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Experiments with an Interferometric Seismometer (iSeis) |
Mark Zumberge, Jonathan Berger, and Jose Otero:
Scripps Institution of Oceanography, University of California San Diego
Erhard Wielandt:
Institute of Geophysics, Stuttgart University, Stuttgart, Germany
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Abstract:
Modern seismometers rely on electronic displacement transducers to sense the motion of an inertial mass suspended by a spring. The more sophisticated systems use electrostatic or electromagnetic force-feedback on the inertial mass to ameliorate the shortcomings of the spring and the displacement transducer. Recent advances in optical fiber technology and digital signal processing offer an alternative to the modern observatory seismometer. We have recently developed an optical fringe resolver to replace the electronic displacement transducer that may lead to an improved seismometer. The use of optical fiber interferometer in place of electronics adds other important benefits, including immunity to noise pickup, simplification of remote deployment (in a borehole, for example), the elimination of a heat source in the seismometer (an important cause of noise in the best existing systems) and elimination of electrical connections between the seismometer and the recording system.Our first test of this concept was to apply it to a standard STS-1 seismometer. For this experiment, we added interferometer components to the seismometer frame and a retro-reflector to the seismometer's mass. We removed the feedback electronics and recorded the STS-1 mass displacement with our new interferometric system. Simultaneously we recorded the output of a standard STS-1 set up on the same pier. The results, which include observations of large teleseisms and microseisms, indicate that the new technique is promising. In our second experiment, we measured the inherent noise floor of the displacement transducer. In a 100 Hz bandwidth, the RMS noise was approximately 5 X 10^-12 m. This, when applied to a mass-spring suspension having a 5.4 s period and a Q of 7.4 will resolve the USGS ground noise model up to at least 15 Hz.The use of optical fiber interferometry rather than traditional electronic displacement transducers affords the following advantages:
- A linear, high-resolution displacement detector - the proposed optical sensor includes the functionality of a digitizer providing about a 30-bit digital output.
- Absolute displacement measurement referenced to the wavelength of light.
- Bandwidth sufficient to resolve the USGS Low Noise Model from DC to > 15 Hz.
- Minimum electronics in package - only optical fiber connection to the seismometer, minimizing heat from electronics in the sensor package and noise pickup from electrical cables.
- Smaller package - our design will be applicable to both vault and borehole installations and should be relatively easy to manufacture.
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IRIS Design Goals:
- Sensitive axis orientation accurate to 0.6 degrees minimum.
- Calibrations good to 1% and gain stability of 1% between calibrations.
- Seismometer linearity of 90 dB or greater.
- Bandwidth of 10-4 Hz to about 15 Hz.
- Clip level of 5.8 X 10-3 m/s RMS over the band 10-4 Hz to 15 Hz.
Our goal is to meet most if not all these requirements. At the very least, the design will offer an alternative to the existing very-broadband seismometers.
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| Figure 1: Conceptual mechanical design for vertical component Optical Seismometer. |
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Figure 2: The figure shows a simple Michelson interferometer which has been modified to produce two fringe signals that are in quadrature. A birefringent element (a lambda/8 phase retarder) placed in one of the optical arms, lengthens the optical path for one polarization by lambda/4 per round trip. Illuminating the interferometer with both polarizations (by adjusting a lambda/2 phase retarder before the beam splitter ) and separating the two fringe signals (with a polarizing beam splitter) produces sine and cosine components of the optical phase difference. The two-photodetector output voltages vary as the optical path difference L changes. |
Design Considerations:
- The amplitudes of the displacements to be measured are quite challenging -- ambient ground noise at a quiet station can be as small as 10-12m Hz-1/2 at 10 Hz.
- The free period (T), ground acceleration (g), frequency (f) and the displacement (x) of a seismometer are related by:
where Q is the mechanical quality factor. For a non-feedback system, this equation shows that the ratio of mass displacement to applied acceleration (force) is a function of the free period and Q of the suspension.
- A mass of 0.1 to 0.3 kg and a free period of 3 to 5 seconds is achievable in a 10 cm package. Brownian noise considerations require MTQ > 1 kg s. A leaf-spring geometry provides the required free period.
- Observatory grade seismometers employ a displacement transducer such as a linear variable differential transducer or a variable capacitive sensor. These have difficulties in resolving required displacements (their self noise limits the bandwidth) while producing a linear output and also have a limited dynamic range.
- We have developed an optical displacement transducer that may lead to a greatly improved seismometer (figure 2). The use of optical fiber interferometry (described below) in place of electronics adds benefits, including immunity to noise pickup, simplification of remote deployment (in a borehole, for example), the elimination of heat sources within the seismometer, and the elimination of components that can be damaged in electrical storms (a problem in many field settings.)
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Optical Fringe Resolver
- For seismometry we require resolution in displacement of about 10-12 m Hz -1/2 at 10 Hz, and the ability to follow displacements that span several mm.
- We have developed and tested a digital-signal-processor (DSP) based fringe resolver with a demonstrated resolution of 5 X 10 -13 m Hz -1/2 at 1 Hz and higher.
- Optical fibers allow us to move the laser and two detectors far away from the interferometer. The optical fibers between the laser and detectors, in figure 2, can span several hundred meters if needed. Because the optical path difference sensed by the interferometer is in free space (outside of the fibers), the optical path lengths of the fibers themselves are unimportant.
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Figure 3: The quadrature fringe signals. In (a) we plot the two signals vs time. In (b) we plot x an y against each other, which yields an ellipse. Increasing and decreasing the path length difference causes the x-y ordered pair at any instant to move clockwise or counterclockwise around the ellipse. It is this position on the ellipse that we want to record. |
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Fringe Resolver Specifications
- 12-bit, 100k samples per second analog-to-digital converter directly to a DSP.
- Full scale10 mm displacement and 1.5 X 10-2 m/s velocity.
- Present electronics capable of 500k samples per second, making the full scale velocity 7.5 X 10-2 m/s.
- Phase determined at 100k sps and filtered to 200 sps. Phase resolution at 200 sps is better than 9 X 10-5 radians.
- Measured optical fringe resolver noise floor: 5 X 10-13 m Hz -1/2.
- Pre-prototype optical fiber interferometer can resolve the USGS Low Noise Model ground noise from DC to about 15 Hz.
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Figure 4: Smoothed interferometer and electronic noise spectra compared with the USGS Low Noise Model acceleration spectrum passed through Eq 1 with T = 5.4 s and Q = 7.4, which corresponds to the STS-1. Spikes in the spectra are believed to be an artificial of the fringe processing scheme. |
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Figure 5: There are two limits to this new design. First, the mass stops limit mass motion to about ±1 cm. Second, the optical fringe resolver will lose trace of the mass when the velocity exceeds 7.5 cm/s. The red curve show how these limits translate to large accelerations (examples of which are show with green curves) with our prototype suspension. |
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Pre-Prototype: A Modified STS1
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Figure 6: Photographs of experiments we carried out, comparing a standard STS-1 to one in which we replaced the electronics with optics. Both seismometers were situated on the same pier. The first was operated normally. In the second, the electronic position sensor was disconnected, and the forcing coil was shorted internally to provide damping. No electrical connections were made to the modified STS-1. Laser light entered and exited through a window in the seismometer's vacuum jar to provide position information.
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Figure 7: Seismograms recorded with both the modified Optical STS-1 and a standard STS-1 from a magnitude 6.7 event off South Georgia Island on 15 November 2002, about 115° from San Diego. The signal at IGPP reached an amplitude of ± 2.5 X 10-4 m of mass motion, very close to the clip level of the STS-1 seismometer, but well within the dynamic range of the Optical Seismometer. |
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Prototype Vertical Component Optical Seismometer |
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Figure 8: Prototype vertical optical seismometer. This unit has a mass of 360 grams and a free period of a few seconds. The spring is a single strip of "NiSpan-C" a trade name for a particular alloy of iron-nickel with small amounts of chromium and titanium.
- For more images, showing the construction, testing, and facilities for the SIFO (seismometers incorporating fiber optics) project, please click here.
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Because we are not using force feedback, (i.e. not forcing the mass to always be near its equilibrium point) we must solve the problems of non-linearity and cross coupling. There are two sources of non-linearity in our instrument:
- The displacement transducer tracks the mass's motion along the optical axis when in fact the mass moves in an arc.
- The restoring force does not exactly follow Hooke's Law. Rather, we have numerous higher order terms.
Because the mass moves in an arc, when it is away from the equilibrium position, its sensitive axis changes slightly, resulting in cross coupling.Normally, the differential equation which governs a seismometer suspension is:
where m is the seismometer mass, z is the mass position with respect to the frame, r is the drag coefficient, k is the spring constant, and h is the ground acceleration. With our system, we must modify this equation slightly:
where zc is the position corrected for the arc motion, α is the cross coupling coefficient, and n is the ground displacement normal to the sensitive axis. The displacement is computed by a DSP. Future work will attempt to further develop the DSP code to correct for non linearity and cross coupling. |
Figure 9: A typical ring down time series for the prototype vertical fiber optic seismometer (a). The mass is displaced towards the upper stop and allowed to naturally decay. The shape of the curve and decay time is governed by the damping and the restoring force of the spring. Numerically correlating the computed acceleration with position yields the spring constant. Correlating acceleration with velocity yields the damping. The restoring force, after correcting for damping is shown as a function of mass position (b). The slope of this line is the spring constant, k, over the mass m. The non-linear portion that results from the geometry of the leaf spring suspension, is shown (c). The period is given by:
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Figure 10: Seismograms recorded with SIFO (red) and a standard STS-1 (blue) from a magnitude 9.0 event off the Sumatra coast on 24 December 2005, about 132° from San Diego. The STS1 was located approximately 5 km from SIFO ontop of Mt. Soledad. |
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Additional Information
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Conceptual Videos of iSeis:
- A fly-through video (Quicktime) of how iSeis works: [w/ sound] [w/o sound]
- A second fly-through video (Quicktime) of iSeis, with more attention to the optics: [w/ sound] [w/o sound]
The above videos require Apple's Quicktime viewer to view them. Additional plugins may need to be downloaded. Both can be downloaded, for free, from Apple' Quicktime website. These videos were created by Jose Otero, with assistance from the IGPP Viz Center. Special thanks to Jeremy Smith for making this video a reality.
iSeis Photos:
- SIFO Construction
- SIFO Testing
- Shake Tables
- PFO Vault Construction
- Michelson Interferometers
The above photos and more can be viewed at this here. A pdf presentation outlining the details of iSeis can be found here.
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People
- Mark Zumberge (Principal Investigator)
- Jose Otero (Graduate Student / PhD Candidate)
- Erhard Wielandt
- John Berger
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