Chapter 3. Receiver Function Analysis. 3.1 Introduction

Transcription

1 Chpter 3 Receiver Function Anlysis 3.1 Introduction The receiver function method hs een pplied widely in the lst yers y vrious reserch groups for estimting the prtil impulse response of the crust nd the upper mntle. The technique ws originlly developed y Lngston (1979) nd ws then improved y vrious groups for different spects such s spectrl estimtion, inversion etc. Some of the importnt developments on the technique re given in the studies of Ammon et l. (199); Cssidy (1992); Owens et l. (1988); Prk & Levin (2); Smridge (1999); Shiutni et l. (1996). Briefly, receiver functions rely on teleseismic erthqukes which smple the Erth long the trvel pth. By using the cncelltion of the common fetures from the source nd most of the pth which re recorded on the different components, one cn otin the prtil impulse response of the Erth just eneth the sttion. The estimted function is then used in n inversion schem for the clcultion of velocity-depth model in the vicinity of the sttion. The recorded wvefield on the Erth cn e descried through convolutionl model. The source signl of the erthquke is convolved with mny different opertors from the origin time to rrivl to the sttion. These opertors represent ner source effects, propgtion pth effects, ner receiver effects nd the instrument response. The isoltion of the ner receiver effects corresponds to the clcultion of the receiver function. It should e lso noted tht typicl receiver function trce will lso crry signtures of locl reverertions. Figure 3.1 depicts the propgtion processes ner receiver. Incident teleseismic P wves cn e converted to S wves t discontinuities tht hve steeper pth. P wve nd S wve crustl reverertions contriute to the seismic signl t the receiver. The detils of the contriutions to the convolutionl representtion re given elow: 19

2 f R K P s J Figure 3.1: Propgtion processes ner receiver (Kennett, 22, p 32). f denotes the free surfce. K nd J re the seismic discontinuities. Ner Source Effects-N S Seismic wves emerging from source will first interct with the locl structure. The ner source effects N S include surfce reflections (pp, ps, sp, ss), reverertions in the presence of sedimentry lyer nd internl reflections due to the presence of strong reflector such s the Moho. All of these contriutions shpe the effective source time function for trnsmission to the teleseismic distnce so tht its nture ecomes complicted. Propgtion Pth Effects-P In generl sense, ry theory cn e used to descrie the pssge of seismic energy inside the Erth. But to ccount for the correct energy of the seismic phse, some other contriutions need to e tken into ccount. The ctul pth of ry will e ffected due to lterl velocity vritions s the dominnt vritions with depth. Focusing nd defocusing occur for the trveling wve, which leds to multipthing. This cn e seen s some of portion of the rys tking extr pths in ddition to the min pth (Stein & Wysession, 23, p 188). The recorded wveform is the sum of the coherent prts of the rys which trveled on ll possile pths from source to receiver. Multipthing is n importnt phenomen where strong velocity heterogeneties exist in the Erth, e.g., suduction zones nd mid ocenic ridges. 2

3 For propgting wve, the wvefront will grow long the propgtion pth. From the conservtion of energy, the energy per wvefront decreses with distnce from the source. Since the mplitude is proportionl to the squre root of energy, there will e loss of mplitude for growing wvefronts. The whole process is clled geometric spreding. There re two seprte clsses of geometric spreding for ody wves nd surfce wves. The ody wves pssing through the volume of the mteril spred out more, nd so decy quickly, thn the surfce wves whose energy is trpped ner the surfce. The mjor discontinuities which define the trnsition zone etween upper mntle nd lower mntle re t 41 km nd 66 km depth. Seismic velocities increse ruptly t these depths due to chnge in the minerl structure. These rpid increses in velocity cuse triplictions in the rrivls. Upper mntle trvel times show two triplictions round 1 nd 22 cused y the 41 nd 66 km discontinuities (Stein & Wysession, 23, p 171). For steeply incident wves, the mount of reflection from these zones will e smll nd most of the energy will e trnsmitted. Between 3 nd 9 epicentrl distnces, the effect of structure is simplified, nd this is the zone usully employed for receiver function nlysis. Although the Erth is ssumed to e lrgely n elstic medium, there is considerle mount of nelsticity. During the propgtion of the rys, some seismic energy will e converted to therml energy. The ttenution Q 1 defines this energy loss, nd commonly there is wek frequency dependency on the ttenution process. Generlly speking, n ttenution opertor cts low pss filter. Most studies of ttenution suggest moderte loss fctor in the crust (Q 1 µ.4) slightly lower loss in the lithosphere with n increse in the sthenosphere of the upper mntle (Q 1 µ.1) nd then decrese to crustl vlues, or lower, in the mntle elow 1 km (Kennett, 21, p 147). Ner Receiver Effects-N R As for the ner source effects, the heterogeneous structure in the neighourhood of the receiver domintes the seismic wve. A sedimentry lyer on top of the sement will led to reverertions.there is lso n mplifiction due to free surfce effects on the recorded displcements. The interction of P 21

4 nd S wves t the Erth s surfce leds to differentil mplifiction etween the verticl nd horizontl components. Reding et l. (23) demonstrted method to remove this mplifiction effect from RF trces. The enefit is tht the susequent inversion procedure spends less time fitting the high mplitude of direct P rrivls nd most time fitting the lter prts of the RF tht provide informtion on the crust nd uppermost mntle structure. Comintion of Effects If we wnt to mke physicl reliztion of these vrious processes, the three clsses of propgtion effects ct on the source time function s set of cscde connected liner systems. In ddition to these effects, the instrument response I(t) needs to e dded to the model. The finl output of the lst system cretes the displcement of the Erth t the receiver u(t). The cscde representtion corresponds to convolutionl model, liner system hs superposition properties nd thus cn e implemented s the opertion of convolution. Although our system in generl is liner, some effects like reverertions operte recursively. If we represent the comintion of effects mthemticlly, then the three orthogonl components of the displcement, u V on the verticl, u R the rdil component on the gret circle etween source nd receiver nd u T the tngentil component in the horizontl plne cn e represented s u V (t) = s(t) N S P(t) N RV I(t) u R (t) = s(t) N S P(t) N RR I(t) (3.1) u T (t) = s(t) N S P(t) N RT I(t) where denotes the convolution opertor nd t is time vrile. This reltion is represented in the time domin. However, the multiplictive representtion in the frequency domin of the convolution opertion will e esier for the isoltion of the ner receiver effects. Then we cn rewrite the eq.(3.1) in frequency domin s u V (ω) = s(ω) N S P(ω) N RV I(ω) u R (ω) = s(ω) N S P(ω) N RR I(ω) (3.2) u T (ω) = s(ω) N S P(ω) N RT I(ω). 22

5 The terms common to the three components cn e eliminted y deconvolution, e.g., y tking the spectrl rtios of the rdil component with nother. For the cod of P wves, it is norml to deconvolve the rdil component with the verticl component to emphsize the converted S wves on the rdil component. This opertion is expected to led to the emergence of N RR term from other contriutions. To extrct N RR nd N RT from the ground displcement, vrious deconvolution methods cn e pplied. The motivtion ehind trying different methods is to find the procedure tht results in the optimum structurl response. At present, the deconvolution method in most common use is the spectrl division method which lso corresponds to Wiener Inverse Filter. Other deconvolution methods, homomorphic deconvolution, multitper estimtion nd wvevector pproch, my e preferle in some cses. In the following section, lterntive methods re outlined nd dt exmples from the tsml project re presented. An pprisl of the different methods is then given. 3.2 Method Development A rnge of different pproches for deconvolution hve een investigted. In ech cse I hve written my own code (Fortrn nd Mtl routines) to implement the lgorithms. Spectrl Division Deconvolution vi spectrl division is the generlized version of n optimum inverse filter (lso clled s Wiener Inverse Filter (Prokis & Mnolkis, 1988)). If we know the input nd the output for unknown system, we cn estimte the trnsfer function of the unknown system y using n itertive lest squres method. Let x(t) represent s the input, y(t) the ctul output, d(t) the desired output nd introduce e(t) s the difference etween the desired nd the ctul output. This schem tries to mtch the FIR (finite impulse response) sed system to n unknown system function y minimizing the difference etween desired output nd ctul output. If we denote the coefficients of the FIR sed model s k ; r xx s utocorreltion of input; nd r dx s cross-correltion 23

6 of desired output d(t) nd input x(t) then the finl form of the filter will e s in eq.(3.3). This reltion is known s the Wiener-Hopf eqution. r dx (l) = M k r xx (k l), l =, 1,..., M. (3.3) k= If we tke Fourier Trnsformtion of oth sides of eq.(3.3) then the reltion will e H(ω) = ψ dx(ω) ψ xx (ω). (3.4) In eq.(3.4), H(ω) is the trnsfer function of the unknown liner system, ψ dx (ω) is the cross-spectrl density of x(t), d(t) nd ψ xx (ω) is the density spectrum of x(t) which is lso equivlent to X(ω) 2. After trnsforming to the frequency domin, N RR /N RV cn e found y spectrl division of u R (ω) nd u T (ω) y u V (ω). nd N RT /N RV Becuse of the finite frequency nd, u V (t) cn e thought of s ndpssed delt function in time δ(t), then N RR N RT = u R(ω)u V (ω) u V (ω)u V (ω) (3.) = u T(ω)u V (ω) (3.6) u V (ω)u V (ω), where denotes the complex conjugtion, the reltions in eq.(3.) nd (3.6) re otined y using the reltion in eq.(3.4). In prctice, the denomintor of eq.(3.4) cn hve spectrl gps which cn e viewed s numericl vlues of the spectrum X(ω) 2 close to. The spectrl division in this cse will led to numericl unstility. To void numericlly unstle opertions, spectrl division cn e performed in two different wys. In the first cse, the holes of the denomintor re filled with predetermined constnt vlue (c. mx[u V (ω)u V (ω)]). This opertion is clled Wter-Level Deconvolution. Alterntively ising the denomintor with constnt vlue (c. mx[u V (ω)u V (ω)]) provides numericl stility t the expense of slight systemtic error in the estimte of the trnsfer function. Eq.(3.) cn e rewritten with Wter-Level Deconvolution pplied s N RR = u R(ω)u V (ω), (3.7) φ ss (ω) 24

7 where φ ss (ω) = mx [u V (ω).u V (ω), c. mx[u V (ω)u V (ω)]]. (3.8) In generl, the choice for the wter-level or ising prmeter is found y tril nd error, since the qulity of the receiver function signl is dependent on the individul records. The forementioned section covers the theoreticl sis for the P to S converted receiver function genertion. However, y interchnging the order of components on the deconvolution, one cn estimte the S to P converted phses. This pproch hs een successfully pplied on crustl nd mntle scle y Frr & Vinnik (2). Although the plin spectrl division of the displcements with the wterlevel correction is the most common technique for clculting the receiver functions, numer of different pproches hve lso een investigted to try to improve the estimtion of the RF. In figure 3.2, the effect of the wter-level nd ising prmeters re shown for the stcked rdil receiver functions of sttion TL6 from 4 individul estimtes. The rw spectrl division could not recover the ny of the conversion of the P to S in the rdil receiver function. With the incresing ising prmeter, the deterministic signls pper round sec, 1 sec nd fter 1 sec. Besides the increse in the mplitude of the receiver functions, ising leds to consistent results on the wveform shpes. In the wter-level deconvolution, the incresing vlues of the wter level results in n verging opertion on the wveform shpes which cuses loss of resolution in the wvetrin. This effect is most visile on the lter rrivls (fter 1 sec). Resolution loss on the wveforms cn e n importnt issue on the inversion step of the oserved receiver functions where the inversion lso relies on the shpe of the wveforms. Homomorphic Deconvolution Homomorphic deconvolution ws originlly developed s method for eliminting the echoes on voice records y Oppenheim (1969). In this method, the output signl y(t) is gin ssumed to e the convolution of the input x(t) nd some system function. The difference is tht this method works in cepstrl domin D. If the convolution form of input nd system function, which is the structurl response in our cse, is trnsformed to n ddition

8 WL=. WL=.1 WL=. WL=.1 WL=. WL=.1 Bis=1 8 Bis=1 7 Bis=1 6 Bis=1 Rw Figure 3.2: The effect of wter-level nd ising prmeters on the stcked rdil receiver function estimtes from sttion TL6. For ising the results re consistent with the incresing vlues ut mplitudes grow. In wter-level deconvolution, increse in wter-level prmeter results resolution loss on the estimtes. opertion then filter L cn e pplied to extrct the system function from output. For chieving this, the following opertions re pplied to the input signl x(t). Firstly, Fourier Trnsformtion of the signl is mde. Secondly, the logrithm function will e pplied to the sequence which is in the frequency domin. Finlly, the inverse Fourier Trnsformtion is pplied to the signl. The finl form is clled s the cepstrum. The reltion of the cepstrum x(t) nd the originl signl x(t) is shown in eq.(3.9). 26

9 x(t) = 1 [ ] log x(t)e iωt dt e iωt dω (3.9) 2π Since we know tht our output y(t) is the convolution of input x(t) nd some system function s(t), this reltion (eq. (3.9)) will correspond to ddition in the cepstrl domin. If suitle filter L is pplied then system function cn e extrcted from the output y(t). The convolutionl property is trnslted to dditivity in the cepstrl domin vi tking the logrithm of the signl. The term of cepstrl domin is the spectrum of the log of the spectrum of time wveform (Oppenheim & Schfer, 24). By finding the right filter, one cn eliminte the unwnted contriutions nd isolte ner-receiver effects. However, in prctice, this pproch my e prolemtic for the receiver function cse. The min ssumption is tht the input signl is minimum phse. For erthquke sources, this ssumption is not lwys stisfied. Homomorphic deconvolution is quite sensitive to the presence of noise. This processing schem ws pplied y Crosson & Dewerry (1994) nd Li & Náĕlek (1999) to receiver functions. Bostock (24) proposed shping filter to e pplied to seismic signls to stisfy the minimum phse criteri. In figure 3.3, the comprison etween receiver functions from wter-level nd homomorphic deconvolution is mde. Although the results from the homomorphic deconvolution is promising, the filtering process in the log spectrl domin needs extensive testing for etter results. Multitper Estimtion Since the spectrl division elongs to the clss of spectrl estimtion prolems, the use of pproprite dt windows or tpering is essentil. With the right choice of window, one cn improve the vrince, resolution nd lekge chrcteristics of the finl estimte. Briefly, these terms refer to the vriility of the estimtion for ech of the reliztion of the signl, resolving the right frequency ins nd the mount of unwnted contriutions from the different prt of the signl. Slepin tpers re clss of orthogonl windows which ensure tht the mximum spectrl concentrtion is chieved on nd limited signl. The 27

10 Time (sec) Time (sec) Figure 3.3: The comprison etween two different receiver function estimtion techniques. ) Plin spectrl division with wter-level correction. ) Homomorphic deconvolution vi filtering in log spectrl domin. In oth of the receiver functions, the Moho conversion efore sec is recovered ut Homomorphic deconvolution is much more sensitive to the choices mde with respect to ndwidth, nd other prmeters nd so is more difficult to implement s routine technique. estimtion of the shpe of these windows is n eigenvector prolem nd the corresponding eigenfunction forms the dt window. If we denote x(t) s time limited signl with length T, nd X(f) s ndlimited function with ndwidth W, then the concentrtion in time domin α 2 (t) cn e shown to e expressed s T/2 / α 2 (t) = x(t) 2 dt x(t) 2 dt. (3.1) T/2 Also the concentrtion prolem cn e lso expressed in the frequency domin s n integrl eqution (eq.(3.11)) W W K(f, f ; T)X w (f )df = α(t) 2 X w (f) f W, (3.11) 28

11 where K(f, f ; T) = sin [ πt(f f ) ] π(f f ). (3.12) The prolem is now finding such kernels (windows) K(f, f ; T) tht mximize the concentrtion α 2 (t). The solution of this integrl eqution is n eigenvector prolem. The kth eigenfunction of the kernel ψ with its ssocited lrgest kth eigenvlue λ will form the solution. After mking the sustitutions (x f/w, y f /W, c πwt), the integrl eqution ecomes 1 1 sin [c(x y)] ψ(y; c)dy = λ(c)ψ(x; c), x 1. (3.13) π(x y) The solution set of the eigenfunctions re clled discrete prolte spheroidl sequences or Slepin sequences. This set ws introduced y Slepin (1978). Ech of the possile tpers corresponds to mximum eigenvlue. The multitper method uses n multiple window pproch to construct good lnce etween the vrince nd the is properties of the spectrum y using Slepin Sequences. Eigenspectrums re clculted vi tpering with different spheroidl sequences. The kth eigenspectrum is shown in eq.(3.14) where the h t,k is kth dt tper for input x t N k (f) = t 2 h t,k x t e i2πft t. (3.14) Ŝ mt t=1 Afterwrds, the eigenspectrums re verged to form spectrl estimte with low vrince. The determintion of the pproprite order of the tpers plys mjor role in the chrcteristics of the finl spectrum. For low orders, the is will e smll nd the vrince level will e low for higher orders. The finl spectr is given y eq.(3.1) Ŝ mt (f) = 1 K K 1 k= S mt k (f). (3.1) The detils of the lgorithm re presented in Thomson (1982) nd Percivl & Wlden (1993). The time-ndwidth product determines frequency resolution of the estimtes. Spectrl vrition over smll intervls in the frequency domin corresponds with widely spced fetures in the time domin (Prk & Levin, 29

12 2). On the other hnd lrger K vlues led to lower vrince in the cost of spectrl lekge. In figure 3.4, the estimtes of rdil receiver functions from the multitper method with Slepin tpers re shown with set of different time-ndwidth product vlues (NW) nd different numer of Slepin tpers (K). For comprison n estimte from the plin wter-level deconvolution (wl) ws included. At first glnce, the difference in the estimtes for lower nd higher time-ndwidth product is ovious, e.g., K=2, NW=2. nd K=2, NW=3.. The lrger time-ndwidth product (NW=3.) resolved the lter rrivls ppered fter 2 sec due to the property tht spectrum estimtes with higher vlues of time-ndwidth product will hve more resolution. The multitper estimtes hve some fundmentl differences etween the estimte from the wl on the wveform shpe. Although the mplitudes of wl estimte is higher thn the multitper, the generl signl to noise rtio is lower. This result hs significnce on the inversion step where the nonliner solver tries to fit full wveform for finding solution. In ddition to this, the signls etween the deterministic rrivl due to the noise hve een suppressed in the multitper estimtes. The multitper pproch with the Slepin tpers ws pplied to receiver functions y Prk & Levin (2) with demonstrted improvement in the results compred to simpler methods. However, the implementtion of the Slepin tpers is not strightforwrd. An equivlent nd etter clss of windows ws developed for estimting plsm fluctutions y Riedel & Sidorenko (199). These tpers use the sine functions, therefore they re esier to implement nd cn e lso used in the multitper context. Also recently Helffrich (26) proposed n extended schem for multitper methods pplied to receiver functions. Wvevector Approch The oserved displcement field on the surfce is result of interction of the wvefield nd the free surfce s shown elow. If the Snell s Lw is defined for incoming plne P nd S wves, then p = sin i α = sin j β, (3.16) 3

13 Wter Level K=3,NW=3. K=3,NW=3. K=3,NW=2. K=3,NW=2. K=2,NW=3. K=2,NW=3. K=2,NW=2. K=2,NW= Figure 3.4: Rdil receiver functions from multitper method for set of different time-ndwidth product vlues (NW) nd different numer of Slepin tpers (K) compred with plin wter-level deconvolution of.1. Ech of the trces hs een normlized to unity to emphsize the chnges in the signl. 31

14 where i, j nd α, β re the ngle of incidence nd velocity for P nd S wves nd p is the corresponding ry prmeter. In the cse of n impinging P wve with n mplitude of A, the displcement field in the corresponding components Z u, verticl nd R u, horizontl will e Z u = A cosi, R u = A sin i, (3.17) where i is the ngle of incidence. This reltion does not include ny free surfce effect. The influence of free surfce reflection cn e introduced y inserting mplifiction opertors C 1,2 in eq.(3.17) so tht the eq.(3.17) with the mplifiction ecomes Z = A cosi C 1, R = A sin i C 2. (3.18) After the free surfce interction, the effective incidence ngle chnges, this is clled s the pprent ngle of incidence i f. This cn e seen from the rtio of the Z nd R components s where surfce mplifiction fctor F is F = C 2 C 1 = tn i F = R Z = R u C 2 Z u C 1 = F tni, (3.19) 2 cosicos j 1 2β 2 sin 2 i/α 2 = 2 cosicos j 1 2 sin 2 j. (3.2) The free surfce effect cn e generlized for ll three rotted components Z, R nd T in the direction of source-receiver zimuth. By following the convention of Kennett (1991), we cn write the isolted P, S V nd S H wvefields from the displcement which ws recorded on the components s P V PZ V PR Z = V SZ V SR R S V S H V HT where free surfce correltion coefficients re V PZ = (1 2β 2 p2 )/(2α q α ) (3.21) V SR = (1 2β 2 p2 )/(2β q β ) (3.22) V PR = pβ 2 /α (3.23) V SZ = pβ (3.24) V HT =. (3.) T 32

15 nd verticl slownesses re q α = α 2 p 2, q β = β 2 p 2. (3.26) This correction is crried nd y empiriclly chosen pproprite velocities. Wvevector form of the receiver function hs een used y Reding et l. (23) for improving the inversion methodology. Also Bostock (1998) used the trnsformtion for the suppression of multiples nd the wvefield decomposition. Unlike the coordinte rottion with chosen ngle such s LQT trnsformtion (Vinnik, 1977), this method ssigns the correct energy on the components y trnsformtion with the velocity informtion. This is illustrted in n exmple using dt from sttion TL6. The wvevector form of the rdil receiver functions were computed with P wve velocity of.8 km/sec nd S wve velocity of 3.4 km/sec. The ry prmeter ws computed vi ry trcing with the model AK13 (Kennett et l., 199) for the corresponding epicentrl distnce of the erthquke. In figure 3., the S-wvevector receiver functions re shown with the conventionl rdil receiver functions. In the wvevector form, the min pek due to the P rrivl is suppressed; however, the P to S wve conversion t sec is preserved including the lter rrivls. With the wvevector form of the receiver functions, the inversion of the wveforms will concentrte more on the region of interest (Moho conversion rrivl nd lter rrivls) thn the conventionl form of the rdil receiver functions, where the min P phse hs dominnt signture on the estimted signl. 33

16 Stck 34 TL6. For oth of the pnels, the ottom trce ws produced from stcking ll of the shown receiver functions. Figure 3.: ) Rdil receiver functions (lck) from TL6. ) S-wvevector form of the rdil receiver functions (lue) from Stck 3 3 Chpter 3. Receiver Function Anlysis

17 3.2.1 Apprisl of Different Methods The methods given in the previous sections cn e compred together with their dvntges nd weknesses in prticulr situtions. Plin spectrl division with wter-level correction is the simplest nd lest rigorous method of the computtion of receiver functions. Despite its simplicity, it hs some mjor drwcks. Unless proper windowing is pplied in frequency domin, the control on the vrince, lekge nd is will e minimum. These prmeters cn e quite importnt, if the signl to noise is low. The closely relted technique ising cn produce etter estimtes with the right prmeter choice. In frequency domin, the ising will e equivlent to the pre-whitening of the spectrum. In some cses, this is required to roden the spectrum. Although the ppliction is quite different from the genertion of receiver functions, this method ws successfully pplied on rodening the spectrum of mient noise wvefield in lter prt of this study. Homomorphic deconvolution is powerful deconvolution technique, first pplied on eliminting the echoes on the voice records y Oppenheim (1969). However, the properties of homomorphic systems mke it difficult to fulfill with teleseismic signls. The minimum phse condition is often not stisfied y the seismic records. Bostock (24) ssumed the incoming P wve hs minimum phse chrcter nd then pplied shping filter to normlize the P wve nd therefore emphsize the direct rrivls. As result, multichnnel type of deconvolution on the source normlized P wve signls in log spectrl domin gve etter Green s function estimtes. Another wy to exploit the homomorphic filtering in the context of receiver function, is to pply filter in log spectrl domin to suppress the unwnted prt. However, to pply this successfully, precise knowledge of the spectrum is needed, which is commonly not known. Multitper estimtion is one of the most significnt techniques pplied to spectrl estimtion prolems. The windowing of the dt efore the spectrl estimtion is common prctice to suppress some of the unwnted effects on the finl estimtes, e.g., reducing spectrl lekge, controlling vrince etc. In multitper estimtor cse, multiple prmeters cn e controlled t the sme time to hve etter result. The power of multitper technique comes from the specilized windows pplied on the signl, which offer mximum 3

18 spectrl concentrtion for ndlimited signl, e.g., seismic signls. Then with the right type of verging, the vrince chrcteristics of the estimtes cn e controlled. The plin spectrl division with wter-level or ising correction cn not offer these controls on the estimtes. It cn e concluded tht the multitper technique is corrected form of the plin spectrl division. There re two difficulties ssocited with multitper estimtion. In the clssicl form, the chosen windows re Discrete Prolte Slepin tpers, which cn e computtionlly intensive to clculte. However, sinusoidl type of tpers with similr properties of Slepin tpers were introduced y Riedel & Sidorenko (199) with less computtionl complexity. The second potentil difficulty with the multitper estimtion for the receiver function genertion is out the choice of design prmeters. The incresed frequency resolution cn result in widely spced fetures in time domin, therefore loss of resolution in this domin (Prk & Levin, 2). As result, the time-ndwidth product (NW) hs to e tested extensively efore processing igger dtsets. The lst technique which cn improve the estimtes, is the wvevector pproch pplied y Reding et l. (23) to receiver functions for eliminting the free surfce response. Unlike the forementioned techniques, this method does not rely on the signl processing schemes. This pproch gins considerle importnce on the type of inversion where the full wveform is modelled. The removed free surfce response on the records emphsizes the lter rrivls. The mjor difficulty of this technique is the requirement of good velocity knowledge of P nd S wves to successfully remove the free response. This priori informtion my not e ville in ll cses. The wvevector method works est when the surfce velocities re quite high. It cn e dpted to suppress ner surfce sediment multiples, ut this requires very detiled knowledge of the ner surfce conditions nd is rther tricky to use. In this work, multitper estimtor ws used with the following prmeters of time-ndwidth product: NW=2. nd tper order: K=3 in the receiver function genertion oth for the oserved nd synthetic dt. The computer progrms used in the genertion of the exmples given for ech technique nd for the receiver functions of the whole tsml experiment were written s prt of this work. The wvevector pproch hs een used to check the identifiction of the Moho rrivl, ut not directly in the inversion. 36

19 3.3 Geophysicl Inversion Before going into the detils of the geophysicl inversion used for the extrction of ner-receiver velocity informtion from receiver function, we need to ddress some generl issues such s the definitions of the forwrd nd inverse prolems. The forwrd prolem cn e defined s clculting the dt from given physicl model. This cn e visulized s clculting the position vector h of free-flling oject for some time intervl t y using the sic reltion of h = 1/2gt 2 where the resistnce of the ir is neglected nd g is the ccelertion of grvity. This is simple exmple of forwrd prolem. On the other hnd if we hd only mesured the position vector vlues h of this free-fll motion, how cn we estimte the time vlues t which corresponds to our oserved vlues of position h, with chosen model. This estimtion prolem nd its solution set s pprisl correspond to the inverse prolem. The forwrd prolem cn e defined in 2 different wys. First, it cn e represented s nonliner prolem s in eq. (3.27), where d is the clculted dt, G(m) is the functionl opertor, nd m is the model prmeters d = G(m). (3.27) The second pproch is to think of the prolem directly in liner sense in which cse it cn e written s in eq. (3.28) with discrete prmeteriztion. If the dt corresponding to reference model m is d, then locl lineristion gives d i d G ij (m j m i ) with G(m) = d i / m j, where d i = j G ij m j. (3.28) In ll cses, misfit criteri should e defined for fitting the dt to the model. Commonly minimiztion of the difference etween the oserved nd clculted dt is chosen nd shown in eq. (3.29) in lest squres sense, φ(d,m) = (d os Gm) T (d os Gm), (3.29) 37

20 where the d os is the oserved dt nd Gm product represents the clculted dt. If we write the liner forwrd prolem in mtrix form, Gm = d then, solution cn e otined using the lest squres solution m est = (G T G) 1 G T d. (3.3) In the nonliner cse, the prolem cn not e directly stted s d = Gm. The solution strtegies will vry ccording to the scle of the nonlinerity. It cn e linerized nd solved s ove, or y using some dvnced lgorithms such s direct serch procedures. Most geophysicl prolems exhiit nonlinerity. With incresing computtionl power, it is desirle to solve nonliner inverse prolems with etter estimtion techniques. The liner geophysicl inverse theory is widely given in Menke (1984), Trntol (1987), Prker (1994), nd Snieder & Trmpert (1999). Neigourhood Algorithm The stcked receiver function dt hs to e mpped from time section to depth in order to model the velocity structure underneth sttion. Generlized inversion plys mjor role on this trnsformtion. However, there is strong nonliner dependency of the receiver function signl on the sher wve velocity. This dependency hs profound effect on the inversion schem to e crried out. Ammon et l. (199) showed the effects of the lineriztion nd the nonuniqueness of the receiver function inversion. Shiutni et l. (1996) pplied nonliner genetic lgorithm type of inversion to dt from n erlier Austrlin deployment nd ws le to recover the velocity structure for the crust. An improved lgorithm ws proposed y Smridge (1999,) with fully nonliner, derivtive free direct serch lgorithm (Neighourhood Algorithm; herefter clled NA) ssisted y the geometricl constructs of Voronoi cells. This pproch is conceptully simpler thn ny linerized schemes (these methods re dependnt on the clcultion of the prtil derivtives). NA is used for inverting the oserved receiver function in this study. The evolution of the Voronoi cells in n NA inversion exmple is given in figure 3.6 for different numers of points in 2-D spce. The summry steps which re tken y the NA re s follows. 38

21 c d Figure 3.6: Regions of Voronoi cells for different smpling points. ) 1. ) 1. c) 1. d) Contours of the test ojective function (Smridge, 1999). 1. Genertion of model smples n s uniformly in prmeter spce with ssocited Voronoi cells. 2. Clcultion of the misfit functions from the generted models nd rnk the lowest misfit models n r. 3. Cretion of new models n s inside the Voronoi cells of lowest misfit models n r y uniform rndom wlk. 4. Reiterte from step 2. The style of the crustl model for Austrli which is used in the inversion stge hs een inherited from the work of Shiutni et l. (1996). The generl lyout of the model is sediment lyer on the top, sement lyer, upper crust, middle crust, lower crust nd uppermost mntle. Ech lyer consists of S wve velocities V s for the upper nd lower prts, thickness h nd V p /V s rtio. As result, 24 prmeters re clculted during the inversion of the dt. Another importnt feture of the NA lgorithm is tht it cretes n ensemle of models rther thn single est model. This cretes the opportunity to ssess the set of serched nd compre well-fitting models. 39

22 3.4 Dt In the recent pst, numerous rodnd seismic experiments hve tken plce cross the Austrlin continent. The tsml experiment rn etween 23 to with 2 sttions with the im of reveling the structurl oundry of Precmrin nd Phnerozoic locks in centrl nd estern Austrli. To chrcterize the Gwler Crton nd its surroundings in south Austrli, 4 dditionl rodnd sttions were deployed in the similr time frme of tsml ut rn for shorter time thn the tsml experiment. The collected dt from these deployments were used with the receiver function method to chrcterize the Moho depth nd its nture. 1 o S TL1 TL2 2 o S TL6 TL7 TL3 TL4 TL TL9 TL12 TL8 TL1 TL11 3 o S TL13 TL14 TL1 GA6GATL17 TL16 GA7 TL18 TL19 GA8 TL2 4 o S 11 o E 12 o E 13 o E 14 o E 1 o E 16 o E Figure 3.7: The loction of three component rodnd sttions of the tsml experiment (TL) nd its Gwler Crton extension (GA) shown with white tringles. Seismic dt from epicentrl distnces of etween 3 nd 9 were used to void tripliction in the mntle (s discussed in n erlier section) nd to ensure tht the rriving seismic wves will e steeply incident nd hence, the conversion rtio of the seismic phse will e high enough. The mgnitude intervl for events ws chosen etween. nd 6. which is sufficient for high signl to noise rtio nd voids the complicted nd elongted wveforms of higher mgnitude events. 4

23 For mpping the energy to the components, the horizontl components were rotted geometriclly to rdil nd trnsverse prts y using the connecting zimuth plne of the source nd the receiver. Ech of the rrivls ws picked y using the theoreticl rrivl time generted y the model AK13 (Kennett et l., 199) with time window of 6 seconds. Multitper spectrl estimtion with Slepin tpers ws used on the oserved receiver function genertion. The wter-level for the deconvolution which is shown t eq.(3.8) ws set s.1 fter severl tests. By visul inspection, the generted receiver functions were clssified ccording to the wveform shpe. It should e stted tht the receiver function genertion is quite sensitive to the noise levels nd other rtifcts on the dt. Roughly, for ech of the sttions 1% of the records proved stisfctory due to forementioned limittions. The receiver function wveforms re clssified ccording to their ckzimuths. In tle 3.1, the detils of the generted receiver functions for ech of the sttion re given. Due to the nonuniform coverge of seismicity round the Austrlin continent, some of the ckzimuthl rnges offer higher numer of events suitle for receiver function nlysis, e.g., therefore used frequently. Also y compring the rdil receiver functions of the other ville ckzimuthl rnges, the geometry of the structure ws ssessed. Although the plnr structure of the lyering is the min ssumption, numericl studies show tht in the presence of dipping lyers or nisotropy, energy will e vrile on the rdil nd trnsverse receiver functions which elong to different ckzimuths (Cssidy, 1992). These type sttions were mrked with 3-D. However for some of the sttions, e.g., TL1, TL11, under the strong influence of sedimentry structures, different ckzimuthl rnges hve similr record sections. In relity, this my not reflect the presence of 1-D crustl structure, since Moho conversion is msked in these receiver functions. In figure 3.8, for two different sttions; TL4 nd TL11, the rdil receiver functions re presented which elong to two different ckzimuthl rnges. In figure 3.8, the Moho trnsition is cler t sec. However, figure 3.8 shows the cler effect of the surfce sediments on the receiver functions, where Moho conversion is msked with reverertions. 41

24 Sttion Good RF Events Structure Bckzimuth Rnge TL D TL2 8 1-D TL D TL4 4 1-D 3 TL 1-D TL6 6 1-D 8 12 TL D TL D TL D 8 12 TL D TL D TL D TL D TL D TL1 3 3-D TL D TL D TL D 2 1 TL D TL D GA 18 3-D GA6 2 1-D GA D GA8 7 3-D Tle 3.1: The detils of the rdil receiver functions used in this study. The numer of receiver functions, estimted structure geometry nd ckzimuth rnge used in the finl stck re given. 42

25 TL4 contins the cler Moho conversion t sec. TL11 shows the influence of the thick surfce sedimentry lyer on the receiver functions. Figure 3.8: Rdil receiver functions for ) TL4 with ckzimuths etween 3, nd ) TL11 with ckzimuths etween Chpter 3. Receiver Function Anlysis

26 3. Results of Inversion The oserved rdil receiver functions were inverted with the NA for vrious different prmeter rnges to exploit the dependence of the inversion results to the strting choice of the model prmeters. Results were then merged nd weighted inversely ccording to the misfit vlues. This pproch ims to show the vrince of the results for ech inversion run. Since the scope of this study is to delinete the crustl structure of the region, Moho depth estimtes were mde for the ville sttions. The estimtes were then clssified into different clsses ccording to the shrpness of the discontinuity. Wveforms with the ringing shpe often indicte the presence of the sedimentry lyers in the shllow crust. With the decresing velocity, impinging wves ecome su-verticl nd the conversion etween the lyers ecome less effective. This leds to low mplitude, delyed signls nd corrupted Moho conversion signture on the wveforms. This type of receiver functions hve een oserved on severl sttions. Since it is not possile to constrin the Moho depth from these receiver functions, interprettions were not pursued except mrking them s the sedimentry fetures. The event distriution, merged models for ll of the inversion runs nd the wveform fits re given for ech of the sttion t figure The estimted Moho depths for ech of the sttions re given in tle 3.2 with comment. Results re clssified s shrp, intermedite nd rod. For some of the sttions, Moho estimtes were not mde due to the sedimentry lyer presence. 44

27 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.9: ) The distriution of the erthqukes for different distnce rnges from TL1. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) receiver functions. 4

28 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.1: ) The distriution of the erthqukes for different distnce rnges from TL2. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 46

29 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.11: ) The distriution of the erthqukes for different distnce rnges from TL3. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 47

30 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.12: ) The distriution of the erthqukes for different distnce rnges from TL4. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 48

31 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.13: ) The distriution of the erthqukes for different distnce rnges from TL. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 49

32 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.14: ) The distriution of the erthqukes for different distnce rnges from TL6. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions.

33 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.1: ) The distriution of the erthqukes for different distnce rnges from TL7. ) Best 1 models from the comintion of ll inversions. c) The oserved (lck) nd inverted (lue-dshed) rdil receiver functions. 1

34 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c. Amplitude Figure 3.16: ) The distriution of the erthqukes for different distnce rnges from TL8. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 2

35 Misfit=[ ] Depth (km) 2 3 TL c Amplitude V s (km/s) Figure 3.17: ) The distriution of the erthqukes for different distnce rnges from TL9. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 3

36 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.18: ) The distriution of the erthqukes for different distnce rnges from TL1. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 4

37 Misfit=[ ] Depth (km) 2 3 TL c Amplitude V s (km/s) Figure 3.19: ) The distriution of the erthqukes for different distnce rnges from TL11. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions.

38 Misfit=[ ] Depth (km) 2 3 TL c Amplitude V s (km/s) Figure 3.2: ) The distriution of the erthqukes for different distnce rnges from TL12. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 6

39 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.21: ) The distriution of the erthqukes for different distnce rnges from TL13. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 7

40 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c.4 Amplitude Figure 3.22: ) The distriution of the erthqukes for different distnce rnges from TL14. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 8

41 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.23: ) The distriution of the erthqukes for different distnce rnges from TL1. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 9

42 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.24: ) The distriution of the erthqukes for different distnce rnges from TL16. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 6

43 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c Amplitude Figure 3.: ) The distriution of the erthqukes for different distnce rnges from TL17. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 61

44 Misfit=[ ] Depth (km) 2 3 TL c Amplitude V s (km/s) Figure 3.26: ) The distriution of the erthqukes for different distnce rnges from TL18. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 62

45 Misfit=[ ] Depth (km) 2 3 TL c Amplitude V s (km/s) Figure 3.27: ) The distriution of the erthqukes for different distnce rnges from TL19. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 63

46 Misfit=[ ] Depth (km) 2 3 TL V s (km/s) c 1.1 Amplitude Figure 3.28: ) The distriution of the erthqukes for different distnce rnges from TL2. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 64

47 Misfit=[ ] Depth (km) 2 3 GA V s (km/s) c Amplitude Figure 3.29: ) The distriution of the erthqukes for different distnce rnges from GA. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 6

48 Misfit=[ ] Depth (km) 2 3 GA V s (km/s) c Amplitude Figure 3.3: ) The distriution of the erthqukes for different distnce rnges from GA6. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 66

49 Misfit=[ ] Depth (km) 2 3 GA V s (km/s) c Amplitude Figure 3.31: ) The distriution of the erthqukes for different distnce rnges from GA7. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 67

50 Misfit=[ ] Depth (km) 2 3 GA V s (km/s) c Amplitude Figure 3.32: ) The distriution of the erthqukes for different distnce rnges from GA8. ) Best 1 models nd verge model (red) from the comintion of ll inversions. c) The oserved (lck) nd inverted (luedshed) rdil receiver functions. 68

51 Sttion Moho Depth (km) Clssifiction Prolem TL1 X Sediments - 27 km? TL2 39 Intermedite TL3 41 Brod TL4 31 Intermedite TL 37 Brod TL6 42 Shrp TL7 38 Shrp TL8 33 Brod TL9 X Sediments - 4 km?? TL1 34 Intermedite TL11 X Sediments - 3 km?? TL12 32 Shrp TL13 X Poor Fit -3 km? TL14 X Poor Fit -3 km? TL1 34 Shrp TL16 29 Intermedite TL17 X Sediments - 3-D? TL18 34 Brod TL19 X Limited Fit-36 km? TL2 X Poor Fit GA 37 Intermedite GA6 X-4 km? Poor Fit GA7 33 Brod GA8 39 Brod Tle 3.2: The estimted Moho depths for TL nd GA sttions. X stnds for the poorly estimted depths due to the sedimentry zones nd receiver function qulity prolems. Clssifiction column comments on the nture of the Moho nomly on the models. Prolem column shows the ssocited prolem with the prticulr sttion with poorly estimted Moho depths. 69

52 3.6 Crustl Depth Results In this section, new crustl depth results from the receiver function nlysis of tsml project sttions re presented in the context of the geologicl setting of the sttions. Crustl depth determintions from est Austrli from the previous study y Clitheroe et l. (2), with sprser sttion distriution, re lso included. The current study improves considerly on the coverge ville to previous workers nd delinetes the geologicl trnsition etween est nd centrl Austrli. The crustl thicknesses derived in this study, nd y Clitheroe et l. (2) for the region of the interest, re shown on top of the surfce geology mp of Austrlin continent t figure The crustl thickness vries significntly from centrl Austrli to estern Austrli in the vicinity of the Tsmn Line (shown with gry line). In the northern prt of centrl Austrli, the crustl thicknesses re 38, 42 nd 41 km eneth the region corresponding to the est Arunt nd north Mt. Is Blocks. At the southest edge of the Mt. Is Block, crustl depths, including result from Clitheroe et l. (2), re shllower (t 3 nd 31 km depth). Beneth the centrl prt of the Thomson Orogen, crustl depths re rther shllow, nd quite consistent (32, 32, 33, 3, 34 nd 36 km) with deeper vlues eing determined in the estern Thomson Orogen (37, 39, 38 nd 44 km). In sttions locted within the New Englnd Orogen, crustl depth is firly consistent (37, 36, 36 nd 39 km). The results from the Gwler Crton leg of the experiment show Moho depths of 39 nd 4 km, with shllower vlues eing otined from sttions covering the Adelide Block (33, 37, 34, 36, nd 34 km depth). There is stedy increse eginning from the Adelide Block (Proterozoic Sediment) to the Gwler Crton. Clitheroe et l. (2) noted tht the Gwler Crton hs similr Moho nture with the Kimerley Crton in the north. Although geologiclly older thn the Gwler Crton, Reding et l. (23) found similr Moho depths in verge 4 km under Yilgrn Crton of Western Austrli. In the Delmrin Orogen, crustl depth vlue of 3 km ws otined while results from the Lchln re generlly deeper (38, 44 nd 41 km) ut re quite vrile. The new deployment hs filled significnt gps in the knowledge of the crustl depth of the region of est Austrli. In receiver function nlysis, it is often tht the delyed pek nd the 7

53 12 o S 18 o S 24 o S 3 o S 36 o S 36 X X X X X X X X o S 117 o E 126 o E 13 o E 144 o E 13 o E Figure 3.33: The crustl thicknesses derived from receiver function inversions. The red tringles show the results of this study nd lck tringles show the results from Clitheroe et l. (2). Sttions where crustl thickness could not e determined re mrked X. The gry dshed line is Tsmn Line which mrks the trnsition from the Precmrin west nd centrl Austrli to the Phnerozoic est. ringing wveform indicte the presence of thick low velocity lyers. The Moho signture is hevily msked in this sitution therefore n inversion cn not e pursued for constrining the crustl thickness. However, signls of this kind re good to chrcterize the vicinity of the sttions with sedimentry fetures. In figure 3.33, these sttions were mrked with X. It should e noted tht loction of the sttions lso mrks the trnsition etween tectonic elements which mtches the results of the receiver function study. The Moho depths estimted from receiver functions exhiit trend from the centrl Austrli to estern Austrli, the imges from group wvespeed tomogrphy (given in Chpter 4) for the midcrust did not revel uniform 71