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2. SEISMIC SOURCE PARAMETERS
The Bible contains several descriptions of earthquakes. One of them, takenfrom Samuel 17 gives the following description of these phenomena:
“And there was trembling in the host, in the field and among all the people. The garrison and the spoilers also trembled and the earth quaked, so it was a very great trembling”
What is seismology ?
The word seismology originates from the Greek language:
Seismos - earthquakeLogos - science
“ the science of earthquakes “
The exact translation of this would be:
SEISMOLOGY
The science of elastic (seismic) waves
1. Their origin - earthquakes, explosions
2. Their propagation through the earth’s interior
3. Their recording and interpretation
APPLIED SEISMOLOGY INCLUDES THE FOLLOWING:
1. EXPLORATION SEISMOLOGY
- Search for economically significant resources, eg oil, coal, minerals, etc
2. ENGINERING SEISMOLOGY
-Depth to bedrock, sink holes, dams, runways, and other construction applications
3. TECTONIC SEISMOLOGY
- Study of earthquakes, volcano's, plate movements etc
4. MILITARY SEISMOLOGY
- Detection of submarines, nuclear explosions
5. MINE SEISMOLOGY
- Study of mine induced seismicity
Some ancient mythical and popular beliefs
Xhosas believed that there is a snake under the ground and thatwhen it moves the earth shakes
The western world had Atlas with the world on his shoulders, every timehe moved the earth shook
The Indians believed that an elephant carries the world on his back and that every time it went for a wee the earth shook
The Japanese believed in a large cat fish under the ground whoshook the whole earth and a small cat fish that caused the after shakes
The subject we will be discussing is mine induced seismicity,its source parameters and interpretation of recorded seismicity
INDUCED SEISMICITY
An increase in seismicity in seismic areas andgeneration of seismicity in a-seismic areas has beenobserved as a result of:
-Deep underground mining
-Large scale surface quarrying
-Filling of reservoirs behind high dams
-Injection of fluids in rocks at depth
-Removal of fluids from subsurface formations
-Detonation of large underground explosions
This type of seismicity is called induced seismicity
The primary requirement for induced seismicity is humanactivity where the rocks are in pre-stressed condition
Largest mine tremors
Date Magnitude Place
13/03/1989 ML = 5.6 Potash mining district, South Germany
23/06/1975 ML = 5.2 As above
07/04/1977 ML = 5.2 Klerksdorp, South Africa
24/03/1977 ML = 4.5 Lubin Copper Mining District, Poland
March 2005 ML= 5.4? Klerksdorp, South Africa
MONITORING
1908 First seismological observatory Bohum, Ruhr, Germany In operation until World War II
1910 Witwatersrand, South Africa, a single seismograph
1920 First seismic network, Upper Silesia Coal Basin 4 stations, one underground at Rozbark Coal Mine Still in operation
1939 First seismic network in South Africa, Witwatersrand 5 seismographs
-----------------------------------------------
1970 KMMA Regional Seismic Network, Klerksdorp, South Africa
Area 107 km27 stations 197020 stations 197824 stations 198129 stations 1988
Above magnitude 3.5
Above magnitude 4.0
ML = 1.45log D + 0.12 where D is duration (in seconds) of the recorded motions
Magnitude of this event is 3.8
ML = 1.45Log D + 0.12 D – duration
Log Mo = 1.5 ML + 9.1 [Nm] ( Hanks & Kanamori 1979)
Log E = 1.5 ML – 1.2 [MJ] (Gutenberg & Richter 1956)
Date: 31 December 1988Time: 14h50m02s
ML = 3.8
Mo = 6.3E+14 NmE = 3.2E+04 MJ
PROBLEMS
Over 24 000 people underground at one time
Probability of a seismic related accident
09h- 10h probability 0.0912h – 13h probability 0.0715h – 16 h probability 0.10
20h -21h probability 0.1422h- 23h probability 0.32
The aim of seismic monitoring is to record the rockmass response to mining activities
Magnitude 4.6
TOTAL CLOSUREWITH F/W HEAVE
42 stations by the end of 1993
1972 – 1988 Magnitude range
From 0.8
1989 – 1999 magnitude distribution
From 0.5
2. SEISMIC SOURCE PARAMETERS
1. MAGNITUDE CONCEPT2. SEISMIC MOMENT3. SEISMIC ENERGY4. STRESS ESTIMATES
Today with the modern digital seismic networks the magnitude is calculated only after the seismic moment and energy are calculated in the process of
spectral analysis.
For example the PMC local magnitude is calculated from the following formulae:
ML = 0.272log E + 0.392logMo - 4.63
Single event
The Council for Geosciences runs the National South African Seismic Network. Their magnitudes are based on the maximum recorded amplitude.
The formulae used to calculate this magnitude is:
ML = log (A) + 1.11LogD +0.00189D -2.09
Where:
A- maximum recorded amplitude on a seismogram after applying a correction for the instrument in nanometers (10E- 09 m)
D – hipocentral distance in km
Mw = 0.667 x log Mo – 6.01
PMC magnitude = 0.272 x log E + 0.392 x log Mo - 4.63
Where:Mw – moment magnitudeMo – seismic momentE – seismic energy
It is not possible to convert one into other magnitude accurately but it is possible to estimate their relation
PMC relation between seismicmoment and magnitude
Relation between seismic momentand moment magnitude
PMC magnitude is about 0.4 or 0.5 lower from the moment magnitudeso the -0.9 moment magnitude is equal to -1.4 local magnitude.
PMC magnitude
Spectral analysis has become a standard technique used to estimate the sourceparameters of seismic events recorded by mine digital seismic networks.
Simple source models of circular dislocations are used for the interpretation of seismic spectra and for the purpose of deriving source parameters.
Seismic moment, corner frequency and seismic energy are inverted from the spectra that are corrected for:
the instrumental, distance and attenuation effects of each waveform and then averaged.
Seismogram
Signal as we assume at the source
The seismic moment (Mo) is a measure of earthquake strength.
It is defined using a pure shear source model. This is not totally correct as it will be presented later with the events recorded at the mines.
Seismic moment is defined as:
Mo = µ ū A
Where: µ is the shear modulus at the source ū is the average displacement across the fault A is the fault area
Such definition implies that theoretically the value of seismic moment could becalculated if there would be access to the source area. Such cases are very rare.
In case of the spectral analysis the seismic moment is calculated from thefollowing relation:
Mo = (4πρoco3RCΏo)/(FcRcSc)
Where: ρo is the density of source material co is either P-wave velocity or the S-wave velocity at the source Rc is the distance between the source and the receiver Ώc is the low frequency level, this is a spectral parameter Fc accounts for the radiation of either P or S waves Cc accounts for the free-surface amplification of either P or S wave amplitudes Sc is the site correction for either P or S waves
From the spectrum two independent source parameters are calculated orrather estimated
Seismic moment Mo [Nm]
Seismic energy E [J]
The estimate of the seismic source parameters is based on number of assumptions:
1. We know the source location
2. We know the seismic wave velocity
3. We know the rock mass density
4. We are able to correct the spectra for attenuation and scattering effects along the travel paths of seismic waves
5. We know the site correction value
Seismic energy and electric energy comparison
MagnitudeElectric energy consumption for a
town with 100 000 inhabitants
1.6 For 1 second
6.8 For 1 year (290 million KWh)
8.7 For 270 years
In comparison a tropical hurricane can release in twenty four hours as much energy as a rich, medium size nation as Britain or France uses in a year.
Seismic energy and energy released during TNT explosions
Exploded amount of TNT
Magnitude
Released energy [J]
Remarks
1kg -1.9 90 U/g explosion
1 ton 0.2 1.3E+05 U/g explosion
1 kt 2.3 1.8E+08 U/g explosion
20 kt 3.2 4.0E+11 U/g explosion20kt = atom bomb dropped at Hiroshima
20 kt 2.1 8.9E+07 Explosion in the air as in Hiroshima
1.0 Mt 4.5 3.5E+11 U/g explosion
2.0Mt 4.6 5.0E+11 U/ g explosion
5.0Mt 5.0 2.0E+12 U/ g explosion
10Mt 5.2 4.0E+12 U/ g explosionLargest recorded U/g event in underground
mine
100Mt 5.9 4.5E+20 U/ g explosion
1000Mt 6.6 5.0E+21 U/ g explosion
Stress release estimates
There are four different estimates of stress release in use
1. Static stress drop – average difference between the initial and final stress levels over the fault plane
2. Dynamic stress drop – difference between the initial stress and the kinetic friction level
3. Apparent stress – quantity based on the radiated energy and seismic moment
4. Brune stress drop – when a complete stress release is assumed
And back to the 2.0 magnitude event …
DateTimeXYZMagnitudeMomentEnergyStress drop
Date 27/02/2004X=23931Y=-12717Z=-500mMagnitude 2.0Energy = 1.25E+07 JMoment =7.9E+11 NmStress = 0.9 MPa
Seismic source parameters – are they measured or estimated values?
Central Fault
Mica Fault
Southwest Fault
Dykes
W E
N S
W E
Date Time X -Y -Z Error Mag E Mo No of Stations
23865 13014 258 38 2 1.90E+07 8.80E+11 3
23871 12526 787 16 2.1 3.90E+07 1.00E+12 4
23873 12534 788 16 2 2.10E+07 9.00E+11 5
23882 12589 723 28 2.1 4.00E+07 9.40E+11 6
23929 12632 652 33 2.1 4.60E+07 9.20E+11 7
24108 12678 545 42 2.1 3.70E+07 1.00E+11 8
24028 12643 581 40 2.1 3.00E+07 9.70E+11 9
23997 12722 508 44 2.1 2.00E+07 9.80E+11 10
24/2/2004 23:15:55 23931 12717 500 46 2 1.40E+07 7.40E+11 11
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
1 2 3 4 5 6 7 8 9
Seismic energy E+07 J
No 3 4 5 6 7 8 9 10 11
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8 9
Seismic Moment E+11 Nm
No 3 4 5 6 7 8 9 10 11
Error
05
101520253035404550
1 2 3 4 5 6 7 8 9No 3 4 5 6 7 8 9 10 11
X
23700
23800
23900
24000
24100
24200
1 2 3 4 5 6 7 8 9
X coordinate
No 3 4 5 6 7 8 9 10 11
Y
12200123001240012500126001270012800129001300013100
1 2 3 4 5 6 7 8 9
Y coordinate
No 3 4 5 6 7 8 9 10 11
Z
-900
-800
-700
-600
-500
-400
-300
-200
-100
0
Z
Z [m]3 4 5 6 7 8 9 10 11
Source parameters depend on software version
Data recalculated with latest version
Different versions of seismic software
4 years of data
Energy index time history based poor quality data
Software version
No of events
Cumulative energy [J]
Cumulative moment [Nm]
No of events above 1.0
9.2.1 1662 1.10E+07 (100%) 2.05E+12 (100%) 5
10.1.3 1662 7.39E+05 (7%) 2.64E+13 (1287%) 135
10.1.4 1662 2.95E+05 (3%) 6.80E+12 (331%) 67
Latest Jmts
1758 6.70E+05 (6%) 2.68E+13 (1307) 138
Version 9.2.1 Version 10.1.3
Version 10.1.4 Version Java
Cumulated seismic energy and seismic moment
Moment magnitude values depending on software version
Magnitude range
Software version
9.2.1 10.1.3 10.1.4 Jmts
-2.0<M<-1.5 1 4 3 3
-1.5<M<-1.0 46 37 38 39
-1.0<M<-0.5 515 373 371 371
-0.5<M<0.0 620 611 609 607
0.0<M<0.5 377 345 368 353
0.5<M<1.0 98 157 206 151
1.0<M<1.5 5 79 66 80
1.0<M<2.0 55 1 57
2.0<M<2.5 1 1
V 9.2.1
V 10.1.3
V 9.2.1
V 10.1.3
Energy release estimate for magnitude 0.7
According toEnergy [J]
Version 9.2.1 2.1E+05
Version 10.1.3 1.4E+03
Version 10.1.4 6.3E+02
Jmts 1.1E+03
Kanamori estimate 5.0E+05
Guttenberg and Richter estimate
7.1E+05
Kanamori (1977) estimate of radiated seismic energy (for larger size events):
Energy = Moment/20000
Guttenberg and Richter (1956) estimate of seismic energy:Log E = 1.5M -1.2 where the energy is in MJ.
Moment Magnitude
Kanamori estimate
Guttenberg & Richter estimate
PMC average
1.3 5.0E+06 J 5.6E+06 J 9.7 E+05 J
1.9 9.6E+06 J
2.0 5.0E+07 J
Why PMC average?
Average monthly energy release by events magnitude 0.5
Maximum 1.0 E+05 JMinimum 1.0 E+04 J
How good is the recorded seismic data?
Reliable seismic data (XYX and source parameters)is the one that was recorded inside of the seismic network
The seismic source is surrounded by seismicsensors ( also located below and above)
PMC seismic data base
138029 eventsIn this:Events above 0.0 – 5189 eventsEvents above 1.0 - 135 events
Network fully installed only from January 2004
This reduces the data by 30751 (22%)
Only 30731 events inside (22% of total)In this:Events above 0.0 – 889 events (17% of total)Events above 1.0 - 15 events (11% of total)
Seismicity recorded inside of the network
Only 3645 events inside (3% of total)In this:Events above 0.0 – 224 events (4% of total)Events above 1.0 - 2 events (1% of total)
Exclude events locating close to the network borders and accept events recorded with minimum 6 stations
Seismic data base consists of unreliable data.
This means that the events XYZ coordinatesas well as their source parameters are not accurate and might be very different from the real values.
If we understand this limitation of the data we still mightbe successful with its interpretation.
Unfortunately that still is not the end of bad news……
Seismic source parameters – are they measured or estimated values?
Seismogram
Signal as we assume at the source
In case of the spectral analysis the seismic moment is calculated from thefollowing relation:
Mo = (4πρoco3RCΏo)/(FcRcSc)
Where: ρo is the density of source material co is either P-wave velocity or the S-wave velocity at the source Rc is the distance between the source and the receiver Ώc is the low frequency level, this is a spectral parameter Fc accounts for the radiation of either P or S waves Cc accounts for the free-surface amplification of either P or S wave amplitudes Sc is the site correction for either P or S waves
From the spectrum two independent source parameters are calculated orrather estimated
Seismic moment Mo [Nm]
Seismic energy E [J]
The estimate of the seismic source parameters is based on number of assumptions:
1. We know the source location
2. We know the seismic wave velocity
3. We know the rock mass density
4. We are able to correct the spectra for attenuation and scattering effects along the travel paths of seismic waves
5. We know the site correction value
And then the source parameter values change depending on:
1. Geometry (the location of event in relation to the sensors)
And then the source parameter values change depending on:
1. Geometry (the location of event in relation to the sensors)
2. With time ( with the caving process progress) the rock mass changes so for example the seismic velocities also change
3. New software new source parameters
Estimation is an approximation of a quality based on information available
It is an educated guess
There is a lot of examples that an estimate might lead towards a disaster (sometimes large sometimes small)
Example:John is planning a wedding partyToday you can hire professionals – wedding manager and his teamJohn sees this option as expensive “I can do it myself”
But there is a lot involved - Catering - Flower arrangements - Drinks - Music - Photographer - Transport and accommodation arrangements…. and probably much more
“But there is still time so it will be OK”
Time passes and John is very busy …… and time is running out
A day or two before the wedding party John remembers that he needs tohire some tables and chairs
There will be 240 people attending
John phones around and find out the following: -Standard table size sitting comfortably 4 people is 200cm by 90cm (0.45m² per person)
-Easy 1.8 m² seats 4 people, for 240 people I will need 60 tables and the price is so and so
-He then remembers that some time ago he was driving by a hire company and he asked for prices and yes they were much cheaper and the tables looked OK for size………………John phones and orders the tables
On the wedding day (for sure Sunday) the tables arrive but they are 180cm by 90cm.
Johns problem:
The standard 200cm by 90cm table times 60 gives area of 108m²The table that arrived is 180cm by 90cm times 60 gives an area of 97.2m²
Comfortable sitting of each invited person requires 0.45m² per person
John is short of 10.8m² table surface that is place to seat comfortably 24 people
Bad luck? No but it is there:
-Remember it is Sunday (all places are closed)-And … all quests arrive
Estimate of the table size resulted in a disaster for John
3. Seismic source parameters – part 2
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