1. Noise and Sensitivity of RasClic 91
10 days of measurement
frame rate 12.4 Hz
periods of enhanced perturbations excluded (human presence)
223 frames (8.4 Mio) included in analysis

2. Raw Noise Spectrum of the Signal
FFT of x and y signal
step elimination at data gaps has no discernible effect
discard lowest 16 components for lack of relevance
16 component bins for reduced scatter (x0.25)

3. Noise Spectrum in Physical Units
amplitude in mm Hz-1/2 as a square root of a spectral power density
white noise at high f ( > 250 mHz )
1/f noise at low f ( < 10 mHz )
broad resonances at 220 and 440 mHz
some structure at 10— 100 mHz

4. Current Limits to RasClic Sensitivity
Noise (white noise) and drifts (1/f noise) in the signal:
white noise: uncorrelated single-point uncertainty s = 200 nm
Improvement potential:
up to 100x : better algorithm for image position (Kramer-Rao-limit)
up to 4x on noise amplitude: increase sample rate to 200 Hz
1/f noise: random-walk of the image position
up to 100x (1000x?) by temperature control (insulation and supervision)

5. Compare Sensitivity with Seismometers
Limitation as given by empirical noise; comparison with seismometers requires:
determining RasClic sensitivity as a function of wavelength
converting wavelengths into seismic oscillation frequencies
converting noise levels at these frequencies into equivalent seismic accelerations
comparing with seismometer specifications

6. RasClic Sensitivity as a Function of Wavelength
Assume that the Earth radius is modulated by r(f) = R0 + a with a = A cos kf, and k the number of periods around the circumference.
The resulting local radius of curvature is (to first order) r(f) = R – (k2–1) a .
For the value x measured by RasClic (the shift of the end point with respect to a straight line pointing through the start point and the center) with length L follows:
E.g., with L = 91m the sensitivity parameter for the quadrupole mode (k = 2) is:
x/a = 5.1*10–11.

7. Converting Wavelengths into Seismic Frequencies
Typical seismic waves have phase velocities of 4-6 km/s, corresponding to earth round trip times of 3 to 2 hours. The graphs show phase velocities and frequency vs. wavelength of 0Sn modes, used in this analysis.

8. Sensitivity as Function of Seismic Frequency
x / a as a function of frequency for 0Sn modes
comparison for three different L values: 91 m, 500 m, 20 km.
The maximum value is 4, when the wavelength equals L; for shorter wavelength the sensitivity oscillates, becoming zero at integer fractions of L/2.

9. Convert Noise Levels into Equivalent Accelerations
For comparison with seismometers, convert position noise into accelerations. g – g
dB units refer to the scale unit m2s–4Hz–1.
E.g., –100 dB means (10-5m)2s–4Hz–1
These are motions of the SIGNAL (x), not of the EARTH (a)!

10. Noise-Equivalent Earth Surface Acceleration
Dividing accelerations of signal (x) noise by the sensitivity parameter x/a provides a value of what seismic acceleration at a given frequency would be required to equal the observed (status quo) noise.

11. Comparison RasClic (status quo) – KNMI
Noise background comparison RasClic (status quo) vs. state- of-the-art seismometer (KNMI)
Projected improvements will result in:
40 dB white noise reduction by improved image position analysis
12 dB white noise reduction by increased data rate
40–60 dB 1/f -noise reduction by temperature control
every doubling of L (up to the seismic wavelength) gives an improvement of 12 dB

12. Fundamental Noise Limit
There is no intrinsic random walk  no intrinsic 1/f noise
Noise limit to sensitivity determined by: (figures current  projected)
individual uncertainty(180 nm  1 nm)
repetition rate (12.4 Hz  1 kHz)
length dependent sensitivity (91 m  140 m  500 m  20 km)