Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 650

_____________________________ _____________________________

Dynamic Source Models of IcelandicEarthquakes and Teleseismic

Tomography along the TOR Array

BY

Z. HOSSEIN SHOMALI

ACTA UNIVERSITATIS UPSALIENSISUPPSALA 2001

Dissertation for the Degree of Doctor of Philosophy in Geophysics presented at UppsalaUniversity in 2001

ABSTRACTShomali, Z.H. 2001. Dynamic source models of Icelandic earthquakes and teleseismictomography along the TOR array. Acta Universitatis Upsaliensis. ComprehensiveSummaries of Uppsala Dissertations from the Faculty of Science and Technology 650. 31pp. Uppsala. ISBN 91-554-5098-9.

This thesis describes new inversion-oriented methodological developments and theirseismological applications. In the first study presented the dynamic source parameters ofsome local Icelandic earthquakes are studied by employing a time domain moment tensorinversion method. A windowing method for direct P and S phases was used and theinversion was performed for frequencies lower than the associated corner frequency underthe double-couple constraint. The inversion algorithm could determine the dynamic sourceparameters correctly, even under conditions of poor azimuthal coverage. The second studydeals with a new method for calculating the empirical Green’s function based on inversionof earthquake radiation patterns. The resulting Green’s functions then may contain bothbody and surface waves. The validity of the method was then confirmed by applying themethod to some Icelandic earthquakes. The lithosphere-asthenosphere transition along theTOR array is investigated in the last two studies. Separate and simultaneous teleseismic Pand S relative arrival-time residuals were inverted via different methods (a singular valuedecomposition and a quadratic programming method) to investigate the reliability and theresolution of the model. The data were corrected a priori for the effect of travel-timeperturbations due to crustal structure. The results indicate that the transition between thinnerlithosphere in Germany to the thicker Baltic Shield in Sweden occurs in two sharp and steepsteps. A sharp and steep subcrustal boundary is found below the Tornquist Zone, with a lesssignificant transition below the Elbe Lineament. The lithospheric structure appears to beabout 120 km thick under the Tornquist Zone, increasing to more than 200 km beneath theBaltic Shield.

Z. Hossein Shomali, Department of Earth Sciences, Uppsala University, Villavägen 16, SE-752 36 Uppsala, Sweden

© Z. Hossein Shomali 2001

ISSN 1104-232XISBN 91-554-5098-9

Printed in Sweden by Fyris-Tryck AB, Uppsala 2001

List of papers

This thesis consists of the following papers, which will be referred to in the text by theirroman numerals :

I. Body wave moment tensor inversion of local earthquakes: an application to the South Iceland Seismic Zone. Shomali, Z.H. and Slunga, R., Geophys. J. Int, 140, 63-70, 2000.

II. Empirical Green's functions calculated from the inversion of earthquake radiation patterns. Shomali, Z.H., Geophys. J. Int, 144, 647-655, 2001.

III. Nonlinear body wave teleseismic tomography along the TOR array. Shomali, Z.H., Roberts, R.G. and the TOR Working Group submitted to Geophys. J. Int, 2001.

IV. Lithospheric structure of the Tornquist Zone resolved by nonlinear P and S teleseismic tomography along the TOR array. Shomali, Z.H., Roberts, R.G., Pedersen, L.B. and the TOR Working Group, submitted to J. geophys. Res., 2001.

Reprints (I) and (II) were made with kind permission from Blackwell Science.

4

Contents

1. Introduction....................................................................................................................... 5

2. Representation theorem ................................................................................................... 7

3. Waveform modelling ........................................................................................................ 7

3.1 Moment tensor inversion applied to local Icelandic earthquakes.................................. 9

4. The empirical Green’s function method....................................................................... 11

4.1 Empirical Green’s functions applied to local Icelandic earthquakes .......................... 12

5. Teleseismic tomography along the TOR array ............................................................ 13

5.1 ACH travel-time tomographic inversion ..................................................................... 145.2 The mean squares error method................................................................................... 155.3 The quadratic programming method ........................................................................... 165.4 Separate and simultaneous P and S relative arrival-time residuals inversion ............. 165.5 Resolution analysis ...................................................................................................... 195.6 Tectonic evolution of the TOR area inferred from the teleseismic results.................. 22

6. Summary of papers......................................................................................................... 23

6.1 Paper I.......................................................................................................................... 236.2 Paper II ........................................................................................................................ 246.3 Paper III ....................................................................................................................... 256.4 Paper IV....................................................................................................................... 26

7. Acknowledgements ......................................................................................................... 28

8. References........................................................................................................................ 30

5

1. Introduction

Earthquakes are the expression of the sudden release of energy within the Earth due to asudden movement, mostly along a fracture or fault. Understanding how earthquakes ”work”is of great scientific interest because they describe the ongoing deformation processeswithin the Earth, and therefore provide a vital key to understanding the Earth’s ongoingdevelopments. Furthermore, large earthquakes can be very destructive, claiming manythousands of lives and causing vast destruction of property. A deeper understanding ofearthquakes may allow society to mitigate the effects of these natural disasters. In studyingearthquakes, analysis of recorded surface vibrations is complicated because the form of theobserved waveforms depends both upon the characteristics of the source and upon theproperties of the wave-path from the source to the receiver. Any complete analysis of thedata requires the separation of the source (e.g. Paper I) and propagation path effects (e.g.Paper II).

Detail knowledge of Earth structure is a key-element in understanding the physicsbehind the Earth’s evolution including plate tectonics. Although our detailed resolution ofEarth structure generally diminishes with depth but we obtain increasingly complete globalcoverage (Lay and Wallace, 1995). The basic concept of modern plate tectonics is related tolithospheric structure. The lithosphere is a high-viscosity region, the components of whichtranslate coherently on the Earth’s surface (Lay and Wallace, 1995). The lithosphere istoday on average about 100 km thick, but in some areas is significantly thicker or thinnerthan this. Maximum earthquake size is limited by the lithospheric thickness available forbrittle failure (Lay and Wallace, 1995) excluding the deep earthquakes. Below thelithosphere is the asthenosphere (low-viscosity materials), a region of relatively lowstrength that may be nearly decoupled from the lithosphere. It is warmer and more plasticthan the lithosphere above. While much cooler than it was at the time of the Earth’screation, the interior of the Earth is still much warmer than the exterior. Therefore heatenergy is continuously exported through the Earth’s surface. Within the Earth, much of theheat transport through the mantle occurs via convection. This does not imply that the mantleis molten, but that on long time scales and over large distances it can behave in a viscousmanner, the movements being allowed by various microscopic creep mechanisms. Coupledto the movements within the mantle, and in a sense driving these movements, aremovements of the lithosphere. These movements are often lateral, but lithosphere is alsoconstantly created and at other places destroyed by “subduction” into the mantle. As a resultof these motions, the lithosphere consists of a number of different “plates”, in constant,slow motion relative to each other. Most significant geological evolution occurs at theboundaries between these plates, e.g. a mountain range is created when lithospheric platescollide. The upper 250 km of the mantle is particularly heterogeneous, with strong regionalvariations associated with surface provinces (Lay and Wallace, 1995). The lithosphericmovements are the primary driving force of geological development. Due to the great age ofthe Earth, previous patterns of motion and the corresponding geological evolution has inmany places been complex. Older areas of the lithosphere contain records of this previous

6

geological evolution, in the form of geological structures within the lithosphere. Byanalysing these structures we can therefore make deductions about the previous geologicalevolution of the area studied.

The oldest, coldest, and thickest parts of today’s lithosphere are sometimes called the“shield” areas. One such area is the Baltic Shield, of which Sweden is a part. To the souththe Baltic Shield ends roughly where Sweden meets Denmark. To the south of thisboundary the geology is radically different, with “Mainland Europe” having much youngerlithosphere than the shield to the north. Therefore, a major lithospheric boundary – probablyextending to a few hundred kilometres depth – must exist in this area. Analysis of thestructure of this boundary zone achieved with the help of teleseismic tomography (e.g.Papers III and IV), can be expected to elucidate the previous geological evolution of thisgeologically very significant boundary zone.

This thesis presents new inversion-oriented methodological developments as describedwith more detail in Papers I-III while Paper IV analyses a new dataset. In Paper I, observedP and S waveforms data are inverted in order to evaluate the dynamic source parameters(scalar seismic moment, strike, rake and dip) of earthquakes assuming known Green’sfunctions. The inversion uses a windowing method for the direct P and S phases on thedifferent components for frequencies lower than the corresponding corner frequency at theindividual seismic stations. In Paper II, empirical Green’s functions were estimated basedon the same set of equations used for studies of the seismic source. The basic equationunderlying the theory used is the representation theorem (Aki and Richards, 1980) thatrelates observed waveforms to source parameters of an earthquake through the Green’sfunction components. The normal equations used in the inversion were based on knowndynamic source parameters, allowing evaluation of empirical Green’s functions between asource area and the individual seismic stations. In Paper III two new concepts related to theinverse problem are discussed. A modified version of the Mean Squares Error (MSE)algorithm of Xu (1998) is introduced to drop insignificant eigenvalues (produced by asingular value decomposition method) that probably do not contain useful informationabout the posed problem. The algorithm was implemented in a nonlinear ACH (Aki et al.,1977) teleseismic tomography method, to reveal the lithosphere-asthenosphere transitionacross the Tornquist Zone. In order to investigate if boundaries and blocks resolved in theinverted model are required by the data or are artificially caused by the inversion, a newalgorithm based on a quadratic programming method (Parker, 1980; Schittkowski, 2000)was developed. The algorithm allows for the flexible application of various constraints onthe model parameters for testing of various hypotheses.

Thus this thesis can be divided into two parts based on the seismological applications ofthe inversion procedures. In the first part (Papers I and II) dynamic source parameters ofsome local Icelandic earthquakes recorded by the SIL network are studied. The second part(Papers III and IV) describes new results achieved for the lithosphere-asthenospheretransition across the Tornquist Zone, based on separate and simultaneous P and S relativearrival-time residuals.

In this thesis first basic theoretical concepts corresponding to each part are briefly

7

discussed, followed by an application of the method. For the teleseismic data a possibletectonic evolution deduced from the models is presented. At the end in “Summary ofpapers” concrete descriptions of each paper is discussed.

2. Representation theorem

The representation theorem is used to synthesise the displacement field from thedisplacement produced by a realistic source which is localised precisely in both space andtime (Aki and Richards, 1980). The displacement field from such a source is called aGreen’s function. Green’s functions can be calculated analytically or empirically. Therepresentation theorem for the displacement un(x,t) due to a general displacementdiscontinuity at the source point ( , ) is (Aki and Richards, 1980)

)0,;t,x(G*),(Mt)(x,u qnp,pqn (1)

where Mpq is the moment tensor, Gnp,q represents spatial derivatives of the Green’s function,the asterisk convolution and Einstein’s implicit summation convention is used over indicesp,q=1,2,3. If x is many wavelengths away from , then convolution with the Green’sfunction gives a field at (x,t) that depends on what occurs at only at “retarded time”, i.e. tminus the propagation time between and x , t- (Aki and Richards, 1980).

The seismic moment tensor depends on source length and fault orientation, andcharacterises the information about the source that can be derived from observing waveswhose wavelengths are much longer than the linear scale of the fault. A single Green’sfunction in eq. (1) can include various categories of waves including body waves, surfacewaves and free oscillations. The representation theorem given in eq. (1) is the basicequation underlying the seismic moment tensor inversion method.

3. Waveform modelling

The Fourier transform of the observed displacements at the free surface of the Earth in acylindrical coordinate system is defined as (Herrmann and Wang, 1985; Jost and Herrmann,1989)

w(r, 0, ) = ZSS A1 + ZDS A2 + ZDD A3

q(r, 0, ) = RSS A1 + RDS A2 + RDD A3 (2) v(r, 0, ) = TSS A4 + TDS A5

where w, q and v are vertical, radial and tangential displacements respectively, and rdenotes epicentral distance. The functions Zii ,Rii and Tii are the components of the Green’sfunction required to evaluate a whole waveform excited by a double-couple source (theisotropic components of the Green’s function are ignored). The subscripts ‘SS’, ‘DS’ and‘DD’ are the three fundamental faults; vertical strike slip (dip: 90 o and rake: 0o), vertical dipslip (dip: 90 o and rake: 90 o) and 45o dipping dip slip (dip: 45o and rake: 90o), respectively.

8

Equation (2) shows that any displacement can be synthesised using a weighted summationof the Green’s functions associated with the three fundamental faults. The coefficients Ai

are the azimuthal radiation patterns of the waveform for a double couple source and aredefined as

A1 = 0.5 (Mxx - Myy) cos2 + Mxy sin2 A2 = Mxz cos + Myz sin A3 = -0.5 (Mxx + Myy) (3) A4 = 0.5 (Mxx - Myy) sin2 - Mxycos2 A5 = -Myz cos + Mxz sin

in the notation chosen here is the forward azimuth and Mij are components of the seismicmoment tensor and are related to the orientation (strike, dip and slip) of the fault andauxiliary planes as given by Aki and Richards (1980) for a double-couple source.Substituting eq. (3) into eq. (2) provides the linear relations between the observeddisplacements and the moment tensor given by

u(w, q, v, ) = Gm (4)

the vector u contains the Fourier transformations of the observed displacements, the matrixG is composed of the Green’s function components and the vector m represents momenttensor components. Equation (4) is in fact a specific form of the representation theoremwhich signifies that the displacement on a source, i.e. a fault, is enough to determine theresulting displacement everywhere, given the Green’s functions (Aki and Richards, 1980).The normal system of equations introduced in (4) can be solved under the deviatoricconstraint , Mzz = -(Mxx + Myy), to give the trace elements of the moment tensor. The fiveunknown moment tensor components can be estimated using a weighted least squaresapproach, by using more (than five) observed data (Paper I). Having determined themoment tensor components the fault plane orientations (strike, dip and slip) can becomputed based on relations between the moment tensor and fault plane orientations (Akiand Richards, 1980; Paper I).

The coefficient A3 is poorly determined for a source with a significant volumetriccomponent, because it is directly constrained by the deviatoric constraint (see eq. (3)). Thiscoefficient mostly contributes in simulating P and SV waves. Therefore it is often moredifficult to achieve high degree of similarity between the observed data and correspondingsynthetics for P and SV waves than for SH waves because the deviatoric constraint may bepartially violated (Paper I). The coefficient A3 appears only in relation to the Green’sfunction associated with 45o dipping dip slip faulting, the estimation of which differsslightly from the other two fundamental Green’s functions as defined in eq. (2), because it isevaluated at fixed azimuth of 45o (Lay and Wallace, 1995).

9

3.1 Moment tensor inversion applied to local Icelandic earthquakes

The algorithm explained above was applied to determine focal mechanisms of four localIcelandic earthquakes. The earthquakes were recorded by the SIL network (Stefánsson etal., 1993) and have epicentral distances ranging from 9 to 42 km with moment magnitude2.2 Mw 3.1. The frequency-wavenumber (F-K) integration method (Bouchon, 1981;Saikia, 1994) was used to compute the Green’s function. Both observed and correspondingsynthetics were bandpass filtered for frequencies larger than those of dominant oceanicnoise and lower than the corner frequency (1.0 f(Hz) 6.0). A windowing method wasapplied for the moment tensor inversion. Around each P and S waveform on eachcomponent at the individual seismic stations, suitable Hanning windows were designed. Theinversion was then carried out inside each window simultaneously for all components at theindividual seismic station. The results of the inversion were classified as a sum of double-couple and CLVD (compensated linear vector dipole) sources. The results were thencompared with those routinely produced by the SIL network, using a spectral amplitudemethod (Rögnvaldsson and Slunga, 1993). Earthquakes within the SIL area down to amagnitude ML=-0.5 are selected and located, and magnitudes and focal mechanisms areestimated automatically by the network (Stefánsson et al., 1993). The spectral amplitudemethod is based on a ray theory algorithm, giving simple Green’s functions for the far-fieldwaves. Figure 1 compares focal mechanisms estimated by the waveform modelling basedon both amplitude and phase information with corresponding results produced by theautomatic spectral amplitude method using only amplitude information. Figure 2 illustratesthe result of inversion for the event #3 (Paper I).

Figure 1. Moment tensor inversion results for four local Icelandic earthquakes (Paper I).

10

Figure 2. Moment tensor inversion results for event #3 for P and S waveform inversion (Paper I).The solid lines are the observed data, and the dashed lines are synthetics. The numbers beneath eachwaveform refer to the station azimuth (°) and epicentral distance (km).

11

4. The empirical Green’s function method

Although models of the Earth’s internal structure may nowadays be quite detailed, there aremany instances where computed theoretical Green’s functions are not reliable. This is verycommon for broadband recording of secondary body waves with complex paths in the Earth(PP, SSS, etc) as well as for shortperiod surface waves (Lay and Wallace, 1995). Thegeneral idea of the classical empirical Green’s functions methods is to account for realisticpropagation path and site effects by using observed records of a small earthquake located inthe rupture area of a large earthquake to estimate a suitable Green’s function for the largerevent. A group of small earthquakes can also be used for calculating empirical Green’sfunction. These approaches are based on the assumption that the Earth’s response isindependent of the magnitude of the seismic excitation, therefore records of a smallearthquake can be used to reproduce the propagation path effect for a larger earthquakelocated nearby (e.g. Capuano et al., 1994; Tumarkin and Archuleta, 1994). Under generalassumptions of linearity and comparable source regions, the same Earth response isachieved if the source depth and focal mechanism of the two earthquakes are identical (Layand Wallace, 1995).

In this section a method for calculating the empirical Green’s function is introduced thatis based on the inversion of earthquake radiation patterns. The method utilises several close-lying earthquakes with known focal mechanisms that are recorded by a common seismicstation. The method is developed based on the system of eqs. (2) and (3) which are usuallyused for seismic moment tensor inversion as described above. By using some earthquakeswith known focal mechanisms (strike, dip, rake and scalar seismic moment), thecomponents of the moment tensor for a double-couple source can be calculated based uponthe known relations (Aki and Richards, 1980; Paper II). Using these components, theradiation pattern coefficients can then be computed for a given earthquake and seismicstation from eq. (3). Thus, the only remaining unknown terms are the Green’s functionsassociated with the three fundamental faults in eq. (2). This equation is only valid for oneearthquake and seismic station. Expanding eq. (2) to include a group of close-lying(clustered) earthquakes that are received by a common seismic station can be done asfollows

wi (r, 0, ) = ZSS A1i + ZDS A2

i + ZDD A3i

qi (r, 0, ) = RSS A1i + RDS A2

i + RDD A3i (5)

vi (r, 0, ) = TSS A4i + TDS A5

i (i=1, ... N)

where N stands for the number of earthquakes. Equations (5) imply that the Earth responseis the same for all N earthquakes. The matrix form of eqs. (5) for the vertical component canbe written as

12

)(r,0,w

)(r,0,w)(r,0,w

n

2

1

n3

n2

n1

23

22

21

13

12

11

AAA

AAA

AAA

DD

DS

SS

ZZZ

(6)

There is a corresponding matrix form for the radial and tangential components (Paper II).The w’s in eq. (6) are the Fourier transforms of the observed (known) displacements and theA’s are the radiation patterns coefficients. By using several observations a least squaresapproach can be employed to calculate the empirical Green’s functions. The system oflinear equations in (6) is solved in the frequency domain for the real and imaginary parts ofthe time-series independently according to a damped least squares method.

Plicka and Zahradník (1998) introduced a new method for calculating the empiricalGreen’s function which was the motivation of the method introduced here. According totheir method Empirical Green’s Tensor spatial Derivatives (EGTD), are calculated based onthe representation theorem (Aki and Richards, 1980) by removing the focal mechanisms ofearthquakes from the waveforms. In contrast to Plicka and Zahradník (1998) whodetermined the Green’s function in the usual manner as a response to excitation byelementary dipoles along the coordinate axes of a fixed Cartesian system, in the presentapproach the Green’s function is defined as a response to excitation by the threefundamental faults. The Green’s function is calculated in accordance with assumedknowledge of the source using the same equations as used for the moment tensor inversion.

4.1 Empirical Green’s functions applied to local Icelandic earthquakes

The method was applied to eight selected local earthquakes, 1.4 < ML<2.8, taken from theSouth Iceland Seismic Zone (SISZ). The earthquakes are recorded by the SIL network andthe focal mechanisms of the earthquakes are routinely determined by the SIL network usingthe spectral amplitude method (Stefánsson et al., 1993). The empirical Green’s functionswere estimated for each event at four SIL seismic stations. These Green’s functions werethen used to model another earthquake at the given seismic stations. The modelling wascarried out by substituting the resulting Green’s function into eq. (2), recalling that at thisstage the radiation pattern coefficients are also known because the focal mechanism of theearthquakes is known. Figure 3 shows an example of the application of the empiricalGreen’s function method to a local Icelandic earthquake. All time-series are bandpassedbetween 0.5-3.5 Hz. The wavelength associated with the upper limit of the filter is expectedto be higher than the size of cluster.

13

Figure 3. Comparison between observed (solid lines) and calculated (dashed lines) data of theIcelandic earthquake #8 at seismic station SOL. To the left the data in the time domain are shownwith arbitrary starting time and to the right the spectral amplitude of each component is depicted. Alltime-series are bandpassed between 0.5-3.5 Hz. The numbers to the right are the maximum value ofthe normalised cross correlation function between the corresponding spectral amplitudes of theobserved and the calculated data. The time-series data are in counts. (Paper II).

5. Teleseismic tomography along the TOR array

The TOR (Teleseismic TOmography TORnquist) project investigates the lithosphere-asthenosphere transition under the Tornquist Zone between Denmark and Sweden(Gregersen et al., 1999). Around 150 seismic stations were employed in a rectangular arrayacross the Tornquist Zone from July 1996 to August 1997. The Tornquist Zone region

14

consists of the northwestern part of the Trans European Suture Zone (TESZ), which is theboundary between the ancient Precambrian lithosphere of the East European Craton and theyounger lithosphere beneath the latest Neoproterozoic-Palaeozoic mobile belts of westernEurope. The former is characterised by a thick crust, low heat flow and a tectono-thermalage of about 3000 to 800 Ma, the latter by a thinner crust, higher heat flow and a tectono-thermal age of 560-290 Ma (Pharaoh et al., 1997). The Phanerozoic geological evolution ofthe region around the Tornquist Zone has been governed by four major tectonic events : 1)Caledonian collision tectonics (~ 450 Ma), 2) the distant Variscan orogeny (~ 250 Ma), 3)Mesozoic rifting and graben formation (~ 220 Ma) and 4) Late Cretaceous to EarlyCenozoic inversion (caused by Alpine compressional stresses) (~ 65 Ma) (Thybo, 2000).

Fifty-one high quality earthquakes were used for the teleseismic tomography study. Allseismograms were restituted to simulate a shortperiod and longperiod WWSSN (the WorldWide Standardised Seismographic Network) for P and S phases picking respectively. Therelative arrival-time residuals were then used as observed datasets.

5.1 ACH travel-time tomographic inversion

The ACH (Aki et al., 1977) method is applicable to all “restricted-array” seismictomography problems, that is, when the receiver array does not span the entire distancefrom the source (Evans and Achauer, 1993). In the ACH method the 3D structure of thetarget volume is not really retrieved, but instead the velocity contrasts relative to the layervelocity average is estimated, the average value remains unknown (Lévêque and Masson,1999). The final velocity model from the inversion based on relative residuals is consideredto reflect deviations about some unknown average. If the target volume is large enough thenthe layer-average velocities can be considered close to some commonly accepted 1Dbackground/reference Earth model (Lévêque and Masson, 1999). The IASP91 travel-timemodel (Kennett and Engdahl, 1991) was used as a starting model in the inversion (Paper III;Paper IV).

The source effect and the propagation path due to lower mantle effects are assumed tobe removed by using relative arrival-time residuals, thus they can be used to model thevelocity anomalies right below the array. There is a risk of leakage of deeper mantlevelocity perturbations into our model (Masson and Trampert, 1997) but because of theexperimental configuration any such leakage is unlikely to significantly degrade the results.In teleseismic tomography the Earth outside the target volume is assumed to be the 1Dreference model, and therefore the velocity anomalies are measured with respect to thegiven model. The ACH method is robust because ray turning points are excluded from themodelled volume (Evans and Achauer, 1993).

A weighted damped least squares algorithm for a linearized system was employed forthe inversion (Paper III; Paper IV). The linearized system was solved iteratively andnormally the optimum solution was achieved by less than four iterations. Two differentinverse methods (a singular value decomposition, SVD and a quadratic programming, QP)were implemented to investigate whether or not the blocks and major boundaries in theinversion are required by the data or are artefacts of the inversion.

15

5.2 The mean squares error method

The SVD (singular value decomposition) (Menke, 1989) method was used to calculate theinverse of the matrix presented in the posed objective function. Because of the mixeddetermined nature of the problem (even with smoothing, some model parameters remainunderdetermined) a method using SVD is well suited to the inversion (Weiland et al., 1995).In order to drop insignificant eigenvalues, i.e. those which probably do not contain usefulinformation, a modified version of the MSE algorithm of Xu (1998) was introduced asfollows (Paper III)

ak

k

1i

tak

2i

2dk x)(x)()x(MSE RIRI (7)

where d2 is the variance of the data, i’s are eigenvalues (sorted in decreasing order), Rk

the a posteriori resolution matrix based on k eigenvalues and corresponding eigenvectorsand xa is a general optimum solution that in a linear problem it can be a damped leastsquares solution. xa is assumed to be the velocity perturbations from the first iteration.Equation (7) consists of two terms which represent the trade-off between uniqueness(solution resolution) and error associated with the solution estimated (model variance). Thefirst term measures the error in the estimated model parameters by summing up thecorresponding eigenvalues and the second term measures the solution uniqueness bycalculating the apparent number of degrees of freedom in the model estimated in the nullspace. With increasing k, the first term (error) increases and the second term decreases froma value that indicates an unresolved solution toward 0, which implies a unique solution (seeTable 1).

Table 1. Minimum and maximum values of the MSE equation. min max

first term2

1

2d

t

2d

second term 0 ata x)(x * is a vector containing all the eigenvalues.

Therefore, by adding more eigenvalues the estimated solution tends to be determined moreuniquely at the expense of the increasing the variance. In other words, the error variance ofxk

MSE is a monotonically increasing function of k, while the solution resolution is amonotonically decreasing function of k (Xu, 1998). The relative crossover of thesefunctions, properly scaled, is considered to be a suitable indicator of the number ofsignificant eigenvalues (Paper III).

16

5.3 The quadratic programming method

In order to find out if boundaries and blocks observed in the inverted model are required bythe data or are unconstrained or have been artificially introduced by the inversion process,the data are inverted under different constraints. To allow sufficient flexibility in theapplication of constraints, an alternative inversion method based on quadratic programming(Parker, 1980; Schittkowski, 2000) was developed. Quadratic programming allows theinclusion of equality and inequality constraints and is a well established method in manyfields. It has been used in geophysics by e.g. Parker (1980). The minimisation was thencarried out by posing lower and upper bounds for unknown model parameters throughsuitable equality and inequality constraints (Paper III). Given the quadratic programmingformulation, constraints to be applied to the inverse problem can be defined with greatflexibility. The constraints can be defined based on an interpretation of the previous resultof the inversion, produced using the SVD method, and thus have a geological meaning. Byapplying suitable constraints in the inversion, we can then assess whether or not particularspecific features observed in the unconstrained inversion are required by the data. This isessentially done by comparing goodness of fit of the constrained and unconstrainedinversions. This type of relative model testing is a standard approach in many statisticalproblems. Those features that are considered to be of geological significance can then beassessed by posing a question to the dataset: Is this feature required by the data, or can anequivalent fit be achieved without the feature? (Paper III).

5.4 Separate and simultaneous P and S relative arrival-time residuals inversion

The error associated with teleseismic arrival-time residuals is usually lower than the travel-time perturbations due to crustal structure. The station spacing is relatively large in relationto the crustal structures as is the lateral block size in the inversion (50x50 km in thehorizontal directions) in the current study. Therefore teleseismic tomography cannot resolvenear-surface structures well. The relative P and S arrival-time residuals were thereforecorrected a priori in the inversion for the travel-time perturbations due to the crust. For Pphase corrections a 3D crustal model developed by Arlitt et al. (1999) was used, and for Sphase the correction was performed in accordance with the previous P-velocity model, andall interpreted Vs and Vp/Vs information about the area as discussed in Paper IV. Thecorrection was applied with respect to the 1D IASP91 travel-time model (Kennett andEngdahl, 1991) and the inversion was conducted with fixed crustal layers.

A cross-section along the TOR array when P phase data are inverted using the SVDmethod is shown in Figure 4a. The velocity perturbation is relative to the IASP91 startingmodel. Thus blue and red regions are the regions with relatively higher and lower velocitywith respect to the background model. Generally the seismic asthenosphere is expected tohave relatively low P- and S-velocities. Thus, a naive interpretation is to associate the highand the low velocity regions with lithospheric and asthenospheric materials respectively.The transition between the areas of relatively low and relatively high velocity is delineatedby white strips.

17

Figu

re 4

. Inv

ersi

on r

esul

ts a

t 3rd

ite

ratio

n fo

r di

ffer

ent

data

sets

. The

res

ults

are

sho

wn

as v

eloc

ity d

evia

tions

fro

m t

he I

ASP

91 s

tarti

ngm

odel

. Pos

itive

and

neg

ativ

e si

gns

indi

cate

the

rela

tivel

y hi

gher

and

low

er v

eloc

ity re

gion

s. Tw

o ob

lique

line

s lim

it th

e m

ost r

elia

ble

area

of th

e re

sult

base

d on

inci

denc

e an

gle

of th

e se

ism

ic ra

ys fo

r the

P p

hase

. Tec

toni

c ab

brev

iatio

ns: E

L, th

e El

be L

ine,

RFH

, Rin

gkøb

ing

Fyn

Hig

h, S

TZ, S

orge

nfre

i Tor

nqui

st Z

one,

LA

B, l

ithos

pher

e as

then

osph

ere

boun

dary

as

defin

ed in

the

text

and

HV

B, h

igh

velo

city

bod

y. N

ote

LAB

in a

ll fig

ures

are

dra

wn

base

d on

the

P ph

ase

inve

rsio

n re

sult.

a) P

pha

se in

vers

ion

usin

g th

e SV

D m

etho

d. b

) P p

hase

inve

rsio

n us

ing

the

QP

met

hod.

Not

e th

at th

is m

odel

is n

ot s

moo

thed

. c) V

p/V

s va

riatio

ns. d

) Sim

ulta

neou

s P

and

S ph

ase

inve

rsio

n us

ing

the

SVD

met

hod

(Pap

ers I

II a

nd I

V).

18

The two oblique lines confine the well resolved area in the inversion and are calculatedbased on ray coverage of the P phase data. Therefore the areas outside the lines can beexpected to be less well resolved (Paper III). Figure 4a shows a general increase (certainlypartially discontinuous) in P-velocity from the south towards the north along the TOR array.This increase is seen together with a south-north increase in Moho depth in the crustalmodel used (Paper III).

Figure 4b shows a P phase inversions produced using the QP method with only a generalconstraint 3.0x0.3- kms-1 posed to the model parameters, x . Note that the modelweighting matrix which represents a smoothing operator in the SVD results, is dismissedfrom the QP algorithm. Smoothing is inconvenient because the way in which the constraintsare applied (e.g. the presence of a sharp boundary) (Paper III). The images shown in Figures4a and 4b are not identical in details. However, slightly different assumptions are implicit inthe inversions, including that the QP inversion is not smoothed in the same way as the SVDinversion. In terms of the general conclusions about Earth structure, it can be judged that theresults of the two inversions (SVD and QP methods) are fully consistent. The implication isthat the differences between the two images are related to the different inversionmethodologies, rather than the information content on the data, i.e. they are unconstrainedor weakly constrained by the data. Furthermore, it should be stressed that the main aim ofusing the QP algorithm is not to produce a “best” image, but to conduct relative model tests.Applying different constraints to the model revealed that the state of the lithosphere-asthenosphere boundary in the northern part of the Tornquist Zone is related to the existence(or not) of the high velocity body (HVB) to the south of the model (the surface expressionof which coincides with the Elbe Lineament) (Paper III).

Figure 4c illustrates Vp/Vs perturbations along the TOR array. The ratio is calculatedbased on separate P and S phase inversion results using the SVD algorithm (Paper III; PaperIV). The white strip indicates Vp/Vs=1.8, which is the average value of the ratio for thedepth range 50-420 km according to the IASP91 model. Therefore the red and blue regionsshow areas where the ratio is relatively lower and higher than the given average value,respectively (Paper IV).

Simultaneous P and S phase inversion is also illustrated in Figure 4d (based on the SVDmethod). The ray tracing was carried out based on a P-velocity model taken initially fromthe IASP91 model. For the corresponding S phases, the P-velocity model was converted toS-velocity based on the Vp/Vs ratio of the IASP91 model. In other words, a 1D Vp/Vs ratiotaken from the IASP91 model was used to relate the P- and S-velocities. The relationshipwas fixed in this inversion. The P and S phases were weighted in accordance with theircorresponding data errors (Paper IV).

Figure 4 shows inversion results using different methods, including the SVD and QPmethods, and for different P and S phase datasets. The major blocks and boundaries shownin Figure 4, are resolved consistently. The thin lithospheric block under Central Europe isobserved next to a 100-120 km thick lithospheric block beneath the Tornquist Zone area andmore than 200 km continental lithosphere in the Baltic Shield (Figures 4a, 4b and 4d). The

19

results also revealed near-vertical transitions at both sides of the Tornquist Zone. Thetransitions are accompanied by abrupt near-vertical changes in Vp/Vs ratio if it is assumedthat Vp/Vs=1.8 is an average value for the upper part of mantle.

5.5 Resolution analysis

The most important problems in many tomography studies are the lack of resolution and thelarge errors in the data (Nolet, 1993). An a posteriori resolution matrix is often used topresent how well the solution represents the “true” Earth. Dropping eigenvalues orinappropriate smoothing or damping the inversion may decrease the resolution. Each row ofthe a posteriori resolution matrix or resolution kernel shows the amount of informationavailable and the direction of smearing in all three dimensions. The reliability of the modelobtained in the inversion can be examined by analysing the resolution kernel for differenttarget points (specific nodes in the model). A-delta-function like resolution kernel indicatesa well resolved part of the model. Figure 5 shows resolution kernels for four importanttarget points in the model for the simultaneous P and S phase inversion case. The diagonalelements of the resolution matrix are not so large. They are relatively low partly due to thechoice of parameterisation. Large values for diagonal elements may be achieved usinglarger block sizes relative to station spacing (Evans and Achauer, 1993). Vertical smearingis a dominant effect recognised in the resolution kernels. Target point d) is not delta-likeand spreads over a wider area. Thus only an average value of the corresponding modelparameter can be inferred.

The diagonal elements of the a posteriori resolution matrix are simplest to display andcompare, but may not be informative for damped inversions (Eberhart-Phillips, 1993). Thediagonal elements of the resolution matrix for the simultaneous inversion case are shown inFigure 6a. In order to obtain a realistic picture of the solution resolved, both diagonal andoff-diagonal elements of the resolution matrix have to be considered. The effect of the off-diagonal elements should be considered allowing for their spatial positions which depend onthe parameterisation. The effect was allowed for using a width function weighted by thedistance between nodes (Weiland et al., 1995; Paper IV). Therefore the best resolved partsof the model should have relatively large diagonal elements and a relatively low widthfunction. The distribution of the normalised width value is illustrated in Figure 6b.According to the diagonal elements and the corresponding width values (Figures 6a and 6b),the lithosphere-asthenosphere transition (LAB in the corresponding figures) is resolved withhigher accuracy than the high velocity body (HVB).

In order to evaluate these results synthetic modelling tests were also conducted alongwith the resolution analysis described above. The ray geometry corresponding to thesimultaneous inversion case was used to generate synthetic relative arrival-time residualsbased on the hypothetical test model shown in Figure 6c. Gaussian noise with 0.1 secstandard deviation was added to the synthetic data to account for errors due to phasepicking, crustal variations and event statics (Dueker et al, 1993).

20

Figu

re 5

. Res

olut

ion

kern

els

for f

our t

arge

t poi

nts.

a) T

arge

t poi

nt 5

3.6°

N, 1

1.2°

E, 7

0-90

km

. b) T

arge

t poi

nt 5

3.0°

N, 1

1.0°

E, 2

40-

270

km. c

) Ta

rget

poi

nt 5

5.8°

N, 1

3.2°

E, 1

20-1

50 k

m. d

) Ta

rget

poi

nt 5

5.8°

N, 1

3.2°

E, 1

80-2

10 k

m. T

ecto

nic

abbr

evia

tions

as

inFi

gure

4.

21

Figu

re 6

. Res

olut

ion

stud

y fo

r si

mul

tane

ous

P an

d S

inve

rsio

n ca

se. a

) D

iago

nal e

lem

ents

of

the

reso

lutio

n m

atrix

. b)

Cor

resp

ondi

ng w

idth

of t

he re

solu

tion

mat

rix. c

) A h

ypot

hetic

al te

st m

odel

. d) R

esol

ved

mod

el a

t 3rd

iter

atio

n. T

ecto

nic

abbr

evia

tions

as i

n Fi

gure

4 (P

aper

IV).

22

The inverted result, Figure 6d, shows that the lithosphere-asthenosphere boundary at theSorgenfrei-Tornquist Zone is resolved well with a small deviation from the true model atshallower depths. This deviation is also predicted by relatively large width values for thearea as in Figure 6b. The high velocity body (HVB) is resolved, but with less accuracy atboundaries in comparison to the major boundary resolved to the north (Paper IV).

Relative modelling tests achieved by inverting the relative residuals under differentconstraints also revealed that the state of the lithosphere-asthenosphere boundary at thenorthern part of the Tornquist Zone is related to the presence of the high velocity body(HVB) (Paper III).

5.6 Tectonic evolution of the TOR area inferred from the teleseismic results

According to the results obtained by separate and simultaneous P and S phase inversions,the lithospheric structure under northern Germany is thin but reaches to an intermediatethickness of about 120 km in the Tornquist Zone area. A continental lithosphere with morethan 200 km thickness characterises the Baltic Shield. The transition between the thinlithosphere in Germany and the continental lithosphere under the Baltic Shield occurs intwo sharp and steep steps. A sharp and steep subcrustal lithosphere-asthenosphere boundaryis found below the Tornquist Zone with surficial expression coincident with the Sorgenfrei-Tornquist Zone. The major near-vertical boundary is observed with changes in P- and S-velocities of several percents to depths of 250 km. Another less significant near-verticaltransition is recognised under the central part of the Tornquist Zone, more or less beneaththe Elbe-lineament. This boundary is sharply resolved in both the P phase and simultaneousinversions. The observed variations from a thin lithosphere beneath northern Germany to anintermediate thick lithosphere under the Tornquist Zone and a thick continental lithosphereunder the Baltic Shield are supported by other geophysical data such as heat-flowvariations. Thermal modelling shows that these features are closely related to an increase ofmantle heat-flow towards the younger areas of Central Europe (Balling, 1995). Thelithospheric block under the Tornquist Zone is characterised by relatively higher Vp/Vs thanthe lithospheric block under the Baltic Shield. The existence of low S-velocities under theTornquist Zone can be seen from relatively high Vp/Vs in the area. The area is coincidentwith a gravity high which supports the idea of extensive mafic intrusions (Thybo, 2000).Tectonic evolution of the area suggests the amalgamation of a micro continent or a series ofterranes of Avalonian origin (to the south of the studied area) onto the Baltic Shield (Thybo,2000) with subduction of the materials between these areas. The high velocity body (HVB)to the south (the surface expression at which coincides with the Elbe-lineament ) can beidentified as a relic of the subducting slab, with the boundary at about 53.5° and 50-100 kmdepth delineating the edge of Avalonia at that time. Variscan tectonics induced right lateraldisplacement that caused distributed lateral displacement across the faults of the TornquistZone (Thybo, 2000). Therefore it is possible that the deeper near vertical boundary to thenorth, under the Sorgenfrei-Tornquist Zone is of later origin, being the product of lateraldislocation parallel to the Tornquist Zone. Generally it can be summarised that the observedhigh gravity anomaly, extensive mafic intrusions, low average velocities because of the

23

thicker crust, and high mantle heat flow indicate dominant extensional tectonic features inthe Tornquist Zone. This idea is further supported by the observed crustal thinning and canbe confirmed as well by the models obtained in the present project. Relatively high valuesof Vp/Vs or low S-velocities may be interpreted as an indication for mantle up-wellingbeneath the Tornquist Zone area (Paper III; Paper IV).

6. Summary of papers

6.1 Paper IBody wave moment tensor inversion of local earthquakes:

an application to the South Iceland Seismic Zone

This paper deals with an application of time domain moment tensor inversion method fordetermining focal mechanisms of some local Icelandic earthquakes. The epicentral distancesof the earthquakes used are in the range 9-42 km with moment magnitudes between 2.2 Mw 3.1. The data were recorded by the South Iceland Lowland (SIL) network. The SILnetwork routinely determines focal mechanisms of the earthquakes based on the spectralamplitude method (Rögnvaldsson and Slunga, 1993). The frequency-wavenumber methodwas used to compute the Green's functions associated with an arbitrary shear dislocationpoint source in a plan layered elastic medium (Bouchon, 1981; Saikia, 1994). The Green’sfunctions associated with the three fundamental faults are related to the rotated componentsof the displacements at the free surface of the Earth through the coefficients describing theradiation pattern (Herrmann and Wang, 1985;Jost and Herrmann, 1989). The threefundamental faults (vertical strike slip, vertical dip slip and 45° dipping dip slip fault) arenecessary to evaluate waveforms excited by a double-couple source. The radiation patterncoefficients are also linear functions of seismic moment tensor components for a givenazimuth. Thus the focal mechanism of the earthquakes is determined in two steps. First, thecomponents of moment tensor are determined through a linear damped least squares methodand then fault plane orientations and scalar seismic moment are computed based on theknown moment tensor components. In order to allow the use of a Heaviside function as asource time function the observed waveforms and corresponding synthetics were filteredbelow the corner frequency of the data. A windowing method was implemented for theinversion. Around each P and S waveform on each component at the individual seismicstations, Hanning windows were designed (the window may contain some of the convertedphases too). P and SV waves on the vertical and radial components and SH waves on thetangential component were used in the waveform modelling. The moment tensor inversionwas then performed inside each window simultaneously for all components at the individualseismic stations. The inversion was optimised by applying a cross-correlation routine toalign the synthetic seismograms with the observed data. The alignment is necessary tocompensate for uncertainties in the structural velocity model used, error in the estimation ofepicentral distances, filtering and other relevant sources of error and was applied before themechanism had been estimated. It is assumed that the best solution is the solution withmaximum variance reduction. The inversion was done for three groups of datasets. P and S

24

waveforms were inverted separately and simultaneously. The results of the inversion werethen classified as a sum of double-couple and CLVD (compensated linear vector dipole)sources. The S waveform was usually the dominant phase for the events studied andexcluding the nodal seismic stations, the fit between the observed data and synthetics werecontrolled by them. Generally, the waveform fit is best for tangential components. Thevertical components show a better fit than the corresponding radial components. The resultswere then compared with the fault plane solutions obtained by the automatic spectralmethod routinely used in the SIL network. The spectral amplitude method is based on a raytheory algorithm, giving simple Green's functions (delayed impulse pulses) for the far-fieldwaves. Therefore the comparison shows focal mechanisms determined from both amplitudeand phase information (waveform modelling) with those estimated using only the amplitudeinformation (automatic spectral amplitude method). Good agreement between the results ofwaveform modelling and spectral amplitude method was achieved.

6.2 Paper IIEmpirical Green's functions calculated from the inversion of earthquake radiation

patterns

The classical empirical Green's function methods use a small earthquake occurring in thesource area of a large earthquake as an empirical Green's function for the large earthquakeat a given seismic station. The most important criteria that have to be taken into account forchoosing the small earthquake are 1) the corner frequency of the small earthquake has to behigh enough relative to the corner frequency of the large earthquake and 2) the twoearthquakes should have the same focal mechanism. In this article a method is introducedfor calculating the empirical Green's function based on inversion of radiation patterns ofearthquakes. Some close-lying earthquakes with known focal mechanisms recorded by acommon seismic station are used to compute the empirical Green's functions between thegiven source area and the seismic station. The method is based on the expression that relatesGreen's function components to different displacement components of a rotated seismicstation at the free surface of the Earth (Herrmann and Wang, 1985;Jost and Herrmann,1989). The expressions are widely used for moment tensor inversion but in the currentresearch were manipulated to be used for determining the empirical Green's functions. Theinversion was carried out in the frequency domain for the real and imaginary parts of thetime-series independently for a given frequency range. The frequency limits were selectedto allow the use of a Heaviside function as a source time function and to ensure that thecorresponding wavelength is higher than the size of cluster. Thus by removing the effect offocal mechanisms from the waveforms and combining the remaining terms based on adamped least squares approach, the empirical Green's function is calculated. The functionrepresents the characteristics of the propagation path after the waves have left the sourcearea until they are received by a given station. The method in fact enhances the commonphases among the time-series and damps those that are not common. It assumes knownfocal mechanism of the earthquakes, therefore uncertain focal mechanisms might degradethe results. The resulting Green's function may contains both body and surface waves. The

25

application of the method is not limited by any requirement to make separation of seismicphases and the earthquakes used are not required to have the same focal mechanisms. In thisarticle the method is applied to two different datasets, including Icelandic and regionalIranian earthquakes.

For the case of the Icelandic data, the empirical Green's functions were calculated forselected local earthquakes , 1.4 < ML < 2.8 with data from the South Iceland Seismic Zone(SISZ) recorded by the SIL (South Iceland Lowland) network. The empirical Green'sfunctions between the given source area and four seismic stations from the SIL networkwere calculated for frequencies in the range 0.1-0.7 Hz. The Green's functions calculatedwere used to model another earthquake at the same stations. The modelling was performedby substituting the resulting Green's function into the expression that relates the functions tocomponents of the displacement at the free surface.

The method was also applied to model the mainshock of the 1990 June 20 Iranianearthquake (Rudbar earthquake) with Mw=7.4 at the broad-band seismic station KIV inRussia. First the empirical Green's function was calculated for the rupture area of theRudbar earthquake and seismic station KIV based on some earthquakes that occurred in thesource area with known focal mechanisms (including five aftershocks). The Green'sfunction calculated was then used to model the Rudbar earthquake at the station using thefocal mechanism of the earthquake. The inversion was carried out for the frequency rangebetween 0.01-0.08 Hz. The similarity between the observed and calculated time-series isless pronounced than for the Icelandic earthquakes. This might be due to the more scatteredspatial distribution of the earthquakes and larger magnitude differences betweenearthquakes used to calculate the empirical Green's function and the main event.

6.3 Paper IIINonlinear body wave teleseismic tomography along the TOR array

The TOR project investigates the lithosphere-asthenosphere structure under the TornquistZone between northern Germany and southern Sweden. The Tornquist Zone is a postcollisional feature (Thybo, 2000) that formed as a northwestward widening splay of lateCarboniferous to early Permian fault zones in the area of Denmark. The zone has to somedegree been reactivated by Mesozoic extensional tectonics and late Cretaceous to earlyTertiary inversion (Thybo, 1997). The Tornquist Zone is a north-west part of the Trans-European Suture Zone (TESZ). The TESZ is considered to be the boundary between theancient Precambrian lithosphere of the East European Craton and the younger lithospherebeneath the latest Palaeozoic mobile belts of western Europe (Pharaoh et al., 1997). TheTOR array consists of 150 seismic stations (108 shortperiod, 28 broadband and 14 otherpermanent stations) along a 900 km long by 100 km wide strip from northern Germanythrough Denmark to Southern Sweden across the Tornquist Zone. The stations wereoperated from July 1996 to August 1997 in the TOR experiment. The average stationspacing is 20 km in the centre of the array in Denmark and southern Sweden and 25-35 kmin northern Germany and central Sweden. 51 high quality teleseismic earthquakes wereselected and arrival-times of P phases were then picked visually. The IASP91 travel-time

26

model (Kennett and Engdahl, 1991) was used as a starting model in the inversion. The ACH(Aki et al., 1977) tomography method was used based on a weighted damped least squaresalgorithm for a linearized system. Two different inverse methods (a singular valuedecomposition method, SVD and a quadratic programming method, QP) were implementedin order to investigate whether or not the blocks and major boundaries resulted in theinversion are required by the data or are artefacts of the inversion. The QP (Parker, 1980;Schittkowski, 2000) inverse method was used to allow sufficient flexibility in theapplication of constraints and consequently testing various hypotheses regarding the SVDimage. Therefore an evaluation of the blocks and major boundaries in the SVD image wasachieved by posing different constraints on the model parameters and inverting the data.The relative teleseismic residuals cannot resolve near-surface structure well in the currentresearch because (1): the error associated with teleseismic arrival-time residuals is usuallylower than travel-time perturbations in the crust and (2): the station spacing is relativelylarge in relation to crustal structure, as is the lateral grid spacing in the inversion (50x50km). In the current research a 3D crustal model developed by Arlitt et al. (1999) was used apriori in the inversion for correcting for the travel-time variations due to the crust (upper 50km of the model). The correction was applied with respect to the IASP91 model. As thecrustal model has a significant influence on the inversion results, there may be a risk of biasif it were incorrect. In order to evaluate the possible bias due to inaccuracies in the crustalmodels, the inversion was repeated using the SVD method, but now with a crustal modelcorrection based on the model developed by Pedersen et al. (1999). Comparisons betweenthese results, and also with inversions where crustal structure was unconstrained, showconsistent features. According to the results, there is a thin lithosphere under Central Europethat is underlain by relatively low velocity materials (asthenospheric region). In theTornquist Zone area (i.e. below the central part of the array) the lithospheric thicknessappears to reach 100-120 km thickness, and in the Baltic Shield more than 200 km ofcontinental lithosphere are recognised. Abrupt lateral changes in P-wave velocityperturbations are observed in either side of the Tornquist Zone. The lithosphere-asthenosphere transition in the northern part of the TOR area is characterised by a near-vertical boundary at depth 150-250 km. More details are also seen in the model, includingwhat appears to be a high velocity body (HVB) under Mainland Europe (depth about 250km at about 53 N).

6.4 Paper IVLithospheric structure of the Tornquist Zone resolved by

nonlinear P and S teleseismic tomography along the TOR array

The Trans European Suture Zone (TESZ) is the boundary between the ancient Precambrianlithosphere of the East European Craton and the younger lithosphere beneath the latestNeoproterozoic-Palaeozoic mobile belts of western Europe (Pharaoh et al., 1997). TheTornquist Zone region consists of the northwestern part of TESZ which is the area ofPalaeozoic amalgamation of the crust and lithosphere of Central Europe onto theProterozoic Baltic Shield and East European platform. The lithosphere under Central

27

Europe is characterised by a thin crust and high heat flow while under the Baltic Shieldthere is a thicker crust and lower heat flow (Pharaoh et al., 1997). The main aim of the TOR(Teleseismic TOmography TORnquist) project is to resolve the lithosphere-asthenospheretransition under the Tornquist Zone. Teleseismic P and S phase relative arrival-timeresiduals from 51 high quality earthquakes recorded by 150 seismic stations along the TORarray (perpendicular to the general trend of TESZ in the Tornquist Zone area) were used todelineate the transition zone. The relative arrival-times residuals cannot be used to producean absolute velocity model. The final velocity model from the inversion based on relativearrival-times is considered to reflect deviations about some unknown average Earth model,since relative arrival-time residuals data are used. The IASP91 model (Kennett andEngdahl, 1991) was used as a starting model in the inversion. Travel-time perturbations inthe crust are higher than the error associated with teleseismic arrival-times residuals. Thusthe residuals were corrected for crustal travel-time variations based on a 3D crustal modelalong the TOR array for P- and S velocities respectively. The ACH tomography method(Aki et al., 1977) was implemented and the inversion was carried out based on a singularvalue decomposition method (Paper III). Nonlinear teleseismic tomography for S phasesand simultaneous P and S phase inversion results shows consistent features when comparedwith P phase inversion case (Paper III). The existence of a major near-vertical change in P-and S-velocities of several percent to depths 250 km below the Tornquist Zone is resolvedby P and S phases separately and simultaneously. The transition coincides at the surfacewith the Sorgenfrei-Tornquist Zone. Beyond the Ringkøbing Fyn High, another lesssignificant transition is marked by the different inversion cases (P, S and simultaneous Pand S phases). The final model shows that the transition zone between the thin lithospherein Germany and the Shield in Sweden is not purely gradual and it includes two very sharpand steep steps. Vp/Vs variations along the TOR array further signify different tectonical-lithological lithospheric units in the Tornquist Zone area and the Baltic Shield along theTOR array.

28

7. Acknowledgements

My first day experience being in Europe, let’s say clearly in Uppsala (with all my fantasy)began with taking part in the time-series analysis course delivered by Roland Roberts.While he was lecturing on refracted-reflected waves, I was thinking about those waves thattook me far away from home. I suddenly stopped thinking, because it was time for coffee-breaks. I did not know that Roland would finally become my supportive supervisor. I wouldlike to express my sincere thanks to Roland for his support, intensive constructivediscussions, encouragement, guidance, advise and especially his friendship throughout mystudy. Thanks Roland for also teaching me, how to write a good scientific paper andspending time on correcting my papers. Laust B. Pedersen deserves a special thanks forhelping me in different occasions with his remarks and comments on my research topics. Iam also grateful to him for his excellent courses, especially the inversion. Both Roland andLaust sent me to many workshops and conferences to different nice places on the world,where I met many colleagues and friends. Now I can say that I have visited further north,Iceland to further south, Portugal, thanks a lot. I have enjoyed working with ReynirBöðvarsson and Ragnar Slunga, that I hereby express my special appreciation to them. OtaKulhánek is warmly thanked for his support throughout my study. Taking part in the weeklyseismic meeting arranged by Christopher Juhlin and presenting our (semi-recent) resultswas a good opportunity to remain fresh on my research topics. I also enjoyed working withhim when I was the computer administrator at the department, thanks Chris. I wish to thankCarl-Erik Lund, for his support. Dan Dyrelius is gratefully acknowledged and IrinaArtemieva is especially thanked for many useful comments on my paper. I appreciatesupportive concerns from Hemin Koyi.

I was lucky to take part in the fieldwork of the SVEKALAPKO project in Finland. Theknowledge I have gained about Orion and fieldwork is due to the valuable supports fromLars Dynesius and Hans Palm, my extreme appreciation. I will never forget the time I spentwith Hasse in the field, while learning different things including the beauty of social life.Conny Holmqvist accompanied me in one of my trips, which was excellent mainly on theboat on the way back, I express my best wishes to him. I like to give my grateful regards toMartin Engels, who has always been ready to help. I have benefited a lot talking to him ondifferent oriented geophysical and social subjects. I also wish to thank Maxim Smirnov.

Without fellow students, it would not have been possible to enjoy the life whilestudying. Mehrdad Bastani (the real GOOLI) and his family, Fariba and Yas have beenwonderful friends to me, and I am greatly indebted to them for their friendship and supportover the past years. We have had quite fun together including unforgettable time, whileMehrdad was living with me in the student corridor. I will always remember the first timethat we tried to eat what we had cooked together (Ghormeh Sabzi). Thanks for everything. Ihave a good memory of the time that I spent with Mehran Gharibi and his family, thus Itake the chance and wish them all the best. Behrooz Tavakoli is a good old friend. Hereminds me a lot of adventures while we were both students in Tehran, thanks to him andhis family.

I spent many nights with David Monterroso (the CD man), Ronnie Quintero (Dr. qué

29

pasó), Jaime Toral (the leader) and Diego Caceres at the V-Dala nation to have a relaxed,friendly and enjoyable time. I always remember their kind friendships. My especial thanksgoes to Sverker and Ingrid Olsson especially for their hospitality and incredible mid-summer 2001. Sverker (a man who knows the best restaurants in Europe) has also been sokind to read through the introduction of my thesis. I firstly learned C-shell scriptprogramming from Ari Tryggvason, thanks Ari, for too many other things (!). I like to thankPuy Ayarza (Hola), for her nice supportive friendship. Johiris Rodriguez my office-companion, is really thanked for her adorable talent. One of her specialities is to create thebest summer vacation time, gratcias señorita. Coffee breaks and long talks about all semi-funny things with Magnus Friberg were quite pleasurable. He showed me how the thingscan be easier, including renting a flat in Uppsala. Mehrdad and Magnus gave me valuablepoints about my thesis. I gratefully like to thank, Artem Kashubin (-r), for too many thingsbut firstly his brave decision on taking over the most time-night-consuming computer job.Björn Bergman (a Mac fellow) is a real cheerful colleague, many thanks to him. LenaFrenje is thanked for picking the S-phase of the TOR dataset. I also wish to thankAlexandros Savvaidis (a fellow from Greece), Richard Ferdinand, Leif Persson, PatirkNilsson, Henning Lorenz, Niklas Juhojuntti, Atalay Ayele, Johannes Schmidt, Björn Lundand Patrik Johansson.

I enjoyed fruitful cooperation among the TOR working group. I notably thank Prof.Soren Gregersen, Prof. Hans Thybo and Peter Voss from Denmark.

I appreciate the assistance and valuable helps from Siv Pettersson, Ingegerd Ohlsson andJane Söderström.

On the way to this thesis, many other people have supported and encouraged me in oneway or the other to complete this thesis. I express my special warm grateful regards to AnitaMofidi, for great support and sympathy. My especial thanks goes to Orang Hedayati, a nicegreat friend that has been always there for me whenever I needed (Goole Cheragh). Ahmad-Reza Hedayati (Bacheh Fil) is warmly thanked.

And last not least I am indebted to endless kindness of my mother, who has been withme during the time of writing the thesis. A great source of love and kindness, I trulyappreciate you mom, and express all my wishes to you. My mother’s presence and greatmemory of my late father have been extremely valuable resources to make this thesis done. For me at least not now, but some weeks later, “TOR” would mean nothing more thanTime TO Relax.

30

8. References

Aki, K., Christoffersson, A. and Husebye, E., 1977. Determination of the three-dimensionalseismic structure of the lithosphere., J. geophys. Res., 82, 277-296.Aki, K. and Richards, P. G., 1980. Quantitative Seismology: Theory and Methods, vol I,W. H. Freeman and Co., San Francisco, CA.Arlitt, R., Kissling, E., Ansorge, J. and TOR Working Group, 1999. 3-D crustal structurebeneath the TOR array and effects on teleseismic wavefronts, Tectonophysics, 314, 309-319.Balling, N., 1995. Heat flow and thermal structure of the lithosphere across the BalticShield and northern Tornquist Zone, Tectonophysics, 244,13-50.Bouchon, M., 1981. A simple method to calculate Green’s functions for elastic layeredmedia, Bull. seism. Soc. Am., 71, 959-971.Capuano, P., Zollo, A. and Singh, S. H., 1994. Source characteristics of moderate sizeevents using empirical Green functions: an application to some Guerrero (Mexico)subduction zone earthquakes, Ann. Geofis., 37, 1659-1677.Dueker, K., Humphreys, E., and Biasi, G., 1993. Teleseismic imaging of the western UnitedStates upper mantle structure using the simultaneous iterative reconstruction technique, inSeismic Tomography: Theory and Practice, pp.265-298, eds Iyer, H.M. and Hirahara, K.,Chapman & Hall, London.Eberhart-Phillips, D., 1993. Local earthquake tomography:earthquake source regions, inSeismic Tomography: Theory and Practice, pp.613-643, eds Iyer, H.M. and Hirahara, K.,Chapman & Hall, London.Evans, J. and Achauer, U., 1993. Teleseismic velocity tomography using the ACH method:Theory and application to continental-scale studies, in Seismic Tomography: Theory andPractice, pp.319-360, eds Iyer, H.M. and Hirahara, K., Chapman & Hall, London.Gregersen, S., Pedersen, L.B., Roberts, R.G., Shomali, H., Berthelsen, A., Thybo, H.,Mosegaard, K., Pedersen, T., Voss, P., Kind, R., Bock, G., Gossler, J., Wylegala, K.,Rabbel, W., Woelbern, I., Budweg, M., Busche, H., Korn, M., Hock, S., Guterch, A., Grad,M., Wilde-Piorko, M., Zuchniak, M., Plomerova, J., Ansorge, J., Kissling, E., Arlitt, R.,Waldhauser, F., Ziegler, P., Achauer, U., Pedersen, H., Cotte, N., Paulssen, H. and Engdahl,E.R., 1999. Important findings expected from Europe’s largest seismic array, EOS, Trans.Am. geophys. Un., 80, 1&6.Herrmann, R. B. and Wang, C. Y., 1985. A comparison of synthetic seismograms, Bull.seism. Soc. Am., 75, 41-56.Jost, M. L. and Herrmann, R. B., 1989. A student’s guide to and review of moment tensors,Seism. Res. Lett., 60, 37- 57.Kennett, B.L.N. and Engdahl, E.R., 1991. Travel times for global earthquake location andphase identification, Geophys. J. Int., 105, 429-465.Lay, T., and Wallace, T. C., 1995. Modern Global Seismology, Academic Press, New York.Lévêque, J.J., and Masson, F., 1999. From ACH tomographic models to absolute velocitymodels, Geophys. J. Int., 137, 621-629.Masson, F. and Trampert, J., 1997. On ACH, or how reliable is regional teleseismic delay

31

time tomography?, Phys. Earth planet. Inter., 102, 21-32.Menke, W., 1989. Geophysical Data Analysis: Discrete Inverse Theory, Academic Press,Inc., New York.Nolet, G., 1993. Solving large linearized tomography problems. in Seismic Tomography:Theory and Practice, pp.227-247, eds Iyer, H.M. and Hirahara, K., Chapman & Hall,London.Parker, R. L., 1980. The inverse problem of electromagnetic induction: Existence andconstruction of solutions based on incomplete data, J. geophys. Res., 85, 4421-4428.Pedersen, T., Gregersen, S. and the Tor Working Group, 1999. Project Tor: Deeplithospheric variation across the Sorgenfrei-Tornquist Zone, Southern Scandinavia, Bull.Geol. Soc. Den., 46, 13-24.Pharaoh, T.C., England, R.W., Verniers, J. and ela niewicz, A., 1997. Introduction:geological and geophysical studies in the Trans-European Suture Zone, Geol. Mag., 134,585-590.Plicka, V. and Zahradník, J., 1998. Inverting seismograms of weak events for empiricalGreen’s tensor derivatives, Geophys. J. Int., 132, 471-478.Rögnvaldsson, S. Th. and Slunga, R., 1993. Routine fault plane solutions for localnetworks: A test with synthetic data, Bull. seis. Soc. Am., 83, 1232-1247.Saikia, C. K., 1994. Modified frequency-wavenumber algorithm for regional seismogramsusing Filon’s quadrature: modelling of Lg waves in eastern North America, Geophys. J. Int.,118, 142-158.Schittkowski, K., 2000. Fortran Subroutine. Mathematisches Institut, UniversitaetBayreuth, Germany.Stefánsson, R., Bödvarsson, R., Slunga, R., Einarsson, P., Jakobsdóttir, S., Bungum, H.,Gregersen, S., Havskov, J., Hjelme, J. and Korhonen, H., 1993. Earthquake predictionresearch in the South Iceland Seismic Zone and the SIL project, Bull. seism. Soc. Am., 83,696-716.Thybo, H., 1997. Geophysical characteristics of the Tornquist Fan area, northwest Trans-European Suture Zone: indication of late Carboniferous to early Permian dextraltranstension, Geol. Mag., 134, 597-606.Thybo, H., 2000. Crustal structure and tectonic evolution of the Tornquist Fan region asrevealed by geophysical methods, Bull. Geol. Soc. Den., 46, 145-160.Tumarkin, A.G. and Archuleta, R.J., 1994. Empirical ground motion prediction, Ann.Geofis., 37, 1691-1720.Weiland, C.M., Steck, L.K., Dawson, P.B. and Korneev, V., 1995. Nonlinear teleseismictomography at Long Vally caldera, using three-dimensional travel time ray tracing, J.geophys. Res., 100, 20379-20390.Xu, P., 1998. Truncated SVD methods for discrete linear ill-posed problems, Geophys. J.Int., 135, 505-514.

Errata

Page Error Corrected form

23, 2nd paragraph damped weighted