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Computation of seismic parameters and its interpretation from the recorded earthquake signal is empowered by digital data acquisition systems. This enables seismologist to automatically compute all …

Computation of seismic parameters and its interpretation from the recorded earthquake signal is empowered by digital data acquisition systems. This enables seismologist to automatically compute all the relevant parameters. Futuristic applications require extensive software development to implement seismic prediction and forecasting models. While developing such models, software developer prefer to write their own in-house analysis & modeling software with complete control over the required computations and models. This paper presents simplified mathematical framework of the seismic events and back-end computational software logic & algorithm to provide a simple framework to software engineers develop customized seismic analysis & computation software.

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- 1. R. Attri Instrumentation Design Series (Seismic), Paper No. 3, Sept 20051 | P a g e Copyright © 2005 Raman K. AttriAbstract— Computation of seismic parameters and itsinterpretation from the recorded earthquake signal isempowered by digital data acquisition systems. This enablesseismologist to automatically compute all the relevantparameters. Futuristic applications require extensive softwaredevelopment to implement seismic prediction and forecastingmodels. While developing such models, software developer preferto write their own in-house analysis & modeling software withcomplete control over the required computations and models.This paper presents simplified mathematical framework of theseismic events and back-end computational software logic &algorithm to provide a simple framework to software engineersdevelop customized seismic analysis & computation software.Index Terms— Earth quake signals, Seismic Instrumentation,Earthquake monitoring, Software approach to seismicmeasurements, seismic parametersI. INTRODUCTIONHE seismological study is closely linked with theimplementation of right kind of the seismicinstrumentation when it comes to recording theseearthquakes, interpreting them, storing their history over theyears. Software systems enhance the power of suchinstrumentation by performing the major job of signalanalysis, complex computation of parameters, datainterpretation, fetching inference, statistical trend analysis ofseismic activity at a place of interest over the years. Inassociation with instrumentation systems, the complexsoftware system deployment sometime ensure rightforecasting and generating warning systems for earthquake.This makes the job of seismologist more accurate, objective,automated and quick.Although a range of off-the-shelf software is available inthe market, however, those sometimes fail to address theneeds of futuristic modeling. In order for a seismologist todevelop a prediction model, they need software to computethe basic seismic parameters and a framework upon whichthey can develop their prediction or forecasting model [6].Software developers typically are not seismologists and are1Raman K Attri is an Ex-Scientist, Geo-Scientific InstrumentationDivision, Central Scientific Instruments Organization Chandigarh 160030India (e-mail: rkattri@rediffmail.com).not aware of the complex mathematics behind the geo-physical activities. This paper describes the simplifiedbackend software approach to enable such developers todevelop a software framework to compute and interpretseismic parameters. This paper outlines basic logic/algorithmic approaches build on mathematically equationsintegrated into software algorithms to correlate data points inseismic signal together toII. SEISMIC RECORDING & ANALYSIS CHAINWhen an earthquake occurs, it generates an expanding wavefront from the earthquake hypocenter at a speed of severalkilometers per second. Generally it takes few second fortheses waves front to travel thousands of kilometers [20]. Awave front expansion is shown in Fig. 1. This wave frontconsists of two unique waves: One P-wave which comesearlier due to its faster speed and another S-wave front whichcomes later due to little slower speed of travel [16]. The P-wave front is released first by the earthquake reach the seismicstation (shown as ‘A’) and S-wave front soon follow the P-wave front.Fig. 1. The expanding circles indicate the expanding wave fronts at everysubsequent second after earthquake is originated at hypocenter. S-wave frontfollowing the P-wave front in an actual earthquakeBackend Framework and Software Approach to ComputeEarthquake Parameters from Signals Recorded by SeismicInstrumentation SystemRAMAN K. ATTRI1Ex-Scientist (Geo-Scientific Instrumentation) Central Scientific Instruments Organization INDIAT
- 2. R. Attri Instrumentation Design Series (Seismic), Paper No. 3, Sept 20052 | P a g e Copyright © 2005 Raman K. AttriThus we get two unique wave peaks on the recordinginstruments, each corresponding to it wave-front. A typicalwaveform recorded on a true earthquake with the help ofseismic sensor is shown in Fig. 2 [6].Fig. 2. A typical seismic signal recorded during earthquake has two distinctpeaks spaced with an interval. The first peak corresponds to P-wave andsecond peak corresponds to S-wave. The S-wave is the seismic after-shockwhich causes more impact and consists of series of peaks.As it is can be seen that signal contains lot of backgroundresidual noise as well as very high peaks of the earthquakeevent. Normally an amplifier with a wide dynamic gain /range (> 120 db) is required to faithfully amplify the signalfrom the sensor [13].Earthquakes are monitored with a network of seismometerson the earths surface. Since no single instrument canoperate over a wide bandwidth and dynamic range,therefore, a set of instruments for different bandwidth areneeded to operate in conjunction [12]. The ground motion ateach seismometer is amplified and recorded electronically at acentral recording site. As the wave front expands from theearthquake, it reaches more distant seismic stations. Seismicdata obtained from many stations must be correlated.The data in digital format is downloaded from the system to aPC with the help of interfacing software. This raw data playsan important role in further seismic analysis, interpretationand prediction modeling.II. SOFTWARE APPROACH TO SEISMIC ANALYSISSeismic data acquisition systems come usually with interface,downloading and analysis software. If not, the researchengineer needs to develop their own data acquisition andseismic analysis software. Seismic Data Analysis andInterpretation Process start with raw data retrieved from dataacquisition system and downloaded into a PC. Specializedsoftware is used to process the data, retrieve parametricinformation and frame inferences.There are few characteristics which are of the interest to aseismologist [14]. The parameters, a seismologist would beinterested in are:Timing Parameters:Arrival time of P and S wave (Time of occurrence)Coda length (total event duration)Location Parameters:Focal Point (where earthquake originated)Epicentral distance (point exactly above focal point)Focal length (depth of origin)Magnitude Parameters:Ritchet Scale,Coda MagnitudeIntensity Parameters:Intensity/ EnergyMomentGround motionThis computation is done by seismic processing software. Asshown in Fig. 3, the input to the software is raw analogseismic signal which is digitized by signal digitizer in realtime. Event detection module selectively detects the seismicevents and the framework computes time, location, magnitudeand energy parameters of the seismic event. The frameworkalso contains display and analysis module. Advanced softwareframework interfaces the output to prediction and forecastmodeling software.Fig. 3. Software based processing and analysis framework for seismicparameters computation and interpretation.IV. COMPUTING TIMING PARAMETERS USING SOFTWARELOGICThe timing parameters in seismology are taken with respectto arrival of P- and S-wave. Generally there are two types oftiming parameters namely: S-P time interval and Coda Lengthwhich are of prime importance to seismologists [7]. These aredepicted in the Fig. 4.Fig. 4. Time Parameters of a seismic signal shown on a recorded seismogram.Difference between the arrival time of P-wave and S-wave is SP-interval andtime from arrival of P-wave till the settlement of ground motion in after shockis called coda length.A. Identifying Arrival Time for P and S Waves UsingSoftware LogicIn software, peak amplitude capturing algorithms is used todetect the arrival of first P-wave. However, before capturingarrival time of P- and S-wave, it is important to detect theoccurrence of the earthquake.
- 3. R. Attri Instrumentation Design Series (Seismic), Paper No. 3, Sept 20053 | P a g e Copyright © 2005 Raman K. Attri1. STA- LTA Ratio Software Algorithm to Detect SeismicEvent Occurrence: One of the software technique to detectearthquake selectively and isolating it from extraneous eventsis STA-LTA averaging. Method involves the computing of thelong-term and short-term averages. In this algorithm, samplesof data are stored well before the current time in form of ahistory and average is computed over a long period. This isthe average ground noise level persisting in general at thatlocation at all time when there is no seismic activity. This istermed as long-term average (LTA). For calculating LTA,data samples of past few seconds (say Y seconds) areaccumulated. The value Y varies from 1 to few tens ofseconds [18].The sample average is also calculated in small time framesas well. These small time frames are usually selectable basedon the seismic profile of the location. Usually these are shortduration in the range of few one-tenth of a second (say 0.Xseconds). This is termed as short-term average (STA). Moderndata acquisition systems have circular memory implementedin it to record the historical data samples prior to current timesamples.Fig. 5. Concept of LTA/ STA computation on seismic signal. A) Filteredseismic signal b) STA and LTA averages calculated on input signal c) Triggeractivated based on set STA/ LTA trigger threshold. Data acquisition systemrecords the seismic event data including PEM (pre-event minutes) before thetrigger until PET (post-event time) after the trigger d) actual recorded signalbased on PEM and PET values (Courtesy: Trnkoczy, 1998, Kinematrics Inc[18])The moment the earthquake is occurring the short-temaverage is expected to be more than long-term average. Asuitable threshold point is chosen depending upon generalground motion history of the site (termed as alpha ratio) asshown in Fig 5. The moment the ratio of STA and LTA crossthis threshold, the earthquake is supposed to have occurred.Generally a ratio of > 1 is good indicator of earthquakeactivity and once triggered the system keeps recording theearthquake event till the end of the activity. This kind ofapproach ensures that we have sufficient data before and afterthe earthquake to carry pre-earthquake studies too. The idea oftaking the average is to rule out some sudden spikes occurringin the signals due to some artificial means or some other ways.This approach will ensure that only seismic data is recordedand hence P and S wave is detected for true seismic event only[1].2. Peak Amplitude Vs Ground Noise Algorithm: Anothertechnique to detect P and S peaks is to detect the peaks onlywith peak detector and finding the ratio of the peak amplitudewith average noise level. The peak capturing generallyindicate the arrival of P-wave and S-wave. In this algorithmsoftware is configured to spot the beginning of such P-wavesor S-waves through discrimination and adaptive differential ofadjacent samples to know when a particular wave has started.These algorithms selectively detect the arrival of P-wave andS-wave.Both of the above algorithms can be implementedsimultaneously in the software. This has the advantage thatsoftware accurately pin-points the arrival time of P-wave andS-wave separately and the computation will be for earthquaketrue signal only.B. Computing S-P Time Interval Using Software LogicThis is the difference between arrival time of P and arrivaltime of S. The seismologists analyze the S-P time differencedata over the years for a particular location and can come upwith minimum time difference available between reception ofP wave and actual heavy disastrous S-wave. How closely Sand P waves follows each other provides important inferencesregarding creation of some early warning systems for somestrategic locations.Once the time of arrival of P-wave and S-wave are marked,the S-P time internal can be computed very accurately. Forthis, the clocks of almost all the seismic data acquisitionssystems are synchronized with some universal timingstandards like WWV or ATA.S-P interval (in sec)= Absolute arrival time of S wave– Absolute arrival time of P wave (1)C. Computation of Coda Length Duration Using SoftwareLogicCoda length is basically the time in seconds starting from P-wave time to the end of wave up to noise level. This timegives an indication for how long a seismic shock prevailedand how much time was taken by the earth to calm down afterthe shock. This time is very important is relating the amountof destruction with the time interval of the earthquake. Thistime measurement starts from right from occurrence of the P-wave. For a given earthquake, coda length is measured bydifferent stations and average value of these durations is taken[17].Coda Length duration is computed by software afterascertaining the start of the P-wave till the waveformamplitude and pattern matches with what it was before thestart of P-wave. From measurement and electronics systemperspective, all time prevailing ground motion converted intoinduced EMF in the sensor can be taken as the measure ofprevailing noise. This noise can be further averaged over the
- 4. R. Attri Instrumentation Design Series (Seismic), Paper No. 3, Sept 20054 | P a g e Copyright © 2005 Raman K. Attritime. A software system computes the average value of noisesamples to specify ‘settled’ ground activities prevailing at alltime. Refer to Fig. 4 to see Coda length marked on theseismogram recording.The coda length can be found out by clubbing the algorithmwhich detects the P-wave arrival time with the algorithmwhich detects the prevailing noise level. When the signalamplitude and earth vibration falls below the stipulatedthreshold, the earthquake is said to be settled and that time isfound out by subtracting the time of arrival of S-wave fromthe time of settlement of earthquake.Coda length (in seconds) = Absolute time of settlement –Absolute time of arrival of P-wave (2)V.COMPUTING LOCATION PARAMETERS USING SOFTWARELOGICTwo important parameters in locating the earth quake are:Epicenter and hypocenter. Epicenter is the point exactly abovethe earthquake on the earth surface. The point where theearthquake generates is called hypocenter. Hypocenter is alsocalled focal point sometime, this is shown in Fig. 6. EpicentralDistance is the straight line distance between the point ofobservation of earthquake and the point exactly above thefocal point on the earth surface. This is measured in degreesand can be converted in kilometers depending upon theparameter constants of the location where the earthquake isbeing measured [17].Fig. 6. The point where earthquake is originated is called focus or hypocenter.The point directly above this on the earth surface is called epicenter.A. Using S-P Time Interval to Find Epicentral Distance(Location of Earthquake) Through Software Logic1. Backend Mathematical Framework: As stated earlier, theearthquake is measured by a network of seismic stationswhich are located at different locations. When an earthquakeoccurs, we observe the times at which the wave front passeseach station. We find the unknown earthquake source byknowing these wave arrival times at different seismic stations[10]. Since P waves travel faster than S waves, the timedifference between the arrival of the P wave and the arrival ofthe S wave depends on the distance the waves traveled fromthe source (earthquake) to the station (seismograph).Louie [10] and IRIS white paper [19] present a method oftriangulation to compute earthquake location. This is anexcellent method which be used in the software logic.Software logic use the fact that P and S-waves each travel atdifferent speeds and therefore arrive at a seismic station atdifferent times and time interval between arrival of S and Pwave can be used to find the location of the earthquake. Pwaves travel the fastest, so they arrive first. S waves, whichtravel at about half the speed of P waves, arrive later. Aseismic station close to the earthquake records P waves and Swaves in quick succession. With increasing distance from theearthquake the time difference between the arrival of the P-waves and the arrival of the S-waves increases. This conceptis made clearer in Fig. 7, where three different seismic stationslocated at different distance record the same event.Fig. 7. Same earthquake recorded by three distant stations where P-wave andS-wave arrives are different time. Velocity of P-wave and S-wave can becomputed from these three data points. S-P interval is used to calculate thedistance of the station from the point of earthquake origin [10, 20].IRIS white paper [19] outlines a method of triangulation tocomputer epicentral distance/ location from recordedseismogram. The IRIS white paper illustrates the earthquakeoccurred in Mexico (Courtesy: IRIS Consortium) to illustratecomputation of epicentral distance [19]. The original signalimages have been reproduced here in Fig. 8 The arrival timeof p-wave and S-wave as well as S-P interval is different atthree locations depending upon the distance from theearthquake.From observing and analyzing many earthquakes, we knowthe relationship between the S-P time and the distancebetween the station and the earthquake. We can thereforeconvert each measured S-P time to distance. In software asimple look-up table can be made to simplify suchcomputations. A time interval of 1.5 minutes corresponds to adistance of 900 kilometers, 3 minutes to 1800 kilometers, and5 minutes to 3300 kilometers. Multiply the seconds of S-Ptime by 8 km/s for the kilometers of distance [10]
- 5. R. Attri Instrumentation Design Series (Seismic), Paper No. 3, Sept 20055 | P a g e Copyright © 2005 Raman K. AttriFig. 8. Seismic signal recorded at three stations from same earthquake. SPinterval increases as the distance of the station increases from the earthquakeepicenter. (Image reproduced with permission from IRIS [I9])2. Software Implementation: Once the distance to theearthquake for three stations is known, the location of theearthquake can be determined using software logic as under:If an earthquake occurred a given distance from a station, itcould have been anywhere on a circle whose radius is thatdistance, centered on the station. If distances from twostations are known, two locations are possible: the twointersection points of two circles. If distances from threestations are known, the earthquake can be unambiguouslylocated. This is the principle of triangulation. For each stationwe draw a circle around the station with a radius equal to itsdistance from the earthquake [19].The earthquake occurred at the point where all three circlesintersect, as found in Fig. 9. In software, this method oflocating the earthquake from data available from at least threesources can be programmed in an algorithm using inherentfunctions in the programming.Fig. 9. Method of Circle intersection to find earthquake location. A circle isdrawn around distance translated from SP interval and intersection of thecircle is actual location or epicenter of the earthquake (Images reproducedwith permission from IRIS [19])The algorithm is simple to state: guess a location, depth andorigin time; through software itself compare the predictedarrival times of the wave from your guessed location with theobserved times at each station; then move the location a littlein the direction that reduces the difference between theobserved and calculated times. Then this procedure is repeatedby the software, each time getting closer to the actualearthquake location and fitting the observed times a littlebetter. Software stops when its adjustments have becomesmall enough and when the fit to the observed wave arrivaltimes is close enough [10]. Above method of triangulationgives the epicentral distance in kilometers.B. Computing Epicentral Distance Using Lookup Tables inSoftware LogicEpicenter Distance in degrees is computed from this S-Ptime interval. The exhaustive table is available which listsepicentral distance in degrees corresponding to each SPinterval in seconds [3, 4]. This lookup table has beengenerated by seismologists by years of research. The basicconcept of these tables is based on the time taken by S-waveto reach after P-wave is directly proportional to the velocity ofthe ground waves and the distance of the originating point tothe point where S-P interval is being observed. This readilyavailable table can be integrated into the software using anydatabase technique in form of tabulation of S-interval vsepicentral distance in degrees. Once integrated into software,the epicentral distance can be determined by the software fromthe database on the basis of previously determined S-Pinterval.The epicenter distance in kilometers can be found from theepicentral distance in degrees by another lookup table [3, 4].This table lists the conversion factor that must be used toconvert the epicentral distance found in degrees intokilometers. Every location on earth has particularcharacteristics which defined this constant. For example for aplaced named, Chandigarh (India Latitude: 30° 42 N,Longitude: 76° 54 E) this constant has already been computedby seismologists to be 111.1 as shown in equation (3). Thisgives a straightforward calculation of epicentral distance inkilometers once epicentral distance in degrees is known.Epicentral Distance (in Km) = 111.1 x Δ (3)Where Δ the epicentral distance in degrees calculated usingtriangulation methodThis table can also be integrated into the software usingdatabase techniques as described earlier. However in this casethe location of the recording is either to be stored with the dataduring data acquisition or it is to be input by the seismologist.Depending upon city string in the input, software willautomatically calculate Epicentral distance in kilometers fromcomputed Epicentral distance in degrees.Another easy and straightforward technique to findepicentral distance in kilometers is from equation (4) forwhich we need to know the velocities of P-wave and S-wave,which are very much known. The equation (4) can find theepicentral distance using S-P time interval. This will save thealgorithms and processing needed for lookup tablemanagement in software. Normally we know the velocity of P& S waves. We can calculate the Epicentral distance ∆ in kmsfrom the S-P interval as under:Epicentral Distance in Kms, ∆ = Vp / (Vp/Vs-1) (Ts- Tp) (4)
- 6. R. Attri Instrumentation Design Series (Seismic), Paper No. 3, Sept 20056 | P a g e Copyright © 2005 Raman K. AttriWhere Vp and Vs are the velocities of P-wave and S-waverespectively. Tp and Ts are their respective arrival times, asrecorded by the software systemFor crustal rocks typical Vp is 6 km/s and Vp/Vs isapproximately 1.8 km. Epicentral distance in kilometers isabout 7.5 times S-P interval in seconds. If three or moreEpicentral distances measure by various seismic stations areavailable, it is possible to use a map to plot these data. Theepicenter may be placed at intersection of circles with stationsas centre and appropriate ∆ as radii. This point of intersectionmay be an aerial distance giving the uncertainty in locatingexact epicenter.C. Computing Focal Depth Using Software LogicFocal Depth is the vertical distance from focal point to theepicenter (i.e. point exactly above it vertically on the earthsurface) is called Focal Depth. This gives the depth of thefocus or hypocenter beneath the earth’s surface. A distance“Hypocenter Distance” is defined to indicate the distancebetween focus (or hypocenter) and the point of observation orthe point where earthquake has produced its effect. This is astraight line distance [17].At software logic, a triangulation method can be used tocompute hypocenter distance as well as depth. For moresophisticated systems, at back-end, mathematically, theproblem is solved by setting up a system of linear equations,one for each station. The equations express the differencebetween the observed arrival times and those calculated fromthe previous (or initial) hypocenter, in terms of small steps inthe 3 hypocentral coordinates and the origin time. We mustalso have a mathematical model of the crustal velocities (inkilometers per second) under the seismic network to calculatethe travel times of waves from an earthquake at a given depthto a station at a given distance. The system of linear equationsis solved by the method of least squares which minimizes thesum of the squares of the differences between the observedand calculated arrival times. The process begins with an initialguessed hypocenter, performs several hypocentral adjustmentseach found by a least squares solution to the equations, anditerates to a hypocenter that best fits the observed set of wavearrival times at the stations of the seismic network [8, 20].Above software system structure is shown in Fig. 10 whichcomputes timing information, epicentral distance in degreesand in kilometers and performs triangulation method to locatethe earth quake.Fig. 10. Comprehensive software framework for locating earthquakeVI. COMPUTING MAGNITUDE PARAMETERS USINGSOFTWAREAlthough each earthquake has a unique magnitude, itseffects will vary greatly according to distance, groundconditions, construction standards, and other factors. Arelatively small magnitude earthquake that happens near thesurface can cause shaking of great intensity, whereas a largemagnitude earthquake that happens in a depth of severalhundred kilometers will not necessarily produce intenseshaking at the surface. The magnitude on the Richter scalerelates to the energy released by the earthquake, and it isindependent of possible damages on the surface of the earth.A.Computing Ritchet Scale Magnitude Using Software Logic1. Backend Mathematical Framework: Ritchet scale isnormally determined on the basis if maximum amplitudeshown on Wood-Anderson seismograph (which have nearlyconstant displacement amplification over the frequency rangeof local earthquake). Ritchet scale defined the LocalEarthquake Magnitude, observed at the place of observation,denoted by ML irrespective of the direction and its origin andempirically given by equation (5) as under:ML = Log A – Log AO (∆) (5)Where A, Maximum amplified in millimeters on Wood-Anderson seismographs, ∆, the Epicentral distance inkilometers and AO (∆) is maximum amplitude at ∆ kilometersfor a standard earthquakeLocal Magnitude is thus a number characteristic ofearthquake and independent of location of the recordingseismographs. The second factor was scaled by certainassumptions by Ritchet. In order to solve above equation (5), atable of –log AO as a function of Epicentral distance inkilometers is needed. Ritchet arbitrarily chose –log AO = 3 at∆ = 100 Kilometers and other entries in the table wereconstructed from observed amplitudes of a series of welllocated earthquakes [3, 4].Gutenberg & Ritchet (1940) extended local scale magnitudeof distant earthquakes to call it as Surface Wave Magnitude,denoted by MS and empirically given in equation (6) as under:MS = Log A – log AO (∆O) (6)Where ∆O is epicentral distance taken in degrees to take intoaccount and origin of the origin of the earthquake, A ismaximum combined horizontal ground amplitude inmicrometers for surface waves with a period of 20 sec and –log AO is tabulated as function of epicentral distance ∆ indegrees, similar to that for local magnitude.This was applicable to shallow earthquakes generatingobservable surface waves. However for distant earthquakes atvarious depths inside the earth only body waves areobservable as P and S-waves. So the magnitude had to bedefined on the basis of observed P-wave and S-waveamplitudes. A new relationship for body waves was defined
- 7. R. Attri Instrumentation Design Series (Seismic), Paper No. 3, Sept 20057 | P a g e Copyright © 2005 Raman K. Attrias Body wave Magnitude, denoted as MB and empiricallygiven by equation (7) as under:MB = log (A/T) –f (∆. h) (7)Here (A / T) is the maximum amplitude to period ratio inmicrometer per second, F (∆, h) is a calibrated function of Δand focal depth h. This function has been characterized foralmost all major locations across the globe and empirically itcan be written in equation (8) as:MB = log (A/T) + ∆ + C (8)Where A is amplitude of highest S-wave Peak, T is the timeperiod of the same peak, as shown in Fig. 11. C is placespecific constant. This distance factor comes from a table thatcan be found in Richters [15] book Elementary Seismology.Theoretically it is logarithmic value of the amplitude ofhighest peak with the time period of that peak.Higher the amplitude, higher the strength of the earthquakeand higher the time period lower will be the strength. This isinterpreted like this that high peaks which are sharpest mostindicate the highest strength of the earthquake occurrence.Fig. 11. A (amplitude) and T (time period of highest peak) of S-wave formsthe basis of Ritchet scale calculation2. Software Implementation: In practice the software willcompute the magnitude of Body waves using Ritchet Scale.This magnitude MB is dependent upon maximum amplitude ofthe signal detected, its frequency and locational characteristicsof the site of observation. The Ritchet scale of a recordedearthquake is computed using the equation (8). The locationconstant is again integrated into the software using the readilyavailable tables. The maximum amplitude ‘A’ can bedetermined by the peak detector software algorithm.Computing the time period of the highest peak requires goodamount of processing. This needs detection of zero crossingimmediately preceding and succeeding the highest peakdetected by the peak detector algorithm. This can be done byincremental time steps below and above the time mark of thepeak, and marking the time marks where signal becomes zeroon both sides. The difference between these two points is thetime period the peak. The Epicentral distance from previousalgorithms and constant ‘C” value determined from look-uptable along with the computed time period enable software tocompute the Ritchet scale [3, 4]. Software system architectureto compute amplitude of P-wave, S-wave and local magnitudeis shown in Fig 12.Fig. 12. Software framework for calculating magnitude and energy of theearthquakeB. Computation of Coda Length Magnitude1. Backend Mathematical Framework: It is an estimate oflocal magnitude ML calculated using the coda-length/magnitude relationship [17]. Coda Magnitude isdirectly related to the coda length and epicentral distance. Thisapproach is based on using the signal duration rather than themaximum amplitude to estimate the earthquake magnitude,because it will make it independent of necessarily usingWood-Anderson Seismograph. Bisztricsany [12] and Lee etal. [9] correlated Ritchet magnitude with signal duration oflocal earthquake through an empirical formula given inequation (9).MD = -0.87 + 2 log D + 0.0035 Δ (9)Where D is Coda length, Δ is epicentral DistanceSimilar empirical relationships in many forms integratingmany dependent factors have been suggested by manyresearchers, the more general form of the same is shown inequation (10) as under:MD = a1 + a2 log D + a3 Δ + a4 h (10)Where h is the focal depth and a1, a2, a3 are empiricalconstants.The above equation can be empirically established for alocation of interest depending upon certain empiricalrelationship. For example the generalized empiricalrelationship reduces to that given in equation (11) for a citylike Chandigarh (India Latitude: 30° 42 N, Longitude: 76° 54E) as under:MD = -0.57 + 1.38 log D + 0.29 Δ (11)The underlying concept is that coda magnitude is a measureof impact of earthquake which occurs at a specified epicenterin a particular direction, specified epicentral distance andsustains for a specified duration in seconds.2. Software Implementation: Software can very easilycompute the Coda magnitude from Coda length and Epicentral
- 8. R. Attri Instrumentation Design Series (Seismic), Paper No. 3, Sept 20058 | P a g e Copyright © 2005 Raman K. Attridistance in degrees from equation (10) with appropriateempirical coefficients depending upon the location. Theseempirical coefficients may be entered by the seismologist or alookup table on the basis of location entered could beprovided. Or alternatively the software could workspecifically with customized empirical relationship e.g forChandigarh using equation (11) or generalized equation (9).This coda length is one type of indicator of the earthquakeintensity. The software system to compute coda magnitude isshown in Fig. 12.VII. COMPUTATION OF SEISMIC ENERGY USING SOFTWAREA.Backend Mathematical FrameworkSeismologists use a Ritchet Magnitude scale to express theseismic energy released by each earthquake. Both themagnitude and the seismic moment are related to the amountof energy that is radiated by an earthquake. Richter andGutenberg (1940) developed a relationship betweenmagnitude and energy. Their relationship is given by equation(12):Log ES = 11.8 + 1.5MS (12)Where ES is energy in ergs from the surface wavemagnitude Ms Note that ES is not the total intrinsic energy ofthe earthquake, transferred from sources such as gravitationalenergy or to sinks such as heat energy. It is only the amountradiated from the earthquake as seismic waves, which ought tobe a small fraction of the total energy transferred during theearthquake process. The Richter scale is based on themaximum amplitude of certain seismic waves, andseismologists estimate that each unit of the Richter scale is a31 times increase of energy [11].Seismologists have developed a standard magnitude scalethat is completely independent of the type of instrument. It iscalled the moment magnitude, and it comes from the seismicmoment. Earthquakes are caused by internal torques, from theinteractions of different blocks of the earth on opposite sidesof faults. The moment of an earthquake is fundamental toseismologists understanding of how dangerous faults of acertain size can be and is expressed by equation (13) below:Mo = μ A d (13)Where M0 is moment of an earthquake (given in units ofdyne-cm), μ is rigidity of the rocks, A is fault area, D is theslip distance.Kanamori [5] gave a relationship between seismic momentand seismic wave energy, given by equation (14) below:ES = Mo / 20000 (14)B. Software ImplementationThe seismic energy can be computed by the software usingthe equation (12). This takes the Surface wave Ritchetmagnitude, MS as input. The surface wave magnitude can becomputed by equation (3) where the factor –log AO isavailable in form of exhaustive tables which can be dulyentered in software using database approaches. The seismicenergy is computed in ergs.The moment can be calculated from equation (13) ifphysical characteristics of earth layer where earthquakeerupted are known. Alternatively equation (14) is goodapproximation for the same. A software system whichcomputes moment and energy from surface wave amplitudeshown in Fig. 12.VIII.CONCLUSIONSoftware based approach to seismic analysis exploits themaximum processing capability of the computer. Rather thanmanually solving complex equations, the function is handledby software. The above highlighted software approach wouldhave advantages like manual and automatic Data viewing withauxiliary information, correlation of the conclusions andinferences drawn from individual recorded data andidentification of seismicity of the site. This paper is animportant research aids for development of customizedsoftware to convert manual framework into an automatedsystem which extends its capability to the prediction process.ACKNOWLEDGMENTSAuthor acknowledges the previous work, consulting andfeedback provided by following individuals which helpedshaping the structure of this paper.1. Naresh Kumar, Ex-Seismologist, CSIO Chandigarh2. Satish Kumar, Senior Geo-Scientific InstrumentsScientist, CSIO Chandigarh3. B.K. Sharma, Deputy Director & Senior Scientist, Geo-Scientific Instruments Division, CSIO Chandigarh4. Incorporated Research Institutions for Seismology(IRIS) Consortium, Washington DC USA.http://www.iris.edu for permissions to use white paper5. Kinemetrics Inc. http://www.kinemetrics.com forpermission to use its white paperREFERENCES[1]. Ambuder, B.P. and Soloman, S.C., (1974), An event recording systemfor monitoring small earthquakes, Bulletin of Seismological Society ofAmerica, Vol 64, pp 1181-1188[2]. Bisztricsany E. 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