• 沒有找到結果。

Multiscale, finite-frequency P and S tomography of the upper mantle in the southwestern Fennoscandian Shield

N/A
N/A
Protected

Academic year: 2021

Share "Multiscale, finite-frequency P and S tomography of the upper mantle in the southwestern Fennoscandian Shield"

Copied!
29
0
0

加載中.... (立即查看全文)

全文

(1)

Geophysical Journal International

Geophys. J. Int. (2015)202, 190–218 doi: 10.1093/gji/ggv130

GJI Seismology

Multiscale, finite-frequency

P and S tomography of the upper mantle

in the southwestern Fennoscandian Shield

Marianne L. Kolstrup,

1

Shu-Huei Hung

2

and Valerie Maupin

1 1Department of Geosciences, University of Oslo, N-0371 Oslo, Norway. E-mail:m.l.kolstrup@geo.uio.no 2Department of Geosciences, National Taiwan University, Taipei, Taiwan

Accepted 2015 March 16. Received 2015 March 12; in original form 2014 September 22

S U M M A R Y

We image the P- and S-wave structure of the upper mantle in southwestern Scandinavia using a wavelet-based, multiscale parametrization and finite-frequency theory to model wave propagation. Relative traveltime residuals of direct P and S waves are measured in a high- and low-frequency band and are corrected for crustal structure using a detailed model for the study area. A range of resolution tests are used to find optimal damping values not only for variations in VPand VSseparately, but also for perturbations in their ratio VP/VS. The tests show that features down to a size of 100 (150) km can be well resolved in the P (S) tomography. To ease comparison with previous studies we also perform ray-theoretical multiscale tomographies, and to test the degree of vertical smearing we evaluate different parametrizations in the vertical direction (wavelet-based multiscale and convolutional quelling). Our finite-frequency, multiscale images of variations in VP and VS confirm the existence of low velocities below southern Norway and Denmark and high velocities beneath the shield proper in Sweden, as seen in previous studies, but add more details to this simplified picture. The low velocities below southern Norway and Denmark are confined to a channel-like structure at about 100–200 km depth, and the lateral transition from low to high velocities follows zones of Carboniferous-Permian extension and magmatism very closely. A deeper low-velocity anomaly below central southern Norway emerges from the channel at 150 km depth and extends to a depth of 350 km. In the Swedish area we infer high-velocity anomalies in VP and VS, and negative anomalies in VP/VSthat indicate a strongly depleted mantle. We propose that the episodic erosion and convective removal of an originally thick mantle lithosphere below southern Norway to its current thickness of about 100 km could have been a trigger for episodic uplift in the Mesozoic and Cenozoic.

Key words: Body waves; Seismic tomography; Intra-plate processes; Cratons; Dynamics of

lithosphere and mantle.

1 I N T R O D U C T I O N

Recent geophysical studies in the western Fennoscandian Shield have revealed a region of anomalously low seismic velocities in the uppermost mantle below southern Norway compared to the other-wise high velocities of the Fennoscandian Shield mantle (Weidle & Maupin2008; Maupin2011; Medhus et al.2012; Wawerzinek

et al.2013). The general picture of a low-velocity anomaly and a transition to the Fennoscandian Shield is present in all studies, but different seismic models show differences in amplitude and location of the anomaly (Medhus et al.2012; Wawerzinek et al.2013) that have not been explained.

The low-velocity anomaly grossly coincides with the high to-pography in southern Norway, which has an unknown and highly debated origin (e.g. Lidmar-Bergstrom & Bonow2009; Nielsen

et al.2009a,b; Gabrielsen et al.2010). It is in particular important

to ascertain whether the low-velocity upper mantle contributes to the isostatic compensation of the high topography (e.g. Pascal & Olesen2009; Ebbing et al.2012; Medhus et al.2012; Gradmann

et al. 2013). A robust estimate of the magnitude and location of the low-velocity anomaly and the transition to the Fennoscandian Shield proper is therefore crucial.

The Fennoscandian Shield contains an Archean core (3.7–2.6 Ga) in the northeast and progressively younger domains towards the southwest (Ga´al & Gorbatschev1987) that accreted to the Archean core in the Palaeoproterozoic (e.g. Ga´al & Gorbatschev 1987; Nironen 1997; H¨ogdahl et al. 2004). The study region (Fig. 1) covers most of the youngest part of the Fennoscandian Shield in the southwest (Ga´al & Gorbatschev1987), which is mainly the prod-uct of Mesoproterozoic continental growth (Ga´al & Gorbatschev

1987; Bingen et al.2005) and late Mesoproterozoic deformation in the Sveconorwegian Orogeny (1.25–0.90 Ga, Ga´al & Gorbatschev

190 CThe Authors 2015. Published by Oxford University Press on behalf of The Royal Astronomical Society.

(2)

Multiscale P and S tomography 191

Figure 1. Station network and tectonic overview of the study region. Left: Seismological stations with topography and a regional map in the lower left corner. Numbers xx are abbreviations of the MAGNUS station names NWGxx. Right: Major tectonic features with topography and seismic events from 1980 to

2011 with M≥ 2.0 (FENCAT2011). CDF, Caledonian front; MZ, Mylonite Zone; OG, Oslo Graben; SG, Skagerrak Graben; SN, Sveconorwegian; SNF,

Sveconorwegian front; STZ, Sorgenfrei-Tornquist Zone; TTZ, Teisseyre-Tornquist Zone; WGR, Western Gneiss Region.

1987). The southern part of the study area was created by the dock-ing of the microcontinent Avalonia (440 Ma), and the later Caledo-nian Orogeny (420–400 Ma) (Roberts2003; Cocks & Torsvik2006) that also heavily deformed the northwestern part. The last major tec-tonic events in the study region were the late Carboniferous-Permian rifting with extension and magmatism in the Oslo and Skagerrak Grabens and along the Sorgenfrei-Tornquist Zone (305–220 Ma, Neumann et al.2004; Larsen et al.2008) and formation of the Dan-ish Basin (Sørensen1986; Frederiksen et al.2001) before the North Atlantic breakup∼55 Ma.

Regional tomographies based on Rayleigh wave dispersion or full-waveform inversion covering our study area (Weidle & Maupin

2008; Rickers et al.2013) infer VSVand VSHvelocities 6 per cent

lower than in AK135 (Kennett et al. 1995) below southern Nor-way and high velocities below neighbouring Sweden. Local studies drawing on surface waves (Maupin2011; K¨ohler et al.2012) infer

VSVvelocities 2–3 per cent lower than AK135 (Kennett et al.1995).

New tomographies of Europe using full waveform inversion (Zhu

et al.2012,2013; Fichtner et al.2013) invert jointly for V, VSHand

VSVand cover our study area, but do not provide enough details on

a local scale to accurately image the lateral variations in the western Fennoscandian lithosphere.

The regional P- and S-wave tomographies in the area (Medhus

et al.2012; Wawerzinek et al.2013) have better resolution than the surface waves studies but generally lower amplitudes. The relative

VS anomalies in the ray-based tomography of Wawerzinek et al.

(2013) are up to±1.5 per cent, an amplitude similar to the one found for VP velocities in Medhus et al. (2012). It is not clear

whether this similarity in magnitude stems from an actual similarity

in nature, or from a higher degree of smoothing in the S-wave tomography.

The preservation of amplitudes of velocity anomalies is critical when it comes to the tectonothermal interpretation of tomogra-phies. As seismic velocities are more sensitive to temperature than to composition (e.g. Goes et al.2000; Cammarano et al.2003), velocity anomalies are usually interpreted as temperature anoma-lies. Below southern Norway the velocity anomaly measured with surface waves has been interpreted as a temperature anomaly of about 200◦C (Maupin2011; Maupin et al.2013), but integrated petrological modelling suggest that a difference in composition is also needed to explain the transition from low to high seismic ve-locities (Gradmann et al.2013). The VP/VSratio is often used as a

diagnostic of compositional anomalies (e.g. Lee2003; Artemieva

2007) but we cannot access this ratio from tomographies of VPand

VSderived using different parametrizations and regularizations, as

tomographic images are non-unique and strongly dependent on the choice of regularization (Trampert & Snieder1996; Chiao & Liang

2003; Chiao et al.2010).

We wish to close the gap between local relative traveltime tomog-raphy and regional full-waveform inversion and present in this study tomographic models of VP and VSHthat can be compared

quanti-tatively. The models are derived using a wavelet-based multiscale parametrization combined with finite-frequency theory to model wave propagation (Hung et al.2010,2011) and a finite-frequency data set of traveltime residuals from Kolstrup (2015).

Traveltimes measured in multiple frequency bands are sensitive to heterogeneities at different spatial scales and hence increase the amount of information available for each source–receiver pair in

(3)

192 M.L. Kolstrup, S.-H. Hung and V. Maupin

the data set, giving better recovery of the magnitude of velocity anomalies in tomographic models (Hung et al.2004; Sigloch2008). Multiscale parametrizations based on wavelet transforms (Chiao & Kuo 2001; Chiao & Liang2003; Chevrot & Zhao 2007; Loris

et al.2007; Charl´ety et al.2013) are data adaptive and preserve the long-wavelength amplitude spectra in sparsely sampled regions without losing resolution in densely covered regions. This is an advantage compared to using a detailed local parametrization, for example blocks as often used in regional body wave tomography, which emphasizes spatial resolution but reduces the magnitude of long-wavelength anomalies through the high need of smoothing regularization.

We outline the main features of multiscale, finite-frequency to-mography in Section 3, after a summary of the data sets (Section 2). Preferred tomographic models are presented in Section 4.1 and fol-lowed by extensive tests of the results (Sections 4.2–4.5). We discuss our findings in relation to thermal and dynamic modelling of the area and the current debate about the origin of the Scandinavian Mountains (Section 5).

2 D AT A

The data used in this study were recorded by the temporary MAGNUS network between 2006 September and 2008 June (Wei-dle et al.2010), by the temporary DANSEIS network from 2008 April to 2008 June, by the temporary CALAS stations (Medhus

et al.2009), and by permanent stations in the study area (Fig.1). The data examined come from earthquakes with magnitude M> 5.0 that occurred at epicentral distances of 30 to 91.5◦(Fig.2). Most events occurred at distances greater than 70◦, making the separation of phases like P(S) and PcP (ScS) difficult and giving a weak PcP (ScS) signal (Kolstrup2015). Therefore, only the direct P and S phases are included in the data set for the tomography.

P waves are measured on the vertical component of the

seis-mograms and S waves are measured on the transverse component. The data are bandpass filtered using different second-order, zero-phase Butterworth filters. For P waves, the high- and low-frequency bands are 0.3–0.125 Hz (33–8 s) and 0.5–2 Hz (2–0.5 s), respec-tively. This isolates the secondary noise peak at around 0.2 Hz (5 s) in southern Norway. S waves are bandpass filtered in the ranges 0.03–0.077 Hz (33–13 s) and 0.077–0.125 Hz (13–8 s). Due to the relatively high noise level above 0.125 Hz (8 s), it was not possible to measure higher frequency S waves, as also found by Wawerzinek

et al. (2013). Traveltimes are measured using an automated pro-cessing procedure tailored for measuring traveltimes in several fre-quency bands (Kolstrup2015). The multichannel cross-correlation method (MCCC) of VanDecar & Crosson (1990) is preceded by several steps of automatic data rejection and by a preliminary pick-ing of arrival times uspick-ing the iterative cross-correlation and stack algorithm (ICCS) of Lou et al. (2013).

The multichannel cross-correlation method measures all relative delays between stationstijand solves in a least-squares sense for

the optimized arrival times ti at each station under a constraint of



ti= 0. This implies that the measured traveltimes are relative to

the mean traveltime for each event, removing uncertainty regard-ing source location and timregard-ing (VanDecar & Crosson 1990) but also removing information about absolute velocities in the study region.

The relative arrival times are then transformed to traveltime resid-uals by subtracting demeaned theoretical arrival times calculated in the spherically symmetric, continental earth model AK135 (Kennett

et al.1995). The traveltime residuals are corrected for the ellipticity of the Earth and for variations in topography and crustal structure (Kennett & Gudmundsson1996; Euler2014; Kolstrup2015) using a detailed crustal model based on information from a wide range of sources and compiled in Kolstrup (2015). Especially useful for the crustal corrections are the Moho depths and S-wave velocity

Figure 2. Map of earthquake sources used in the tomographies. The events displayed have given traveltime data in at least one frequency band. Left: Events used in the P-wave tomography. Right: Events used in the S-wave tomography.

(4)

Multiscale P and S tomography 193

models from joint inversion of P-receiver functions and surface waves (Kolstrup & Maupin2013) beneath the temporary Magnus stations and beneath permanent stations in Norway and Sweden, as these models give information directly beneath the stations with no need for interpolation.

The crustal corrections are performed using ray theory and are therefore equal for both high and low-frequency bands. It is well-established that crustal reverberations cause a significant differ-ence between traveltimes of long- and short-period waves that must be taken into account in global absolute traveltime tomography (Obayashi et al.2004; Yang & Shen2006; Ritsema et al.2009). For regional relative tomography, though, the data are demeaned in each frequency band and it is therefore only the relative variation of crustal traveltimes in the study region that is important (Maupin & Kolstrup2015, in revision). Ray-theoretical corrections in some cases overestimate the influence of the crust on low-frequency trav-eltimes (Maupin & Kolstrup2015, in revision), and we therefore also invert for a tomographic model without crustal corrections (Section 4.3).

The resulting data set consists of 4205 and 3927 direct P arrivals in the high and low-frequency bands, respectively, from 110 events (Fig.2). For S waves, the corresponding numbers are 3766 and 3187, from 96 events (Fig.2).

Fig. 3shows map views of P-wave traveltime residuals from opposite backazimuths, corrected for crustal structure and ellipticity of the Earth. The residuals are calculated for each station as weighted averages of all residuals from the northeastern and southwestern quadrants, respectively, using the inverse of the estimated standard deviations in measurement error (VanDecar & Crosson1990) as weights.

The high-frequency residuals from the northeastern quadrant (Fig.3a) show a simple, almost bimodal, picture of early resid-uals in the east and late residresid-uals in the west, whereas the high-frequency residuals from the southwestern quadrant (Fig.3c) are early in both the southwestern and easternmost areas. This indi-cates a more complicated 3-D subsurface structure than suggested by the northeastern residuals, with the presence of high velocities off coast southwestern Norway.

The P-wave residuals from the lower frequency bands do not differ in magnitude from the higher frequency residuals, but differ in the spatial distribution of positive and negative residuals (Figs3b and d), especially in the southern part of the of the study area where the long-period waves are less sensitive to the presence of sedi-mentary layers (Maupin & Kolstrup2015, in revision). For events from the southwestern quadrants the changed pattern in negative residuals in the southwestern areas suggest the presence of a high velocities off coast western Denmark that are sensed by the lower frequency residuals due to their broader kernels. Hence, providing data from several frequency bands clearly increases the amount of information about subsurface structure and calls for finite-frequency tomography.

3 T H E O RY A N D M E T H O D

Multiscale, finite-frequency tomography was described in detail by Hung et al. (2011) and we only review the main points and features important for our results.

The basis of linearized traveltime tomography is the formulation

δt =

 K (x)δs(x)d

3x, (1)

whereδt is the observed traveltime residual with respect to given spherically symmetric, standard earth model, and K (x) is the sensi-tivity kernel that relatesδt to perturbations in P- or S-wave slowness

s(x) at every point x in the region. To construct the kernels K (x) we use the finite-frequency theory developed by Dahlen et al. (2000) in which the Born approximation for forward scattering is combined with ray theory for body waves and the paraxial approximation for wavefronts away from the central ray.

As mentioned in Section 2, the traveltime residualsδt are de-meaned for each event. This implies that the appropriate kernel for a relative traveltime measurement is the one associated with this particular source-station path minus the average kernel for all the data from this particular source (e.g. Chevrot & Zhao2007). For most network configurations though, the difference between the usual kernels and the relative ones is small enough not to bias the tomography (Maupin & Kolstrup2015, in revision). Another effect of the demeaning is that the model inverted from the relative trav-eltime residuals will be relative to the unknown 1-D average model of the study region (Aki et al.1977).

The seismic network used in this study covers an area of ap-proximately 500 km by 800 km and is discretized into a grid of 65 (26 + 1) by 65 (26 + 1) by 33 (25+ 1) (=139 425) nodes with a

grid spacing of 25 km and until a depth of 800 km. Even though we correct the traveltime residuals for crustal structure, we include two layers in the crust and upper mantle at 0–25 and 25–50 km, as crustal corrections are never perfect (Martin et al.2005; Maupin & Kolstrup2015, in revision) and the model most be free to account for those imperfections in the uppermost layers.

Numerical integration of the kernels K (x) around each node leads to a data equation that relates the slowness perturbation at each node to the traveltime measurements:

d= Gm, (2)

where d is the data vector containing the N traveltime measurements

δtiand m is the model vector containing the M (139 425) slowness

parameters. The elements Gi jof the matrix G represents the

sensi-tivity of the ith datum with respect to the slowness perturbation at the jth node.

Instead of solving eq. (2) directly for the model parameters m, using regularizations like norm damping and smoothing, the multi-scale parametrization expands the model parameters m in terms of wavelet basis functions in 3-D (e.g. Chiao & Kuo2001; Chevrot & Zhao2007; Hung et al.2011), giving an equation similar to eq. (2), but with both G and m transformed into wavelet space, utilizing the CDF (2,2) wavelet (Cohen et al.1992) and the lifting scheme (Sweldens1996). This decomposes the model into a hierarchy of wavelet coefficients at various scales, with up to six scale-levels of successive refinements. The coarsest level (=1) is at a length-scale of the entire domain and the finest level (=6) is at a length-scale of the grid spacing (25 km).

Hence, the model parameters that are inverted for, using weighted, damped least-squares solution (DLS; e.g. Menke1984), are wavelet coefficients associated with each grid node. Minimum norm damp-ing (2 norm) in the DLS solution therefore acts on the wavelet

coefficients and at several scale levels at a time, instead of uni-formly on the entire model. This has the desirable effect that the finest scales being resolved are spatially varying, minimizing the need for regularization through a priori information, and preserv-ing the amplitudes of long wavelength structures to a larger degree than conventional grid-based parametrizations (Chiao & Kuo2001; Hung et al.2011).

(5)

194 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 3. Average P-wave traveltime residuals from the northeastern and southwestern quadrants. The arrow shows the direction of the incoming wave. (a) High-frequency residuals from the northeastern quadrant. (b) Low-frequency residuals from the northeastern quadrant. (c) High-frequency residuals from the southwestern quadrant. (d) Low-frequency residuals from the southwestern quadrant.

The conventional2norm is used in the DLS-solution as it allows

for convenient linearization of the inversion problem, but recent work suggests that the use of the1 norm on wavelet coefficients

gives a sparser and hence more robust solution (Loris et al.2007; Charl´ety et al.2013) that better recovers sharp discontinuities in the model. In a later work, Loris et al. (2010) performed more realistic synthetic experiments where the classic2 norm penalty

on the Laplacian of the model (smoothing) worked almost as well or even better than some of the0- and1-wavelet methods. The

proper choice of wavelet transformation and regularization strategy therefore seems to be dependent on the target of the study (Loris

et al.2010), being for example recovery of amplitudes or sharpness

of boundaries, and is an ongoing field of research (Simons et al.

2011; Chevrot et al.2012; Charl´ety et al.2013; Yuan & Simons

2014).

4 R E S U L T S

4.1 Images ofδ lnVP,δlnVSandδln(VP/VS)

Preferred models ofδlnVP (=δVP/VP) and δlnVS(=δVS/VS) are

shown in map views in Figs 4and 5, respectively, and in four profiles across the study region in Figs6and7.

(6)

Multiscale P and S tomography 195

Figure 4. Map views ofδlnVPfrom at depths from 50 to 450 km derived using the full 3-D multiscale parametrization. Deep crustal structures from Fig.1are drawn with solid black lines (Mylonite Zone, Oslo and Skagerrak Grabens, Sorgenfrei-Tornquist Zone, Sveconorwegian Front, and Teisseyre-Tornquist Zone). Regions with poor resolution have been masked out.

Figure 5. The same as Fig.4forδlnVS.

(7)

196 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 6. Profiles ofδlnVPderived using the 3-D multiscale parametrization. Regions with poor resolution have been masked out.

To visualize regions that are well sampled by the data, we plot the square root of the diagonal elements of the matrix GT

G, where GT is the transpose of the matrix G in eq. (2). GTG is used as a

proxy for the resolution matrix, as each of its diagonal elements is associated with a grid node and is the squared sum of the sensi-tivity kernels that contribute to this node. Comparison of the GTG

images (Fig.8) with resolution tests (Section 4.4) indicates that robustly constrained regions have GTG values exceeding 0.5 per

cent of the overall maximum at all nodes, and that the data pro-vide reliable images down to a depth of approximately 500 km for P and 400–500 km for S. In all images we do not display the model at nodes with a value below the threshold of 0.5 per cent (Figs4–7).

The most striking structure of the models is a low-velocity region extending from western Norway to Denmark, strongest in the up-permost layers at depths between 100 and 200 km. Higher velocities are found both west and east of this region, and the low-velocity anomaly therefore has a horizontal, channel-like appearance. The

channel seems to be adjacent to, and distinct from, a more circular anomaly below the northwestern end of the Oslo Graben, which extends deeper down to 350 km. The high-velocity area inferred off coast southwestern Norway and Denmark is present in both the

P- and S-wave images and was predicted already from the raw data

(Section 2). In the eastern part of the study area, high velocities extend from north to south and until a depth of around 300–350 km. The highest VPanomalies of+2.5 per cent are found east of the

Sve-conorwegian Mylonite Zone, while the high VSanomalies of up to

+4 per cent are distributed more uniformly in the Sveconorwegian and Svecofennian areas (Fig.1).

The wiggly boundary between the high velocities in the east and low velocities in the west has a steep, almost vertical angle in the southern part between Denmark and Sweden, and is more gently dipping between Norway and Sweden in the northern part (Figs6

and7). The boundary follows the Sorgenfrei-Tornquist Zone very closely in southern Sweden and Denmark and continues along the west side of the Skagerrak and Oslo Grabens before it terminates

(8)

Multiscale P and S tomography 197

Figure 7. The same as Fig.6forδlnVS.

in the northern part of the study area with no association to major tectonic structures (Fig.1).

The P- and S-wave images are very similar in all features but the magnitude of the anomalies, which is larger for S as expected (e.g. Kennett et al.1998; Goes et al.2000). The amplitude variations are around−2.0 and +2.5 per cent for P waves and around −3.5 and +4.0 per cent for S waves. The S-wave models also appear slightly more smooth, possibly due to the longer wavelength of the S-wave data.

In order to compare the images ofδlnVP and δlnVS

quantita-tively we calculate the perturbations in the ratio VP/VS, that is

δln(VP/VS)= δlnVP− δlnVS(Fig.9; e.g. Chou et al.2009). The

ratio VP/VSis often used as a diagnostic of compositional anomalies

(Lee2003; Artemieva2007; Afonso et al.2010), and it is therefore more straightforward to compareδln(VP/VS) to petrological results

than the ratioδlnVP/δlnVS. In addition,δln(VP/VS) is more stable

in numerical computations (Chou et al.2009).

A consistent data set of common source–receiver pairs is usu-ally preferred when computing VP/VS-ratios from tomographies

(Chou et al.2009; Hung et al.2011) or when jointly inverting P-and S-wave data sets (Kennett et al.1998). In our study we keep all available data to computeδln(VP/VS), as the event coverage is

almost equal for the two data sets (Fig.2) and evaluation of the resolution matrix proxy GTG shows comparable data coverage for

the P- and S-wave tomographies (Fig.8). In addition, equal source– receiver combinations do not guarantee compatibility of the P and

S models as the wavelengths and kernels of the P- and S-wave data

sets are anyway different for the two wave types and result in dif-ferent resolutions. The perturbations in VP/VSare quite sensitive

to small-scale variations in the models and it is important not to interpret underdamped solutions or regions of the images with low resolution (Hung et al.2011). We use therefore a stronger cut off criteria of 1 per cent for the square root values of the diagonal elements of GTG in the plots ofδln(V

P/VS) (Fig.9).

(9)

198 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 8. Images of the square root of the diagonal elements of the matrix GTG. Left: For the P-wave tomography. Right: For the S-wave tomography.

The values ofδln(VP/VS) reflect the covariation of VPand VSand

point consistently to high values of VP/VSunder southern Norway

and low values below Sweden down to a depth of 500 km (Fig.9). The difference is about 3 per cent between east and west at 150– 200 km depth, and even larger in the shallowest part of the mantle. All anomalies in VPand VS, except for the circular low-velocity

anomaly in the middle of the study area, have smaller magnitudes

below depths of 200 km. Whether this is due to strong heterogeneity in the lithospheric mantle and/or loss of resolution at greater depths is an important question to answer to properly interpret the results. It is also interesting to investigate if the circular low-velocity anomaly could be connected to the deeper mantle but appear disconnected due to decreased resolution at depth, and to estimate the amount of vertical smearing upwards from such a deep anomaly. Equally

(10)

Multiscale P and S tomography 199

Figure 9. The same as Figs4and5forδln(VP/VS).

important is the quantification of horizontal smearing between sep-arate anomalies in the uppermost mantle, before we interpret the channel-like low-velocity region as a hot finger reaching out from Norway to Denmark, especially as the data coverage is best in the east-west direction. As we calculate anomalies in the VP/VSratio

it is also important to quantify uncertainties inδln(VP/VS). Before

going to a more detailed interpretation of the models in Section 5, we will investigate their robustness in Sections 4.2–4.4

4.2 Vertical multiscale versus vertical convolutional quelling

The inverted multiscale model is built from synthesizing the largest scale-level first, and hence there is a risk that the resulting struc-ture will be vertically smoothed if the incoming waves are steeply incident with few ray crossings at greater depths. In our data set, epicentral distances are greater than 70◦ for most events and this might increase the risk of vertical smearing from the multiscale parametrization.

The degree of vertical smearing can be tested by switching off the multiscale parametrization in the vertical direction and use instead convolutional quelling (Meyerholtz et al.1989; Chiao et al.2010) for vertical regularization. Convolutional quelling penalizes model roughness by assigning an a priori correlation length to the model (Hung et al.2004; Chiao et al.2010).

We therefore invert for subsurface structure using both the full 3-D multiscale parametrization (hereafter called multiscale) and

using a hybrid parametrization with multiscale in the horizontal directions and convolutional quelling with a correlation length of 25 km in the vertical direction (hereafter called hybrid).

Fig. 10 shows tradeoff curves comparing the multiscale and the hybrid schemes for models inverted using the same range of damping values. Model variance, defined as in Chiao et al. (2006), is a measure of model uncertainty resulting from data error. This quantity is more appropriate than the usual model norm to calculate L-curves in tomographies with wavelet parametrization, where focus is not on damping the small scales but removing the non-constrained features. It is therefore the model variance which is shown as a function of data misfit, calculated as the squared difference between observed and predicted data normalized by the sum of the squares of the observed data.

Preferred models are chosen near the point of maximum cur-vature and shown with solid symbols in Fig.10. The difference between models with damping values around the point of maximum curvature is quite small, with higher damping values suppressing the amplitudes of resulting anomalies slightly. As we perform both

P- and S-wave tomographies, we also perform tests like in Chou et al. (2009) to find optimal damping values not only forδlnVPand

δlnVSseparately but also forδln(VP/VS). In these tests we calculate

synthetic data for a range of synthetic models with similar mag-nitude forδlnVPandδlnVS(Section 4.4). Hence, the anomalies in

VP/VS should be zero and we search for the damping values

giv-ing the smallest artificial anomalies in VP/VS. The chosen damping

values in Fig.10represent a compromise between model variance, data misfit and stability of the perturbations inδln(VP/VS).

(11)

200 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 10. Trade-off between model variance and data misfit for the 3-D multiscale parametrization and the hybrid parametrization with vertical convolutional

quelling. (a) P-wave models. (b) S-wave models. Solid symbols denote the preferred solutions that are shown in Figs4–7(multiscale) and Figs11–12(hybrid).

The full multiscale inversion clearly has a higher data fit than the hybrid scheme and is the best inversion scheme in that sense. To compare the models derived from the two parametrizations we present in Figs11and12map views of the hybrid solutions for P and S, corresponding to the multiscale map views in Figs4and5. The greatest difference between the models is that the multiscale ones have larger anomalies and more small-scale perturbations than the smooth-looking hybrid models.

A wide range of resolution tests of the hybrid and multiscale schemes, whereof some are presented in Section 4.4, show that the full multiscale inversion is better at recovering the amplitude and location of the anomalies. Overdamped multiscale inversions are very similar to underdamped hybrid inversions, and damping values can be chosen such that the results are close to be indistinguishable. As smoothing regularizations are very common, smooth images are typically preferred over more rough pictures of the subsurface by geophysicists, either consciously or unconsciously. The hybrid scheme produces the more smooth and typical tomographic pictures, but all resolution tests (Section 4.4), as well as the data misfit, point out the 3-D multiscale as the superior parametrization. Hence, our preferred model is the one obtained with the full 3-D multiscale inversion. When testing our results in Section 4.4 we pay special attention to vertical resolution and perform all tests using both parametrizations.

4.3 Influence of crustal traveltime corrections

The vertical smearing is most severe in the uppermost parts where the overlap between kernels is smallest, making the influence of crustal corrections quite important. Fig.13shows P-wave velocities in the uppermost layers inverted from the data set without crustal corrections (Kolstrup2015), and Fig.14shows the corresponding velocities inverted from the corrected data set. The models are grossly similar, but the corrected images have significantly weaker low-velocity anomalies below southern Norway and Denmark in the depths from 0 to 150 km and stronger high-velocity anomalies in the eastern part of the study area. Similar conclusions are drawn for the S-wave models (Supporting Information Figs S4 and S5).

The increased magnitude of the channel-like low-velocity re-gion in the uncorrected tomography (Fig. 13) is due to the crust in southern Norway being thicker inland than at the coast, and due to the much thicker sedimentary layers in Denmark compared to the rest of the study area. This gives positive (late) crustal trav-eltime corrections in central southern Norway and Denmark. In addition, the thinner crust at the Norwegian coast gives negative (early) traveltime corrections that, when not corrected for, result in an overestimation of the high velocities off coast southern Norway. These effects combine to give the expression of a more narrow low-velocity channel with greater magnitude of associated anomalies than in our corrected images (Fig.14).

It is important to note that the ray-theoretical crustal correc-tions applied here are not entirely consistent with the finite-frequency measurements, as crustal reverberations have a signif-icant frequency-dependent effect on absolute traveltimes derived with waveform cross-correlation methods (Obayashi et al.2004; Yang & Shen 2006; Ritsema et al. 2009). Frequency-dependent crustal corrections (Obayashi et al. 2004; Yang & Shen 2006; Ritsema et al. 2009) have heretofore been based on the reflec-tivity method that does not take into account 2-D and 3-D effects (Yang & Shen2006), making them difficult to apply in a region with a high level of 3-D variation. Recent work shows that, com-pared to reflectivity-based corrections, ray-theoretical corrections in general overestimate the influence of sedimentary layers and of a thin crust (<30 km) on arrival times measured in the lowest frequency bands (Maupin & Kolstrup2015, in revision). In our case, ray-theory and reflectivity-based corrections do not differ by more than 0.05 s in Norway and Sweden, but differ by up to 0.6 s for the low-frequency P-wave band and for both S-wave bands in Denmark due to the overestimation by ray-theory of the influence of the sedimentary layers. The ray-theoretical corrections can there-fore be viewed as a maximum bound on the crustal corrections, and the true model in the southwestern part therefore lies some-where between the ray-theoretically corrected model (Fig.14), and the model with no corrections (Fig. 13) in the upper 150 km. Similarly for the S-wave model (Supporting Information Figs S4 and S5).

(12)

Multiscale P and S tomography 201

Figure 11. The same as Fig.4using the hybrid parametrization.

Figure 12. The same as Fig.5using the hybrid parametrization.

(13)

202 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 13. Images ofδlnVPin the uppermost layers. Input data are the raw traveltime residuals without the crustal and topographic corrections from Kolstrup

(2015).

Figure 14. As Fig.13but with input data corrected for topography and crustal structure.

Our results show that a robust estimate of the crustal correc-tions below each station is important to avoid artefacts in the upper 150 km in the tomographic images. In addition, it is important not to lock the crust during inversion, such that the crustal

lay-ers can allow for additional perturbations (Martin et al.2005). We also add station and event correction terms in the inversion but as-sign them a quite low weight, giving them little influence on the results.

(14)

Multiscale P and S tomography 203

Figure 15. Synthetic input for a chequerboard test with squares of size 200× 200 × 200 km3,δlnVP= ±3 per cent, and δlnVS= ±3 or ±5 per cent. Upper left map shows location of profiles and grid discretization. The apparent lateral variation of the box size in the profiles is due to the obliquity of the profiles with respect to the chequerboard pattern.

4.4 Resolution tests

We calculate synthetic traveltime data using the G matrices built from the actual P- and S-wave data sets with 3-D finite-frequency kernels, hence using exactly the same source–receiver configuration as in the real tomographies. Random errors with a mean amplitude of about 5 per cent of the average size of the synthetic data is added prior to inversion.

For each synthetic model we test velocity perturbations of 3 per cent in VP, and both 3 and 5 per cent in VS. Equal anomalies in VP

and VSof 3 per cent are used to determine the damping values that

give the smallest fluctuations in theδln(VP/VS) as in Chou et al.

(2009).

4.4.1 Horizontal and vertical resolution

We use a range of classical chequerboard tests to estimate the size of objects that can be resolved horizontally and vertically. The start-ing point is chequerboards of size 200 × 200 × 200 km3, and

Fig.15shows the synthetic input for VP. The full 3-D multiscale

inversion results for P and S waves are shown in Figs16and17, and the corresponding hybrid results for P waves are shown in Fig.18.

It is obvious from Figs16and18that both the hybrid and mul-tiscale parametrizations recover the input model quite well, but the full multiscale inversion is significantly better at recovering the am-plitude and location of anomalies. This result is consistent for all

resolution tests, and we show only results for the 3-D multiscale after this first example.

Comparing P- and S-wave results (Figs 16 and 17), we see that the P-wave tomography has better resolution, especially be-low 200 km depth, but objects of size 200 × 200 × 200 km3

are quite well resolved in both tomographies. It is also seen that the S-wave tomography has more damped anomalies at depth than the P-wave tomography. The apparent loss of amplitude in the S-wave tomography below depths of 200 km (Fig.5) might therefore be partly due to loss of resolution at this depth.

Chequerboard tests were also performed using squares of 150× 150× 150 km3and 100× 100 × 100 km3, and with rectangular

boxes where the horizontal or vertical length scale was kept con-stant at 200 km in order to investigate the horizontal and vertical resolution separately. Boxes of size 100× 100 × 200 km3 could

be well resolved in the P-wave tomography, also below 250 km depth. For S waves, the horizontal limit of resolution was found to be about 150 km, best in the upper part of the model. Keeping the horizontal length scale constant at 200 km, we found that the limit of vertical resolution was about 150 km in the upper part of the model and 200 km in the lower part, again with the P-wave tomography having the best resolution. Hence, we can resolve fea-tures with a horizontal scale of about 100 (150) km quite well in the

P(S)-wave tomography, but vertical resolution is limited to about

150–200 km.

The limits of resolution inferred from the chequerboard tests are well below the main features of the models in Figs4–7. The

(15)

204 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 16. Recovered P-wave model using the 3-D multiscale parametrization for the chequerboard test shown in Fig.15and synthetic velocity perturbations

δlnVP= ±3 per cent. Upper left map shows location of profiles and grid discretization.

channel-like low-velocity region is on its thinnest around 150 km wide, though, and the deep cylindrical low-velocity anomaly is quite narrow. In addition, the chequerboard tests created in all cases strong artificial anomalies in the VP/VSratio. We analyse therefore in the

following sections some synthetic models that simulate naturally occurring anomalies to a larger degree.

4.4.2 The low-velocity channel extending from Norway and Denmark

Regional tomographies on a scale larger than ours (Weidle & Maupin2008; Rickers et al.2013) show a low-velocity channel from Iceland to southern Norway and Denmark at shallow depths. The ray-theoretical S-wave tomography of Wawerzinek et al. (2013) shows this channel-like feature at depths of 250–410 km, and the

P-wave tomography of Medhus et al. (2012) shows a tendency of a channel at depths of 100–300 km, but much more blurred than in our images. As the channel imaged in this study might be part of a larger regional feature with geodynamic implications (Weidle & Maupin

2008; Rickers et al.2013), it is important to ascertain whether the

channel could result from horizontal smearing of separate anoma-lies in the uppermost mantle below Norway and Denmark. We place therefore two cylinders extending from 100 to 200 km depths with

δlnVP= −3 per cent and δlnVS= −3 or −5 per cent. The cylinder

below Norway has a diametre of 180 km and the cylinder below Denmark a diametre of 150 km. From the chequerboard tests we know that anomalies of this size are on the lower limit of resolution, and hence the risk of smearing the synthetic input is large.

The synthetic P-wave model is shown in Fig.19and the multi-scale inversions forδlnVPandδlnVSare displayed in Figs20and21.

The inversion clearly separates the two cylindrical anomalies and does not smear them into a channel. This indicates that the channel-like feature is indeed a channel and does not represent smearing of separated anomalies in the shallow mantle. The hybrid inversions (not shown) have weaker amplitudes and give a more channel-like appearance of the recovered anomalies.

Using equalδlnVPandδlnVSof−3 per cent shows that damping

values around 10 000 for both P and S give the least amount of artificial fluctuations in δln(VP/VS), withδln(VP/VS) being close

to zero. These damping values are also reasonable with respect to the trade-off between model variance and data misfit (Fig.10).

(16)

Multiscale P and S tomography 205

Figure 17. Recovered S-wave model using the 3-D multiscale parametrization for the chequerboard test shown in Fig.15and synthetic velocity perturbations

δlnVS= ±3 per cent. Upper left map shows location of profiles and grid discretization.

Fig. 22 shows the resulting δln(VP/VS) for a synthetic input of

+2 per cent (δlnVP= −3 per cent and δlnVS= −5 per cent). The

recoveredδln(VP/VS) is below 1 per cent and much smaller than

the anomalies in the real tomography (Fig.9), implying that the real anomalies have a larger contrast in VP/VS, or that they are better

recovered than the small synthetic objects.

The vertical smearing ofδln(VP/VS) is also much more severe

than for VPand VSseparately, due to the larger degree of vertical

smearing of the S-wave tomography and the combined uncertainties of the P- and S-wave data sets. This test, along with the chequerboard tests, shows that we cannot interpret depth variations of the VP/VS

ratio, but that we have robust estimates of horizontal variations averaged over depth. Hence, we can interpret the strong west to east variation inδln(VP/VS) in Fig.9.

4.4.3 The deep cylindrical low-velocity anomaly below central southern Norway

The cylindrical low-velocity anomaly in the centre of the study area extends from depths of approximately 150–350 km (Figs4

and5). As the resolution decreases at greater depths, we test if a cylinder located from 150 to 500 km depth gives a similar image as a cylinder confined to depths of 150–350 km. The synthetic cylinder has a diametre of 100 km and a velocity perturbation ofδlnVP=

−3 per cent and δlnVS= −3 per cent or −5 per cent.

The synthetic input model is shown in Fig.23and the inverted

P-wave model is shown in Fig.24. Obviously, the P-wave anomaly is recovered down to depths of around 450–500 km. The results for a similar cylinder extending only to a depth of 350 km (not shown) are much more similar to the anomaly found in the tomographic images in Figs4and5. Similar tests were also performed using broader cylinders with diametres of 120 and 150 km, giving similar results but much stronger recovered anomalies. Hence, we can be quite confident that the cylindrical low-velocity anomaly does not extend below 350–400 km depth and that it is indeed quite narrow with a diametre of about 100 km.

We also tested if the cylindrical low-velocity anomaly could re-sult from vertical smearing of separate anomalies by placing two cylinders at depths from 100 to 200 km and 300 to 400 km. Both cylinders have a diametre of 100 km and velocity perturbations

(17)

206 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 18. The same as Fig.16using the hybrid parametrization.

of δlnVP = −3 per cent and δlnVS = −5 per cent (Supporting

Information Fig. S1). The recovered anomalies (Supporting In-formation Figs S2 and S3) are smeared into a continuous cylin-der, but with much smaller amplitudes than the input anomalies: about −1 per cent in Vp and −1.5 per cent in Vs. It is

there-fore more likely that the strong cylindrical anomaly in the tomog-raphy represents a continuous feature than the result of vertical smearing.

4.5 Ray-theoretical multiscale tomographies

As an additional check of our results, we also perform an inversion of the data with a ray-theoretical approach instead of the finite-frequency kernels, facilitating comparison of our results with the recent ray-theoretical tomographies of Medhus et al. (2012) for

P waves and Wawerzinek et al. (2013) for S waves. These two studies use the same databases as we do, but different methods to measure traveltimes. We invert the high-frequency band of our data sets using the same multiscale parametrization and gridding as in the finite-frequency tomography. Resolution tests were also performed but are not shown.

The resultingδlnVPmodel is displayed in Fig.25and shows more

similarity with the relative tomography of Medhus et al. (2012) than

the finite-frequency model in Fig.4. The important difference be-tween the ray-theoretical images (Fig.25) and the finite-frequency images (Fig.4) is that the inclusion of the low-frequency data in-creases the sensitivity to velocity anomalies off coast and across the Skagerrak Sea between Norway and Denmark. In our ray-theoretical inversions, we lose the clear image of a channel and only sense the western high-velocity anomaly in a small area close to the south-western coast of Norway. This is very similar to the relative tomog-raphy of Medhus et al. (2012), and confirms that the inclusion of low-frequency data increases resolution due to the different spa-tial sensitivity of finite-frequency measurements in different pass bands.

A ray-theoretical S-wave tomography is shown in Fig.26. Com-pared to the finite-frequency images in Fig. 5the ray-theoretical tomography has smaller anomalies and less resolution off coast. The main features of the VSH images in Figs5and26 are

simi-lar to the images of Wawerzinek et al. (2013) but the amplitudes are much larger. Wawerzinek et al. (2013) infer a quite deep low-velocity anomaly down to depths of 410 km where our images confine this deeply going anomaly to depths of around 350 km and to a smaller horizontal area. The increased recovery of amplitudes in our images can be ascribed to both the multiscale parametrization and the finite-frequency kernels.

(18)

Multiscale P and S tomography 207

Figure 19. Synthetic input for a test with two cylinders in the depth range from 100 to 200 km and with diametres of 150 and 180 km. The velocity perturbations

areδVP= −3 per cent and δVS= −3 or −5 per cent. Upper left map shows location of profiles and grid discretization.

5 D I S C U S S I O N

Resolution tests show that we have three main well-resolved fea-tures in our models: a low-velocity channel extending from western Norway to Denmark, a deeper cylindrical low-velocity anomaly be-low central southern Norway, and a belt of high velocities bebe-low Sweden. The lateral boundary between the high and low veloci-ties is imaged with great detail in the horizontal directions, and its development with depth is also robustly constrained. For VP/VS

ratios, resolution tests show a high degree of vertical smearing, implying that vertical variations are very poorly constrained, but (depth-averaged) lateral variations are robustly constrained down to 250–300 km depth.

5.1 Comparison to previous seismological studies

Our study reproduces the low velocities below southern Norway and Denmark and high velocities of the Fennoscandian Shield found by recent local geophysical investigations (Maupin2011; Medhus et al.

2012; K¨ohler et al.2012; Wawerzinek et al.2013; Maupin et al.

2013) and regional studies of western Europe (Weidle & Maupin

2008; Zhu et al.2012; Fichtner et al.2013; Rickers et al.2013; Zhu et al.2013). Our study adds to this large-scale picture some important details that have not been imaged in previous studies. The low velocities below southern Norway and Denmark consist of two clearly distinct features: a quite narrow channel at shallow depths to the west, and a deeper, cylindrically shaped anomaly centred at the northern end of the Oslo Graben.

On a larger regional scale, Zhu et al. (2012,2013) image a low-velocity channel in VSVand isotropic VSat shallow depths below

southern Norway, and quite interestingly, also an inversion of the low velocities at depths below 475 km where a high-velocity anomaly is placed below southern Norway and Denmark. The low velocities below southern Norway are also seen in the regional tomographies of Weidle & Maupin (2008) and Fichtner et al. (2013).

Rickers et al. (2013) focuses on the North Atlantic region and image a channel with approximately−4 per cent anomaly in VSH

(with respect to a European 1-D average model) connecting the Ice-land hotspot to southern Norway and Denmark. The low-velocity channel has its maximum between depths of 100–200 km but ex-tends to a depth of 300 km. In the North Sea, northwest of southern Norway, the anomaly increases in strength and depth. This is also

(19)

208 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 20. Recovered P-wave model using the 3-D multiscale parametrization in a test with the synthetic model shown in Fig.19and velocity perturbation

δlnVP= −3 per cent. Upper left map shows location of profiles and grid discretization.

the region where we infer the lowest velocities, especially in the

S-wave tomography (Fig.5). In the Central Graben area, southwest of Norway and Denmark, Rickers et al. (2013) find high-velocity anomalies between 2 to 3 per cent, confirming the high velocities off coast southern Norway and Denmark in our images. Although the relative magnitudes of anomalies in our images cannot be com-pared directly to the absolute velocity anomalies in the tomography of Rickers et al. (2013), we find a very similar low-velocity channel in VSH, the only difference being the higher degree of detail in our

tomography.

Local studies based on surface waves (Maupin 2011; K¨ohler

et al.2012) also confirm this general picture of low velocities below southern Norway, but on this scale it is even more natural to compare our results with the recent P- and S-wave tomographies of Medhus

et al. (2012) and Wawerzinek et al. (2013) already mentioned in the previous sections.

Medhus et al. (2012) were the first to clearly image the lateral boundary between low and high P-wave velocities that continues quite surprisingly from the Tornquist-Teisseyre Zone (TTZ) and Sorgenfrei-Tornquist-Zone (STZ) in northern Germany and Den-mark into southern Norway. Our tomographic images show a

bound-ary between low and high velocities in both VPand VSHthat follows

the STZ (Fig.1) to an even larger degree than in the tomographies of Medhus et al. (2012) and with a correlation that extends to depths of around 300 km. The greatest difference between our study and the work of Medhus et al. (2012) is that we infer high velocities off coast western Denmark and Norway, which confines the low velocities to a shallow channel, instead of a boundary between two half-spaces. In addition, we image much more clearly the presence of a deeper low-velocity structure below the northwestern end of the Oslo Graben, and infer in general higher magnitudes of velocity anomalies.

Where the P-wave study of Medhus et al. (2012) and S-wave study of Wawerzinek et al. (2013) estimate velocity anomalies of about equal magnitudes, our study images VSHanomalies with magnitudes

about twice the size of the VP anomalies, as expected from both

theoretical calculations (e.g. Goes et al.2000) and seismological models (e.g. Kennett et al.1998). In addition our P- and S-wave tomographies show much less difference in the spatial distribution of anomalies than the tomographies of Medhus et al. (2012) and Wawerzinek et al. (2013), showing the importance of regularization and parametrization for seismic models (e.g. Trampert & Snieder

(20)

Multiscale P and S tomography 209

Figure 21. The same as Fig.20forδlnVS= −5 per cent.

1996; Chiao & Kuo2001; Nolet2008; Chiao et al.2010). Estimating robust perturbations of VP/VSis therefore only possible when using

similar parametrization and regularization of the P- and S-wave models, or when making joint inversions of the P- and S-wave data sets.

5.2 Comparison to non-tomographic studies

It seems clear that main structures we image are concordant with previous seismological studies but we recover more realistic mag-nitudes of the P- and S-wave anomalies.

It is very interesting to note that the gravity modelling of Ebbing

et al. (2012) shows a quite strong contribution to surface topography from some non-crustal source, for example the upper mantle, in the location where we image the low-velocity channel, but they do not estimate any contribution to topography where we image the deep circular anomaly. This could mean that the causes of the two low-velocity anomalies are different. Care should be taken that part of this estimated buoyancy from the mantle could be caused by uncertainties in Moho depth, as receiver function studies and active seismics infer different Moho depths, with up to 8 km difference, in the Western Gneiss Region (WGR, Fig.1) at the nortwestern coast

of southern Norway (Svenningsen et al.2007; Stratford & Thybo

2011; Frasetto & Thybo2013; Kolstrup & Maupin2013). Another gravity study that estimates a contribution to the surface topography from the mantle is the study of Jones et al. (2002). They use the long-wavelength (>750 km) free-air gravity anomaly field to estimate the dynamic contribution to topography and infer a contribution on the order of 500–1000 m in southern Norway. Rickers et al. (2013) noted a strong correlation between the low-velocity anomalies in their North Atlantic tomography with both the areas of positive residual topography in Jones et al. (2002) and with continental regions estimated to have experienced major Neogene uplift (e.g. Japsen & Chalmers2000). This suggests that the correlation between the low-velocity anomalies in our images and the mantle contribution to topography in Ebbing et al. (2012) is not coincidental.

It is also interesting that the low-velocity channel is associated with a high degree of intraplate seismic activity (e.g. Lindholm et al.

2000; Bungum et al.2010) that continues from the North Sea along the coast of western Norway and to northwestern Denmark (Fig.1). The cause of the seismic activity is not believed to be post-glacial rebound and is more likely caused by a combination of for example ridge push, sedimentation and/or lateral lithospheric differences

(21)

210 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 22. The same as Figs20and21forδln(VP/VS)= 2 per cent.

(Bungum et al.2010). A similar concentration of intraplate stresses and seismicity in lithospheric ‘thin spots’ has been described in the case of SE Brasil (Assumpc¸˜ao et al.2004). Our study clearly images lateral lithospheric differences and suggests that intraplate stresses concentrate in areas with a thinner lithosphere. The narrow and deep cylindrical low-velocity anomaly in the northwestern end of the Oslo Graben is not associated with any centre of seismic activity, and this again suggests that it is different from the more shallow channel-like anomaly.

5.3 Tectonophysical implications—δlnVP,δlnVSand

temperature variation

If low seismic velocities below the passive margins of the North Atlantic are indeed associated with dynamic support of topography from the mantle and Neogene uplift, as suggested by Rickers et al. (2013), it is quite important to quantify the anomalies in terms of temperature and/or composition and investigate their tectonic implications.

Within the upper subcontinental mantle and away from the hy-drated regions close to subduction zones, seismic velocity anomalies are best explained by variations in temperature (from either

con-vection, changes in lithospheric thickness and/or changes in heat production) and iron content (from melt extraction or metasomatic refertilization; e.g. Goes et al.2000; Poudjom Djomani et al.2001; Griffin et al. 2009). Separating the effects of the two parameters is notoriously difficult (Cammarano et al.2003) and perhaps only possible in extreme cases where Archean and tectonically young lithospheres are compared (Goes et al.2000).

As anhydrous variations in composition give seismic velocity variations smaller than 1–2 per cent in Proterozoic and younger tectonic regions (Goes et al.2000; Cammarano et al.2003; Griffin

et al. 2009; Hieronymus & Goes 2010), we can make an end-member interpretation of the high- and low-velocity anomalies in terms of temperature. Using for example derivatives of VS

veloc-ity with respect to temperature from the literature (∂lnVS/∂T ≈

−1 per cent/100 K, Lee2003), VS velocity anomalies of±3 per

cent translate into temperature anomalies about∓300◦C.

The main problem with this linear interpretation of seismic high-and low-velocity anomalies into hot high-and cold, is that shear anelas-ticity makes the temperature derivatives of VP and VS strongly

temperature-dependent and the absolute value of the derivatives increases with increasing temperature (Cammarano et al.2003). Velocity anomalies of different sign therefore give temperature

(22)

Multiscale P and S tomography 211

Figure 23. Synthetic input for a test with one cylinder extending from 150 to 500 km depth and with a diametre of 100 km. The velocity perturbations are

δlnVP= −3 per cent and δlnVS= −3 or −5 per cent. Upper left map shows location of profiles and grid discretization.

anomalies of different magnitude, and absolute seismic velocities are needed to make a thermal interpretation (Goes et al. 2000; Cammarano et al. 2003). In addition, the anelasticity param-eters used in calculating velocities and velocity derivatives (e.g. Berckhemer et al.1982; Sobolev et al.1996; Jackson et al.

2002; Shapiro & Ritzwoller 2004) also have a significant effect on the magnitude of estimated velocities (e.g. Goes et al.2000; Cammarano et al.2003; Kolstrup et al.2012).

Due to these complications we take a more indirect approach in the interpretation of the velocity anomalies in Figs4–7and compare our results to those obtained by thermal lithosphere modelling in the study area (Kolstrup et al.2012; Gradmann et al.2013).

Kolstrup et al. (2012) modelled the temperature field and pre-dicted seismic velocities in southern Norway using several geo-physical data sets (Moho depth, geoid, surface heat flow), taking into account the dependence of seismic waves on temperature, composi-tion and anelasticity at high temperature and pressure. To limit the range of possible models fitting the data sets, they used a constraint of local isostatic equilibrium for the lithospheric column overly-ing an adiabatic asthenosphere. Kolstrup et al. (2012) inferred a thin and warm lithosphere (∼100 km) in western Norway and a thick and cold lithosphere in eastern Norway and Sweden (∼200 km), and

additionally a slightly thinner and warmer area associated with the Oslo Graben. The maximum relative difference in synthetic seismic shear wave velocity between the thin western lithosphere and the thick eastern lithosphere in Kolstrup et al. (2012) is up to 8.5 per cent at 100 km depth (T ≈ 400◦C) and 5.5 per cent at 150 km depth (T ≈ 300C). In our tomographic images of VSwe find a

maxi-mum relative anomaly between southeast and northwest of around 7.5 per cent at 100 km depth and around 5 per cent at 150 km depth (Fig. 5).

Using a more complete 3-D modelling approach of the litho-sphere in southwestern Scandinavia, Gradmann et al. (2013) es-timated an abrupt change in lithospheric thickness from 100 to 200 km across the Oslo Graben, but also needed a change in com-position between a fertile southern Norwegian mantle and a depleted Fennoscandian Shield to fit absolute VSV velocities in southern

Norway (Maupin2011) and Sweden (Cotte & Pedersen2002). Both modelling approaches show that a lithosphere in local iso-static equilibrium can exhibit strong variations in seismic velocities just from variations in lithospheric thickness and associated temper-ature variations. It is therefore not necessary to invoke a plume or diapir in the uppermost mantle below southern Norway (Rohrman & van der Beek1996; Rohrman et al.2002) to explain the low

(23)

212 M.L. Kolstrup, S.-H. Hung and V. Maupin

Figure 24. Recovered P-wave model using the 3-D multiscale parametrization with the synthetic model shown in Fig.23and a velocity perturbationδlnVP= −3 per cent. Upper left map shows location of profiles and grid discretization.

seismic velocities. A direct translation of the relative velocity anomalies in Figs4and5into relative temperature anomalies could easily be taken as evidence for anomalously hot temperatures and diapiric upwelling of the asthenosphere into the lithosphere.

Neither the lithospheric modelling of Kolstrup et al. (2012) nor Gradmann et al. (2013) is able to explain the details in our tomo-graphic images, but suggests that the low velocities in the channel-like structure between Denmark and Norway may be due to a thin but stable lithosphere of about 100 km overlying convecting as-thenosphere. The high velocities in Sweden and the sharp transition from low to high velocities can likewise be explained by a rapid increase in lithospheric thickness, possibly associated with a higher degree of depletion of the lithospheric mantle below Sweden.

What we cannot explain by variations in lithospheric thickness and mantle depletion is the deep cylindrical low-velocity anomaly that does not fit at all with the uniform asthenosphere assumed below the lithosphere in Kolstrup et al. (2012) and Gradmann et al. (2013). Above 200 km depth, the cylinder merges with the low-velocity channel and could be ascribed to lithospheric thickness

variations, but between depths of 200 and 350 km it is a much stronger feature than the deep part of the channel and it has its own distinct geometry. The location of the structure is slightly west of the northern end of the Oslo Graben and it might therefore have an origin in the extensive Permian magmatism of the Oslo Graben (Neumann et al.2004; Larsen et al.2008; Torsvik et al.2008).

The perhaps most natural explanation for such a structure is a centralized small-scale upwelling, but numerical simulations using a uniform composition for the asthenosphere indicate that upwelling would not give a velocity anomaly as strong as−3 per cent in VSand

1.5–2 per cent in VP(Hieronymus et al.2007). Hence, the narrow

cylinder needs to be anomalously hot or to have an anomalous composition, with for example a higher water content or increased heat production.

The interpretations in this section are based mainly on the anoma-lies in VS. The covariation of VP and VSin δln(VP/VS) provides

additional information on the causes of the velocity anomalies, es-pecially on compositional variations, and will be explored in the following section.

(24)

Multiscale P and S tomography 213

Figure 25. The same as Fig.4for theδlnVPmodel obtained using only the high-frequency P-wave data set and a ray-theoretical approach. The same 3-D

multiscale parametrization and damping value as in Fig.4is used in the inversion.

Figure 26. The same as Fig.5for theδlnVSmodel obtained using only the high-frequency S-wave data set and a ray-theoretical approach. The same 3-D

multiscale parametrization and damping value as in Fig.5is used in the inversion.

數據

Figure 1. Station network and tectonic overview of the study region. Left: Seismological stations with topography and a regional map in the lower left corner.
Figure 2. Map of earthquake sources used in the tomographies. The events displayed have given traveltime data in at least one frequency band
Figure 3. Average P-wave traveltime residuals from the northeastern and southwestern quadrants
Figure 5. The same as Fig. 4 for δlnV S .
+7

參考文獻

相關文件

Other instruments and appliances, used in dental sciences, with low-frequency, high-frequency, ultrasonic and ultra-short wave

For goods in transit, fill in the means of transport in this column and the code in the upper right corner of the box (refer to the “Customs Clearance Operations and

6 《中論·觀因緣品》,《佛藏要籍選刊》第 9 冊,上海古籍出版社 1994 年版,第 1

Wang, Solving pseudomonotone variational inequalities and pseudocon- vex optimization problems using the projection neural network, IEEE Transactions on Neural Networks 17

Hope theory: A member of the positive psychology family. Lopez (Eds.), Handbook of positive

Define instead the imaginary.. potential, magnetic field, lattice…) Dirac-BdG Hamiltonian:. with small, and matrix

For ASTROD-GW arm length of 260 Gm (1.73 AU) the weak-light phase locking requirement is for 100 fW laser light to lock with an onboard laser oscillator. • Weak-light phase

 name common laboratory apparatus (e.g., beaker, test tube, test-tube rack, glass rod, dropper, spatula, measuring cylinder, Bunsen burner, tripod, wire gauze and heat-proof