Abstract

A ring laser unlocked by the Earth's Sagnac effect has attained a frequency resolution of 1 part in 3 × 1021 and a rotational resolution of 300 prad. We discuss both theoretically and experimentally the sideband structure of the Earth rotation-induced spectral line induced in the microhertz–hertz region by frequency modulation associated with extra mechanical motion, such as seismic events. The relative sideband height is an absolute measure of the rotational amplitude of that Fourier component. An initial analysis is given of the ring laser record from the Arthur's Pass–Coleridge seismic event of 18 June 1994.

© 1995 Optical Society of America

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  1. R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
    [CrossRef]
  2. R. Rodloff, “Gibt es den optische superkreisel?” Z. Flugwiss. Weltraumforsch. 18, 2–15 (1994).
  3. G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).
  4. G. E. Stedman, M. T. Johnsson, Z. Li, C. H. Rowe, H. R. Bilger, “T violation and microhertz resolution in a ring laser,” Opt. Lett. 20, 324–326 (1995).
    [CrossRef] [PubMed]
  5. G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, H. R. Bilger, “Harmonic analysis in a precision ring laser with backscatter-induced pulling,” Phys. Rev. A 51, 4944–4958 (1995).
    [CrossRef] [PubMed]
  6. E. O. Schulz-Dubois, “Alternative interpretation of rotation rate sensing by ring laser,” IEEE J. Quantum Electron. QE-2, 299–305 (1987).
  7. C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992).
    [CrossRef] [PubMed]
  8. W. Schleich, P. Dobiasch, V. E. Sanders, M. O. Scully, “Nonequilibrium statistical physics in a dithered ring laser gyroscope, or quantum noise in pure and applied physics,” in Frontiers of Nonequilibrium Statistical Physics, Vol. 135 of NATO Advanced Study Institute Series B, G. T. Moore, M. O. Scully, eds. (New York, Plenum, 1986), pp. 385–408.
    [CrossRef]
  9. J. R. Wilkinson, “Ring lasers,” Prog. Quantum Electron. 11, 1–103 (1987).
    [CrossRef]
  10. R. J. Neutze, “Ring interferometer with angular acceleration,” Phys. Rev. A (to be published).
  11. I. Vetharaniam, G. E. Stedman, “Accelerated observers: synchronisation and tests of local Lorentz invariance,” Class. Q. Gravity 11, 1069–1082 (1994).
    [CrossRef]
  12. G. E. Stedman, H. R. Bilger, “Could a ring laser reveal the QED anomaly via vacuum chirality?” Phys. Lett. A 122, 289–292 (1987).
    [CrossRef]
  13. L. Cooper, “Axion detection by ring lasers,” M.Sc. thesis (University of Canterbury, Christchurch, New Zealand, 1994).
  14. F. Aronowitz, “The laser gyro,” in Laser Applications, M. Ross, ed. (Academic, New York, 1971) Vol. 1, pp. 133–200.
  15. M. A. Riedesel, R. D. Moore, J. A. Orcutt, “Limits of sensitivity of inertial seismometres with velocity transducers and electronic amplifiers,” Bull. Seismol. Soc. Am. 80, 1725–1752 (1990).
  16. M. J. Usher, R. F. Burch, C. Guralp, “Wide-band feedback seismometers,” Phys. Earth Planet. Inter. 18, 38–50 (1979).
    [CrossRef]
  17. H. Kanamori, Seismological Laboratory, California Institute of Technology, Pasadena, Calif. 91103 (personal communication), 1992.
  18. S. W. Smith, K. Kasahara, “Wave and mode separation with strain seismographs,” Bull. Earthquake Res. Inst. 47, 831–848 (1969).
  19. “Panel discussion,” in Proceedings of the International Symposium on Earthquake Disaster Prevention (CENAPRED, Mexico City, 1992), pp. 333–338.
  20. K. Aki, P. G. Richards, Quantitative Seismology, Theory and Methods (Freeman, San Francisco, Calif., 1980).
  21. K. R. Gledhill, M. J. Randall, M. P. Chadwick, “The EARSS digital seismograph: system description and field trials,” Bull. Seismol. Soc. Am. 81, 1380–1390 (1991).
  22. R. D. Adams, “The New Zealand seismographic network,” Phys. Earth Planet. Inter. 18, 114–120 (1979);A. J. Haines, “Research in seismology and the physics of the Earth's interior in New Zealand 1987–1990,” presented by the New Zealand National Committee for Geodesy and Geophysics to the International Association of Seismology and Physics of the Earth's Interior, Vienna, Austria, August 1991.
    [CrossRef]
  23. M. R. Sayeh, H. R. Bilger, “Flicker noise in frequency fluctuations of lasers,” Phys. Rev. Lett. 55, 700–702 (1985);T. A. Dorschner, H. A. Haus, I. M. Holz, I. W. Smith, H. Statz, “Laser gyro at the quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980);H. Statz, T. A. Dorschner, M. Holtz, I. W. Smith, “The multioscillator ring laser gyroscope,” in Laser Handbook, M. L. Stitch, M. Bass, eds. (North-Holland, Amsterdam, 1985), Vol. 4, pp. 229–332, equation 4.5.10.
    [CrossRef] [PubMed]
  24. R. Rodloff, “A laser gyro with optimised resonator geometry,” IEEE J. Quantum Electron. QE-23, 438–445 (1987). Eq. (12a).
    [CrossRef]
  25. A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing, (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  26. T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
    [CrossRef]
  27. M. Ewing, F. Press, “Surface waves and guided waves,” in Geophysics I, Vol. 47 of Encyclopaedia of Physics (Springer-Verlag, Berlin, 1956), pp. 119–139.
    [CrossRef]
  28. K. E. Bullen, B. A. Bolt, “An introduction to the theory of seismology,” 4th ed. (Cambridge U. Press, Cambridge, En-gland, 1985).
  29. M. Bath, Introduction to Seismology, 2nd ed. (Birkhauser, Basel, 1979).
  30. A. H. Nuttall, “Some windows with very good sidelobe behav-iour,” IEEE Trans. Acoust. Speech Signal Process ASSP-29, 84–91 (1981).
    [CrossRef]
  31. This distance assumes Northridge, Los Angeles, California to be at 34°14′N, 118°33′W, and the Cashmere cavern, Christchurch, New Zealand to be at 43°35′S, 172°38′E. The Northridge–Kelburn course and distance are 10,764 km, 224.3°; the Northridge–Cashmere course and distance are 223°, 11,105 km; the Kelburn–Cashmere figures are 214°, 309 km. For the comparison with the Kelburn data presented here, the help of T. H. Webb of the Institute of Geophysical and Nuclear Research, Wellington, New Zealand, is gratefully acknowledged.
  32. G. G. Sorrells, T. T. Goforth, “Low frequency Earth motion generated by slowly propagating organised pressure fields,” Bull. Seismol. Soc. Am. 63, 1583–1601 (1973).
  33. G. G. Sorrells, E. J. Douze, “A preliminary report on infrasonic waves as a source of long period seismic noise,” J. Geophys. Res. 79, 4908–4917 (1974).
    [CrossRef]

1995 (2)

G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, H. R. Bilger, “Harmonic analysis in a precision ring laser with backscatter-induced pulling,” Phys. Rev. A 51, 4944–4958 (1995).
[CrossRef] [PubMed]

G. E. Stedman, M. T. Johnsson, Z. Li, C. H. Rowe, H. R. Bilger, “T violation and microhertz resolution in a ring laser,” Opt. Lett. 20, 324–326 (1995).
[CrossRef] [PubMed]

1994 (3)

I. Vetharaniam, G. E. Stedman, “Accelerated observers: synchronisation and tests of local Lorentz invariance,” Class. Q. Gravity 11, 1069–1082 (1994).
[CrossRef]

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

R. Rodloff, “Gibt es den optische superkreisel?” Z. Flugwiss. Weltraumforsch. 18, 2–15 (1994).

1993 (2)

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
[CrossRef]

1992 (1)

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992).
[CrossRef] [PubMed]

1991 (1)

K. R. Gledhill, M. J. Randall, M. P. Chadwick, “The EARSS digital seismograph: system description and field trials,” Bull. Seismol. Soc. Am. 81, 1380–1390 (1991).

1990 (1)

M. A. Riedesel, R. D. Moore, J. A. Orcutt, “Limits of sensitivity of inertial seismometres with velocity transducers and electronic amplifiers,” Bull. Seismol. Soc. Am. 80, 1725–1752 (1990).

1987 (4)

G. E. Stedman, H. R. Bilger, “Could a ring laser reveal the QED anomaly via vacuum chirality?” Phys. Lett. A 122, 289–292 (1987).
[CrossRef]

J. R. Wilkinson, “Ring lasers,” Prog. Quantum Electron. 11, 1–103 (1987).
[CrossRef]

E. O. Schulz-Dubois, “Alternative interpretation of rotation rate sensing by ring laser,” IEEE J. Quantum Electron. QE-2, 299–305 (1987).

R. Rodloff, “A laser gyro with optimised resonator geometry,” IEEE J. Quantum Electron. QE-23, 438–445 (1987). Eq. (12a).
[CrossRef]

1985 (1)

M. R. Sayeh, H. R. Bilger, “Flicker noise in frequency fluctuations of lasers,” Phys. Rev. Lett. 55, 700–702 (1985);T. A. Dorschner, H. A. Haus, I. M. Holz, I. W. Smith, H. Statz, “Laser gyro at the quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980);H. Statz, T. A. Dorschner, M. Holtz, I. W. Smith, “The multioscillator ring laser gyroscope,” in Laser Handbook, M. L. Stitch, M. Bass, eds. (North-Holland, Amsterdam, 1985), Vol. 4, pp. 229–332, equation 4.5.10.
[CrossRef] [PubMed]

1981 (1)

A. H. Nuttall, “Some windows with very good sidelobe behav-iour,” IEEE Trans. Acoust. Speech Signal Process ASSP-29, 84–91 (1981).
[CrossRef]

1979 (2)

R. D. Adams, “The New Zealand seismographic network,” Phys. Earth Planet. Inter. 18, 114–120 (1979);A. J. Haines, “Research in seismology and the physics of the Earth's interior in New Zealand 1987–1990,” presented by the New Zealand National Committee for Geodesy and Geophysics to the International Association of Seismology and Physics of the Earth's Interior, Vienna, Austria, August 1991.
[CrossRef]

M. J. Usher, R. F. Burch, C. Guralp, “Wide-band feedback seismometers,” Phys. Earth Planet. Inter. 18, 38–50 (1979).
[CrossRef]

1974 (1)

G. G. Sorrells, E. J. Douze, “A preliminary report on infrasonic waves as a source of long period seismic noise,” J. Geophys. Res. 79, 4908–4917 (1974).
[CrossRef]

1973 (1)

G. G. Sorrells, T. T. Goforth, “Low frequency Earth motion generated by slowly propagating organised pressure fields,” Bull. Seismol. Soc. Am. 63, 1583–1601 (1973).

1969 (1)

S. W. Smith, K. Kasahara, “Wave and mode separation with strain seismographs,” Bull. Earthquake Res. Inst. 47, 831–848 (1969).

Adams, R. D.

R. D. Adams, “The New Zealand seismographic network,” Phys. Earth Planet. Inter. 18, 114–120 (1979);A. J. Haines, “Research in seismology and the physics of the Earth's interior in New Zealand 1987–1990,” presented by the New Zealand National Committee for Geodesy and Geophysics to the International Association of Seismology and Physics of the Earth's Interior, Vienna, Austria, August 1991.
[CrossRef]

Aki, K.

K. Aki, P. G. Richards, Quantitative Seismology, Theory and Methods (Freeman, San Francisco, Calif., 1980).

Anderson, R.

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

Aronowitz, F.

F. Aronowitz, “The laser gyro,” in Laser Applications, M. Ross, ed. (Academic, New York, 1971) Vol. 1, pp. 133–200.

Bath, M.

M. Bath, Introduction to Seismology, 2nd ed. (Birkhauser, Basel, 1979).

Bilger, H. R.

G. E. Stedman, M. T. Johnsson, Z. Li, C. H. Rowe, H. R. Bilger, “T violation and microhertz resolution in a ring laser,” Opt. Lett. 20, 324–326 (1995).
[CrossRef] [PubMed]

G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, H. R. Bilger, “Harmonic analysis in a precision ring laser with backscatter-induced pulling,” Phys. Rev. A 51, 4944–4958 (1995).
[CrossRef] [PubMed]

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

G. E. Stedman, H. R. Bilger, “Could a ring laser reveal the QED anomaly via vacuum chirality?” Phys. Lett. A 122, 289–292 (1987).
[CrossRef]

M. R. Sayeh, H. R. Bilger, “Flicker noise in frequency fluctuations of lasers,” Phys. Rev. Lett. 55, 700–702 (1985);T. A. Dorschner, H. A. Haus, I. M. Holz, I. W. Smith, H. Statz, “Laser gyro at the quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980);H. Statz, T. A. Dorschner, M. Holtz, I. W. Smith, “The multioscillator ring laser gyroscope,” in Laser Handbook, M. L. Stitch, M. Bass, eds. (North-Holland, Amsterdam, 1985), Vol. 4, pp. 229–332, equation 4.5.10.
[CrossRef] [PubMed]

Bolt, B. A.

K. E. Bullen, B. A. Bolt, “An introduction to the theory of seismology,” 4th ed. (Cambridge U. Press, Cambridge, En-gland, 1985).

Bullen, K. E.

K. E. Bullen, B. A. Bolt, “An introduction to the theory of seismology,” 4th ed. (Cambridge U. Press, Cambridge, En-gland, 1985).

Burch, R. F.

M. J. Usher, R. F. Burch, C. Guralp, “Wide-band feedback seismometers,” Phys. Earth Planet. Inter. 18, 38–50 (1979).
[CrossRef]

Centeno Neelen, R.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992).
[CrossRef] [PubMed]

Chadwick, M. P.

K. R. Gledhill, M. J. Randall, M. P. Chadwick, “The EARSS digital seismograph: system description and field trials,” Bull. Seismol. Soc. Am. 81, 1380–1390 (1991).

Cooper, L.

L. Cooper, “Axion detection by ring lasers,” M.Sc. thesis (University of Canterbury, Christchurch, New Zealand, 1994).

Danzmann, K.

T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
[CrossRef]

Dobiasch, P.

W. Schleich, P. Dobiasch, V. E. Sanders, M. O. Scully, “Nonequilibrium statistical physics in a dithered ring laser gyroscope, or quantum noise in pure and applied physics,” in Frontiers of Nonequilibrium Statistical Physics, Vol. 135 of NATO Advanced Study Institute Series B, G. T. Moore, M. O. Scully, eds. (New York, Plenum, 1986), pp. 385–408.
[CrossRef]

Douze, E. J.

G. G. Sorrells, E. J. Douze, “A preliminary report on infrasonic waves as a source of long period seismic noise,” J. Geophys. Res. 79, 4908–4917 (1974).
[CrossRef]

Etrich, C.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992).
[CrossRef] [PubMed]

Ewing, M.

M. Ewing, F. Press, “Surface waves and guided waves,” in Geophysics I, Vol. 47 of Encyclopaedia of Physics (Springer-Verlag, Berlin, 1956), pp. 119–139.
[CrossRef]

Gledhill, K. R.

K. R. Gledhill, M. J. Randall, M. P. Chadwick, “The EARSS digital seismograph: system description and field trials,” Bull. Seismol. Soc. Am. 81, 1380–1390 (1991).

Goforth, T. T.

G. G. Sorrells, T. T. Goforth, “Low frequency Earth motion generated by slowly propagating organised pressure fields,” Bull. Seismol. Soc. Am. 63, 1583–1601 (1973).

Guralp, C.

M. J. Usher, R. F. Burch, C. Guralp, “Wide-band feedback seismometers,” Phys. Earth Planet. Inter. 18, 38–50 (1979).
[CrossRef]

Johnsson, M. T.

Kanamori, H.

H. Kanamori, Seismological Laboratory, California Institute of Technology, Pasadena, Calif. 91103 (personal communication), 1992.

Kasahara, K.

S. W. Smith, K. Kasahara, “Wave and mode separation with strain seismographs,” Bull. Earthquake Res. Inst. 47, 831–848 (1969).

Li, Z.

G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, H. R. Bilger, “Harmonic analysis in a precision ring laser with backscatter-induced pulling,” Phys. Rev. A 51, 4944–4958 (1995).
[CrossRef] [PubMed]

G. E. Stedman, M. T. Johnsson, Z. Li, C. H. Rowe, H. R. Bilger, “T violation and microhertz resolution in a ring laser,” Opt. Lett. 20, 324–326 (1995).
[CrossRef] [PubMed]

Mandel, P.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992).
[CrossRef] [PubMed]

McGregor, A. D.

G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, H. R. Bilger, “Harmonic analysis in a precision ring laser with backscatter-induced pulling,” Phys. Rev. A 51, 4944–4958 (1995).
[CrossRef] [PubMed]

Moore, R. D.

M. A. Riedesel, R. D. Moore, J. A. Orcutt, “Limits of sensitivity of inertial seismometres with velocity transducers and electronic amplifiers,” Bull. Seismol. Soc. Am. 80, 1725–1752 (1990).

Neutze, R. J.

R. J. Neutze, “Ring interferometer with angular acceleration,” Phys. Rev. A (to be published).

Niebauer, T. M.

T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
[CrossRef]

Nuttall, A. H.

A. H. Nuttall, “Some windows with very good sidelobe behav-iour,” IEEE Trans. Acoust. Speech Signal Process ASSP-29, 84–91 (1981).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing, (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Orcutt, J. A.

M. A. Riedesel, R. D. Moore, J. A. Orcutt, “Limits of sensitivity of inertial seismometres with velocity transducers and electronic amplifiers,” Bull. Seismol. Soc. Am. 80, 1725–1752 (1990).

Poulton, M. P.

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

Press, F.

M. Ewing, F. Press, “Surface waves and guided waves,” in Geophysics I, Vol. 47 of Encyclopaedia of Physics (Springer-Verlag, Berlin, 1956), pp. 119–139.
[CrossRef]

Randall, M. J.

K. R. Gledhill, M. J. Randall, M. P. Chadwick, “The EARSS digital seismograph: system description and field trials,” Bull. Seismol. Soc. Am. 81, 1380–1390 (1991).

Richards, P. G.

K. Aki, P. G. Richards, Quantitative Seismology, Theory and Methods (Freeman, San Francisco, Calif., 1980).

Riedesel, M. A.

M. A. Riedesel, R. D. Moore, J. A. Orcutt, “Limits of sensitivity of inertial seismometres with velocity transducers and electronic amplifiers,” Bull. Seismol. Soc. Am. 80, 1725–1752 (1990).

Rodloff, R.

R. Rodloff, “Gibt es den optische superkreisel?” Z. Flugwiss. Weltraumforsch. 18, 2–15 (1994).

R. Rodloff, “A laser gyro with optimised resonator geometry,” IEEE J. Quantum Electron. QE-23, 438–445 (1987). Eq. (12a).
[CrossRef]

Rowe, C. H.

G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, H. R. Bilger, “Harmonic analysis in a precision ring laser with backscatter-induced pulling,” Phys. Rev. A 51, 4944–4958 (1995).
[CrossRef] [PubMed]

G. E. Stedman, M. T. Johnsson, Z. Li, C. H. Rowe, H. R. Bilger, “T violation and microhertz resolution in a ring laser,” Opt. Lett. 20, 324–326 (1995).
[CrossRef] [PubMed]

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

Rüdiger, A.

T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
[CrossRef]

Sanders, V. E.

W. Schleich, P. Dobiasch, V. E. Sanders, M. O. Scully, “Nonequilibrium statistical physics in a dithered ring laser gyroscope, or quantum noise in pure and applied physics,” in Frontiers of Nonequilibrium Statistical Physics, Vol. 135 of NATO Advanced Study Institute Series B, G. T. Moore, M. O. Scully, eds. (New York, Plenum, 1986), pp. 385–408.
[CrossRef]

Sayeh, M. R.

M. R. Sayeh, H. R. Bilger, “Flicker noise in frequency fluctuations of lasers,” Phys. Rev. Lett. 55, 700–702 (1985);T. A. Dorschner, H. A. Haus, I. M. Holz, I. W. Smith, H. Statz, “Laser gyro at the quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980);H. Statz, T. A. Dorschner, M. Holtz, I. W. Smith, “The multioscillator ring laser gyroscope,” in Laser Handbook, M. L. Stitch, M. Bass, eds. (North-Holland, Amsterdam, 1985), Vol. 4, pp. 229–332, equation 4.5.10.
[CrossRef] [PubMed]

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing, (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Schilling, R.

T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
[CrossRef]

Schleich, W.

W. Schleich, P. Dobiasch, V. E. Sanders, M. O. Scully, “Nonequilibrium statistical physics in a dithered ring laser gyroscope, or quantum noise in pure and applied physics,” in Frontiers of Nonequilibrium Statistical Physics, Vol. 135 of NATO Advanced Study Institute Series B, G. T. Moore, M. O. Scully, eds. (New York, Plenum, 1986), pp. 385–408.
[CrossRef]

Schnupp, L.

T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
[CrossRef]

Schulz-Dubois, E. O.

E. O. Schulz-Dubois, “Alternative interpretation of rotation rate sensing by ring laser,” IEEE J. Quantum Electron. QE-2, 299–305 (1987).

Scully, M. O.

W. Schleich, P. Dobiasch, V. E. Sanders, M. O. Scully, “Nonequilibrium statistical physics in a dithered ring laser gyroscope, or quantum noise in pure and applied physics,” in Frontiers of Nonequilibrium Statistical Physics, Vol. 135 of NATO Advanced Study Institute Series B, G. T. Moore, M. O. Scully, eds. (New York, Plenum, 1986), pp. 385–408.
[CrossRef]

Smith, S. W.

S. W. Smith, K. Kasahara, “Wave and mode separation with strain seismographs,” Bull. Earthquake Res. Inst. 47, 831–848 (1969).

Sorrells, G. G.

G. G. Sorrells, E. J. Douze, “A preliminary report on infrasonic waves as a source of long period seismic noise,” J. Geophys. Res. 79, 4908–4917 (1974).
[CrossRef]

G. G. Sorrells, T. T. Goforth, “Low frequency Earth motion generated by slowly propagating organised pressure fields,” Bull. Seismol. Soc. Am. 63, 1583–1601 (1973).

Spreeuw, R. J. C.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992).
[CrossRef] [PubMed]

Stedman, G. E.

G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, H. R. Bilger, “Harmonic analysis in a precision ring laser with backscatter-induced pulling,” Phys. Rev. A 51, 4944–4958 (1995).
[CrossRef] [PubMed]

G. E. Stedman, M. T. Johnsson, Z. Li, C. H. Rowe, H. R. Bilger, “T violation and microhertz resolution in a ring laser,” Opt. Lett. 20, 324–326 (1995).
[CrossRef] [PubMed]

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

I. Vetharaniam, G. E. Stedman, “Accelerated observers: synchronisation and tests of local Lorentz invariance,” Class. Q. Gravity 11, 1069–1082 (1994).
[CrossRef]

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

G. E. Stedman, H. R. Bilger, “Could a ring laser reveal the QED anomaly via vacuum chirality?” Phys. Lett. A 122, 289–292 (1987).
[CrossRef]

Usher, M. J.

M. J. Usher, R. F. Burch, C. Guralp, “Wide-band feedback seismometers,” Phys. Earth Planet. Inter. 18, 38–50 (1979).
[CrossRef]

Vetharaniam, I.

I. Vetharaniam, G. E. Stedman, “Accelerated observers: synchronisation and tests of local Lorentz invariance,” Class. Q. Gravity 11, 1069–1082 (1994).
[CrossRef]

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

Wells, P. V.

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

Wilkinson, J. R.

J. R. Wilkinson, “Ring lasers,” Prog. Quantum Electron. 11, 1–103 (1987).
[CrossRef]

Winkler, W.

T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
[CrossRef]

Woerdman, J. P.

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992).
[CrossRef] [PubMed]

Ziyuan, Li

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

Am. J. Phys. (1)

R. Anderson, H. R. Bilger, G. E. Stedman, “‘Sagnac’ effect: a century of earth-rotated interferometers,” Am. J. Phys. 62, 975–985 (1994).
[CrossRef]

Aust. J. Phys. (1)

G. E. Stedman, H. R. Bilger, Li Ziyuan, M. P. Poulton, C. H. Rowe, I. Vetharaniam, P. V. Wells, “Canterbury ring laser and tests for nonreciprocal phenomena,” Aust. J. Phys. 46, 87–101 (1993).

Bull. Earthquake Res. Inst. (1)

S. W. Smith, K. Kasahara, “Wave and mode separation with strain seismographs,” Bull. Earthquake Res. Inst. 47, 831–848 (1969).

Bull. Seismol. Soc. Am. (3)

M. A. Riedesel, R. D. Moore, J. A. Orcutt, “Limits of sensitivity of inertial seismometres with velocity transducers and electronic amplifiers,” Bull. Seismol. Soc. Am. 80, 1725–1752 (1990).

K. R. Gledhill, M. J. Randall, M. P. Chadwick, “The EARSS digital seismograph: system description and field trials,” Bull. Seismol. Soc. Am. 81, 1380–1390 (1991).

G. G. Sorrells, T. T. Goforth, “Low frequency Earth motion generated by slowly propagating organised pressure fields,” Bull. Seismol. Soc. Am. 63, 1583–1601 (1973).

Class. Q. Gravity (1)

I. Vetharaniam, G. E. Stedman, “Accelerated observers: synchronisation and tests of local Lorentz invariance,” Class. Q. Gravity 11, 1069–1082 (1994).
[CrossRef]

IEEE J. Quantum Electron. (2)

E. O. Schulz-Dubois, “Alternative interpretation of rotation rate sensing by ring laser,” IEEE J. Quantum Electron. QE-2, 299–305 (1987).

R. Rodloff, “A laser gyro with optimised resonator geometry,” IEEE J. Quantum Electron. QE-23, 438–445 (1987). Eq. (12a).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process (1)

A. H. Nuttall, “Some windows with very good sidelobe behav-iour,” IEEE Trans. Acoust. Speech Signal Process ASSP-29, 84–91 (1981).
[CrossRef]

J. Geophys. Res. (1)

G. G. Sorrells, E. J. Douze, “A preliminary report on infrasonic waves as a source of long period seismic noise,” J. Geophys. Res. 79, 4908–4917 (1974).
[CrossRef]

Opt. Lett. (1)

Phys. Earth Planet. Inter. (2)

R. D. Adams, “The New Zealand seismographic network,” Phys. Earth Planet. Inter. 18, 114–120 (1979);A. J. Haines, “Research in seismology and the physics of the Earth's interior in New Zealand 1987–1990,” presented by the New Zealand National Committee for Geodesy and Geophysics to the International Association of Seismology and Physics of the Earth's Interior, Vienna, Austria, August 1991.
[CrossRef]

M. J. Usher, R. F. Burch, C. Guralp, “Wide-band feedback seismometers,” Phys. Earth Planet. Inter. 18, 38–50 (1979).
[CrossRef]

Phys. Lett. A (1)

G. E. Stedman, H. R. Bilger, “Could a ring laser reveal the QED anomaly via vacuum chirality?” Phys. Lett. A 122, 289–292 (1987).
[CrossRef]

Phys. Rev. A (2)

C. Etrich, P. Mandel, R. Centeno Neelen, R. J. C. Spreeuw, J. P. Woerdman, “Dynamics of a ring-laser gyroscope with backscattering,” Phys. Rev. A 46, 525–536 (1992).
[CrossRef] [PubMed]

G. E. Stedman, Z. Li, C. H. Rowe, A. D. McGregor, H. R. Bilger, “Harmonic analysis in a precision ring laser with backscatter-induced pulling,” Phys. Rev. A 51, 4944–4958 (1995).
[CrossRef] [PubMed]

Phys. Rev. D (1)

T. M. Niebauer, A. Rüdiger, R. Schilling, L. Schnupp, W. Winkler, K. Danzmann, Phys. Rev. D 47, 3106–3123 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

M. R. Sayeh, H. R. Bilger, “Flicker noise in frequency fluctuations of lasers,” Phys. Rev. Lett. 55, 700–702 (1985);T. A. Dorschner, H. A. Haus, I. M. Holz, I. W. Smith, H. Statz, “Laser gyro at the quantum limit,” IEEE J. Quantum Electron. QE-16, 1376–1379 (1980);H. Statz, T. A. Dorschner, M. Holtz, I. W. Smith, “The multioscillator ring laser gyroscope,” in Laser Handbook, M. L. Stitch, M. Bass, eds. (North-Holland, Amsterdam, 1985), Vol. 4, pp. 229–332, equation 4.5.10.
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

J. R. Wilkinson, “Ring lasers,” Prog. Quantum Electron. 11, 1–103 (1987).
[CrossRef]

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R. Rodloff, “Gibt es den optische superkreisel?” Z. Flugwiss. Weltraumforsch. 18, 2–15 (1994).

Other (12)

M. Ewing, F. Press, “Surface waves and guided waves,” in Geophysics I, Vol. 47 of Encyclopaedia of Physics (Springer-Verlag, Berlin, 1956), pp. 119–139.
[CrossRef]

K. E. Bullen, B. A. Bolt, “An introduction to the theory of seismology,” 4th ed. (Cambridge U. Press, Cambridge, En-gland, 1985).

M. Bath, Introduction to Seismology, 2nd ed. (Birkhauser, Basel, 1979).

This distance assumes Northridge, Los Angeles, California to be at 34°14′N, 118°33′W, and the Cashmere cavern, Christchurch, New Zealand to be at 43°35′S, 172°38′E. The Northridge–Kelburn course and distance are 10,764 km, 224.3°; the Northridge–Cashmere course and distance are 223°, 11,105 km; the Kelburn–Cashmere figures are 214°, 309 km. For the comparison with the Kelburn data presented here, the help of T. H. Webb of the Institute of Geophysical and Nuclear Research, Wellington, New Zealand, is gratefully acknowledged.

R. J. Neutze, “Ring interferometer with angular acceleration,” Phys. Rev. A (to be published).

W. Schleich, P. Dobiasch, V. E. Sanders, M. O. Scully, “Nonequilibrium statistical physics in a dithered ring laser gyroscope, or quantum noise in pure and applied physics,” in Frontiers of Nonequilibrium Statistical Physics, Vol. 135 of NATO Advanced Study Institute Series B, G. T. Moore, M. O. Scully, eds. (New York, Plenum, 1986), pp. 385–408.
[CrossRef]

L. Cooper, “Axion detection by ring lasers,” M.Sc. thesis (University of Canterbury, Christchurch, New Zealand, 1994).

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A. V. Oppenheim, R. W. Schafer, Discrete-Time Signal Processing, (Prentice-Hall, Englewood Cliffs, N.J., 1989).

H. Kanamori, Seismological Laboratory, California Institute of Technology, Pasadena, Calif. 91103 (personal communication), 1992.

“Panel discussion,” in Proceedings of the International Symposium on Earthquake Disaster Prevention (CENAPRED, Mexico City, 1992), pp. 333–338.

K. Aki, P. G. Richards, Quantitative Seismology, Theory and Methods (Freeman, San Francisco, Calif., 1980).

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Figures (4)

Fig. 1
Fig. 1

Sidebands arising (a) from the motor-driven elastic band (0.625 Hz) taken from an 11-min segment of run czg 1205 (2 December 1994, 64 k at 10 sample/s, with the cutoff for dedrifting of 0.1 Hz), (b) in a 54-min segment of run g18 (18 January 1994, 64 k at 2 sample/s, with the cutoff of 0.05 Hz). The upper trace in (a) is the raw FFT of the data, and the effect of dedrifting with the routine gside is evident in the lower trace.

Fig. 2
Fig. 2

Set of parallel seismic records during an important sequence of seismic events in the South Island, New Zealand. The upper and middle traces are the filtered instantaneous phase obtained from the ring laser signal in the respective frequency ranges 0.05–1 Hz and 1–10 Hz. The lowest trace is a schematic indication of seismic activity at a conventional seismograph in a networked station at MQZ.

Fig. 3
Fig. 3

Magnified version of the main shock of Fig. 2. The first trace is plain time-domain data with the dominant (largely unaffected) Sagnac component from Earth rotation removed through appropriate frequency filtering. Two samples, of lengths 256 (dashed curve) and 512 (dotted curve) respectively, are superposed. The middle and lower traces correspond to the upper traces of Fig. 2 and are the filtered instantaneous phase for the respective frequency ranges 0.05–1 Hz and 1–10 Hz. Arrows indicate estimates from observations at MQZ of the arrival time of the p and s waves at the ring laser site.

Fig. 4
Fig. 4

Spectrum from a run (m4mhap 4) on 4 April 1994 of length 200 ks (∼60 h) at 2 s/s, in which the noise floor develops sidebands in the region 10–100 μHz. The carrier frequency, FWHMP, and height are fitted by 70,516,500 6 ± μHz, 28 6 ± μHz, and 80 6 ± dB, respectively.

Tables (1)

Tables Icon

Table 1 Basic Seismic Data for Arthur's Pass–Coleridge Events (43.04° S, 171.45° E), on or after 18 June 1994

Equations (26)

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f b = 4 A Ω / λ P .
d E ± d t = ( i ω ± + π a ) E ± + r E exp i ,
1 2 π d ψ d t = f l sin ψ ,
f = f e S f m sin 2 π f m t ,
ψ f ( t ) = 2 π f e t + S cos 2 π f m t .
ψ = ψ P ( t ) 2 arctan v f e = 2 arctan sin ( π p t + χ ) cos π p t ,
p ( f e 2 l 2 ) 1 / 2 , v l + p tan π p t , χ tan 1 ( l p ) .
D f + l sin ( 2 π p t + χ ) ,
V ( t ) = 1 + Re [ exp i ( 2 π f e t + S cos 2 π f m t ) ] = 1 + Re { exp ( 2 π i f e t ) × [ 0 ( S ) + n = 1 i n n ( S ) cos ( 2 π n i f m t ) ] } ,
n ( S ) = ( S 2 ) n k = 0 ( 1 ) k ( S 2 ) 2 k / [ k ! Γ ( n + k + 1 ) ] = ( S 2 ) n [ 1 n ! ( S 2 ) 2 1 ( n + 1 ) ! + ( S 2 ) 4 1 2 ( n + 2 ) ! ] .
0 ( S ) 1 ¼ S 2 , 1 S ( 8 S 2 ) / 16 , 2 S 2 ( 12 S 2 ) / 96 .
B = 10 log 10 [ 2 0 ( S ) 1 ( S ) ] 10 log 10 [ 4 S ( 1 1 8 S 2 ) ] 6 10 log 10 S
d d t ( D X ) = 2 π p l cos ( 2 π p t + χ ) cos 2 π f m t ,
X = plN ( p 2 f m 2 ) D ,
N p sin ( 2 π p t + χ ) cos 2 π f m t f m cos ( π p t + χ ) sin 2 π f m t .
V ( t ) { f + f cos 2 π p t S ( cos 2 π f m t + X ) × [ l + f sin ( 2 π p t + χ ) ] } / D .
Ω N ~ Ω δ f / f b = c P A Q ( h f 0 8 P o T ) 1 / 2 ,
Z ( t ) = V ( t ) + i W ( t ) = R ( t ) exp i Φ ( t ) ,
X ( t ) = A e cos 2 π f e ( t ) t + A cos [ 2 π f e ( t ) t 2 π f m t + β ] ,
Z ( t ) = A c exp i 2 π f e ( t ) t [ 1 + A A c exp i ( 2 π f m t β ) ] .
Ω = 1 2 × d u d t .
u = ayf ( y , z ) sin κ ( x c s t ) ,
Ω = ½ u ( t ) c s κ 2 ,
u = a ( exp α κ z 1 + β 2 2 exp β κ z ) sin κ ( x c s t ) x ̂ + a ( α exp α κ z + α β exp β κ z ) cos κ ( x c s t ) ,
β ( 2 3 ) 1 / 2 / 3 1 / 4 = 0.39 ) , α ( 1 + β 2 ) 2 4 β = 0.85 ,
u = a 1 β 2 2 [ 1 + ( 1 + β 2 2 β ) 2 ] 1 / 2 Ω R = ( 1 + 3 ) 1 / 2 2 u ( t ) c s κ 2 .

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