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