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An Optimization Method on Joint Inversion of Different Types of Seismic Data

An Optimization Method on Joint Inversion of Different Types of Seismic Data. ¹ Mathematical Science, Computational Science Program, ²Geological Sciences, ²Computer Science. M. Argaez¹, R. Romero 3 , A. Sosa¹ , L. Thompson² L. Velazquez¹ , A. Velasco².

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An Optimization Method on Joint Inversion of Different Types of Seismic Data

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  1. An Optimization Method on Joint Inversion of Different Types of Seismic Data ¹ Mathematical Science, Computational Science Program, ²Geological Sciences, ²Computer Science M. Argaez¹, R. Romero3, A. Sosa¹, L. Thompson² L. Velazquez¹, A. Velasco² Cyber-ShARE Steering Committee Meeting‏ December 8, 2009

  2. Forward and Inverse Problems Forward Problem Inverse Problem Inverse Problem Difficulties may have infinitely many solutions is numerically unstable (ill conditioned) Implement an efficient solver for the linear system Given an operator and find “Easy” to solve • Given an operator and find the true such that • Hard to solve

  3. Goal • To characterize the Earth structure underneath a station by using velocity distributions

  4. Experiment Design Body waves Surface waves We use data from different EQs at a given station Each EQ can be recorded in a 3 component seismogram First arrivals Longer periods Smaller amplitudes Slower velocities Shorter periods Higher amplitudes

  5. What does a seismogram tell us? From the Body waves we have (Developed by L. Braile)http://web.ics.purdue.edu/~braile/edumod/waves/WaveDemo.htm

  6. What does a seismogram tell us? • From the Surface waves (Developed by L. Braile)http://web.ics.purdue.edu/~braile/edumod/waves/WaveDemo.htm

  7. How do we find the velocities x? From the body waves From the surface waves Gives high resolution of velocities near the surface • Gives more resolution for deeper layers • Helps to define layer thicknesses Each data set provides different VALUABLEinformation Question : How to join each data set to obtain a better characterization of the given site ? Answer : Joint Inversion!!!

  8. Joint Inversion methods Uses indirect method : Conjugate Gradient* • Uses direct methods: • QR Factorization • Cholesky Factorization • SVD Factorization* * We are using the fortran 77 code provided by C. Ammon et al. with synthetic data sets

  9. Numerical Results Inversion SVD

  10. Numerical Results Inversion our CG

  11. Future Work To study the choice of the regularization parameter to improve the rate of convergence of the algorithm To implement the code for solving large scale real geophysical problems To implement state-of-the-art optimization techniques using the norm (using current research Dr. Argaez). That is:

  12. References • Joint inversion of receiver function and surface wave dispersion observations. J. Julia, C. J. Ammon, R. Hermann, M. Correig. Geophysics Int. J (2000). . 99-112. • References On the Nonuniqueness of Receiver Function Inversion. C. J. Ammon, G. Randall, G. Zandt. Journal of Geophysical Res. Vol. 95. (1990) • An Introduction to Seismology Earthquakes and Earth Structure, • S. Stein and M. Wysession, Blackwell Publishing, 2006 • Numerical Optimization. J. Nocedal, and S. J. Wright. Springer. Second Edition. 2006 Acknowledgements Computational Science and Department of Mathematical Sciences at University of Texas at El Paso (UTEP) This work is being funded by NSF Crest Cyber-ShARE HRD-0734825

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