Republic of Iraq Ministry of Higher Education and Scientific Research University of Baghdad College of Science Department of Geology

Determination Formula of Local Earthquake Magnitude for Iraqi Seismological Network

A Thesis Submitted to the Council College of Science

University of Baghdad in Partial Fulfillment of the Requirements for the Degree of Master of Science in (Geophysics)

By:

Maythem Abdul Qadir Al Dabbagh B.Sc. Geology, College of Science, University of Baghdad

1997

Supervised by Prof. Dr. Nawal Abd Al ridha

1435 2014

( )

The Supervisor Certification

I certify that this thesis entitled Determination Formula of Local Earthquake Magnitude for Iraqi Seismological Network has been prepared under my supervision in the department of Geology, College of Science, University of Baghdad in partial fulfillment of the requirements for the degree of master of science in Geology (Geophysics).

Recommendation of the head of the department of Geology:

In view of the available recommendation, I forward this thesis for the debate by the examining committee.

Signature Name: Nawal A. ALridha Title: Professor Address: Department of Geology College of Science University of Baghdad Date:

Signature Name: Title: Professor Address: Department of Geology College of Science University of Baghdad Date:

Committee Certification

We certify that we have read this thesis entitled Determination Formula of Local Earthquake Magnitude For Iraqi Seismological Network and as the examination committee examined the student in its content and in our opinion it adequate for award of the degree of Master of Science in Geology (Geophysics).

Signature Name: Fitian R. AL Rawi Title: Professor Address: Department of Geology Collage of Science University of Baghdad Date: (Chairman)

Approved by the Deanery of the collage of Science:

Signature Name: Salman Zainalabdin Khorshid Title: Assist. Prof. Address: Department of Geology Collage of Science University of Baghdad Date: (Member)

Signature Name: Hussein Hammeed Karim Title: Professor Address: Building and Constructing Engineering Department University of Technology Date: (Member)

Signature Name: Nawal A. ALridha Title: Professor Address: Department of Geology Collage of Science University of Baghdad Date: (Supervisor)

Signature Name: Dr.Saleh Mahdi Ali Title: Professor Address: Dean of the collage of Sciences Date:

Declaration

This is to certify the thesis titled:

Determination Formula of Local Earthquake Magnitude for Iraqi Seismological Network

Submitted by : Maythem Abdul Qadir Al-Dabbag

Department: Geology department

College: College of science

Has been written under my linguistic supervision and its language, in its present form, is quite acceptable.

Name: Dr. Ameen I. AL-Yasi

Address: Asst. professor

Signature:

Contents Item Subject Page Chapter(1): An introduction

1.1 Introduction 1

1.2 Aim of Study 2

1.3 Procedure of Study 2

1.4 location of Studded Area 2

1.5 Previous Studies 2

1.5.1 World Studies 2

1.5.2 Some Regional Studies 3

1.5.3 Calculating Magnitude in Iraqi Seismological Network

4

1.6 Tectonics and Seismotectonics of the Studied Area 4

1.6.1 Tectonic Framework of Arabian Plate 4

1.6.2 Tectonic and Seismotectonics of Iraq 6

1.7 Seismic Activities in Iraq 8

Chapter(2):Local magnitude scale derivation

2 Preface 10

2 Introduction 10

2.2 Moment Magnitude 11

2.2.1 Definition 11

2.2.2 Seismic Moment From Seismic Record 11

2.2.3 Seismic Moment_ Corner Frequency Relationship and Saturation 13

Item Subject Page 2.3 Historical Development of the Local Magnitude Scale 16

2.3.1 Richter Scale as Richter Represented 16

2.3.2 Instrument and Syntheses 19

2.3.3 Attenuation Function 21

2.3.4 ML Scale Derivation, Formulation and Methodology 22

2.4 Hypocenter_ Station Distance Calculation 25

2.5 Structure of Seisan Software 25

Chapter(3):Instrument response removal to read amplitude

3 Preface 27

3.1 Magnification of the Digital Recording System Used in ISN 27

3.2 Ground Motion Determination 29

3.3 Wood-Anderson Seismometer Magnification 32

3.4 Synthetic WA Amplitude 34

3.5 Wood Anderson Synthesis from Digital Data 36

3.6 Reading Amplitude by Seisan Sofware 37

3.7 Verification of Seisan Software 41

Chapter(4):Working with data

4.1 Data Collection and Preparation 44

4.2 Data Set Used in the Present Study 47

4.3 Hutton and Boor, 1987 Study, a Review 52

4.4 Linear Least Square Fitting Execution 53

Item Subject Page 4.4.1 Examining Formula (4-3) and Formula (4-4) Statistically 54

4.4.2 A Comparison Between Hutton, 1987 and MLH (ISN) Formula 55

4.5 Attenuation Curve Study 58

4.6 Relationship between average Wood-Anderson amplitude to the vertical and horizontal componants

58

4.7 ISN Two formulas, Mathematical relationships 60

4.8 ML for Dataset Used in Present Study as Reported by ISK(Turkey) and TEH (Iran)

64

5 Chapter(5):Conclusion 67

List of Figures Figure Subject Page ( 1-1) General tectonics of the Arabian and surroundings plate 6

( 1-2) The three tectonic zones of Iraq 8

(1-3) Epicenters of seismic events recorded by ISN between 1900 and 2011

9

(2-1) Shape of the seismic displacement spectrum 12

(2-2) Example of seismic displacement spectra of a local earthquake 13

(2-3) Theoretical S-source spectra for different size earthquakes 14

(2-4) Relationship between different kinds of magnitudes and moment magnitude

15

(2-5) Decay curves of (6) magnitude units 19

(2-6) Attenuation curve ( log A? as a function of distance) for some ML formulas

22

(2-7) S-file to the first event of the dataset used to make the linear least square fitting operation

26

(3-1) Displacement magnification curve of streckisen STS-2 seismometer as a function of frequency

31

Figure Subject Page (3-2) Velocity magnification curve of STS-2 seismometer as a

function of frequency 31

(3-3) Velocity magnification curve of STS-2 seismometer, taken from the seismometers manual

32

(3-4) Displacement magnification of Wood Anderson Seismometer as a function of frequency

33

(3-5) (WA gain/ ISN gain) as a function of period 36

(3-6a) Z-component for a seismic event recorded by MSL station and reviewed by Seisan software in raw data form

38

(3-6b) Zoomed trace to the same event of Fig(3-6a) 38

(3-6c) Synthetic Wood Anderson trace to the record of Fig (3-6a) 39

(3-6d) Reading amplitude on synthetic Wood Anderson trace of Fig (3-6a)

39

(3-6e) Velocity trace to the record of Fig (3-6a) 40

(3-6f) Zoomed view to the velocity trace of Fig (3-6a) 40

(3-6g) Reading maximum velocity on the velocity trace 41

(3-8) MS calculated from reading maximum amplitude on velocity trace(MS seisan) minus MS calculated from reading maximum amplitude on raw data after making the correction(MS raw)

42

(3-9) ML calculated by use of maximum amplitude read on synthetic Wood Anderson trace minus ML calculated by use of raw data

42

(4-1) A histogram shows the distribution of data records according to hypocenter- station distance, for records used in deriving MLV

45

(4-2) A histogram shows the distribution of data records according to hypocenter- station distance, for records used in deriving MLH

45

(4-3) A histogram shows Distribution of seismic events used in the study according to mb(USGS)

46

(4-4) Epicenters of seismic events projected on a map represents the studied area

47

(4-5) Residuals according to MLV(ISN) 55

Figure Subject Page (4-6) Residuals according to MLH (ISN) 55

(4-7) Residuals according to Hutton and Boor,1987 formula 57

(4-8) Residuals according to MLH(ISN) formula 57

(4-9) Attenuation curve (-Log Ao = a*Log(distance)+b*distance+c) of ISN, Norway and southern California

59

(4-10) Attenuation curve( LogAo valuse as a function of distance ) taken from ML formula of some regions

59

(4-11) Residuals according to mb(IDC)_MLV relationship 61

(4-12) Residuals according to MS(IDC)_MLV(ISN) relationship 61

(4-13) Residuals according to mb(USGS)_MLV(ISN) relationship 62

(4-14) Residuals according to mb(USGS)_MLH(ISN) relationship 62

(4-15) Residuals according to mb(IDC)_MLH(ISN) relationship 63

(4-16) Residuals according to MS(IDC)_MLH(ISN) relationship 63

List of Tables Table Subject Page (1-1) Parameters a, b and c constant of the ML scale at different

localities 3

(2-1) Distance correction according to Richter, 1935 17

(3-1) Constants used to construct a response curve to ISN seismic recording system

27

(3-2) Displacement and velocity gain of strakisen STS-2 seismometer for periods between (4 and 0.1) second

28

(3-3) Magnification of Wood Anderson seismometer 34

(3-4) The ratio of WA gain to ISN system gain and the corresponding periods

35

(4-1) Information about ISN stations and their contribution in providing data records used in the study

44

Table Subject Page (4-2) Date, origin time, location, depth and magnitude of seismic

events used in present study 49

(4-3) Station corrections, after the execution of the linear least square fitting operation to derive MLV , for the five stations

53

(4-4) Station corrections , after the execution of the linear least square fitting operation to derive MLH, for the five stations

54

(4-5) Relationships to calculate predicted ML ISN by use of mb,MS of IDC and mb of USGS

60

(4-6) MLV(present study),MLH(present study),ML(ISK),ML(TEH) and ML calculated according to Ambrasseys,1990 relationship to calculate ML from mb

64

List of Abbreviation IASPEI International Association of Seismology and Physics of the Earth

Interior. IDC International Data Centre one of the (Comprehensive Nuclear-Test-Ban

Treaty) organizations. USGS United States Geological Survey.

NEIC National Earthquake Information Center.

ISC International Seismological Centre.

ISN Iraqi seismological network

ISK Kandilli Observatory and Research Institute.( A Turkish agency)

TEH Tehran University

WA Wood-Anderson

mb Short period body wave magnitude

Ms Surface wave magnitude

MS Broad band surface wave magnitude

Mw Moment magnitude

Abstract Two magnitude formulas have been derived to be used in calculation of local magnitude (ML) for seismic events recorded by Iraqi seismological network. Nine hundred seventeen (917) amplitude readings from 78 recorded seismic events for the period from year 2010 to the end of year 2012 contributed in deriving the two formulas. The following model (Hutton and Boor, 1987) is adopted to derive the two formulas: ML (A, R) = log10 A + a*log10 R + b*R + c + S Three hundred five (305) and (612) amplitude readings on vertical and horizontal components respectively are contributed in in deriving the two scales (MLV and MLH), which are valid for maximum amplitude read on synthetic Wood-Anderson trace of the vertical and horizontal component respectively (A) and epicenter- station distance (R) up to 1060 Km. The standard deviation (SD) to the single station magnitude about event magnitude obtained by averaging single station magnitude are 0.143 and 0.155 for MLV and MLH respectively. Slope and level of the two attenuation curves taken from the two formulas derived in the present study reflect tectonic environment a mid between the active and the stable. By use of simple linear regression analyses, three mathematical relationships between [mb(USGS), mb(IDC) and MS(IDC) ] and every one of the two formulas , are derived, and it is found that (MLV-MS(IDC)) and (MLH-mb(IDC)) relationships gave the least standard deviation. It is found that MLH is greater than MLV with (0.289) magnitude unit (as an average for the seismic events used in the study) and that reflects soil cover existence which enlarges the shear waves. It is found that MLH values are closer than MLV to ML reported by some nearby networks to the same events, therefore the study recommends adopting MLH as a formal local magnitude scale for Iraqi seismological network.

Chapter (1)

An introduction

1

1.1 Introduction Calculating the magnitude of earthquake is a basic and essential task of any seismological network, globally as well as locally. When an earthquake occurs, the first question from the press is about the Richter magnitude and the second about location (Havskov and Ottemoller, 2010). The concept of magnitude was introduced by Richter (1935) to provide an objective instrumental measure of the size of earthquakes. Richter used the term magnitude in distinction to the name intensity scale, which is based on the assessment and classification of shaking damage and human perceptions of shaking and thus depends on the distance and depth of the seismic source. Magnitude M uses instrumental measurements of the ground motion adjusted for epicentral distance and source depth (Bormann, 2002). Magnitudes of earthquakes are calculated with the objectives to: Express energy release to estimate the potential damage after an earthquake. Express physical size of the earthquake. Predict ground motion and seismic hazard. Calculating magnitude is thus a basic and essential task of any seismological network, globally as well as locally (Havskov and Ottemoller , 2010). One of the ultimate goals of earthquake- source studies is to understand the physical processes of a seismic source in as much details as possible. There are two possible approaches to this problem. In the first approach, we make a very detailed analysis of all the data available including those on seismic body waves, surface waves, near-field data, foreshocks and aftershocks etc. However, this type of study is time consuming and is not possible for every earthquake. In the second approach we use a relatively simple method, and process a large number of events in a very short time. This approach provides the public quick information on the earthquake. More importantly, it provides fundamental data to be included in the earthquake catalogs which are the basis of a variety of scientific research. The earthquake magnitude introduced by Richter (1935) is one of the important parameters to be used in the second approach (Kanamori , 1983). Due to local variation in attenuation and ground motion site amplification as well as of the station position with respect to the source radiation pattern, large variations in the measured amplitudes might occur, leading to large variance in magnitude estimates at individual stations. Thus, magnitude calculation is not an exact science and in the first hours following an earthquake, the magnitude is often revised several times (Schubert, 2007).

2

1.2 Aim of Study The aim of study is to derive local magnitude scale to be used in calculating the magnitude for local seismic events recorded by Iraqi seismological network (ISN). 1.3 Procedure of Study In year 1987 Hutton and Boor derived a local magnitude scale for southern California by following a procedure similar to that of Richter when he derived a magnitude scale in the same region. According to the IASPI , the procedure of Hutton and Boor , 1987 became a standard for local magnitude determination, and in the present study , the same procedure will be followed. 1.4 location of Studied Area Studied area is the area limited by the international borders of Iraq, Iraq-Turkey border region and Iraq-Iran border region. 1.5 Previous Studies 1.5.1 World Studies Richter (1935) used maximum trace amplitude for the seismic event as recorded by standard Wood-Anderson torsion seismometer, to derive ML scale for southern California.He presented a magnitude formula in the form [m = logA+ (-logAo)], where (-logAo) is the distance correction term presented as a tabulated values. Bakun and Joyner (1984) used 957 synthesized Wood-Anderson horizontal component records to derive ML scale for central California, they used just the Lg phase to present a local magnitude formula in the form (ML = logA+a*log distance+b*distance+c ) . Where a=1, b=0.00301 and c=-1.99 Hutton and Boor (1987) used 9941 peak amplitude on Wood- Anderson (or simulated Wood-Anderson instrument), to derive a local magnitude scale for southern California. By using the linear least square fitting method, they presented a formula in the same form that Bakun and Joyner (1984) represented, where a=1.11, b=0.00189 and c=-2.09. After 1987 ML formulas took a form similar to that of Bakun and Joyner (1984) and Hutton and Boor (1987). Table (1-1) shows the parameters (a), (b) and(c) for various regions.

3

Table (1-1). Parameters a, b and c constant of the ML scale at different localities Region a b c Distance

range(km) reference

Central Europe

1.11 0.00095 -2 10 - 1000 Stange(2006)

Norway 0.91 0.00087 -1.68 0 - 1500 Alsaker et al.(1991) N.Italy 1 0.0054 -2.22 10 - 300 Bindi et al.(2005)a Ethiopia 1.2 0.00107 -2.17 200 - 600 Keir et al.(2006) Vietnam 1.74 0.00048 -

3.202 0 - 750 Nguyen et al.(2010)

South Africa

1.15 0.00063 -2.04 10 - 1000 Saunders et al.(2012)

Craiu et al. (2011) derived a local magnitude formula for the Intermediate-depth earthquakes in Romania. The parameters in the magnitude relation are determined through multiple regression method using as reference the duration magnitude previously used in routine magnitude estimation for the earthquakes occurred on the Romania territory. The amplitude (A) was measured on the horizontal components of broadband seismograms filtered to reproduce synthetic Wood-Anderson seismograms (in millimeters). 1.5.2 Some Regional Studies (Al-Amri, et al., 1999) derived a local magnitude scale for seismographic sub-network in NW Saudi Arabia, they applied linear regression teqnique between the two amounts [mb(USGS)-log (amplitude)] and log(distance) for seismic events used in the study. They derived the following formula: [ML=log(amplitude/period)+3.4*log(distance/111.2)+2.55] Bindi et al.(2005) used seismic and strong motion records to calibrate the local magnitude scale over a hypocentral distance range from 10 to 190 km In NW Turkey. By analyzing the unit covariance matrix and the resolution matrix, researchers show how the source-to-station geometries of the seismic and strong motion networks affect the uncertainties of the computed station corrections, attenuation coefficients, and magnitudes. Horizontal component is used to derive the following ML formula for NW Turkey: (ML=logA+log(distance)+0.00152*distance-1.61). (Askari, et al. ,2009) derived a local magnitude scale for Alborz region Norther Iran. They used the same procedure followed by Hutton and Boor, 1987 to derive

4

the following formula for a distance rang from (8.5 to 550) kilometer: ML=logA+1.1725log(distance)+0.0021*distance-3.12. Nassir and Al-Humidan(2011) derived a local magnitude scale for Kuwait national seismic network (KNSN) by applying simple linear regression analysis between the two amounts: [mb(USGS)-log (amplitude)] and log(distance) for seismic events used in their study. They used vertical component to derive the following relationship: (ML=log A+1.43*log (distance/111.2) +1). Rezapour and Rezaei(2011) derived a local magnitude scale for northwest Iran. Their investigation showed that using one-half the peak-to-peak value tends to underestimate the magnitude of an event by as much as 0.07 magnitude units in comparison with using the zero-to-peak value. Additionally, using a vector sum of horizontal measurements overestimates the ML values by 0.16 magnitude units in comparison with magnitude values that are determined using arithmetic means of horizontal measurements. The distance attenuation curve, station correction terms, and the magnitude of events were simultaneously estimated using parametric and nonparametric approaches. The distance attenuation curves that resulted in a nonparametric approach are given by: logA0=0.9252log () +0.0030+0.8496 and logA0=0.9993log () +0.0029+0.7114 for the vertical and horizontal components, respectively, where is the epicentral distance in kilometers. 1.5.3 Calculating Magnitude in Iraqi Seismological Network According to ISN published bulletins, the following two durational magnitude formulas are depended, to calculate the magnitude of the local and distant events recorded by the network: MD =1.31*log (D) +1.19 epicenter-station distance must not exceed 100 kilometer. For epicenter- station distance more than 100 kilometer the following formula is used: MD = 0.99*log (D) +0.76*log(R) +0.38 Where: D is the duration of seismic events in seconds; R is epicenter- station distance in kilometer. 1.6 Tectonics and Seismotectonics of the Studied Area 1.6.1 Tectonic Framework of Arabian Plate The Arabian subcontinent Plate is one of the Earths largest blocks that was held together and moved many kilometers as a unit since the late Cretaceous experiencing relative transitional motion with respect to the Eurasian, African, Somalian, Iranian, Anatolian, and Aegean Plates (AlSinawi, 2002).

5

Tectonic setting of the Arabian plate shows that it is almost surrounded by a variety of types of active plate boundaries which are characterized by complex faulting and Tertiary dike injections and volcanism: continental collision with the Eurasian Plate ( south of Anatolian fault zone along the Zagros Belt and Bitlis Sutures ), continental transform ( Dead Sea Fault system ), young seafloor spreading ( Red Sea and Gulf of Aden ) and oceanic transform(Omar, 2006). The majority of earthquakes and other tectonic activities are concentrated along the Zagros fold belt, the Dead Sea transform, the Gulf of Aqaba and the Red sea belt ( Al-Damegh et al., 2004). The Arabian and Eurasian plates are colliding along the Zagros suture zone in western Iran. This collision zone has experienced two major episodes of collision orogeny during late Mesozoic and Miocene time (Stocklin 1974; Sengor and Kidd, 1979). Continental collision is occurring along the Bitlis suture zone in southern Turkey and the Zagros suture zone in western Iran. The current counter-clockwise rotation and northward motion of the Arabian plate relative to Eurasia is accommodated along these collision zones ( Seber, et al., 2001 ). Tectonic setting of the Arabian plate shows that it is almost surrounded by active plate boundaries. The Arabian Subcontinent Plate is subducted under the Anatolian and Iranian Plates.

6

Fig( 1-1). General tectonics of the Arabian and surroundings plate ( After JSO, 2004 ). 1.6.2 Tectonic and Seismotectonics of Iraq Iraq is located in the northern Arabian Platform including the western edge of the Zagros Mountain range, where the convergent tectonic boundary between the Eurasian and Arabian plates forms a fold and thrust belt(Gok et al,2006).

7

The high Bitlis-Zagros Mountains in the north and eastern part of the country are a folded belt in a NW-SE direction along the western part of Iran and northeast Iraq (Gok et al, 2006). The Zagros sedimentary cover is folded into a mountain belt for a distance of about 1500km along the southwestern part of Iran and northeastern Iraq. The Zagros folded belt lies on the northeastern margin of the underthrusting Arabian continental crust ( Ni and Barazangi, 1986 ). The folding probably started during the Upper Miocene-Lower Pliocene, and the belt is still considered to be one of the most active orogens on earth (Gok et al, 2006). Iraq can be divided into three tectonic zones:

Unfolded Zone (stable platform) the northern part of African-Arabian Pre- Cambrian platform and is characterized by unfolded stable zone, an almost horizontal dipping strata and smooth relief

Folded Zone The Mesopotamian foredeep covers an intermediate structural position between the Alpine geosynclinal area of Zagros in N-NE part of Iraq and the Pre- Cambrian African-Arabian platform to the west.

Thrust zone a zone of approximately 200 km width, which runs parallel to the folded belt(Kadinsky-Cade and Barazangi, 1982). The majority of the moderate-to-large historical events in eastern Iraq have occurred along this belt(Alsinawi and A1-Shukri, 1979).

This division is called The Triple Division and it is adopted by Henson (1940), Dunnington (1958), Al Naqib (1959) , Alsayyab (1968) , Ditmar et al (1971) and Jassim and Goff( 2006). Fig(1-2) shows the three tectonic zones of Iraq

8

Fig( 1-2). The three tectonic zones of Iraq. (After Gok et al,2006). 1.7 Seismic Activity in Iraq Most of the seismic activities in Iraq are restricted to the north and northeastern part along the Alpine folded thrusted area, near that there is a sharp boundary in seismic distribution between the folded and unfolded regions; indicating that the stresses resulting from the movement of the Arabian plate to the north and northeast with respect to the Iranian plate are not transported to the unfolded region but only causes deformation to the folded area ( Al-Sinawi and Issa,

9

1986 ). Fig (1-3) shows epicenters of seismic events recorded by ISN between 1900 and 2011 taken from ISN database

Fig(1-3) epicenters of seismic events recorded by ISN between 1900 and 2011. Data used in the plotting was taken from ISN database

Chapter (2)

Local magnitude scale derivation

10

Preface This chapter includes an introduction to the magnitude types, moment magnitude will be rather explained in details because this type of magnitude dose not suffer from saturation (the problem of all the magnitude scales that depend on amplitude measurement). Adequacy details will be presented about local magnitude scale (subject of present study) in terms of historical development and the problem of the connection between this scale and a certain type of instruments and how this problem was overridden. Hypocenter- station distance is a very important parameter in any magnitude formula. Therefore, the equation used in distance calculation will be specified . A brief introduction about Seisan software (the main tool of the present study) will be presented. At last, method used to derive the ML scale will be explained. 2-1 Introduction The original Richter magnitude (ML) was based on maximum amplitudes measured on records of the standardized short-period Wood-Anderson (WA) seismometer network in Southern California (Kanamori, 1983). Gutenberg and Richter (1936) extended the magnitude concept so as to be applicable to ground motion measurements from medium- and long-period seismographic recordings of both surface waves ( Ms ) and different types of body waves (mb ) in the teleseismic distance range(Bormann,2002). After the deployment of the World Wide Standardized Seismograph Network (WWSSN) in the 1960s it became customary to determine the body-wave magnitude only on the basis of short-period narrow-band vertical component P-wave recordings only. This short-period body-wave magnitude was termed mb(Bormann,2002) . Another effort to provide a single measure of the earthquake size was made by Kanamori (1977). He developed the seismic moment magnitude Mw. It is tied to Ms but does not saturate for big events because it is based on seismic moment M0, which is proportional to the average static displacement and the area of the fault rupture and is thus a good measure of the total deformation in the source region( Kanamori ,1977). 2.2 Moment Magnitude 2.2.1 Seismic Moment and Moment magnitude The moment magnitude scale is the most recent scale and is fundamentally different from the earlier scales. Rather than relying on measured seismogram peaks, the Mw scale is tied to the seismic moment (M) of an earthquake (Hanks and Kanamori, 1979).

11

The moment M0 is measured in Newton*meter. The seismic moment M0 is a direct measure of the tectonic size (product of fault plain area times average static displacement) (Stein and Wysession ,2004). Moment magnitude is calculated from seismic moment using the relation of Kanamori (1977) :

7.10log32

10 -= oMM w -------------------------------------------------------------------- (2-1)

Where: Mw is the moment magnitude and Mo is the seismic moment. The advantage of the Mw scale is that it is clearly related to a physical property of the source and it does not saturate for even the largest earthquakes.(Shearer, 1999). 2.2.2 Seismic Moment From Seismic Record The most common seismic source model used is the Brune model. The model has been used extensively and it has been shown that it gives a good agreement with observations from many different tectonic regions and for a large range of magnitudes(Havskov and Ottemoller , 2010). (The Brune model predicts the following source displacement spectrum S (f):

32 4))(1()(

prno

o

ffMfS

+= ------------------------------------------------------------------ (2-2)

Where: Mo is the seismic moment measured in (Newton* meter), is the density (kg/m3), v is the velocity (m/s) at the source (P or S-velocity depending on spectrum) , f0 is the corner frequency and f is the frequency. This expression does not include the effect of the event-station azimuth variation (Brune, 1970). Displacement spectrum can be obtained by doing Fourier transform to the displacement trace (raw data can be corrected to produce displacement, velocity and acceleration traces. The shape of the log-log spectrum is seen in Fig (2-1). At low frequencies, the spectrum is flat with a level proportional to Mo while at high frequencies, the spectral level decays linearly with a slope of 2. At the corner frequency (f = f0), the spectral amplitude is half of the amplitude of the flat level(Havskov and Ottemoller , 2010).

12

Fig (2-1).Shape of the seismic displacement spectrum. o is the spectral flat level. In the point f=fo , spectral level is half the flat level . After (Havskov and Ottemoller , 2010). Equation (2-1) is valid if the receiver was put on distance (0) from the seismic events epicenter. In the ordinary cases there is a distance between epicenter of seismic event and receiver. Therefore the displacement spectrum at the receiver will be modified by geometrical spreading G (,h) and attenuation. At an epicentral distance (in meter) and hypocentral depth h (in meter), the observed spectrum can be expressed as: (Havskov and Ottemoller , 2010)

)(

32)(*)(*),(*

4))(1(

2*6.0*),( fQft

fk eehG

ff

MtfDp

p

prno

o-

-D+

= -------------------------------------- (2-3)

Where: D(f,t) is the corrected displacement spectrum. ),( hG D is geometrical

spreading term. fke p-)( is soil amplification term. )()( fQft

ep-

is attenuation term. The factor 0.6 account for average radiation pattern effect. The factor 2.0 is the effect of the free surface. The spectrum corrected for attenuation is called Dc and is used to obtain the observed parameters, corner frequency fo and spectral flat level o (ms).

).,())(1(4

2*6.0*

))(1()(

232hG

ff

M

fffDc D

+=

+

W=

oprn

o

o

o ------------------------------------------- (2-4)

Where: cD : Displacement spectrum, corrected for attenuation

),(*2*6.04* 3

hGM

DW

=prnoo ---------------------------------------------------------------------- (2-5)

),( hG D : Geometrical spreading, in simplest case is equal to (1/r), where (r) is

event- station distance.

Log spectral level (Nanometer*second)

Log frequency

Slop= -2

fo

o Flat level

13

2*6.04* 3rM prnoo W= ------------------------------------------------------------------------ (2-6)

Where: Mo is seismic moment in (Newton*meter). o is flat level displacement spectral in (meter*second). is density of rupture area in (kilogram / 3)(meter ) . v is velocity of (P or S) wave in unit (meter /second). r is event- station distance in meter. ( Brune, 1970), (Havskov and Ottemoller , 2010). Fig (2-2). Represents displacement (P-spectrum and S-spectrum) for a real record.

Fig (2-2). Example of seismic displacement spectra of a local earthquake. On top is shown the seismogram (vertical component) with the time windows used for spectral analysis. The top spectral curve is the signal spectrum while the bottom curve is the noise spectrum. The spectrum is corrected for attenuation. Note that the y-axiss unit is in nm/Hz = nm s. flat level for S- spectra is between 2 and 3 and the flat level of P-spectra is between 1 and 2 .After (Havskov and Ottemoller , 2010).

2.2.3 Seismic Moment_ Corner Frequency Relationship and Saturation Havskov and Ottemoller , (2010) , Borman, (2002) and Shearer, (2009 )cited the following equation to express the relationship between the moment magnitude and the corner frequency: Log (fo) = 2.35 0.5Mw-------------------------------------------------------------- (2-7) Using eq (2-7) to calculate the corner frequency for a given Mw, the corresponding Brune spectra can be calculated by use of eq (2-2) and the theoretical source spectra can be plotted as a function of the moment magnitude, as in Fig (2-3).

14

Fig (2-3).Theoretical S-source spectra for different size earthquakes. The curves are calculated using eq (2-2) and eq (2-7) assuming a velocity of 3.5 km/s and a density of 3 g/cm3. The stress drop is 30 bar. The moment magnitude is indicated at each spectrum. A line indicates the corner frequencies where it crosses the spectra. The Ms and mb lines indicate the frequencies of determination(to determine mb, maximum body wave amplitude must be read on a cycle of period 1 second, while for Ms determination maximum surface wave amplitude must be read on a cycle of period 20 second. After (Havskov and Ottemoller , 2010). At frequencies below fo there is a linear relationship between magnitude (log of the measured amplitude) and moment. However, at higher frequencies this linearity breaks down and the magnitude scale does not fully keep up with the increasing size of the events. This phenomenon is called magnitude saturation (Shearer, 2009). For mb, the amplitude is read at around 1 Hz. From the figure(2-3) it is seen that the amplitude at 1 Hz increases linearly with moment until the corner frequency reaches 1 Hz (around magnitude 6) and for larger events, the amplitude at 1 Hz is smaller than the amplitude of the flat level. Thus for events larger than 6, mb will

15

underestimate the magnitude. The same happens for Ms, but at the lower frequency of 0.05 Hz(Shearer,2009). Saturation phnomena of magnitude scales when moment magnitude increase and relationship between different kinds of magnitude scales is shown in Fig (2-4).

Fig(2-4). Relationship between different kinds of magnitudes and moment magnitude. Saturation of these magnitude scales with moment magnitude increasing, can be seen.(after Kanamori,1983). 2.3 Historical Development of the Local Magnitude Scale 2.3.1 Richter Scale as Richter Represented The data that Richter worked with were the data taken from southern California networks where many different size earthquakes have been occurred and for each event there are a number of stations that record it, so there is the ability to follow the decreasing in the energy (amplitude) with the distance increasing.

16

To build his scale, Richter, plotted the maximum ground motion at each station as ordinate with the corresponding epicentral distance as abscissa (Richter 1958). Amplitudes were plotted on a logarithmic scale; since the measurements ranged from 0.1 millimeter to 10 or 12 centimeters, this gave a more manageable chart than linear scale. (Richter 1958). For every seismic event there is a curve of points the y-axis (for each one) is the logarithm of maximum trace amplitude in millimeter and the x-axis is the event-station distance in kilometer. The result is a group of curves each curve represents a seismic event; on the assumption that these curves are parallel to each other and; if this parallelism was exact, the difference between the logarithms of amplitudes of any two given shocks would be independent of distance, the amplitudes themselves would be in constant ratio.(Richter 1958). Till this step and in accordance to the law of parallelism, quality M (the magnitude) can be defined as: M = Log A Log A Where A is the recorded trace amplitude for a given earthquake at a given distance, and A is that for a particular earthquake selected as standard (Richter, 1958) This standard shock has also been called the zero shock, since, if A = A, M =0 (Richter 1958). The zero level (zero magnitude) was intentionally chosen low enough to make the magnitude of the smallest recorded earthquake positive. Table (2-1) represents event-station distance and the corresponding (Log A) as a distance correction according to Richter, 1958

17

Table (2-1). Distance correction according to Richter, 1935. Logarithms of the amplitude (in millimeter) with which a standard torsion seismometer (To=0.8, v=2800, h=0.8) should register an earthquake of magnitude zero (since A is less than 1, its logarithm is negative and Table shows values for Log A). (After Richter, 1958). distance(km) Log A distance(km) Log A 0 1.4 260 3.8 10 1.5 280 3.9 20 1.7 300 4 30 2.1 320 4.1 40 2.4 340 4.2 50 2.6 360 4.3 60 2.8 380 4.4 70 2.8 400 4.5 80 2.9 420 4.5 90 3 440 4.6 100 3 460 4.6 120 3.1 480 4.7 140 3.2 500 4.7 160 3.3 520 4.8 180 3.4 540 4.8 200 3.5 560 4.9 220 3.65 580 4.9 240 3.7 600 4.9

The zero level A can be fixed by naming its value at a particular distance. This was taken to be one thousandth of a millimeter at a distance of 100 kilometers from the epicenter; an equivalent statement is that an earthquake recording with trace amplitude of 1 millimeter measured on a standard seismogram at 100 kilometers, is assigned magnitude 3 (Richter, 1958). Fig (2-5) Represents the frame of Richter scale. If you look carefully to the chart you can see the following:-

Any amplitudedistance pair of a seismic event can be represented as a point it ordinate is the logarithm of maximum trace amplitude in millimeter and it abscissa is the event-station distance in kilometer

According to the assumption of the parallelism of the decay curves and by use of Log A values, For any point (amplitude distance pair of a seismic event), we can draw the decay curve pass through that point; and the numerical value of the magnitude to that point (and all points of the decay curve) will be :

(the y-axis of the point belongs to this curve at 100 x-axis ) + 3

18

Fig (2-5). Decay curves of (6) magnitude units drown by excel by use of -Log A values taken from Table (2-1).

distance vs logA

-6

-5

-4

-3

-2

-1

0

1

2

3

4

0 100 200 300 400 500 600 700

distance(km)

log(amplitude) in millimiter

6

5

4

3

2

1

A

B

zero magnitude curve

(magnitude 6) amplitude decay curve

0

19

(Magnitude of point A is 1+3=4). And that equivalent to: The magnitude of any shock is taken as the logarithm of the maximum trace amplitude, expressed in microns( 610- m), with which the standard short-period torsion seismometer (To = 0.8 sec., V z = 2800, h = 0.8) would register that shock at an epicentral distance of 100 kilometers (Richter 1935).

For any given point : magnitude = Log A Log A , for point A M = (-1-[-5]=4)

for zero magnitude curve 1. The y axis has been chosen arbitrarily (as mentioned above). 2. zero magnitude curve passes through the point (100,-3), which means

that (an earthquake recorded with maximum trace amplitude of 1 millimeter measured at 100 kilometer distance, is assigned magnitude 3. (In the next literatures this point took the name: anchor point, and any magnitude formula must achieve the following condition: by inserting 1 mm as amplitude and 100 km as distance, magnitude of 3 will be obtained.

According to the assumption of paralisem and by use of -Log A values we can draw the decay curve of the amplitude with the distance for any given magnitude unit.

2.3.2 Instrument and Syntheses In his definition to the numerical value of the local magnitude, Richter put the following (2) criteria

Using an instrument of a certain magnification characteristics. Amplitude to be used in ML calculation is the amplitude read on Wood-

Anderson seismograph, and it dose not represent the ground displacement. The magnitude of any shock is taken as the logarithm of the maximum trace amplitude, expressed in microns, with which the standard short-period torsion seismometer (T = 0.8second, v= 2800, h=0.8) would register that shock at an epicentral distance of 100 km) (Richter, 1935). Thus, seismologists are often faced with the task of estimating ML from records registed by instruments radically different from the W-A seismograph( Backun, et al., 1978). For analog data, synthesis may be achieved by converting record amplitudes from another seismograph with a displacement magnification Mag (T) into respective WA trace amplitudes by multiplying them with the ratio MagWA(T)/Mag(T) for

20

the given period of Amax. (Bormann, 2002). This means that (reading amplitude and Period will be done on the raw trace and then correcting the amplitude using a response function for the particular instrument ,manually or automatically; However, this might give a wrong value since the maximum amplitude might appear at different times on the raw and Wood-Anderson simulated traces(Havskov and Ottemoller , 2010). Willmore,(1979) suggested to read more than one peak and corresponding period on raw data and choose the amplitude-period pair that gives the largest converted amplitude. Bakun, et al., (1978) defined the synthetic Wood-Anderson seismogram as : The synthetic W-A seismogram is the record that would have been written at the sensor site of the modern system if a W-A seismograph ,with the appropriate gain and dynamic range, had been in operation there. They describe a method to obtain synthetic Wood-Andeson seismograpm from USGS central California network seismograph (three-component short-period seismograph electronically digitized from magnetic tape at 200 samples/sec.) as the following: The transformation of a signal f(t) recorded on a USGS central California network seismograph into a "synthetic W-A seismogram" fWA(t) can be expressed by

= - )]([

)()()( 1 tf

wTwTtf

USGS

wAwA ----------------------------------------------------------- (2-8)

Where and 1- represent forward and inverse Fourier transforms, )(wTwA is the theoretical transfer function of a W-A seismograph, and w is the angular frequency ( Backun, et al., 1978). Kanamori and Jennings,(1978) described a method to obtain synthetic Wood-Anderson trace from digitized strong-motion accelerograms. Uhrhammer and Collins, (1990) presented a study demonstrates how reliably the waveforms and maximum trace amplitudes recorded by "standard (Ts = 0.8 sec)" Wood-Anderson type torsion seismographs can be synthesized from broadband digital seismographic recordings. WA seismograms are synthesized from the digital records by frequency domain convolution. The procedure is: deconvolve the broadband instrument transfer function to obtain a ground displacement record; convolve the WA transfer function (Uhrhammer and Collins, 1990). After these three studies, the two criteria of Richter have been skipped , it has became possible to use digital records of broad band and strong motion instrument, in ML calculation and it is very easy to get synthetic Wood-Anderson trace from them.

21

2.3.3 Attenuation Function Richter,1958 presents the distance correction as tabulated values and he implied the following limitation: another limitation of log A values that without further evidence it can not be assumed to apply outside the California area(Richter,1958). Which means that log A values may not be valid for other regions. Bakun and Joyner,(1984) separated the distance correction in to two terms (-log A= a*log(R) +b*R +c) where (R) is a distance in kilometer, (a) and (b) are geometrical spreading and attenuation coefficients respectively . In year 1987, Hutton and Boor derive ML scale for southern California by following the same procedure of Bakun and Joyner. After (Hutton and Boor, 1987) study, the term (-log A) took a standard form (-log A= a*log(R) +b*R +c). By plotting -log A values as a function of distance Borman,( 2002) compared between attenuation characteristics of southern California and Norway region. The parameters a, b and c can be expected to have regional variation and should ideally be adjusted to the local conditions (Havskov and Ottemoller , 2010). The difference in attenuation parameters among different regions is due to: different velocity and attenuation structure, crustal age and composition, heat-flow conditions and depth distribution of earthquakes. (Bormann, 2012). Fig (2-6) is a graph of attenuation functions for different regions all over the world.

22

Fig (2-6). Attenuation curve ( log A as a function of distance) for some ML formulas. (Magnitude for continental shield areas revealed significantly lower attenuation when compared with Southern California (e.g., the calibration curve of Alsaker et al., 1991. (After Bormann, 2012).

2.3.4 ML Scale Derivation, Formulation and Methodology The local magnitude (ML) is defined by Richter as ML =log A - Log A +S -------------------------------------------------------------- (2-8) Where A is the recorded trace amplitude in (millimeter) for a given earthquake at a given distance (in kilometer) as written by the standard type of instrument, S is a station correction term and - Log A is the distance correction term. -Log A is a function of earthquake station distance and have values increase with distance. Richter (1935; 1958). Bakun and Joyner, (1984) separated the distance correction in two terms; they presented it in the form: -Log A = a* log (R/100) + b*(R-100) +3 ------------------------------------------ (2-9) Where a and b are coefficients for geometrical spreading and anelastic attenuation, respectively, and R is hypocentral distance.

23

By substitute eq (2-9) in eq (2-8) we will get: ML = log (A) + a* log (R/100) + b*(R-100) +3+S ------------------------------ (2-10) For a dataset composed of m earthquakes, every one is recorded by a number of stations, equation (2-10) will be written in the form:

jijijiij SRbRaMLA ----=+ )100(*)100/log(*3)log( --------------------------------- (2-11) Where i is a counter of m earthquakes and j is a counter of n stations. The station correction is given by S. The system of equations will have m + n + 2 unknowns (magnitudes, station corrections, a and b). For a good number of amplitude observation at a different distance range it is an over-determined system and can be solved by a standard methods, such as linear least-square curve fitting (Havskov and Ottemoller , 2010). To prepare the data set of equations for least squares fitting operation, equation (2-11) must be written in such a way that one single equation contains all the unknowns, as the following:

l

Ns

lljk

Ne

kikrefij

ref

ijijref SMLRRbR

RaAML **)(*)log(*)log(

11

==

-+--=+ dd -----------------(2-12)

Where: Aij is the maximum trace amplitude in (mm) of earthquake i at station j. Rij is hypocentral distance in (km) for earthquake i at station j . ij is the Kronecker delta (1 if i equals j, otherwise 0). Ns is the number of stations. Ne is number of events. MLref is 3. Rref is 100. (Alsaker et al., 1991). For better understanding to eq (2-12). see appendix (1). Equation (2-12) can be rewritten in matrix form as:

24

=

-----

---

------

0

*

001111110000000010010000

00000100010

0010000000100001000001

2

1

1

1

22

11

11

Nej

j

j

j

Ns

j

Ne

NejNej

jj

jj

jj

y

y

yy

ba

S

SML

ML

ur

ur

urur

--------------- (2-13)

Or A * x = y Where rij = log(Rij/Rref). uij = (Rij, - Rref). yij = logAij + MLref. The vector of unknowns (x) can be found by inversion of A, under the constraint that the station corrections sum is equal to zero . Therefore the number of rows in matrix A equal to the number records in the dataset plus one row represents the equation: S1 + S2 + S3 ++++ + Sj =0 (see the last row in matrix A). To apply the linear least square fitting on vertical component records in appendix (4) which contains 305 record which means 305 equation available to the least square fitting operation (plus one equation of the form [0+0+0++++1+1+1+1+1+0+0+++0=0]). The objective is to extract the (78+5+2) unknown. Linear system described above can be resolved by three methods as follows:

1. The normal equation method. 2. QR decomposition method. 3. Singular value decomposition (SVD) method.

In the present study, least square fitting is done by use of program (MAG2) within Seisan software package, and MAG2 program applies singular value decomposition to make the operation ( Ottemoller et al, 2011).

25

2.4 Hypocenter- Station Distance Calculation Seisan software is a package contains several programs; the program which executes the least square fitting is MAG2. In the section (MAG2), Seisan manual ( Ottemoller et al, 2011) did not mention anything about the distance, but in another location (of the manual) the following formula is cited : D = )]cos()cos()cos()sin()[sin(cos 1 ooo llqqqq -+- ----------------------------------- (2-14) Where: D is the epicentral distance in degrees which is calculated along a great circle path, o and are the latitude of the epicenter and station respectively and o and are the corresponding longitudes.To get the epicentral distance in kilometer, D must be multiplied by: (111.2). According to Havskov and Ottemoller ,( 2010), distance used in ML formula must be the distance from hypocenter( not the epicenter) of earthquake to the recording station, therefore the Pythagoras equation must be applied to get that distance, as:

22 )()( depthR +D= -------------------------------------------------------------------- (2-15) Where: R is the distance in kilometer between hypocenter of seismic event and recording station; is the distance in kilometer between epicenter of seismic event and recording station ; depth is the distance between hypocenter and epicenter of the seismic event in kilometer or the depth of the seismic event. Applying formula (2-15) will produce results (distances) very close to distances obtained by MAG2 within Seisan package. 2.5 Structure of Seisan Software A widely used seismic analysis system is the Seisan software developed by J. Havskov and L. Ottemller . It contains a complete set of programs and a simple database for analyzing analog and digital recordings. Seisan can be used, amongst other things, for phase picking, spectral analysis, azimuth determination, and plotting seismograms. Seisan is supported by DOS, Windows95, SunOS, Solaris and Linux and contains conversion programs for the most common data formats (Bormann,2002). The Earthquake Analysis Software, Seisan 9.0.1 is used to simultaneously solve the system of equation used to derive ML scale (the object of the present study). The whole Seisan system is located in subdirectories under a main directory called Seismo(Ottermoller et al, 2011). The system contains many subdirectories containing information that the program needs to run. The following are the main subdirectories:

REA: contains earthquake readings and full epicenter solutions in the database.

WAV: Digital waveform data files. DAT: Default and parameter files, e.g. station coordinates.

26

CAL: System response information files. PRO: Programs, source code and executables. DAT: Default and parameter files, e.g. station coordinates. INF: Documentation and information.

The database of Seisan contains two main directories REA and WAV. The REA directory contains all the readings and information about the earthquakes that needs to be analyzed while the WAV directory contains all the waveform data. The main directory REA is sub divided into a number of directories which correspond to different databases. These sub directories are created by the user and are used to store all the earthquake events that are going to be analyzed. Each event is stored in a single S-file( a text file) in yearly directories and monthly subdirectories. If new datum is entered into the database it is automatically saved as an individual S-file. (Ottermoller et al, 2011). Fig(3-7) represents the S-file of event(1) of the data set used to make the inversion.

Fig (2-7). S-file to the first event of the dataset used to make the linear least square fitting operation. First row is called the header; the header contains informations about the seismic event like: location, date, origin time, depth and magnitude. The following rows contain details about stations, phases, amplitudes, distance and azimuth. S- file is the input file to program MAG2.

Chapter (3)

Instrument response removal to read amplitude

27

Preface Amplitude used in deriving the ML scale is taken either from reading maximum amplitude on synthetic Wood Anderson trace or reading maximum amplitude on raw data and then making the correction manually. The two methods will be explained in this chapter and a comparison will be hold between them to make sure that amplitude used in the study is right and dependable. 3.1 Magnification of the Digital Recording System Used in ISN Digital recording system used in ISN consists of STS-2 Streckisen seismometer and Q330 Quantera digitizer. Constants used to construct a response curve for this system are shown in table (3-1). Table (3-1). Constants used to construct a response curve to ISN seismic recording system. Parameter Symbol device value unit Natural frequency

fo STS-2 seismometer

0.0038 Hertz (Hz)

Damping constant

h STS-2 seismometer

0.707

Generator constant

G STS-2 seismometer

1500 Volt/(meter/second)

Sensitivity Q330 digitizer 419130 Count/volt For the seismometer, displacement magnification (gain) can be calculated:

222222

3

4)()(

ood

wwhwwGwwA

+-= ----------------------------------------------------------- (3-1)

Where 0 = 2f0 and = 2f . To obtain velocity magnification (gain) Av, eq (3-1) is divided by

222222

2

4)()(

oov

wwhwwGwwA

+-= ----------------------------------------------------------- (3-2)

For acceleration, one more division with is needed (Havskov and Ottemoller , 2010). By substituting the first three parameters of table (3-1) in equation (3-1), and equation (3-2) we will get the STS-2 seismometer magnification (gain) in a unit

28

(volt/meter) and (volt/meter/second) as a function of period (frequency). Tabulated values of displacement and velocity magnification of STS-2 seismometer are shown in table (3-2). Table (3-2). Displacement and velocity gain of strakisen STS-2 seismometer for periods between (4 and 0.1) second.

period(Sec)

Frequency (Hz)

displacement gain of STS 2 seismometer

(volt/meter)

velocity gain of STS 2 seismometer

(volt/meter/second) 4 0.25 2356.19 1500.00 3.8 0.26 2480.20 1500.00 3.6 0.28 2617.99 1500.00 3.4 0.29 2771.99 1500.00 3.2 0.31 2945.24 1500.00 3 0.33 3141.59 1500.00 2.8 0.36 3365.99 1500.00 2.6 0.38 3624.91 1500.00 2.4 0.42 3926.99 1500.00 2.2 0.45 4283.99 1500.00 2 0.50 4712.39 1500.00 1.8 0.56 5235.99 1500.00 1.6 0.63 5890.49 1500.00 1.4 0.71 6731.98 1500.00 1.2 0.83 7853.98 1500.00 1 1.00 9424.78 1500.00 0.8 1.25 11780.97 1500.00 0.6 1.67 15707.96 1500.00 0.4 2.50 23561.94 1500.00 0.2 5.00 47123.89 1500.00 0.1 10.00 94247.78 1500.00

The seismometer measures the ground motion and translates it into a voltage. Ground motion can mathematically be described as displacement, velocity or acceleration(Havskov and Ottemoller , 2010). To know the maximum output voltage from STS-2 seismometer resulting from a sine wave ground displacement of 1 second period and 1 nanometer ( 910

1 meter)

amplitude , go to table(3-2), magnification of seismometer in response to a ground displacement when the period is 1 second, is 9424.8(v/m). Maximum Output voltage is:

29

volt

metervoltmeter 99 10

8.94248.9424*101

=

For ground velocity of 2 second period and 3 nanometer/second, output voltage of the seismometer is

volt

ondmetervolt

ondmeter 99 10*4500

sec

1500*)sec

(10*3 -- = .

The process of converting a continuous analog signal to a series of numbers representing the signal at discrete intervals is called analog to digital conversion and this process is performed by the digitizer ( Alguacil and Havskov,2010). Digitizers input is the voltage coming from the seismometer, and its output is a series of digits or what we call counts. Sensitivity of Q330 digitizer is 419430 count/volt, which means that if the input voltage (from the seismometer to the digitizer) is 1 volt , the output of the digitizer will be 419430 count (output of digitizer will be stored in the wave form file ). For the example above (on assumption that the digitizer is Quantrra Q330), output of the digitizer will be:

count 43.95304386419430*10

8.94249 =volt

countvolt

For the second example, output of the digitizer (which represents the value to be stored in waveform file) will be:

countvolt

countvolt 887.1419430*10*4500 9 =-

3.2 Ground Motion Determination In the digital recording system ground motion (represented by displacement, velocity or acceleration) can be calculated from the formula as (Alguacil and Havskov,2010) Ground motion = output / system magnification------------------------------ (3-3). The seismograph can be understood as a linear system where the input is the ground motion and the output is the number (count) in the digital recording system (Alguacil and Havskov,2010). To remove instrument response, apply the formula:

3)a-(3---------)/(419430*)/(gainnt displasemer seismomete

)(voltcountmetervolt

countamplitudeamplitude =

30

To get the displacement in meter unit, or apply the formula:

3)b--(3-------)/(419430*)sec//(gain r velocityseismomete

)(voltcountondmetervolt

countamplitudeamplitude =

To get the velocity in (meter/second) unit. Suppose that the amplitude and period for a certain cycle within the seismic trace were 9000 counts and 2 seconds, to calculate the amplitude of the ground displacement:

From table (2), gain (magnification) of the seismometer in respond to the ground displacement when the period is 2 second is 4712.4 volt/meter.

Apply eq (3-3) a.

nanometermeter

voltcount

metervolt

countamplitude 966- 10*10*55.410*4.55419430*4.4712

9000 -===

To calculate the velocity of the ground motion, apply eq. (3-3) b

ondnanometer

ondmeter

voltcount

meterondvolt

countvelocitysec

10*43.1sec

10*43.1419430*sec.1500

9000 45 === - To see

a high resolution table of displacement and velocity magnification of ISN system see appendix (2). Fig (3-1) is the displacement magnification curve(displacement response curve) of STS-2 seismometer. Fig(3-2) is the velocity magnification curve of STS-2 seismometer obtained by applying eq(3-2) and Fig(3-3) is velocity response(magnification) curve taken from streckisan STS-2 seismometer documents.

31

Fig(3-1) Displacement magnification curve of streckisen STS-2 seismometer as a function of frecuency. Frequency and corresponding displacement magnification are taken from the table in appindex(2).

Fig(3-2). Velocity magnification curve of STS-2 seismometer as a function of frequency. Frequency and corresponding velocity magnification are taken from the table in appendix(2).

0.001 0.01 0.1 1 10 100Frequency(Hz)

0.1

1

10

100

1000

10000

100000Ma

gnific

ation

(v/m)

0.001 0.01 0.1 1 10 100Frequency(Hz)

10

100

1000

10000

Magn

ificati

on(v/

m/s)

32

Fig (3-3). Velocity magnification curve of STS-2 seismometer, taken from the seismometers manual: (Streckeisen STS-2 very-broad-band triaxial seismometer) one of seismometer documents provided by Kinametric company. Comparison between response curve obtaining from applying formula(3-2) and response curve of seismometer documents shows the completely matching in frequency range from 3 milli Hertz to 10 Hertz ( maxima used in the present study are in frequency range between 0.2 Hz to 1 Hz). 3.3 Wood-Anderson Seismometer Magnification Richter represents the displacement magnification of Wood Anderson torsion seismometer in the form:

22 BAvH+

= ----------------------------------------------------------------------------- (3-4)

Where:

2

2

1tTA -=

thTB 2=

H is the magnification with no units (mm trace amplitude to mm of ground motion), T is the period of ground motion in second, v is the static magnification= 2800. (Richter, 1958).

33

(Uhrhammer and Collins, 1990) found that the static magnification of wood Anderson torsion seismometer is 2080 and that value (2080) will be used as the value of static magnification in the present study. is the seismometer free period in seconds and is equal to 0.8 second, h is the damping constant and is equal to 0.8 (Richter, 1958). Tabulated values of Wood Anderson seismometer magnification and corresponding period is generated by substitute H, , ,s and series of numbers represents the period of a rang between (4 and 0.1) second in eq (3-4) . See table (3-3), and Fig (3-4).

Fig (3-4). Displacement magnification of Wood Anderson Seismometer as a function of frequency, according to Uhrhammer and Collins (1990), static magnification is assumed 2080. Wood-Anderson displacement magnification values are taken from table(3-3), and excel is used in drawing.

Wood Anderson displacement magnification

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12

frequency(Hz)

displacement

gain(unitless)

34

Table (3-3). Magnification of Wood Anderson seismometer. Column (3) represents the trace amplitude when the ground motion is 1 millimeter, therefore: magnification of Wood Anderson is unitless (mm/mm).

Period(second) Frequency(Hz) WA displacement gain(unitless) 4 0.25 82.22 3.8 0.26 90.98 3.6 0.28 101.20 3.4 0.29 113.24 3.2 0.31 127.54 3 0.33 144.70 2.8 0.36 165.52 2.6 0.38 191.09 2.4 0.42 222.95 2.2 0.45 263.26 2 0.50 315.14 1.8 0.56 383.19 1.6 0.63 474.20 1.4 0.71 598.11 1.2 0.83 768.66 1 1.00 1001.16 0.8 1.25 1300.00 0.6 1.67 1628.48 0.4 2.50 1896.80 0.2 5.00 2040.68 0.1 10.00 2070.71

3.4 Synthetic WA Amplitude Amplitude must be read on Wood-Anderson seismograph to achieve ML calculations. In the case of reading amplitude on a seismograph with displacement magnification, different amplitude must be synthesized and this can be achieved by applying the formula:

5)-(3--------- system ofoutput *ion magnificatnt displaceme system

ionmagnificatnt displacemeWA amplitude WA Synthetic =

(Bormann, 2002). By using of the Tables (3-2), Table (3-3) and applying eq (3-5)

35

for t between (4 and 0.1) second, table (3-4) is generated, so it can extract Wood Anderson synthetic amplitude in millimeter from the raw data (in count) (see table (3-4). Table (3-4) the ratio of WA gain to ISN system gain and the corresponding periods.

Period(second)

WA seismometer displacement magnification

4 82.22 0.0000832 3.8 90.98 0.0000875 3.6 101.2 0.0000922 3.4 113.24 0.0000974 3.2 127.54 0.0001032 3 144.7 0.0001098 2.8 165.52 0.0001172 2.6 191.09 0.0001257 2.4 222.95 0.0001354 2.2 263.26 0.0001465 2 315.14 0.0001594 1.8 383.19 0.0001745 1.6 474.2 0.0001919 1.4 598.11 0.0002118 1.2 768.66 0.0002333 1 1001.16 0.0002533 0.8 1300 0.0002631 0.6 1628.48 0.0002472 0.4 1896.8 0.0001919 0.2 2040.68 0.0001032 0.1 2070.71 0.0000524

Appendix (2) is a high resolution table which can be used to extract synthetic Wood Anderson amplitude in millimeter and nanometer from the raw data. Suppose that the amplitude for a specific cycle in the raw data was 9000 count and the period was 2 second then: By applying eq (3-5): Synthetic WA amplitude in mm will be: 0.0001594(mm/count)*9000 count=1.4346 mm.

mmcount

gain System

gainnt displacemeWA

36

Fig (3-5). (WA gain/ ISN gain) as a function of period. To calculate synthetic Wood Anderson amplitude in millimeter for a certain cycle follow the two points below:

Measure the amplitude in count Multiply the measured amplitude by the ratio :

countmmgain system

gainWA

3.5 Wood Anderson Synthesis from Digital Data To develop empirical equation for local magnitude ,synthetic Wood Anderson seismogram have become widely used by deconvolution of recording instrument response and convolution the signal with standard Wood Anderson torsion seismograph which has a natural period ( ) of 0.8 second , static magnification (v) of 2080 and damping factor of 0.8 (Kang et al, 2000). After synthesizing Wood Anderson seismograms from each record, maximum amplitude of synthetic seismograms in horizontal and vertical components can be used to determine the coefficients of the empirical formula (Kang et al, 2000).

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Period(second)

WA gain/ISN gain(mm/count)

37

The recording signal(f) obtained at each station can be expressed by convoluting ground motion (g) and instrument response(i) as function of time(Uhrhammar and Collins ,1990). f(t)=g(t).i(t)--------------------------------------------------------------------------(3-6) To obtain the ground displacement g(t):

1. Fourier transform to f (t) to get F (w). 2. Fourier transform to I (t) to get I (w).

[i(t) may be displacement , velocity or acceleration response function] 3. G (w) =F (w)/I (w). 4. Inverse Fourier transform for G (w) to get g(t).

To obtain synthetic Wood Anderson seismogram:

5. Convolve g (t) with Wood Anderson displacement response r (t) (Havskov and Ottemoller , 2010).

In Seisan software the trace is corrected for the instrument response in order to produce displacement. The displacement trace is then multiplied with the response of the Wood-Anderson instrument to produce a signal to look exactly like it that would have been seen on a Wood-Anderson seismograph (Ottemoller et al, 2011). 3.6 Reading Amplitude by Seisan Sofware The following steps are followed to read maximum amplitude on synthetic Wood-Anderson trace:

1. Raw data are reviewed by Seisan 2. Generating a synthetic Wood Anderson trace from raw data. 3. Position cursor at the top of the cycle of the maximum amplitude and press

a. Position cursor at the bottom of the same cycle and press (a). Amplitude (zero to peak) and period are now stored. (Seisan manual).

For MS calculation, the same procedure is followed but the readings are taken on the velocity trace. Figures (3-6a) to (3-6g) illustrate how to measure amplitude by Seisan software

38

Fig (3-6a). Z-component for a seismic event recorded by MSL station and reviewed by Seisan software in raw data form. Text in the first line on the top , contains information about the seismic event that the trace belongs to. Date of the seismic event is 25/10/2001, origin time is 14:55:08, coordinates are 38.850 as latitude and 43.600 as longitude, the depth is 10 km. this event is one of the 78 events of the dataset of the present study. the trace belongs to Mousol station(MSL) and the component is Z of 10 sample per second(BHZ). Plot start time is 14:55:31.306 . X-axis is the time and it can be seen that the trace have three ticks the absolute time of the first tick is 14:56:00. The whole time window is about 3.5 minute.

Fig(3-6b). Zoomed trace to the same event of Fig(3-6a) . Zoomed section is the section we expect to find maximum amplitude in it.

39

Fig(3-6c). Synthetic Wood Anderson trace to the record of Fig (3-6a)

Fig(3-6d). Reading amplitude on synthetic Wood Anderson trace of Fig (3-6a). Zero to peak amplitude is 15217.5nm and the period of the cycle of the maximum amplitude is 1.41 second

40

Fig (3-6e). Velocity trace to the record of Fig (3-6a). seisan program can correct the raw data to produce displacement, velocity and acceleration trace.

Fig (3-6f). Zoomed view to the velocity trace of Fig (3-6a), (zooming is in the place of V max).

41

Fig (3-6g). Reading maximum velocity on the velocity trace. 3.7 Verification of Seisan Software Seisan can not generate Wood Anderson or velocity traces unless it reads response information from a file written in specific format and placed in a specific directory. To make sure that Seisan is working well and the amplitude readings taken from Seisan is correct, a sub dataset is randomly chosen from the main dataset and for every record of that dataset, amplitude read twice and surface wave magnitude (MS) is calculated as the following:

Amplitude and period directly read on velocity trace then MS is calculated.(MS calculated from amplitude read on velocity trace is referred to as: MS velocity)

Amplitude and period read on raw data( of the maximum closest to the maximum read in step (1) , correction made by use of eq (3-3b ) and appendix (2) then MS is calculated.( MS calculated from amplitude read on raw data trace is referred to as: MS raw

Details of calculation in appendix (3) and Fig (3-8) is a graph represents ( MS seisan minus MS raw) for every record in the sub dataset used .

42

Fig(3-8). MS calculated from reading maximum amplitude on velocity trace(MS seisan) minus MS calculated from reading maximum amplitude on raw data after making the correction(MS raw). By use of the same procedure , ML is calculated by use maximum amplitude read Wood Anderson trace (ML seisan) and it is calculated by use of amplitude read on raw data to the maximum nearest to the maximum of synthetic Wood Anderson trace (ML raw) . Details of calculation in appendix(3). Fig (3-9) is a graph represents (ML seisan minus ML raw) for every record in the sub dataset used.

Fig (3-9). ML calculated by use of maximum amplitude read on synthetic Wood Anderson trace minus ML calculated by use of raw data.

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0 5 10 15 20 25 30 35

sample number

MS seisan - MS raw

-0.15000

-0.10000

-0.05000

0.00000

0.05000

0.10000

0 5 10 15 20 25 30 35

sample number

ML s

eisa

n- M

L ra

w

43

From the comparison between MS calculated in the two cases and ML calculated in the two cases we can conclude the following: Synthetic Wood Anderson trace generated by seisan software is dependable.

Chapter (4)

Working with data

44

4.1 Data Collection and Preparation When seismic event occurs, some or all stations in the network will record it, so there are a number of seismograms for every seismic event. Because ISN stations are triaxial, every seismogram consists of three components and every one of these component provides one (amplitude-distance) datum (or one record). 78 seismic events recorded at some or all ISN stations at the period between 2010 and 2012 provided the present study with (354) data record to contribute in deriving MLV scale (ML depends on vertical component ) and 691 record to contribute in deriving MLH scale (ML depends on horizontal component). Seismic events selection depends on the following basis

Low noise Sample rate equal or more than 10 sample per second Event is Recorded in more than one station

Minimum hypocenter- station distance to the seismic events contribute in the study was 47.3 Km while maximum distance was 1060 Km. Minimum mb(USGS) of the seismic events of the study was 3.5 while maximum mb(USGS) was 6.2 . Figures (4-1) and (4-2) are two histograms that show the distribution of data records according to hypocenter- station distance, for records used in deriving MLV and MLH respectively. Fig (4-3) is a histogram shows the distribution of seismic events used in the study according to mb(USGS). Fig (4-4) shows epicenters of seismic events used in the study projected on a map. Latitude, longitude, minimum event-station distance, maximum event-station distance, number of records used in deriving MLV and number of records used in deriving MLH for every ISN station , illustrated in table(4-1). Table (4-1). Information about ISN stations and their contribution in providing data records used in the study. Station Latitude

(degree) Longitude (degree)

Min. event-station distance

Max. event- station distance

Number of records used in MLV deriving

Number of records used in MLH deriving

MSL 36.4 43.11 100 1022 62 127 RTB 33.02 40.3 414.2 1060.1 62 130 IKRK 35.4 44.34 47.3 873.1 72 150 IBDR 33.11 45.93 110.7 776.1 57 122 NSR 31.01 46.14 72.8 908 52 83

45

Fig (4-1). A histogram shows the distribution of data records according to hypocenter- station distance, for records used in deriving MLV.

Fig (4-2). A histogram shows the distribution of data records according to hypocenter- station distance, for records used in deriving MLH.

MLV

4

40

50 53

39

50

71

14

28

5

0

10

20

30

40

50

60

70

80

47 100 200 300 400 500 600 700 800 900

100 200 300 400 500 600 700 800 900 1100

event station distance(km)

frequency

MLH

8

8297 105

78

106

140

2542

8

0

20

40

60

80

100

120

140

160

47 100 200 300 400 500 600 700 800 900

100 200 300 400 500 600 700 800 900 1100

event-station distance(km)

frequency

46

Fig(4-3). A histogram shows Distribution of seismic events used in the study according to mb(USGS).

1 0 1 14

12

22

10 10

6

13

1 0 1

0

5

10

15

20

25

3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.9 6.1 6.3

3.3 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.9 6.1

mb(USGS)

frequency

47

Fig (4-4).Epicenters of seismic events projected on a map represents the studied area. Red Oblique is the recording station while green cycle represents the seismic event. 4.2 Data Set Used in the Present Study Data set used in present study was distributed among two tables as illustrated bellow:

Table (4-2) consists of 15 fields: 1. Field (1) headed: ev ID: every single seismic event took a unique

identifier (from 1 to 78). 2. Field (2) to field (7) are the date and origin time of the seismic event.

48

3. field(8),field(9), field(10) are : latitude, longitude and depth of the seismic event

4. Field (11) is the short period body wave magnitude (mbgs) as reported by USGS/NEIC.

5. Field (12) is ML for the event as reported by (TEH) (an Iranian agency).

6. Field (13) is ML for the seismic event as reported by (ISK) (a Turkish agency).

7. Field (14) is the body wave magnitude (mb) of (IDC). 8. Field (15) is the broad band surface wave magnitude (MS) of (IDC).

49

Table (4-2). Date, origin time, location, depth and magnitude of seismic events used in present study.

ev id year month day hour minute second latitude longitude depth(km) mb(usgs) ml tehran

ml isk

mb IDC

MS IDC

1 2010 1 16 20 23 41 32.57 48.38 51 5 4.9 4.4 4 2 2010 2 11 16 29 41 33.34 47.24 10 4.5 4.3 4.1 3.4 3 2010 2 23 10 25 54 32.56 48.26 10 5.2 5.2 4.5 4.5 4 2010 9 27 4 26 9 37.65 43.84 2 3.8 3.5 3.6 3.1 5 2010 11 22 10 38 2 36.98 42.86 5 3.5 4.2 4.2 3.6 3 6 2011 10 23 20 45 37 38.64 43.22 10 5.9 5.7 5.7 5.4 5.7 7 2011 10 24 8 28 27 38.67 43.56 2 4.7 4.4 4.5 4.4 3.6 8 2011 10 24 8 49 20 38.68 43.63 5 4.8 4.6 4.5 4.6 3.7 9 2011 10 24 15 28 8 38.7 43.13 16 5 4.5 4.7 4.3 4 10 2011 10 24 22 13 32 38.72 43.18 5 4.4 4.5 4.4 4.2 3.5 11 2011 10 25 14 55 8 38.85 43.6 10 5.7 5.4 5.4 5.3 5.1 12 2011 10 26 3 16 19 38.7 43.2 7 4.7 4.3 4.5 4.1 3.9 13 2011 10 26 23 42 27.6 38.64 43.16 23 4.6 4.4 4.1 4.3 14 2011 10 27 8 4 22 37.21 43.93 10 5.2 5.5 5.4 4.7 4.4 15 2011 10 28 22 48 4 32.56 48.98 53 4.7 4.7 4.2 4 16 2011 11 2 11 43 3 37.19 43.82 2 4.7 4.8 4.3 3.8 17 2011 11 8 22 5 50 38.71 43.11 6 5.6 5.5 5.4 5 4.6 18 2011 11 12 18 20 2 38.63 43.18 19 4.6 4.3 4 3.7 19 2011 11 14 16 47 17 38.61 43.01 7 4.7 4.7 4.5 4.2 3.7 20 2011 11 14 22 8 16 38.75 43.17 10 5.2 5.2 5 4.8 4.3 21 2011 11 17 2 37 19 39.16 41.59 10 4.8 4.6 4.6 4.4 4.1 22 2011 11 18 17 39 40 38.85 43.87 2 5 4.9 4.5 4.3 23 2011 11 22 3 30 37 38.62 43.31 5 4.6 4.6 4.2 3.9 24 2011 11 29 7 58 14 34.67 45.11 2 4.3 4 4 2.6 25 2011 11 30 0 47 23 38.52 43.41 2 4.9 4.9 5 4.4 4.7 26 2011 12 3 1 30 54 38.76 43.97 2 4.7 4.3 4.3 3.7 27 2011 12 4 22 15 3 38.46 43.3 5 4.7 4.7 4.9 4.3 3.9

50

ev id year month day hour minute second latitude longitude depth(km) mb(usgs) ml tehran

ml isk

mb IDC

MS IDC

28 2011 12 6 2 56 1 38.82 43.64 5 4.6 4.5 4.1 3.8 29 2011 12 27 19 18 54 38.94 43.69 2 4.7 4.4 3.9 3.9 30 2012 2 28 23 18 50 32.57 47.1 0 4.7 4.5 4.2 4.1 31 2012 3 5 6 50 34 35.04 44.09 2 4.5 5.3 3.9 4.4 32 2012 3 10 21 41 4 32.63 46.98 0 4.4 4 4.1 3.4 33 2012 3 25 12 28 54 32.47 46.98 30.6 4.6 4.2 4.1 3.2 34 2012 4 4 9 41 40 38.88 43.57 2.6 4.4 4.2 4.6 4.1 3.7 35 2012 4 18 18 43 1 32.56 47.03 30 5.1 4.9 4.6 4.2 36 2012 4 18 20 4 5 32.48 47.12 0 4.4 4.4 4.1 4 37 2012 4 19 7 42 52 32.39 46.95 10 4.6 4.4 4.2 3.6 38 2012 4 20 1 21 11 32.51 47.07 34.2 5.1 5.1 4.7 4.4 39 2012 4 20 1 21 7 32.5 47.05 20 5.1 5.1 4.7 4.4 40 2012 4 20 3 5 47 32.63 47.02 45.5 5 4.8 4.5 4.4 41 2012 4 20 3 31 39 32.42 46.97 0 4.4 4.1 4 3.7 42 2012 4 20 15 37 5 32.54 47.08 24.4 4.8 5 4.5 3.7 43 2012 4 20 16 17 50 32.52 47.1 24 4.7 4.8 4.3 4.1 44 2012 4 20 16 32 51 32.49 46.97 0 4.2 3.9 3.6 45 2012 4 20 17 19 52 32.43 46.99 44.3 4.6 4.2 3.9 3.1 46 2012 4 22 8 13 52 32.44 47.09 0 4.2 4.2 4.2 3.3 47 2012 4 23 16 42 59 32.65 47.01 0 4.5 4 4.2 2.9 48 2012 4 23 23 0 39 32.51 46.79 38 4.8 4.4 4.3 3.5 49 2012 4 24 18 16 39 32.36 47.17 51.2 4.5 4.3 4 3.3 50 2012 5 3 10 9 36 32.75 47.73 10 5.6 5.5 4.8 4.7 51 2012 5 5 1 57 15 34.87 44.17 42.8 4.4 4.9 4.1 3.8 52 2012 6 8 16 15 12 29.71 50.76 14 4.9 4.8 4.5 4.2 53 2012 6 14 5 52 54 37.29 42.33 5.4 5.3 5.5 4.9 4.5 54 2012 6 15 23 48 17 37.4 42.41 0 4.3 3.5 3.4 55 2012 6 24 20 7 21.5 38.63 43.65 6.2 4.9 4.5 4.5 4.6 3.9

51

ev id year month day hour minute second latitude longitude depth(km) mb(usgs) ml tehran

ml isk

mb IDC

MS IDC

56 2012 7 14 0 55 1 34.6 47.51 5.6 4.6 4.4 4.3 3.3 57 2012 7 20 16 20 22 38.64 43.35 44.2 4.1 3.8 3.1 58 2012 7 24 22 53 39 38.61 43.37 0 4.5 4.4 4 3.4 59 2012 8 5 20 37 24 37.54 43.11 16 4.9 5.4 4.6 4.2 60 2012 8 11 12 23 18 38.33 46.83 10 6.2 6.2 5.4 6.5 61 2012 8 11 12 44 39 38.46 46.64 14.1 4.8 62 2012 8 11 15 21 20 38.63 46.81 10 4.7 4.6 4.3 4.8 63 2012 8 11 15 43 17 38.23 46.7 0 5 4.7 4.7 4.3 64 2012 8 11 16 21 53 38.42 46.68 4 3.9 3.8 3.4 65 2012 8 11 19 52 45 38.27 46.85 10 4.7 4.5 4.3 3.4 66 2012 8 11 22 24 3 38.46 46.72 17.4 5.1 4.9 4.8 4.5 67 2012 8 13 1 56 8 38.25 46.5 0 4.6 4.6 4.1 3.6 68 2012 8 14 14 2 25 38.45 46.79 6 5.1 5.2 4.7 4.2 69 2012 8 15 17 49 5 38.41 46.67 4 5.3 5.1 4.9 4.2 70 2012 8 16 17 14 12 38.37 46.59 0 4.8 4.5 4.3 3.9 71 2012 9 12 23 29 36 37.09 43.63 9.3 4.3 4.3 3.8 3.1 72 2012 9 13 2 42 23 37.28 43.81 0 4.5 4.4 3.9 73 2012 11 7 6 26 33 38.42 46.62 10 5.4 5.1 5 5.3 74 2012 11 27 6 22 30 33.2 49.21 24.5 4.7 4.7 4.1 3.9 75 2012 12 23 6 38 57.1 38.47 44.86 10 5.2 5 4.9 4.3 76 2013 1 19 16 51 38 31.77 46.03 10 77 2013 1 20 17 12 30 31.65 46 0 4.2 78 2013 1 21 18 50 50 31.61 45.98 35 4.1

52

Every single event in Table (4-2) is recorded at more than one of ISN stations. Appendix (4) represents a table shows the recording details for that event which is recorded at some or all of ISN stations. Appendix (4) represents the main dataset used in the present study and almost all calculations made by use of its records. The conjunction between table (4-2) and appendix (4) is the field: evid in the two tables. ( event of ev id=1 in table(4-2) have 8 related records in appendix(4), origin time of that event is 16/1/2010 20:23:41 , recorded at three stations which are IBDR, NSR and RTB , recoding detail are in 8 records of appendix 4, from record of record id=1 to record of record id=8). According to IASPI recommendations 2011 for the triaxial stations which contain two horizontal components in front of one vertical, for MLH derivation, amplitude will be read on each one of the two horizontal components and each amplitude will be treated as a single datum. Therefore, number of data records used to derive MLH almost equal twice the data used to derive MLV

4.3 Hutton and Boor, 1987 Study, a Review From year 1935 to year 1987, ML for southern California is calculated according to the ML scale derived by Richter (by use the values of Log Ao as a distance correction). (Workers who do routine magnitude assignment are aware that distant stations produce magnitudes that are too high, and nearby stations produce magnitudes that are too low, relative to stations at intermediate distances. In general, only the practice of averaging values from all available stations has prevented this from being more of a problem than it is. (Hutton and Boor, 1987). In other word, high residuals in some stations which record the same event is what urge Hutton and Boor to derive a new ML scale. Almost all Hutton and Boors comparisons were built on the comparisons between residuals. According to Hutton and Boor, (1987): residuals refer to the difference between the magnitude computed from a single station and the event magnitude obtained by averaging the individual station magnitudes. Therefore, residual is calculated from the formula Residual= ML(sta) - ML(eq)-----------------------------------------------------------(4-1) Where: ML(sta) is the magnitude computed from a single station. ML(eq) is the event magnitude obtained by averaging the individual station magnitudes.(see Hutton and Boor,1987).

53

Standard deviation of residuals is the square root of mean square value of residuals or:

n

residualn

ii

== 12)(

deviation Standard ------------------------------------------------------(4-2)

Where n is the number of residuals According to the high residual of Mammoth lake, Hutton and Boor decided to exclude Mammoth lakes stations data. According to IASPI recommendation (2011) Hutton formula became a standard in ML calculation (Bormann and Dewey, 2012). 4.4 Linear Least Square Fitting Execution By use of appendix 4 records, linear least square curve fitting is applied on (305) equation to construct MLV scale and (612) equation to construct MLH scale, the results are: 1. for MLV

(a) = 1.028 (b) = 0.00122 (c) = -1.86 78 values of MLV for 78 seismic events. 5 station corrections.

Therefore MLV formula according to Hutton and Boor, 1987 model is: MLV = log (A) + 1.028log(R) + 0.00122(R) 1.86+ S----------------------------(4-3) Where: A is Maximum amplitude in nanometer read on synthetic Wood-Anderson trace to the vertical component. R is hypocenter station distance in kilometer (up to 1060 Km).S is station correction.

Station corrections for the five stations are shown in table(4-3)

Table (4-3). Station corrections, after the execution of the linear least square fitting operation to derive MLV , for the five stations. These values are added to the single station magnitude (MLV sta) when applying formula (4-3). IBDR NSR RTB IKRK MSL 0.021 0.005 -0.134 -0.035 0.144 Formula (4-3) according to the present study is an ML scale that can be applied on the vertical component records and will be referred to as MLV(ISN). 2 . for MLH

(a) = 0.891 (b) = 0.00143 (c) = -1.607 78 values of MLH for 78 seismic events.

54

5 station corrections. MLH formula according to Hutton and Boor,1987 model is: MLH = log (A) + 0.891 log(R) + 0.00143(R) 1.607 +S----------------------- (4-4) Where: A is Maximum amplitude in nanometer read on synthetic Wood- Anderson trace to the horizontal component. Each one of the two horizontal readings to the same event recorded