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- 1. Determination of 2D shallow S wave velocity profile using waveform inversion of P-SV refraction data. AMROUCHE Mohamed YAMANAKA Hiroaki Tokyo Institute of Technology 東京工業大学 24 September 2012 LISBOA - PORTUGAL
- 2. IntroductionDuring earthquakes most of constructions interact directly with the surface layers,structural soil irregularities and lateral S wave variations may generated complexwaves that interfere to disturb the expected response of the buildings.The surface wave exploration became very popular in the last few years. Surfacewaves have dispersive features while propagating that can be utilized for the onedimensional soil exploration of shallow soils.However, the 1D soil profiling assumes that the propagation medium is horizontallylayered and ignores the lateral variations of layers along the profile.Also, since most of the surface wave methods are based on the inversion of thedispersion curves of surface waves, it will be very difficult to invert a twodimensional profile, and only few authors have attempted to invert a 2D soil usingthe Rayleigh waves.We proposed a new approach based on the direct 2D soil numerical modeling andthe full wave inversion of surface Rayleigh waves time series obtained fromconventional seismic refraction survey to estimate the two dimensional soil profile. 1/13
- 3. Inversion of Rayleigh waves STEP02: Source Deconvolution. Waveform Deconvolution STEP01: Acquisition. 2D inverted Soil profile Soil Modelization based on the computed waves STEP03: Numerical modeling. 2/13
- 4. Numerical Modeling: Finite Difference Staggered GridVertical Point Yamada (2000) upgraded 2.5D P-SV Wave field Vertical component Source of receivers - 4th order Approximation for space. - 2nd order Approximation for time. - Non physical boundaries (Clayton, Engquist 1980) based on J.Virieux 1986 3/13
- 5. Numerical Modeling: Soil parameterizationTo materialize the soil structure, we use the combination of the tomographic cell andhomogeneous layered model proposed by Aoi et al.(1993). This technique allows a betterreconstruction of the geological discontinuities using few number of unknown parametersand gives the lateral variation at each layer.The interface of each block can be written as follow: dx：Interface Depth at location x. L: Number of basis functions. Pk：Coefficient determined by inversion. Cx：Basis Function.A smoothing factor is implemented between blocks to balance the velocity/depth trade offduring inversion. 7 Blocks Basis 7 BlocksFunctions Basement. Total parameters for inversion: 14 velocities + 14 depths= 28 unknown parameters 4/13
- 6. Waveforms Deconvolution 5/13
- 7. Generation of a Random initial Inversion Algorithms model (2.5D FD computation) The inversion algorithm used in this study is the Hybrid Heuristic Search Method proposedCal. Of Misfit between Obs. and by Yamanaka (2007). This method combines the Cal. waveforms Genetic Algorithms and Simulated Annealing Algorithms to obtain an optimal solution.Selection – Cross over – Mutation The main goal of inversion is to minimize the misfit function between the Observed New Generation: waveforms and the Computed ones. Calculation of new model The Misfit function can be defined as follows: Cal. Of Misfit for the present generation Change Temp. Where, Oobs and Ocal are respectively the observed and the calculated waveforms at each Optimal model M station along N number of data. 6/13
- 8. Numerical Experiments 250 m/s 200 m/s 400 m/s 650 m/s 650 m/sInversion Parameters: Elasticity parameters: Number of blocks: 30 Vp/Vs Q ρ Initial population: 20 Number of generations: 200 Surface layer 1.7 10 1700Search limits: Velocity: 150 – 500 (m/s) Basement 2.0 12 1900 Depth: 1 – 5 (m) 7/13
- 9. Model01: Irregular Model : Observed Waveforms.Target : Calculated Waveforms.Model 250 m/s 650 m/s 251 m/s 650 m/sInvertedModel 8/13
- 10. Noise and Impedance effectTarget Model 7% Noise corrupted Noise free inversion inversion 250 m/s 251 m/s 248 m/s 650 m/s 650 m/s 650 m/s 251 m/s 500 m/s 423 m/s 650 m/s 650 m/s 9/13
- 11. Target Model02: Lateral velocity variationModel 200 m/s 400 m/s Generation 01 Generation 100 650 m/s Generation 50 210 m/s 406 m/s 650 m/s Generation 200InvertedModel 10/13
- 12. Empirical inversion: Data acquisitionG3 Rear ParkingTokyo Institute of Technology SuzukakedaiCampus Yokohama (JAPAN) Down stream Up Survey line stream Borehole 10mGoogle® map 11/13
- 13. Empirical inversion: Data inversionUp Stream inversion Borehole Data 200 300 500 420 550Down Stream inversion 200 300 500 420 550 : Observed Waveforms. : Inverted Waveforms. 12/13
- 14. ConclusionThrough this method, we have proved the possibility to reconstruct the 2D soilprofile using the full wave inversion of the time series of surface waves in shallowsoils, using numerical soil modeling.The numerical model is simulated using a2.5D P-SV waves FD staggered grid.Deconvolution is used to get rid of the source signature in the wave fors.The numerical experiments shows that the algorithm is able to reconstructcomplex two dimensional soil structures. The effect of noise can me morepronounced in soils with low impedance ratio.An empirical inversion was performed showing acceptable correlation with theexcising bore hole data.Since this method is not based on the inversion of the dispersion curve, all theenergy of the Rayleigh waves encoded in the signal are inverted. 13/13
- 15. Thank you for your kind attention! mohamedamrouche347@hotmail.com

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