EAS 557
Introduction to Seismology
Robert L. Nowack
Lecture 3B
Seismometry II
In Lecture 3A, we investigated two simple mechanical systems for detecting ground motion. These had several limitations, including limited magnification, as well as practical constraints on the free period using mechanical seismometers. One way of addressing these issues is to have the seismometer deflection be proportional to an electrical signal (voltage, current). We will discuss this qualitatively with no differential equations. Then, a discussion of the amplitude response and magnifications achievable in modern seismograph systems will be given.
An important constraint in the recording of seismograms is natural and manmade seismic ground noise and its level as a function of frequency
A principle application of a well calibrated seismometer is the determination of earthquake magnitude. We’ll then explore how magnitude is defined, the different scales in common use, and the advantages and limitations of characterizing an earthquake by a single parameter.
The Electromagnetic
Transducer
- This device converts the deflection of the seismometer mass into a voltage.
- The method of doing this is to put a coil of wire on the moving element (pendulum or mass spring) and surrounding it by a magnetic field (originally Count Galitzin, a Russian nobleman, did this in 1914 and used a permanent horseshoe magnet).
- The coil moving in the magnetic field induces an electromagnic force proportional to the rate of change of the mass deflection. Thus, for a mass and spring deflection, the voltage, V, is given by
where G = coil constant
Thus, the voltage output is proportional to relative mass velocity, , rather than the displacement (i.e., the coil magnet system is a “velocity transducer”). The standard amplitude response of a damped seismometer is modified as
Figure 1a
Figure 1b
where is the input ground motion, is the relative mass motion, and V is the voltage.
The Galvanometer
The current induced in the coil may be amplified and filtered by an electronic device whose output is fed into the galvanometer (a coil and magnet) for the recording system. The galvanometer has an amplitude and phase response of its own, just as the mechanical seismometer does. Thus,
Figure 1c (see
where V is the voltage and S is the seismic output. The galvanometer frequency is and the free period is .
Now, we need to multiply the three responses to get the total response of the seismograph system
Figure 2 - “Magnification response”
where is the ground motion and S is the seismic output.
The phase
response can also be computed (see
Question – Why can’t we electronically amplify the seismic signal indefinitely?
Answer – Ground noise
Ground Noise
Ambient background motion of the Earth’s surface is due to wind, cultural noise (by this we don’t mean music; we mean cars, people, cows, etc), wave beating on the shore, atmospheric pressure fronts. (See Figure 10.11 of Aki and Richards, 1980).
Figure 3
A significant feature of the ground noise spectrum is two peaks at about 0.14 Hz and 0.7 Hz. Both peaks are due to ocean waves and meteorological disturbances. These so called 6 sec microseisms are a fundamental limitation on magnification of long period seismographs. These are found in the middle of continents, but are a bigger problem near the coasts. High frequency (10-100 Hz) cultural noise limits magnification of short period seismographs. At quiet sites, one can have magnifications as high as 107 at 20 Hz!
Two electromagnetic seismograph systems that were used since the 1950’s are the World Wide Standardized Seismograph Network (WWSSN) long and short period instruments. The long period free period is 15 sec (30 sec for some) with a galvanometer period of 100 sec. The short period instrument has a 1 sec free period and a 0.75 sec galvanometer period.
Figure 4 (from Lay and Wallace, 1995)
In the WWSSN Seismic Network, there were a total of six instruments at each site measuring ground motions in the N-S, E-S, and vertical directions for the short and long period instruments. The instrument had several possible gain levels depending on the local ground noise. The long period WWSSN instruments had gains from 375-3000 and the short period instruments had gains of 104-105. A typical seismograph recording was made on chart paper like that in Figure 5, where a pen made horizontal lines on a paper attached to a rotating drum. The minute and hour marks were also put on the record and when the paper was removed from the drum, each line down would be an hour later (depending on the drum speed). The vertical deflections of the pen would then measure the ground amplitude and the horizontal coordinate would represent time.
Figure 5 (from Stein and Wysession, 2003)
In the epicentral region, high frequency sensors are often used at higher magnifications to record small high frequency microseisms. For seismic refraction and reflection prospecting for petroleum, seismograph systems in the period range of 1-100 Hz are often used.
To record ground motions from large earthquakes in the epicentral regions, often so called “strong ground motion” seismometers are used. Early strong motion instruments had a resonant frequency of 25 Hz and effectively measured ground acceleration in the frequency range of interest for many buildings from 1-10 Hz (see Figure 1a).
For teleseismic recording, a number of seismograph systems have been designed to give relatively flat responses as a function of frequency. Figure 6 shows a number of amplitude responses for different seismic instruments that are here flat in ground acceleration over a range of frequencies.
Figure 6 (from Stein and Wysession, 2003)
Currently, most seismograph systems for both local and teleseismic distances recorded seismic data digitally. In fact, an early application of the “digital revolution” was in the recording of seismic signals for oil prospecting starting in the 1950’s. Once the data is in digital form, it can be manipulated on the computer. For example, Figure 7 shows the results of digital filtering of a teleseismic signal to emphasize different arrivals. The original unfiltered signal is shown at the top.
Figure 7 (from Aki and Richards, 2002)
Recent deployments of teleseismic broadband, digital seismograph systems, are shown in Figure 8.
Figure 8 (from Stein and Wysession, 2003)
Regional seismic network deployments in the continental
Figure 9 (from Stein and Wysession, 2003)
As of 2003, the USArray has been
funded to provide a rolling coverage of seismic stations across the continental
Figure 10 (from Stein and Wysession, 2003)
The Magnitude Scale (for earthquakes and blasts)
Reference: Richter, pp. 338-348
One of the principle uses of a well calibrated seismograph is to determine the magnitude of near and distant earthquakes. The magnitude scale was established to answer the age old question, “How big was that earthquake?”
The basic idea: an earthquake generates elastic waves whose amplitude (recorded by a seismograph) decreases with distance from the source.
Figure 11
On Figure 11, we have plotted the amplitude of first arriving waves (compressional or P wave) recorded on a number of seismograph stations at different distances for 3 different earthquakes. The amplitude of the P-wave signal is shown in Figure 12.
Figure 12
Based on the ground motion amplitudes, in some sense, earthquake #1 is the largest and earthquake #3 is the smallest. But, Figure 11 only shows the amplitude of the seismic waves generated by the earthquake and doesn’t measure the size of the earthquake directly.
The ground amplitude of each earthquake at a particular station is different, but the shape of the amplitude versus distance curve is the same (for a given region). This simple fact was the basis for Richter’s establishment of the first instrumental magnitude scale in 1935. The level of this amplitude versus distance curve determines the “magnitude” after we have assigned a magnitude for a reference curve at some particular distance. For example, suppose we chose the curve for earthquake #1 to correspond to M (magnitude) = 0. Then, used in this way, Richter defined a “local magnitude”, ML, in terms of the seismogram trace amplitude measured at a given distance () referenced to the amplitude of a standard or “reference earthquake” at that distance
where is the reference amplitude versus distance curve. Richter used a log scale since the seismic amplitudes for different size earthquakes have a large range. (Actually the shape of the reference curve for a particular region is determined by measuring seismic amplitudes from many earthquakes at many different distances to obtain a suitable average curve.) Thus, once we know how far away an earthquake is, we can measure its amplitude on a seismogram (), go to a table (p. 342 in Richter, table 22-1) to get and, therefore, obtain ML. ML used the largest trace amplitude on the record. In order for this to work, Richter needed a well calibrated seismograph system and for his original magnitude scale ML he used a Wood Anderson seismograph system (Figure 4). Although this seismograph system is not in use today, the idea of Richter to “cancel out” the effects of the Earth and a known seismograph system to find a number measuring the source is still in use today.
Other magnitude scales may be superficially fancier than the ML scale, but they all use the same idea.
Ex) “Body wave” magnitude (mb)
Based on the P-wave amplitude for a distant earthquake , ~ 111 km), recorded on short period WWSSN seismographs. This seismic trace amplitude is corrected for distance and focal depth in basically the same way as ML, although the reference curve corrections are more complicated (see Richter, pp. 688-690). This scale used the P-wave trace amplitude at a frequency of about 1 sec.
Ex) “Surface wave magnitude (Ms)
Based on the maximum amplitude of the 20 sec surface wave for teleseisms ) recorded on long period WWSSN seismographs. Again, reference curve corrections for distance and focal depth have been determined empirically from observations.
Since the
1980’s, another of earthquake size has been developed called the seismic moment,
Although this magnitude scale was designed to give similar estimates as earlier magnitude scales where they are valid, for larger earthquakes. The earlier magnitude scales may underestimate the actual size of the earthquake source. The magnitudes obtained from mb will “saturate” for Mw magnitudes greater than about 5.7. Also, Ms will “saturate” (i.e., not get any bigger) for Mw magnitudes greater than about 8.1 (more on this in later lectures).
Table 1 (from Stein and Wysession, 2003)
The confusion in the different magnitude scales in use today and their different ranges of validity have prompted the Press to request that scientists provide them with a preliminary magnitude, which could be ML, mb or Ms. Then, a final moment magnitude, Mw is provided at some point later. Nonetheless, there are still difficulties in trying to characterize an earthquake by just one number.