III. Demonstration of a seismometer response with amplitude and phase responses at:
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1 GG5330, Spring semester 006 Assignment #1, Seismometry and Grond Motions De 30 Janary Calibration Of A Seismometer Using Java: A really nifty se of Java is now available for demonstrating the seismic response and calibration of an inertial seismograph. It rns in either Netscape or Internet Explorer and is available from the Technical University of Clasthal at: Note that Java mst be trned on in yor web browser. This exercise demonstrates how Java applets can be sed to simlate physical systems. The script basically rns the soltion of the linear differential eqation of an inertial seismograph, namely an S-13, with varios driving signals and mechanical parameters sch as the free period, damping, coil constants, etc. The Java script also calclates the seismometer responses in displacement, velocity and acceleration nits for phase and amplitde. This exercise reqires that yo have access to a website and I sggest the faster the Internet connection the better sch as the college labs or from yor homes if yo want. Here are the main sites to look at. Note the magnetic and geothermic applets at this site also. Go ahead and try them all and get Java ot of yor before going on the assignment. Yor plots can be made from the Internet window and downloaded sing a screen dmp. I. Seismometer principles of operation: II. A description of the S-13 is available from the manfactrer at: III. Demonstration of a seismometer response with amplitde and phase responses at: IV. Calibration of a seismometer: Be carefl rnning in Java and be patient the exection speed depends on the client machine speed. Don t change parameters nless Java is not rnning. Assignment: For this assignment, I want yo to go throgh the calibration of the S-13 seismometer jst as we did in lab bt sing the Java applets. For the write-p I want yo to prepare yo report in any word processor and either make a hard copy or pt yo report into a complete docment (text and figres) sch as in Word or Frame Maker. Steps: GG 5330 Homework #1 1 1/4/06
2 a) Download the principles of the seismometer operation and either print them ot or save them for reference (site I). b) Take a look at the description of the seismometer from Teledyne Co. This seismometer is a very commonly sed in earthqake networks arond the world. It costs, in a three component configration abot $9000 a set (site II). c) Perform a demonstration of the seismometer sing a range of parameters that we sed in the lab for enogh freqencies to show that it is the same. Refer to the lab assignment for the freqencies. Note the visal images of grond motion, mass motion and otpt. i) Make plots of some of the signals, and ii) The corresponding amplitde and phase response for each freqency steps. Note the steady state responses to sinsoidal motions and the transient responses to implses and sqare waves. Yo can make p yor own signal by inptting the motions via the mose at the green btton. Especially, note the visal lags/leads of the grond motion, the seismometer mass and the otpts. These are particlar instrctional for nderstanding how the seismic signal mimics the grond motion. c) Now rn the calibration part of the script especially to see how the transient response operates. To do this yo can do a simlate weight drop or jerk that we talked abot bt we did not perform in lab. Yo can also simlate qiet or noisy site conditions jst as we did on the pier in the bottom of the Browning Bldg. For this part of the virtal experiment yo will see a detailed schematic of the entire seismometer system.. Many of the early pendlm seismographs, ca , are still in operation and provide valable information. They are particlarly sefl for comparing recent earthqakes with older larger events from the same region in terms of waveforms and magnitdes. Milne-Shaw seismographs, with a seismometer free period to of 1 sec, a damping ratio of 0:1, and a magnification of 50 have been operated throghot Erope and the English colonies since 190. The Wood-Anderson torsion seismograph was designed at Cal Tech in the early 190's and employed by C. F. Richter for his famos "Richter" magnitde scale pblished in The Wood-Anderson seismograph has a free period of To 0.8 sec, a damping factor of 0.8, and a magnification of 800. This instrment is still the world standard for local magnitde determinations. Since neither The Milne-Shaw or the Wood-Anderson seismographs are electromagnetic, the eqations derived in class for the motion of a damped seismometer can be applied directly to calclate record amplitdes for grond motion inpts of specified amplitde and freqency. GG 5330 Homework #1 1/4/06
3 a. For each of these seismographs compte the maximm seismometer amplitdes, (t), and instrmental phase shifts, converted to nits of time, i.e. time lag, for the following cases of inpt grond displacement, x(t), which yo may assme to be harmonic with dominant periods of T e : (a) P-wave from a nearby earthqake. T e 1 sec, amplitde 10-4 cm (b) S-wave from a distant earthqake. T e 8 sec, amplitde 6x10-4 cm (c) Rayleigh wave from a distant, large earthqake. T e 0 sec, amplitde 10-4 cm b. Comment on the appearance of the seismograms and the possible applications of each instrment with regard to size of grond motion and freqency of incoming wave. 3. The attached figre gives three responses of a seismometer-galvanometer system as a fnction of period vs. displacement magnification, velocity sensitivity, and acceleration sensitivity. Recall that the galvanometer is the recording end of a seismograph, like the Helicorder drms in the University of Utah Seismograph Stations. Becase it is a pen sspended with a spring system, it is a pendlm and has an eqivalent freqency response. Confirm that the slopes of the graticles of the diagram are correctly oriented to give displacement magnification, velocity sensitivity, and acceleration sensitivity for each of the figres. 4. It is sefl to consider the range of actal amplitdes recorded from earthqakes in terms of magnitdes that can be recorded on a seismograph. Given the log 10 A 0 (Δ) fnction (attached) from Richter, 1958 (Table.1, p. 34), draw a plot showing the range of earthqake magnitdes Mmax and Mmin (on the ordinate) that will prodce detectable and on-scale recordings on a seismic recording system (with a 45 db dynamic range) verss epicentral distance: 0 km < Δ > 600 km. Assme that the minimm measrable amplitde is 0. mm. Recall the definition of Richter magnitde given by: M log A/A 0 log A - log A 0.(From Richter (1958) pg. 34). 5. The eqations of motion for a copled seismometer-galvanometer system with a velocity transdcer can be written:! + "# 0! + # 0! -x + "#0 $ s I This is the eqation for the grond motion copled to the grond and the galvanometer. Note the otpt of the galvanometer or pen (in the case of a Helicorder) is the seismogram record of the grond motion. I +!"0 I + "0 I!" 0 # g $ This is the eqation for the galvanometer copled to the grond. GG 5330 Homework #1 3 1/4/06
4 φ, x, and I are the displacements of the seismometer, the grond and the galvanometer, respectively, and! 0, " 0, #, $, % s, % g are the resonant freqencies, damping, and copling constants for the seismometer and galvanometer, respectively. a. First find the freqency response of the galvanometer, (ω), normalized by the grond spectrm x(ω). Hint keep everything complex, don't take amplitdes at this stage. b. Ignore the copling factor σs (set it to zero) and by groping terms, show how the transfer fnction between the grond, x(ω), and the otpt, I (ω) can be expressed as the cascade (mltiplication in the freqency domain) of three components: the mechanical seismometer, the velocity transdcer and the galvanometer. c. By looking at the sketch of the response fnctions in log-log space, what combination of seismometer and galvanometer periods will prodce a record,, proportional to grond velocity x? Assme damping near critical and band limited grond motion. No calclations are needed. Extra Credit 6. Seismographic recordings, seismograms, are primarily affected by the non-linear response of the transdcer, the seismometer, rather than the recording and plotting system. For this problem I want yo to become acqainted with the affects of the nonlinearity of a seismometer on how grond motion is detected and plotted. To do this I want yo to write a Matlab script(s) that calclate the amplitde, velocity and acceleration responses for some typical freqency ranges of interest to earthqake hazards, 100 Hz < f < 0.5 Hz. This is done by sing are the soltions,,, or, for a Single Degree Of Freedom (SDOF) seismometer response to the eqation, m + c + k -m g given in sections 3..1 and Appendix A..3 of Kramer. a. To do this, first write scripts that calclate and plot the following expressions for the relative displacement response, for varios freqencies that yo will inpt for or freqencies of interest: g g! ( 1"! ) + ( #! ) (1) velocity response, : g GG 5330 Homework #1 4 1/4/06
5 g " 0! ( 1 #! ) + ( $! ) () and acceleration response, : g g! 0 1 ( 1" # ) + ( $# ) (3) Where! " g " is the tning ratio or ratio of grond freqency, ω g, to the natral 0 freqency, ω 0, of the seismometer; freqency, and! c 1 km! 0 k is the ndamped natral circlar m is the damping ratio. Note that the eqations have the same form on the right hand side of the eqation with a simple division of β to go from displacement to velocity and another division by β to get acceleration response. b. Then plot these soltions by with the displacement, velocity and acceleration on the vertical scale vs. freqency, f, from ω πf, as the horizontal axis. Becase of the large range in amplitdes, we take the logarithm of each side and yo will get a figre like Appendix Figre A.9. Use three vales of β: β < 1, β 1, β > 1. This means that yo will have three plots for each β, or nine plots. Note that yo can plot the soltions vs. β and yo will get Kramer Figre 3.3. Be sre and make yor scripts general so that yo can inpt freqencies over a wide range sch as we se in hazards analysis of 100 Hz. to Hz. Appendix Kramer, Figre A.9 is the standard form of the freqency response crve that we se for everyday earthqake hazards problems. c. Explain why the tning or damping ratio, β, is so important to yor calclations. It mst be selected so that the response does not go off scale at when the grond freqency eqals the natral freqency of the seismometer. Also explain why! mst also be selected in conjnction with β to constrain the response not to go off-scale when the grond freqency eqals the natral freqency of the seismometer. GG 5330 Homework #1 5 1/4/06
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