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Theoretical Basis for Rotational Effects in Strong Motion and Some Results

Theoretical Basis for Rotational Effects in Strong Motion and Some Results. Vladimir Graizer vgraizer@consrv.ca.gov California Geological Survey Menlo Park, February 16, 2006.

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Theoretical Basis for Rotational Effects in Strong Motion and Some Results

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  1. Theoretical Basis for Rotational Effects in Strong Motion and Some Results Vladimir Graizervgraizer@consrv.ca.gov California Geological Survey Menlo Park, February 16, 2006

  2. Most common instruments used in seismological measurements of ground motion are pendulum seismographs. Pendulums are sensitive to translational motion and rotations. When seismology started measuring ground motion in the near-field of earthquakes and explosions the assumption that movement of the instrument’s base is purely translational was simply transferred from the far- to the near-source studies. During the last half of century a number of attempts were made to measure or estimate rotational component of strong ground motion (Kharin & Simonov, 1969; Trifunac & Hudson, 1971; Lee & Trifunac, 1985; Niazi,1986; Lee & Trifunac, 1987; Graizer, 1987, 1989, 1991; Oliveira and Bolt, 1989; Nigbor, 1994; Takeo, 1998; Huang, 2003). But we still don’t have consistent measurements of rotations associated with strong-motion. Introduction Most common instruments used in seismological measurements of ground motion are pendulum seismographs. Pendulums are sensitive to translational motion and rotations. When seismology started measuring ground motion in the near-field of earthquakes and explosions the assumption that movement of the instrument’s base is purely translational was simply transferred from the far- to the near-source studies. During the last half of century a number of attempts were made to measure or estimate rotational component of strong ground motion (Kharin & Simonov, 1969; Trifunac & Hudson, 1971; Lee & Trifunac, 1985; Niazi,1986; Lee & Trifunac, 1987; Graizer, 1987, 1989, 1991; Oliveira and Bolt, 1989; Nigbor, 1994; Takeo, 1998; Huang, 2003). But we still don’t have consistent measurements of rotations associated with strong-motion.

  3. Schematic representation of an accelerograph

  4. Equation of pendulum motion Longitudinal: y1” + 21D1y1’ + 12y1 = -x1” + gψ2 - ψ3”l1 + x2”1 Vertical: y3” + 23D3y3’ + 32y3 = -x3” + gψ12/2 - ψ1”l3 +x2”3 Graizer, 1989 Golytsyn (1912) is not considering cross-axis sensitivity (item 4). Aki & Richards (1980) are not considering angular acceleration (item 3).

  5. List of symbols Where: yiis recorded response of the instrument, iis the angle of pendulum rotation, liis the length of pendulum arm, yi = i li , iandDiare respectively the natural frequency and fraction of critical damping of the ith transducer, gis acceleration due to gravity, xi”is ground acceleration in Ith direction, ψiis a rotation of the ground surface about xiaxis.

  6. Errors due to angular acceleration (a), tilt (b) and cross axis sensitivity (c)

  7. “Effective” equations of pendulums in strong-motion Horizontal: y1” + 21D1y1’ + 12y1 = -x1” + gψ2 Vertical: y3” + 23D3y3’ + 32y3 = -x3”

  8. What can be done in absence of rotations y” + 2Dy’ + 2y = - Vx” T1 T W =  [x’(t)]2dt +  [x’(t)]2dt 0 T2 Graizer, 1979

  9. Comparison of shake-table motion with displacement calculations

  10. Comparison of the “true” displacement and displacement calculated using accelerogram contaminated by tilt

  11. Response of Two-Pendulums System

  12. Measurements of Displacement and Tilt in the near-field of 2 explosions using two-pendulums instruments Graizer et al., 1989

  13. Method of estimating tilt using existing strong-motion records Method of tilt evaluation using uncorrected strong-motion accelerograms based on the difference in the tilt sensitivity of the horizontal and vertical pendulums is suggested (Graizer, 1989). Method was tested in a number of laboratory experiments with different strong-motion instruments (Moscow, 1988; Menlo Park, 1993).

  14. “Effective” equations of pendulums in strong-motion Horizontal: y1” + 21D1y1’ + 12y1 = -x1” + gψ2 Vertical: y3” + 23D3y3’ + 32y3 = -x3”

  15. Response of Horizontal Pendulum to Acceleration and Tilt

  16. Comparison of H to V (no tilt present)

  17. Contamination with artificial tilt

  18. Estimates of Tilts during Northridge Earthquake

  19. Pacoima Dam

  20. Fourier spectra and Spectral Ratios of H/V at Pacoima

  21. Tilts at Pacoima Dam Residual tilt extracted from the strong-motion record at the Pacoima Dam – Upper Left Abutment reached 3.10 (0.054 rad) in N450E direction. It was a result of local earthquake induced tilting due to high amplitude shaking (not source generated). This value is in agreement with the residual tilt of 3.50 in N400E direction measured using electronic level few days after the earthquake by CSMIP staff (Shakal et al, 1994). Tilting velocity is estimated to reach about 15 deg/sec (0.26 rad/sec).

  22. Los Angeles – 6-story Office Bldg (24652)

  23. Tilts in a Building Method was applied to the records of Northridge earthquake of 1994 at Los Angeles – 6-story Office Bldg. According to the estimates, this building experienced residual tilting from 0.1 up to 3.5 degrees (0.002 to 0.06 rad) at the 1st and 3rd floors with no significant residual tilting at the basement and roof levels.

  24. Ventura – 12-story Hotel (25339)

  25. Analysis of the equation of motion of horizontal and vertical pendulums has shown that horizontal sensors are sensitive not only to translational motion but also to tilts. In contrast to horizontal sensors, vertical sensors don’t have these limitations, since they are much less sensitive to tilts. Ignoring tilt sensitivity may produce unreliable results, especially in residual displacement and long-period calculations. Tilts at Pacoima Dam and in some CSMIP instrumented buildings reached more than 3 degrees (0.06 rad) during the Mw 6.7 Northridge earthquake. In general, only six-component systems measuring rotations and accelerations, or three-component systems similar to systems used in inertial navigation assuring purely translational motion of accelerometers can be used to calculate “true” displacements. Highlights

  26. References • Aki K., Richards P. G. (1980). Quantitative Seismology, vol. I and II. Freeman, San Francisco • Boore D. M. (2001). Effect of baseline corrections on displacements and response spectra for several recordings of the 1999 Chi-Chi, Taiwan, earthquake. Bull Seism Soc Am 91: 1199-1211. • Boore D. M. (2003). Analog-to-digital conversion as a source of drifts in displacements derived from digital recordings of ground acceleration. Bull Seism Soc Am 93: 2017-24. • Bouchon M., Aki K. (1982). Strain, tilt, and rotation associated with strong ground motion in the vicinity of earthquake faults. Bull Seism Soc Am 72: 1717-38. • Bradner H., Reichle M. (1973). Some methods for determining acceleration and tilt by use of pendulums and accelerometers. Bull Seism Soc Am 63: 1-7. • Farrell W. E. (1969). A gyroscopic seismometer: measurements during the Borrego Earthquake. Bull Seism Soc Am 59: 1239-45. • Golitsyn B. B. (1912). Lectures on Seismometry. Russian Acad Sci, St. Petersburg. • Graizer V. M. (1979). Determination of the true displacement of the ground from strong-motion recordings. Izv USSR Acad Sci, Physics of the Solid Earth 15: 12, 875-85. • Graizer V. M. (1987). Determination of the path of ground motion during seismic phenomena. Izv USSR Acad Sci, Physics Solid Earth 22: 10, 791-94. • Graizer V. M. (1989). Bearing on the problem of inertial seismometry. Izv USSR Acad Sci, Physics Solid Earth 25: 1, 26-29. • Graizer V. M. (1991). Inertial seismometry methods. Izv USSR Acad Sci, Physics Solid Earth 27: 1, 51-61. • Graizer V. M. (2005). Effect of tilt on strong motion data processing. Soil Dyn Earthq Eng 25: 197-204. • Graizer V. M. (2006). Equation of pendulum motion including rotations and its implications to the strong-ground motion. (In print). • Huang B-S. (2003). Ground rotational motions of the 1999 Chi-Chi, Taiwan earthquake as inferred from dense array observations. Geophys. Res. Letters. 30, No.6, 1307-10. • Iwan W. D., Moser M. A., Peng C-Y. (1985). Some observations on strong-motion earthquake measurement using a digital accelerograph. Bull Seism Soc Am 75: 1225-46. • Kharin D. A., Simonov L. I. (1969). VBPP seismometer for separate registration of translational motion and rotations. Seismic Instruments 5: 51–66 (in Russian). • Lee V. W., Trifunac M. D. (1985). Torsional accelerograms. Soil Dyn Earthq Eng 4: 132-142. • Lee V. W., Trifunac M. D. (1987). Rocking strong earthquake accelerations. Soil Dyn Earthq Eng 6: 75-89. • Niazi M. (1986). Inferred displacements, velocities and rotations of a long rigid foundation located at El Centro differential array site during the 1979 Imperial Valley, California earthquake. Earthquake Eng Struct Dyn 14: 531-42. • Nigbor R. L. (1994). Six-degree-of-freedom ground-motion measurements. Bull Seism Soc Am 84: 1665-69. • Oliveira C. S., Bolt B. A. (1989). Rotational components of surface strong ground motion. Earthquake Eng. Struct. Dyn. 18: 517-26. • Rodgers P. W. (1968). The response of the horizontal pendulum seismometer to Rayleigh and Love waves, tilt and free oscillations of the earth. Bull Seism Soc Am 58: 1384-1406. • Shakal A. F., Huang M. J., Graizer V. M. (2003). Strong-motion data processing. In: Lee W. H. K. et al. (eds) “International Book of Earthquake & Engineering Seismology”, part B. Academic Press, Amsterdam, pp 967-81. • Shakal A., Cao T., Darragh R. (1994). Processing of the upper left abutment record from Pacoima dam for the Northridge earthquake. Report OSMS 94-13. Sacramento. 23 p. • Shakal A., Huang M., Darragh R., Cao T., Sherburne R., Malhotra P., Cramer C., Sydnor R., Graizer V., Maldonado G., Peterson C., Wampole J. (1994). CSMIP Strong-motion records from the Northridge, California earthquake of 17 January 1994. Report OSMS 94-07. Sacramento, California. 308 p. • Takeo M. (1998). Ground rotational motions recorded in near-source region of earthquakes. Geophys. Res. Letters. 25, No.6, 789-792. • Todorovska M. I. (1998). Cross-axis sensitivity of accelerographs with pendulum like transducers – mathematical model and the inverse problem. Earthquake Eng Struct Dyn 27: 1031-51. • Trifunac M. D. (1971). Zero baseline correction of strong-motion accelerograms. Bull Seism Soc Am 61:1201-11. • Trifunac M. D., Hudson D. E. (1971). Analysis of the Pacoima dam accelerogram – San Fernando, California, Earthquake of 1971. Bull Seism Soc Am 61:1393-1411. • Trifunac M. D. (1982). A note on rotational components of earthquake motions for incident body waves. Soil Dyn Earthq Eng 1: 11-19. • Trifunac M. D., Lee V. W. (1973). Routine computer processing of strong-motion accelerograms. Earthq Engin Res Lab, Report EERL 73-03. • Trifunac M. D., Todorovska M. I. (2001). A note on the usable dynamic range of accelerographs recording translation. Soil Dyn Earthq Eng 21: 275-86. • Wong H. L., Trifunac M. D. (1977). Effect of cross-axis sensitivity and misalignment on response of mechanical-optical accelerographs. Bull Seism Soc Am 67: 929-56. • Zahradnik J., Plesinger A. (2005). Long-period pulses in broadband records of near earthquakes. Bull Seism Soc Am 95:1928-39.

  27. Method Testing (Menlo Park, 1993) Lee & Graizer, 1993

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