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Charles R. Hutt - One of the best experts on this subject based on the ideXlab platform.
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detection and characterization of pulses in broadband Seismometers
Bulletin of the Seismological Society of America, 2017Co-Authors: David C Wilson, Adam T. Ringler, Charles R. HuttAbstract:Abstract Pulsing—caused either by mechanical or electrical glitches, or by microtilt local to a seismometer—can significantly compromise the long‐period noise performance of broadband Seismometers. High‐fidelity long‐period recordings are needed for accurate calculation of quantities such as moment tensors, fault‐slip models, and normal‐mode measurements. Such pulses have long been recognized in accelerometers, and methods have been developed to correct these acceleration steps, but considerable work remains to be done in order to detect and correct similar pulses in broadband seismic data. We present a method for detecting and characterizing the pulses using data from a range of broadband sensor types installed in the Global Seismographic Network. The technique relies on accurate instrument response removal and employs a moving‐window approach looking for acceleration baseline shifts. We find that pulses are present at varying levels in all sensor types studied. Pulse‐detection results compared with average daily station noise values are consistent with predicted noise levels of acceleration steps. This indicates that we can calculate maximum pulse amplitude allowed per time window that would be acceptable without compromising long‐period data analysis.
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Laboratory and Field Testing of Commercial Rotational Seismometers
Bulletin of the Seismological Society of America, 2009Co-Authors: Robert L. Nigbor, John R. Evans, Charles R. HuttAbstract:Abstract There are a small number of commercially available sensors to measure rotational motion in the frequency and amplitude ranges appropriate for earthquake motions on the ground and in structures. However, the performance of these rotational Seismometers has not been rigorously and independently tested and characterized for earthquake monitoring purposes as is done for translational strong- and weak-motion Seismometers. Quantities such as sensitivity, frequency response, resolution, and linearity are needed for the understanding of recorded rotational data. To address this need, we, with assistance from colleagues in the United States and Taiwan, have been developing performance test methodologies and equipment for rotational Seismometers. In this article the performance testing methodologies are applied to samples of a commonly used commercial rotational seismometer, the eentec model R-1. Several examples were obtained for various test sequences in 2006, 2007, and 2008. Performance testing of these sensors consisted of measuring: (1) sensitivity and frequency response; (2) clip level; (3) self noise and resolution; and (4) cross-axis sensitivity, both rotational and translational. These sensor-specific results will assist in understanding the performance envelope of the R-1 rotational seismometer, and the test methodologies can be applied to other rotational Seismometers.
W. T. Pike - One of the best experts on this subject based on the ideXlab platform.
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SEIS: Insight’s Seismic Experiment for Internal Structure of Mars
Space Science Reviews, 2019Co-Authors: Philippe Lognonné, P. Laudet, W. T. Pike, Domenico Giardini, U Christensen, Sebastien De Raucourt, William B. Banerdt, Peter Zweifel, Simon Calcutt, Marco BierwirthAbstract:By the end of 2018, 42 years after the landing of the two Viking Seismometers on Mars, InSight will deploy onto Mars’ surface the SEIS (Seismic Experiment for Internal Structure) instrument; a six-axes seismometer equipped with both a long-period three-axes Very Broad Band (VBB) instrument and a three-axes short-period (SP) instrument. These six sensors will cover a broad range of the seismic bandwidth, from 0.01 Hz to 50 Hz, with possible extension to longer periods. Data will be transmitted in the form of three continuous VBB components at 2 sample per second (sps), an estimation of the short period energy content from the SP at 1 sps and a continuous compound VBB/SP vertical axis at 10 sps. The continuous streams will be augmented by requested event data with sample rates from 20 to 100 sps. SEIS will improve upon the existing resolution of Viking’s Mars seismic monitoring by a factor of ∼2500$\sim 2500$ at 1 Hz and ∼200000$\sim 200\,000$ at 0.1 Hz. An additional major improvement is that, contrary to Viking, the Seismometers will be deployed via a robotic arm directly onto Mars’ surface and will be protected against temperature and wind by highly efficient thermal and wind shielding. Based on existing knowledge of Mars, it is reasonable to infer a moment magnitude detection threshold of Mw∼3$M_{{w}} \sim 3$ at 40∘$40^{\circ}$ epicentral distance and a potential to detect several tens of quakes and about five impacts per year. In this paper, we first describe the science goals of the experiment and the rationale used to define its requirements. We then provide a detailed description of the hardware, from the sensors to the deployment system and associated performance, including transfer functions of the seismic sensors and temperature sensors. We conclude by describing the experiment ground segment, including data processing services, outreach and education networks and provide a description of the format to be used for future data distribution.
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Isolation of Seismic Signal from InSight/SEIS-SP Microseismometer Measurements
Space Science Reviews, 2018Co-Authors: J Hurley, Naomi Murdoch, Nicholas A Teanby, Simon Calcutt, N. Bowles, T. Warren, David Mimoun, W. T. PikeAbstract:The InSight mission is due to launch in May 2018, carrying a payload of novel instruments designed and tested to probe the interior of Mars whilst deployed directly on the Martian regolith and partially isolated from the Martian environment by the Wind and Thermal Shield. Central to this payload is the seismometry package SEIS consisting of two Seismometers, which is supported by a suite of environmental/meteorological sensors (Temperature and Wind Sensor for InSight TWINS; and Auxiliary Payload Sensor Suite APSS). In this work, an optimal estimations inversion scheme which aims to decorrelate the short-period seismometer (SEIS-SP) signal due to seismic activity alone from the environmental signal and random noise is detailed, and tested on both simulated and Viking data. This scheme also applies a module to identify measurements contaminated by Single Event Phenomena (SEP). This scheme will be deployed as the pre-processing pipeline for all SEIS-SP data prior to release to the scientific community for analysis.
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Seismic Coupling of Short-Period Wind Noise Through Mars’ Regolith for NASA’s InSight Lander
Space Science Reviews, 2017Co-Authors: Nicholas A Teanby, Jelka Stevanovic, Robert Myhill, James Wookey, Naomi Murdoch, J Hurley, Simon Calcutt, N E Bowles, W. T. PikeAbstract:NASA’s InSight lander will deploy a tripod-mounted seismometer package onto the surface of Mars in late 2018. Mars is expected to have lower seismic activity than the Earth, so minimisation of environmental seismic noise will be critical for maximising observations of seismicity and scientific return from the mission. Therefore, the Seismometers will be protected by a Wind and Thermal Shield (WTS), also mounted on a tripod. Nevertheless, wind impinging on the WTS will cause vibration noise, which will be transmitted to the Seismometers through the regolith (soil). Here we use a 1:1-scale model of the seismometer and WTS, combined with field testing at two analogue sites in Iceland, to determine the transfer coefficient between the two tripods and quantify the proportion of WTS vibration noise transmitted through the regolith to the Seismometers. The analogue sites had median grain sizes in the range 0.3–1.0 mm, surface densities of 1.3 – 1.8 g cm − 3 $1.3\mbox{--}1.8~\mbox{g}\,\mbox{cm}^{-3}$ , and an effective regolith Young’s modulus of 2.5 − 1.4 + 1.9 MPa $2.5^{+1.9}_{-1.4}~\mbox{MPa}$ . At a seismic frequency of 5 Hz the measured transfer coefficients had values of 0.02–0.04 for the vertical component and 0.01–0.02 for the horizontal component. These values are 3–6 times lower than predicted by elastic theory and imply that at short periods the regolith displays significant anelastic behaviour. This will result in reduced short-period wind noise and increased signal-to-noise. We predict the noise induced by turbulent aerodynamic lift on the WTS at 5 Hz to be ∼ 2 × 10 − 10 ms − 2 Hz − 1 / 2 $\sim2\times10^{-10}~\mbox{ms}^{-2}\,\mbox{Hz}^{-1/2}$ with a factor of 10 uncertainty. This is at least an order of magnitude lower than the InSight short-period seismometer noise floor of 10 − 8 ms − 2 Hz − 1 / 2 $10^{-8}~\mbox{ms}^{-2}\,\mbox{Hz}^{-1/2}$ .
Y. Hello - One of the best experts on this subject based on the ideXlab platform.
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P‐Delays from Floating Seismometers (MERMAID), Part I: Data Processing,
Seismological Research Letters, 2016Co-Authors: G. Nolet, C. Joubert, S. Bonnieux, Anne Deschamps, J.x. Dessa, Y. HelloAbstract:We present methods of data analysis adapted to Mobile Earthquake Recorder in Marine Areas by Independent Divers (MERMAID) seismograms, obtained with hydrophones mounted on moving underwater floats. If the MERMAID float comes immediately to the surface after recording an earthquake signal, the seismogram location is obtained from the first Global Positioning System (GPS) position, using a correction for the surface drift of the float. In the case of earthquakes recorded without an immediate surfacing, the location is estimated using a linear interpolation between GPS positions. We performed a Bézier interpolation of the GPS positions to estimate a location error. In 67% of the cases, the distance between the two trajectories was less than 500 m. We tested the method on six months of data acquired in the Ligurian basin (Mediterranean Sea). To validate the (manually) picked onset times for P waves, we performed a preliminary tomographic inversion beneath the Ligurian basin of MERMAID data together with a much larger volume of picks from nearby land and ocean‐bottom seismometer stations. After inversion we found that 67% of MERMAID data have a misfit between ±0.17 s, but the distribution of misfits is not Gaussian and shows outliers. We conclude that floating Seismometers are an excellent and accurate means for covering oceanic areas for P‐wave tomography.
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p delays from floating Seismometers mermaid part i data processing
Seismological Research Letters, 2016Co-Authors: C. Joubert, G. Nolet, S. Bonnieux, Anne Deschamps, J.x. Dessa, Y. HelloAbstract:We present methods of data analysis adapted to Mobile Earthquake Recorder in Marine Areas by Independent Divers (MERMAID) seismograms, obtained with hydrophones mounted on moving underwater floats. If the MERMAID float comes immediately to the surface after recording an earthquake signal, the seismogram location is obtained from the first Global Positioning System (GPS) position, using a correction for the surface drift of the float. In the case of earthquakes recorded without an immediate surfacing, the location is estimated using a linear interpolation between GPS positions. We performed a Bezier interpolation of the GPS positions to estimate a location error. In 67% of the cases, the distance between the two trajectories was less than 500 m. We tested the method on six months of data acquired in the Ligurian basin (Mediterranean Sea). To validate the (manually) picked onset times for P waves, we performed a preliminary tomographic inversion beneath the Ligurian basin of MERMAID data together with a much larger volume of picks from nearby land and ocean‐bottom seismometer stations. After inversion we found that 67% of MERMAID data have a misfit between ±0.17 s, but the distribution of misfits is not Gaussian and shows outliers. We conclude that floating Seismometers are an excellent and accurate means for covering oceanic areas for P‐wave tomography.
Philippe Lognonné - One of the best experts on this subject based on the ideXlab platform.
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High Precision SEIS Calibration for the InSight Mission and Its Applications
Space Science Reviews, 2019Co-Authors: L. Pou, Philippe Lognonné, D. Mimoun, R. Garcia, O. Karatekin, M. Nonon-latapie, R. Llorca-cejudoAbstract:Part of the InSight mission, the SEIS instrument (Seismic Experiment for Interior Structures), is planned to arrive on Mars in November 2018. In order to prepare its future recordings on the red planet, special attention was directed towards calibrating the seismometer in-situ on the Martian surface. Besides relative calibrations, we studied the possibility of actively calibrating the two kinds of Seismometers onboard SEIS, the Very Broad Band Seismometers (VBB) and the Short Period Seismometers (SP) and extended the analysis towards a possible absolute calibration. For that purpose, we developed additional noise models at low frequency and elaborate on how they will be sensed by the seismic sensors from long-period data recorded by the seismometer. Such work will improve SEIS capabilities to unveil the inner structure of Mars by checking SEIS well-being and with applications such as gravimetry with the main Phobos tide. The current calibra
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SEIS: Insight’s Seismic Experiment for Internal Structure of Mars
Space Science Reviews, 2019Co-Authors: Philippe Lognonné, P. Laudet, W. T. Pike, Domenico Giardini, U Christensen, Sebastien De Raucourt, William B. Banerdt, Peter Zweifel, Simon Calcutt, Marco BierwirthAbstract:By the end of 2018, 42 years after the landing of the two Viking Seismometers on Mars, InSight will deploy onto Mars’ surface the SEIS (Seismic Experiment for Internal Structure) instrument; a six-axes seismometer equipped with both a long-period three-axes Very Broad Band (VBB) instrument and a three-axes short-period (SP) instrument. These six sensors will cover a broad range of the seismic bandwidth, from 0.01 Hz to 50 Hz, with possible extension to longer periods. Data will be transmitted in the form of three continuous VBB components at 2 sample per second (sps), an estimation of the short period energy content from the SP at 1 sps and a continuous compound VBB/SP vertical axis at 10 sps. The continuous streams will be augmented by requested event data with sample rates from 20 to 100 sps. SEIS will improve upon the existing resolution of Viking’s Mars seismic monitoring by a factor of ∼2500$\sim 2500$ at 1 Hz and ∼200000$\sim 200\,000$ at 0.1 Hz. An additional major improvement is that, contrary to Viking, the Seismometers will be deployed via a robotic arm directly onto Mars’ surface and will be protected against temperature and wind by highly efficient thermal and wind shielding. Based on existing knowledge of Mars, it is reasonable to infer a moment magnitude detection threshold of Mw∼3$M_{{w}} \sim 3$ at 40∘$40^{\circ}$ epicentral distance and a potential to detect several tens of quakes and about five impacts per year. In this paper, we first describe the science goals of the experiment and the rationale used to define its requirements. We then provide a detailed description of the hardware, from the sensors to the deployment system and associated performance, including transfer functions of the seismic sensors and temperature sensors. We conclude by describing the experiment ground segment, including data processing services, outreach and education networks and provide a description of the format to be used for future data distribution.
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Frequency band enlargement of the penetrator seismometer and its application to moonquake observation
Advances in Space Research, 2015Co-Authors: Ryuhei Yamada, Philippe Lognonné, Naoki Kobayashi, Tanguy Nébut, Hiroaki Shiraishi, Satoshi TanakaAbstract:Seismic data obtained over a broad frequency range are very useful in investigation of the internal structures of the Earth and other planetary bodies. However, planetary seismic data acquired through the NASA Apollo and Viking programs were obtained only over a very limited frequency range. To obtain effective seismic data over a broader frequency range on planetary surfaces, broadband Seismometers suitable for planetary seismology must be developed. In this study, we have designed a new broadband seismometer based on a short-period seismometer whose resonant frequency is 1 Hz for future geophysical missions. The seismometer is of an electromagnetic type, light weight, small size and has good shock-durability, making it suitable for being loaded onto a penetrator, which is a small, hard-landing probe developed in the LUNAR-A Project, a previous canceled mission. We modified the short-period seismometer so as to have a flat frequency response above about 0.1 Hz and the detection limit could be lowered to cover frequencies below the frequency. This enlargement of the frequency band will allow us to investigate moonquakes for lower frequency components in which waveforms are less distorted because strong scattering due to fractured structures near the lunar surface is likely to be suppressed. The modification was achieved simply by connecting a feedback circuit to the seismometer, without making any mechanical changes to the short-period sensor. We have confirmed that the broadband seismometer exhibits the frequency response as designed and allows us to observe long-period components of small ground motions. Methods to improve the performance of the broadband seismometer from the current design are also discussed. These developments should promise to increase the opportunity for application of this small and tough seismometer in various planetary seismological missions. (C) 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
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Lunar Surface Gravimeter as a lunar seismometer: Investigation of a new source of seismic information on the Moon
Journal of Geophysical Research. Planets, 2015Co-Authors: Taichi Kawamura, Satoshi Tanaka, Naoki Kobayashi, Philippe LognonnéAbstract:Lunar seismology has always suffered from the limited number of seismic stations and limited coverage of the seismic network. Additional seismic data are necessary to probe the lunar interior in depth. Instead of a costly new deployment of Seismometers, the aim of this study is to investigate the possibility of using the Apollo 17 Lunar Surface Gravimeter (LSG) as a lunar seismometer. The LSG was designed to detect gravitational waves (associated to change in the curvature of spacetime) and tidal ground motion on the Moon, but the data were not investigated for seismic use partially because of a malfunction of the instrument. We first evaluated the influence of the malfunction through comparison with other Apollo seismic data and found that the effect of the malfunction is small, and the LSG detected seismic signals in a manner that was consistent with those of the other Apollo Seismometers. Then we carried out source location with the additional station of the LSG. We relocated previously located deep moonquake nests to evaluate the influence of the LSG data, which are generally noisier than other Apollo seismic data. Then we located deep moonquake nests that were previously unlocatable. Forty deep moonquake nests were examined, and we located five new nests. One newly located nest, A284, was most likely to be located on the farside. This series of analyses indicates that the LSG functioned as a lunar seismometer, and that its data are useful for improving seismic analyses with the previous seismic data set of the Moon.
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on the possibility of lunar core phase detection using new Seismometers for soft landers in future lunar missions
Planetary and Space Science, 2013Co-Authors: Ryuhei Yamada, Philippe Lognonné, Naoki Kobayashi, Nozomu Takeuchi, Tanguy Nébut, Hiroaki Shiraishi, Marie Calvet, Raphael F GarciaAbstract:Abstract Information on the lunar central core; size, current state and composition; are key parameters to understand the origin and evolution of the Moon. Recent studies have indicated that possible seismic energies of core-reflected phases can be identified from past Apollo seismic data, and core sizes are determined, but we have still uncertainties to establish the lunar core parameters. We, therefore, plan to detect seismic phases that pass through the interior of the core and/or those reflected from the core–mantle boundary to ensure the parameters using new Seismometers for future lunar soft-landing missions such as SELENE-2 and Farside Explorer projects. As the new Seismometers, we can apply two types of sensors already developed; they are the Very Broad Band (VBB) seismometer and Short Period (SP) seismometer. We first demonstrate through waveform simulations that the new Seismometers are able to record the lunar seismic events with S/N much better than Apollo Seismometers. Then, expected detection numbers of core-phases on the entire lunar surface for the two types of Seismometers are evaluated for two models of seismic moment distributions of deep moonquakes using the recent interior model (VPREMOON). The evaluation indicates that the VBB has performance to detect reflected S phases (ScS) from the core–mantle boundary mainly on the lunar near-side, and the P phases (PKP) passing through the interior of the core on some areas of the lunar far-side. Then, the SP can also detect PKP phases as first arrival seismic phase on limited regions on the lunar far-side. If appropriate positions of the seismic stations are selected, core-phases can be detected, allowing us to constrain the origin and evolution of the Moon with future lunar soft-landing missions.
Peter W. Rodgers - One of the best experts on this subject based on the ideXlab platform.
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Signal-coil calibration of electromagnetic Seismometers
Bulletin of the Seismological Society of America, 1995Co-Authors: Peter W. Rodgers, Aaron J. Martin, Michelle C. Robertson, Mark M. Hsu, David B. HarrisAbstract:Abstract We show that electromagnetic (em) Seismometers may be easily and accurately calibrated by removing a step of current from their signal coil, and simultaneously switching the signal coil to a recorder to capture the response. A theory is developed that obtains the damped generator constant, resonant frequency, and damping ratio from the output of a system identifier used to analyze the response. Only the seismometer mass (from the manufacturer) and the applied current (measured) need be known for a complete calibration. The coil and damping resistances are not required. The method is confirmed by comparing this signal-coil method with weight-lift and calibration-coil calibrations. For a GS-13 V seismometer, these results were within 1.3% of each other. The undamped generator constant computed from the damped generator constant obtained by the signal-coil method matched the generator constant given by the manufacturer to better than 1%. Calibration of nine new L-4C components resulted in undamped generator constants all within 3% of the values given by the manufacturer. The circuit used in the signal-coil method is shown and explained.
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Self-noise spectra for 34 common electromagnetic seismometer/preamplifier pairs
Bulletin of the Seismological Society of America, 1994Co-Authors: Peter W. RodgersAbstract:Because of a lack of such information, computed self-noise spectra are presented for a total of 34 frequently used electromagnetic-seismometer I preamplifier combinations. For convenience, most of these data are given in three sets of units. Peterson's Low Noise Model is included on each plot for comparison. The self-noises of nine frequently employed electromagnetic (EM) Seismometers properly matched to their operational amplifier (op-amp) preamplifiers are plotted. In terms of amplitude density spectra in (m I s**2) I Hz**0.5, the values of the self-noise spectra at resonance range from a low of 3 x 10-10 for the GS-13, to a high of 1.3 x 1 Q-8 for the HS-I. Between these two Seismometers, in order of increasing noise at resonance, are the SV-1, SL-210V, S-13, SS-I, L-4C, S-6000CD, and the L-22D. In order to show which Seismometers exhibit the lowest noise with which operational amplifierpreamplifiers, the self-noises of the HS-1, L-22D, L-4C, GS-13, SV-1, and SL-210V are plotted each paired with four commomly used op-amps: the LT1028, OP-227, OP-77, and the LT1012. For the GS-13, the LT1012 was the quietest. For the rest, the OP-227 was the best. For a given seismometer, the differences in self-noise between op-amps were frequently a factor of 2 or 3, and as large as 10 in one case. The use of these op-amps in the analog front ends of five current digital seismic recorders is discussed.
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Frequency limits for Seismometers as determined from signal-to-noise ratios. Part 1. The electromagnetic seismometer
Bulletin of the Seismological Society of America, 1992Co-Authors: Peter W. RodgersAbstract:The range of frequencies that a seismometer can record is nominally set by the corner frequencies of its amplitude frequency response. In recording pre-event noise in very quiet seismic sites, the internally generated self-noise of the seismometer can put further limits on the range of frequencies that can be recorded. Some examples of such low seismic noise sites are Lajitas, Texas; Deep Springs, California; and Karkaralinsk, U.S.S.R. In such sites, the seismometer self-noise can be large enough to degrade the signal-to-noise ratio (SNR) of the recorded pre-event data. The widely used low seismic noise model (LNM) (due to Peterson, 1982; Peterson and Hutt, 1982; Peterson and Tilgner, 1985; Peterson and Hutt, 1989) is used as representative of the input ground motion acceleration power density spectrum (pds) at such very low noise sites. This study determines the range of frequencies for which the SNR of an electromagnetic seismometer exceeds 3 db (a factor of 2 in power and 1.414 in amplitude). In order to do this, an analytic expression is developed for the SNR of a generalized electromagnetic seismometer. The signal pds using Peterson's LNM as an input is developed for an electromagnetic seismometer. Suspension noise is modeled following Usher (1973). In order to determine the electronically caused component of the self-noise, noise properties are compared among three commonly used amplifiers. The advantages and disadvantages of the inverting and noninverting configurations in terms of their SNR are discussed. In most cases, the noninverting configuration is to be preferred as it avoids the use of the large gain setting resistances required in the inverting configuration to avoid loading the seismometer output. A noise model is developed for a typical low noise operational amplifier (Precision Monolithics OP-27). This noise model is used to numerically compute the SNRs for the three electromagnetic Seismometers used as examples. The degradation in SNR caused by large gain setting resistances is shown. Numerical examples are given using the Mark Products L-4C and L-22D and the Teledyne Geotech GS-13 electromagnetic Seismometers. For each of the example Seismometers, the calculated range of frequencies for which their SNR exceeds 3 db is as follows: the GS-13, 0.078 to 56.1 Hz; the L-4C, 0.113 to 7.2 Hz; and the L-22D, 0.175 to 0.6 Hz. For the GS-13, the calculated lower and upper frequencies at which the SNR is 3 db are 0.078 and 56.1 Hz. This compares with the values 0.073 and 59 Hz measured in the noise tests on the vertical GS-13. Expressions for the total noise voltage referred to the input of an operational amplifier are developed in Appendix A. It is shown that in the inverting configuration, although no noise current flows in the input resistor, the noise current appears in the expression for the total noise voltage as if it did. In Appendix B, it is shown that any noise current flowing through an electromagnetic seismometer having a generator greater than several hundred V/m/sec generates a back emf that adds significantly to the noise of the system. This implies that system noise tests that substitute a resistor at the noninverting input of the preamplifier or clamp the seismometer mass will tend to underestimate the system noise.
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Frequency limits for Seismometers as determined from signal-to-noise ratios. Part 2. The feedback seismometer
Bulletin of the Seismological Society of America, 1992Co-Authors: Peter W. RodgersAbstract:The range of frequencies that a seismometer can record is nominally set by the corner frequencies of its amplitude frequency response. In recording pre-event noise in very quiet seismic sites, the internally generated self-noise of the seismometer can put further limits on the range of frequencies that can be recorded. Some examples of such low seismic noise sites are Lajitas, Texas; Deep Springs, California; and Karkaralinsk, U.S.S.R. In such sites, the seismometer self-noise can be large enough to degrade the signal-to-noise ratio (SNR) of the recorded pre-event data. The widely used low seismic noise model (LNM) (due to Peterson, 1982; Peterson and Hutt, 1982; Peterson and Tilgner, 1985; Peterson and Hutt, 1989) is used as representative of the input ground motion acceleration power density spectrum (pds) at such very low noise sites. This study determines the range of frequencies for which the SNR of a feedback seismometer exceeds 3 db (a factor of 2 in power and 1.414 in amplitude). Analytic expressions for the SNR are developed for three types of feedback Seismometers. These are the displacement feedback, velocity feedback, and coil-to-coil velocity feedback Seismometers. It was found that the analytic SNRs of the displacement and velocity feedback Seismometers are identical and that the SNRs for the coil-coil feedback seismometer and the electromagnetic seismometer are also the same. The signal pds using Peterson's LNM as an input is developed for each of the three types of feedback Seismometers. Suspension noise is modeled following Aki and Richards (1980). In order to model the electronically caused component of the self-noise, the electronic noise properties of two commonly used operational amplifiers (Precision Monolithics OP-27 and the Burr-Brown OPA2111 FET) are described. Using these, noise models are developed for a synchronous demodulator and a chopper-stabilized amplifier. These noise models are used to numerically compute the SNRs for the two feedback Seismometers used as examples, which are the Guralp Systems CMG-3ESP and Sprengnether Instruments SBX-1000 feedback Seismometers. For each of the example Seismometers, the calculated range of frequencies for which their SNR exceeds 3 db is as follows: the CMG-3ESP, 0.025 to 13.3 Hz; the SBX-1000, 0.098 to 11.3 Hz. The calculated and measured SNRs for the CMG-3ESP are compared. The calculated upper frequency for a SNR of 3 db was 13.3 Hz compared with 18.4 Hz measured in the noise tests. The calculated lower frequency for a SNR of 3 db was 0.025 Hz, whereas the measured value was 0.047 Hz. The difference is most likely due to the fact the CMG-3ESP is cut off at 0.1 Hz. Formulas are developed in Appendix A for calculating the SNR and self-noise of identical, colocated Seismometers from their recorded outputs. The analytic transfer functions, midband gain, upper and lower corner frequencies, and bandwidths for the three types of feedback Seismometers are given in Appendix B for comparison with the frequency limits set by the SNR.
