Autoregressive Analysis for the Detection of Earthquakes With a Ring Laser Gyroscope

Abstract

The second-order autoregressive AR(2) model is used to analyze rotational data for seismic events captured by a large ring laser gyroscope. Both the Sagnac frequency and linewidth estimates obtained from this model sense the rotational components of seismic waves. An event of magnitude M L = 6.5 at a distance of D = 5.4° from a large ring laser gyroscope operating at its quantum limit is used to compare the AR(2) model with the previous analytical phase angle method of analysis. The frequency, linewidth and analytic phase angle data each satisfactorily estimate the rotation magnitude. The direct detection of rotational motion in the P wave coda is observed, demonstrating the conversion to transverse S wave polarizations by the local geology.

The GEOsensor Project: Rotations — a New Observable for Seismology

“…While for the remote earthquake the spectral power density essentially drops off to zero above frequencies of 0.1 Hz, one can still see some signal signature up to about 4 Hz for the regional event. Frequencies with a rate of change above 2 Hz; however, are already outside the regime of reliable representation in phase and amplitude by conventional frequency counting and second order autoregression frequency analysis (McLeod et al, 2001).…”

Compensation of the laser parameter fluctuations in large ring-laser gyros: a Kalman filter approach

“…In Figure 1 we report the results of a Monte Carlo simulation of 10 6 s of ring laser dynamics evolution with I 1 /I 2 = k. We considered the following noise sources in the system: a white frequency noise with standard deviation of 10 −1 on ω(t) (mimic of the output of AR(2) frequency detection algorithm [20]) and a random-walk noise on the parameters r 1,2 , k, and ε. The Allan variance of ω(t) has been calculated for four different cases, denoted with (a), (b), (c) and (d).…”

“…the value of τ where the minimum is attained) of a ring laser can be significantly improved. In fact, the instantaneous Sagnac frequency will depend in general on the full system state [I 1 (t), I 2 (t), ψ(t)], and so dynamic Kalman filtering can be more effective in estimating ω s than other approaches that rely on ψ(t) only (e. g. the standard AR(2) method for frequency estimation [20]).…”

“…(2) taking into account the spectroscopic prop- erties of its active medium and the constraints imposed by the stabilization loops. The use of a special gas mixture, containing 20 Ne and 22 Ne isotopes at 50:50 ratio, avoids mode competition effects, while the perimeter control, by keeping constant the laser optical frequency avoids mode-jumps. In the Appendix A we show that β 1 = β 2 = β, σ 1 = σ 2 , τ 12 = τ 21 = 0, and θ 12 = θ 21 = 0 hold for the closed loop operation of G-Pisa.…”