversion Using a Direct Search Algorithm and its Application to Ambient Vibration Measurements, Near Surface Geophysics (2), 2-22p, 4. 9
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