Complex deep seismic anisotropy below the Scandinavian
Mountains

Corinna Roy · Joachim R. R. Ritter

Received: 28 January 2012 / Accepted: 16 July 2012

© Springer Science+Business Media B.V. 2012

**Abstract** Several seismological projects focused on the deep structure of the Scandinavian Mountains, in Norway and neighbouring Sweden. We use these recordings to study seismic anisotropy by analysing the birefringence of SKS and SKKS phases. These phases, which should be polarised radially, are split into an additional transverse component if they propagate through an anisotropic medium. Our results are directions $\Phi$ of the apparent fast shear wave polarisation and delay times $\delta t$ between the split phases. For station KONO in Southern Norway, we find frequency-dependent $\Phi$ and $\delta t$ values, indicating a depth-dependent anisotropy. Additionally, $\Phi$ and $\delta t$ values vary with epicentre backazimuths in Norway, indicating a complex anisotropic structure in the crust and upper mantle. Stacking of the SKS/SKKS waveforms improves the signal-to-noise ratio along one station line and allows us to better determine the splitting parameters. A unique and complete model of the complex anisotropy cannot be obtained due to the limited observed backazimuth range. Near-surface tectonic structures correlate with the splitting pattern and thus the crust is one anisotropic layer in the region. Partly preferred orientations in the rock fabric at the surface can be correlated with $\Phi$. Below one or

more anisotropic layers must exist to explain the backazimuth- and frequency-dependent observations, as well as the long $\delta t$ values ($>2$ s) which cannot be explained with crustal anisotropy alone. The spatial distribution of the splitting results indicates that different tectonics units, e.g. the Sveconorwegian, the Central and Northern Svecofennian and the Caledonian nappes, are each characterised by specific anisotropic signatures.

**Keywords** Scandinavia · SKS splitting · Anisotropy · Lithosphere

**1 Introduction**

The present high topography of the Scandinavian Mountain range (also called Scandes; Fig. 1) cannot be explained uniquely by existing geodynamic models (e.g. Pascal and Olesen 2009; Lidmar-Bergström and Bonow 2009; Gabrielsen et al. 2010 and references therein). At the same time, seismic anisotropy, which is the direction-dependent propagation velocity of seismic waves and often due to geodynamic deformational processes, is still unknown below the Scandes. Recently, Weidle and Maupin (2008) found a low shear wave velocity zone of –6 % relative to the surrounding mantle of about 70–150 km in depth which reaches from the Iceland plume across the NE Atlantic to Southern Norway. This anomaly might play a role in the Cenozoic uplift phase of the Scandes if it acts as a buoyancy source. Using Rayleigh wave

<footnote>C. Roy · J. R. R. Ritter (✉)
Geophysical Institute, Karlsruhe Institute of Technology,
Hertzstr. 16,
76187 Karlsruhe, Germany
e-mail: joachim.ritter@kit.edu</footnote>
<figure><img src="image_114.png" /><figcaption>**Fig. 1** Relief map displaying the study area with geographical locations and stations used (squares permanent broadband stations, circles MAGNUS temporary stations, diamonds SCANLIPS1 and SCANLIPS2 stations). SS Southern Scandes, NS Northern Scandes, OG Oslo Graben</figcaption></figure>

measurements from the MAGNUS experiment (Weidle et al. 2010), Maupin (2011) confirmed the upper mantle low shear wave velocity anomaly at 150 km in depth directly underneath Southern Norway. If there exists presently an asthenospheric mantle flow from Iceland towards Norway, then one might expect a W–E fast direction for shear wave propagation inside this anomaly due to shear induced alignment of olivine crystals (Tommasi 1998). Another explanation for possible mantle anisotropy is flow of asthenospheric material around the still debated lithospheric root of the mountain range. Observed range parallel fast anisotropy is sometimes interpreted as such a flow pattern in the mantle (Nicolas 1993). The apparent plate motion direction, which is mostly parallel to asthenospheric flow, may be

related also to possible anisotropic patterns. Therefore, observation of seismic anisotropy may be due to several reasons including crustal, lower lithospheric and upper mantle rock fabrics (Plomerová et al. 2008 and references therein).

The Scandinavian Mountains or Scandes at the west of the Baltic Shield are the second largest mountain range in Europe. Together the Southern and Northern Scandes form a 1,400-km-long mountain range at the NW edge of the European continent (Fig. 1). The Southern Scandes at about 59° to 63° N make up a dome-like massif, whereas the Northern Scandes form a SW-NE elongated range at about 65° to 70° N (Fig. 1). In between, the Central Scandes with lower topography are situated. Most of the Scandes' crust was built up and heavily deformed during the Scandinavian Caledonide orogeny 440–420 Ma ago during the collision of Baltica and Laurentia (Torsvik and Cocks 2005). The highly deformed nappes, which were thrusted onto the underlying Proterozoic lithosphere, still make up the prevailing mass of the Scandes. Today, the highest peaks reach as high as 2.4–2.6 km above sea level, and there are numerous hints that Cenozoic uplift added topography to the ancient Caledonian mountain range (Smelror et al. 2007; Anell et al. 2009). Japsen and Chalmers (2000) and Anell et al. (2009) summarise widespread high topography areas, Cenozoic uplift and their geodynamic driving forces around the Northern Atlantic. However, there are two contrasting hypotheses which try to explain the present high topography of the Scandes far away from current plate boundaries and in the absence of active compressional tectonics. The first type of models comprises two or more stages of uplift starting with the initial Caledonian stage and then followed by some 300 Ma of erosion possibly close to sea level until the end of the Mesozoic. The second uplift stage then formed the present topography by a dome-like rising of the Southern Scandes in the Paleogene and Neogene (Smelror et al. 2007). Rohrman et al. (1995) proposed an asthenospheric updoming as buoyancy force for the Scandes which may be maintained by intraplate stresses. Pascal and Olesen (2009) demonstrated with integrated gravity and thermal modelling that the Cenozoic uplift of the Scandes cannot be explained only by an asthenospheric diapir.

The second type of models contains only one uplift event, the Caledonide orogeny with subsequent continuous erosion. The recently proposed isostasy–climate–erosion hypothesis (Nielsen et al. 2009)

<figure><img src="image_115.png" /></figure>
favours this single stage uplift hypothesis, but it is debated (Lidmar-Bergström and Bonow 2009). This controversy is mainly due to our limited knowledge on the deep structure of the Scandes (see “Section 2”) due to sparse data, which prevents the determination of a consistent geodynamic model.

Seismic anisotropy is caused by preferred alignment of anisotropic minerals in rocks due to deformation processes, layering of rocks or alignment of cracks as well as preferred orientation of pores in the rock matrix (Babuska and Cara 1991; Maupin and Park 2007). Anisotropy is a hint for deformation pattern in the lithosphere (Silver 1996) and asthenosphere (Savage 1999) and thus anisotropy measurements help to unravel geodynamic processes. Besides direction-dependent seismic velocity, birefringence of shear waves is observed and used to detect seismic anisotropy. Especially the splitting of mantle shear waves into orthogonally polarised waves is analysed and the recovered anisotropic structures are interpreted as indicators for geodynamic processes (Silver 1996; Savage 1999, Karato et al. 2008). We analyse the splitting of teleseismic shear waves (SKS and SKKS phases; see “Section 3”) in order to determine the elastic anisotropy (apparent direction of fast shear wave polarisation, which is expressed as angle $Φ$ against north, and the apparent delay time $δt$ between the fast and slow shear wave arrivals) below the Scandes.

Up to now, seismic anisotropy below the Scandes is hardly known. Only some SKS phases and their birefringence analysis at station KONO were published yet (Evans et al. 2003). At KONO, the fast shear wave propagation direction is in N–S direction and the average delay time of 1–1.5 s indicates anisotropy also below the crust. To the east, in Sweden, anisotropy was studied in detail at the national Swedish network (Eken et al. 2010). Crossing crustal seismic refraction profiles across the Southern Scandes do not show any signs for anisotropy (Stratford and Thybo 2011), although the lithosphere was heavily deformed during the past collisional events (Torsvik and Cocks 2005).

In this study, we combine seismological measurements at several networks in the region and apply the transverse component minimisation method of Silver and Chan (1991) to determine the splitting parameters $δt$ and $Φ$. In order to improve the signal-to-noise ratio (SNR) at some selected nearby stations, we stack the waveforms and thus achieve waveforms with higher

SNR and more stable splitting results. Frequency dependent splitting is analysed in order to estimate whether small- or large-scale anisotropic regions at depth cause the recovered complicated splitting pattern. The splitting results are compared to major tectonic units of the Scandes and the Baltic Shield.

## 2 Regional seismic structure and station distribution

Several geophysical studies were specifically designed to search for a crustal root or other structural elements which could isostatically sustain the Scandes. Svenningsen et al. (2007) found an up to 10-km-thick crustal thickening under the Southern Scandes based on P wave receiver function modelling along two station lines. This crustal root may sustain the high topography of the mountains by an Airy-type isostasy model. Using seismic refraction measurements, Stratford et al. (2009) determined a 3-D Moho map of Southern Norway based on three new seismic refraction profiles and earlier published models. Their updated Moho map shows a clear increase of crustal thickness from the coast (about 28–30 km) to a maximum of 38–40 km under the Southern Scandes and a thinning to about 36 km underneath the Oslo Graben. This crustal model by Stratford et al. (2009) was interpreted to mean that crustal *and* mantle compensation is required to sustain the high mountains.

The Central Scandes, with up to 1-km-high mountains, do not have a crustal root (England and Ebbing 2012). For the Northern Scandes, the crustal structure is not known in detail yet.

Global mantle tomography models contain a transition from low seismic velocity underneath Norway and the Southern Scandes relative to faster seismic velocity to the east underneath the Baltic Shield (Bijwaard and Spakman 2000). A new regional P wave tomography model has a sharp boundary with low seismic velocity in the upper mantle west of the Oslo Graben and fast velocity towards east under the Baltic Shield. This difference is interpreted as thin lithosphere and shallow hot asthenosphere in the west, contrasting with cold thicker shield lithosphere in the east (Medhus et al. 2012). Using surface waves, Weidle and Maupin (2008) imaged a low S wave velocity zone reaching from the Iceland plume towards Norway and below Southern Sweden. Maupin (2011) confirmed the presence of a low S wave anomaly at ~150 km in depth directly underneath Southern Norway.
None of the cited P or S wave studies found any hint for seismic anisotropy. The crossing seismic refraction models as well as the P and S wave mantle models are all based on isotropic seismic wave propagation, and it seems that anisotropy is not required to explain the travel time observations. Especially the high resolution seismic refraction models, which cover three different azimuths, have the same dominant seismic velocity values at different crustal layers (Stratford et al. 2009). Lateral velocity variations can be explained with lateral heterogeneities correlating with known crustal units. In Norway, only Evans et al. (2003) studied anisotropy using automatic teleseismic shear wave splitting at the permanent station KONO in Southern Norway (see also http://www.isc.ac.uk/SKS/index2.html). They recovered a N–S fast shear wave propagation direction and a split time of 1–1.5 s which requires a significant mantle contribution. In east of Norway, Eken et al. (2010) analysed teleseismic body waves at the Swedish National Seismic Network. They recovered at least four different domains of upper mantle anisotropy. These domains are related to different lithospheric blocks of the Baltic Shield and are interpreted as fossil anisotropy representing early plate tectonics. In “Section 6”, our results are compared with the results of Eken et al. (2010).

Our main data source is the MAGNUS experiment (MAntle investigations of Norwegian Uplift Structures) which is described in detail by Weidle et al. (2010). Within MAGNUS, 30 mobile broadband recording stations of the KArlsruhe BroadBand Array were installed in and around the Southern Scandes from September 2006 until May 2008. The mobile stations were placed in such a way to fill gaps between the few permanent broadband stations (Fig. 1): KONO (Kongsberg), BER (Bergen), HFC2 (Hagfors) and seven stations of the Norwegian Seismic Array (NORSAR). In 2009, the MAGNUS dataset was integrated into the EUROCORE programme TOPO-EUROPE of the European Science Foundation and therein specifically into the Collaborative Research Project *TopoScandiaDeep*. *TopoScandiaDeep* aims at developing a geophysical model for the lithosphere–asthenosphere system under Southern Norway, explaining the mechanisms that led to mountain formation far away from plate boundaries. Within *TopoScandiaDeep*, we could add selected teleseismic recordings from the SCANDinavian LIthosphere P and S wave (SCANLIPS1 and 2) experiments (recording times April–October 2006 and July 2008 to September

2009) across the Central and Northern Scandes (Fig. 1). SCANLIPS was organised by Leicester University (UK) and the Geological Survey of Norway (England and Ebbing 2008, 2012). More details on the seismic stations are listed in Table 1.

## 3 SKS and SKKS waveforms

We selected those earthquakes which should emit potential SKS and SKKS phases during the available recording time periods of the different stations. As selection criteria, we chose 80–140° as epicentre distance and a moment magnitude $M_w$ of at least 6. In a first step, the recordings were visually inspected to search for SKS and SKKS phases with a sufficient SNR of about 3–4 on the horizontal components. Recordings without visible or very weak SKS or SKKS phases were removed from the dataset at this early stage. The finally analysed events are displayed in Fig. 2 and listed in Table 2. The suitable events occurred in four preferred backazimuth (BAZ) ranges: South America (red symbols in Fig. 2, BAZ~240–266°), Hawaii (green, BAZ~345°), South of Fiji (black, BAZ~9°) and NW Pacific (blue, BAZ~40–83°).

The basic data processing for the SKS splitting analysis comprises the following steps: deconvolution of the individual instrument response function, band-pass filtering from 5 s to 15 s, integration to ground displacement, rotation to radial (R) and transverse (T) components with the theoretical BAZ and slowness values and extraction of time windows with the SKS and SKKS phases. In Fig. 3, we present a waveform example from the MAGNUS dataset as a distance-dependent record section. On the R seismograms (Fig. 3a), we can clearly distinguish four main teleseismic phases (SKSac, SKKSac, ScS and SP) which arrive with different slowness values. The T seismograms (Fig. 3b) contain only three clear phases (SKS, SKKS and ScS). The observation of SKS and SKKS phases on the T component is an indication for anisotropy in the mantle, but wave scattering at heterogeneities may be another mechanism. The wavelet on the T component is similar to the derivative of the R signal (e.g. Fig. 4a). Our modelling in the succeeding discussion shows that the wavelets on the T component can be best explained by generation by birefringence of an S wave that is originally polarised only in the radial direction (due to P-to-S conversion at the core mantle boundary). The missing SP phase on the T

<figure><img src="image_116.png" /></figure>
<table><caption>**Table 1** Recording stations used in this study. Sensors since 2006: STS-2: Streckeisen STS-2; CMT-40 T, CMG-3 T, CMG-6TD: Güralp Systems; KS2000, KS54000 (borehole): Geotech Instruments</caption><thead><tr><th>Station code</th><th>Latitude (°)</th><th>Longitude (°)</th><th>Elevation (m)</th><th>Sensor</th></tr></thead><tbody><tr><td colspan="5"><strong>Permanent</strong></td></tr><tr><td>HFC2</td><td>60.13</td><td>13.69</td><td>297</td><td>STS-2</td></tr><tr><td>BER</td><td>60.38</td><td>5.33</td><td>21</td><td>STS-2</td></tr><tr><td>KONO</td><td>59.65</td><td>9.59</td><td>-124</td><td>CMG3-T</td></tr><tr><td colspan="5"><strong>NORSAR</strong></td></tr><tr><td>NAO01</td><td>60.84</td><td>10.89</td><td>426</td><td>KS54000</td></tr><tr><td>NBO00</td><td>61.03</td><td>10.78</td><td>529</td><td>KS54000</td></tr><tr><td>NB201</td><td>61.05</td><td>11.29</td><td>613</td><td>KS54000</td></tr><tr><td>NC204</td><td>61.28</td><td>10.76</td><td>851</td><td>KS54000</td></tr><tr><td>NC303</td><td>61.23</td><td>11.37</td><td>401</td><td>KS54000</td></tr><tr><td>NC405</td><td>61.11</td><td>11.72</td><td>496</td><td>KS54000</td></tr><tr><td>NC602</td><td>60.74</td><td>11.54</td><td>305</td><td>CMG3-T</td></tr><tr><td colspan="5"><strong>MAGNUS mobile</strong></td></tr><tr><td>NWG01</td><td>63.49</td><td>9.74</td><td>88</td><td>STS-2</td></tr><tr><td>NWG03</td><td>62.78</td><td>7.15</td><td>181</td><td>STS-2</td></tr><tr><td>NWG04</td><td>62.78</td><td>8.88</td><td>215</td><td>STS-2</td></tr><tr><td>NWG05</td><td>62.72</td><td>10.04</td><td>564</td><td>STS-2</td></tr><tr><td>NWG06</td><td>62.56</td><td>11.55</td><td>842</td><td>STS-2</td></tr><tr><td>NWG07</td><td>62.13</td><td>5.97</td><td>43</td><td>STS-2</td></tr><tr><td>NWG08</td><td>62.14</td><td>9.99</td><td>822</td><td>CMG-40 T</td></tr><tr><td>NWG09</td><td>62.03</td><td>7.53</td><td>938</td><td>CMG-40 T</td></tr><tr><td>NWG10</td><td>61.84</td><td>11.85</td><td>691</td><td>STS-2</td></tr><tr><td>NWG11</td><td>61.39</td><td>12.68</td><td>441</td><td>KS2000</td></tr><tr><td>NWG12</td><td>61.51</td><td>9.39</td><td>672</td><td>STS-2</td></tr><tr><td>NWG13</td><td>61.19</td><td>7.10</td><td>19</td><td>STS-2</td></tr><tr><td>NWG14</td><td>61.48</td><td>5.26</td><td>17</td><td>STS-2</td></tr><tr><td>NWG15</td><td>60.58</td><td>6.92</td><td>174</td><td>STS-2</td></tr><tr><td>NWG16</td><td>60.62</td><td>8.29</td><td>613</td><td>STS-2</td></tr><tr><td>NWG17</td><td>60.62</td><td>9.69</td><td>511</td><td>KS2000</td></tr><tr><td>NWG18</td><td>60.70</td><td>12.38</td><td>212</td><td>STS-2</td></tr><tr><td>NWG19</td><td>59.85</td><td>11.82</td><td>289</td><td>KS2000</td></tr><tr><td>NWG20</td><td>59.64</td><td>8.03</td><td>829</td><td>KS2000</td></tr><tr><td>NWG21</td><td>59.95</td><td>6.59</td><td>410</td><td>STS-2</td></tr><tr><td>NWG22</td><td>59.27</td><td>5.24</td><td>66</td><td>STS-2</td></tr><tr><td>NWG23</td><td>59.49</td><td>7.39</td><td>834</td><td>STS-2</td></tr><tr><td>NWG24</td><td>59.03</td><td>8.54</td><td>398</td><td>KS2000</td></tr><tr><td>NWG25</td><td>58.99</td><td>9.94</td><td>25</td><td>KS2000</td></tr><tr><td>NWG26</td><td>59.14</td><td>11.44</td><td>131</td><td>STS-2</td></tr><tr><td>NWG27</td><td>58.75</td><td>9.04</td><td>102</td><td>STS-2</td></tr><tr><td>NWG28</td><td>58.62</td><td>7.42</td><td>343</td><td>STS-2</td></tr><tr><td>NWG29</td><td>58.74</td><td>5.68</td><td>24</td><td>STS-2</td></tr><tr><td>NWG31</td><td>58.38</td><td>8.24</td><td>164</td><td>STS-2</td></tr><tr><td>NWG32</td><td>60.21</td><td>10.75</td><td>567</td><td>STS-2</td></tr><tr><td>NWG33</td><td>60.62</td><td>9.69</td><td>481</td><td>KS2000</td></tr></tbody></table>
<table><caption>**Table 1 (continued)**</caption><thead><tr><th>Station code</th><th>Latitude (°)</th><th>Longitude (°)</th><th>Elevation (m)</th><th>Sensor</th></tr></thead><tbody><tr><td>NWG34</td><td>59.12</td><td>11.39</td><td>81</td><td>STS-2</td></tr><tr><td>NWG35</td><td>59.49</td><td>7.39</td><td>839</td><td>STS-2</td></tr><tr><td colspan="5">SCANLIPS1</td></tr><tr><td>N6001</td><td>63.74</td><td>8.83</td><td>19</td><td>CMG-6TD</td></tr><tr><td>N6002</td><td>63.53</td><td>9.06</td><td>56</td><td>CMG-6TD</td></tr><tr><td>N6003</td><td>63.47</td><td>9.49</td><td>0</td><td>CMG-6TD</td></tr><tr><td>N6004</td><td>63.33</td><td>9.65</td><td>305</td><td>CMG-6TD</td></tr><tr><td>N6005</td><td>63.27</td><td>10.04</td><td>69</td><td>CMG-6TD</td></tr><tr><td>N6006</td><td>63.29</td><td>10.44</td><td>158</td><td>CMG-6TD</td></tr><tr><td>N6007</td><td>63.37</td><td>10.77</td><td>179</td><td>CMG-6TD</td></tr><tr><td>N6008</td><td>63.41</td><td>10.93</td><td>150</td><td>CMG-6TD</td></tr><tr><td>N6009</td><td>63.48</td><td>11.23</td><td></td><td>CMG-6TD</td></tr><tr><td>N6010</td><td>63.43</td><td>11.77</td><td>290</td><td>CMG-6TD</td></tr><tr><td>N6011</td><td>63.30</td><td>12.12</td><td>631</td><td>CMG-6TD</td></tr><tr><td>N6013</td><td>63.44</td><td>12.70</td><td>478</td><td>CMG-6TD</td></tr><tr><td>N6014</td><td>63.40</td><td>13.21</td><td>565</td><td>CMG-6TD</td></tr><tr><td>N6016</td><td>63.37</td><td>13.45</td><td>388</td><td>CMG-6TD</td></tr><tr><td>N6017</td><td>63.38</td><td>13.66</td><td>531</td><td>CMG-6TD</td></tr><tr><td>N6018</td><td>63.38</td><td>14.07</td><td>409</td><td>CMG-6TD</td></tr><tr><td>N6019</td><td>63.32</td><td>14.64</td><td>281</td><td>CMG-6TD</td></tr><tr><td>N6021</td><td>63.24</td><td>15.47</td><td>351</td><td>CMG-6TD</td></tr><tr><td>N6022</td><td>63.22</td><td>15.79</td><td>389</td><td>CMG-6TD</td></tr><tr><td>N6024</td><td>62.99</td><td>16.54</td><td>222</td><td>CMG-6TD</td></tr><tr><td>N6025</td><td>62.95</td><td>16.81</td><td>345</td><td>CMG-6TD</td></tr><tr><td>N6026</td><td>62.93</td><td>17.09</td><td>377</td><td>CMG-6TD</td></tr><tr><td>N6027</td><td>62.88</td><td>17.24</td><td>294</td><td>CMG-6TD</td></tr><tr><td>N6028</td><td>62.84</td><td>17.62</td><td>246</td><td>CMG-6TD</td></tr><tr><td>N6029</td><td>62.74</td><td>17.82</td><td>101</td><td>CMG-6TD</td></tr><tr><td>N6130</td><td>62.69</td><td>9.90</td><td>675</td><td>CMG-6TD</td></tr><tr><td>N6132</td><td>63.62</td><td>10.84</td><td>146</td><td>CMG-6TD</td></tr><tr><td>N7001</td><td>68.4</td><td>15.95</td><td>15</td><td>CMG-3 T</td></tr><tr><td colspan="5">SCANLIPS2</td></tr><tr><td>N7001</td><td>68.40</td><td>15.95</td><td>15</td><td>CMG-3 T</td></tr><tr><td>N7002</td><td>68.56</td><td>15.83</td><td>8</td><td>CMG-3 T</td></tr><tr><td>N7003</td><td>68.25</td><td>16.72</td><td>60</td><td>CMG-3 T</td></tr><tr><td>N7005</td><td>68.15</td><td>17.49</td><td>628</td><td>CMG-3 T</td></tr><tr><td>N7010</td><td>67.63</td><td>17.83</td><td>463</td><td>CMG-40 T</td></tr><tr><td>N7014</td><td>67.21</td><td>19.31</td><td>404</td><td>CMG-3 T</td></tr><tr><td>N7017</td><td>66.97</td><td>20.57</td><td>419</td><td>CMG-3 T</td></tr><tr><td>N7018</td><td>66.85</td><td>21.01</td><td>375</td><td>CMG-3 T</td></tr><tr><td>N7020</td><td>66.61</td><td>21.71</td><td>396</td><td>CMG-3 T</td></tr><tr><td>N7023</td><td>66.28</td><td>22.71</td><td>0</td><td>CMG-3 T</td></tr><tr><td>N7025</td><td>66.04</td><td>23.31</td><td>70</td><td>CMG-40 T</td></tr><tr><td>N7027</td><td>65.92</td><td>23.97</td><td>50</td><td>CMG-3 T</td></tr></tbody></table>

<figure><img src="image_117.png" /></figure>
<figure><img src="image_118.png" /><figcaption>**Fig. 2** Epicentre distribution of all analysed events. The *colour code* indicates similar backazimuthal regions relative to the study area (triangle in the centre)</figcaption></figure>

component in Fig. 3b indicates the successful component rotation routine because SP should arrive as a radially polarised wave only. During our data analysis, slowness was measured for each SKS and SKKS phase and compared to the theoretical value of the *iasp91* reference Earth model (Kennett et al. 1991) in order to verify the identification of the phase.

The SNR of the split SKS and SKKS phases on the T component (Fig. 3b) is about 3–4 on average, which is enough for a stable splitting analysis (Vecsey et al. 2008). The SKS and SKKS recordings of the other events were plotted in a similar way and only clearly visible split phases were further analysed.

# 4 Methodology and splitting analysis

## 4.1 Splitting measurement

We applied the minimisation method by Silver and Chan (1991) to analyse the splitting properties of the observed SKS and SKKS phases. In a layered homogeneous isotropic Earth, SKS and SKKS phases

should be polarised in radial direction (R) only because these phases are generated by compressional waves leaving the outer core. Along their travel paths through an anisotropic mantle, the SKS and SKKS phases are split and thus a fraction of their amplitudes appears on the transverse component (T). This splitting can be identified in the T seismograms (Figs. 3b and 4a) or in the particle motion diagram as an elliptical polarisation in the R–T plane (Fig. 4a). Due to the seismic velocity anisotropy, the two split waves propagate with slightly different shear wave velocities, and thus a split time or delay time $δt$ evolves between both waves. Under the assumption of a single homogeneous anisotropic layer with transverse isotropy, the length of $δt$ depends on the strength of the anisotropy, the wave propagation direction relative to the direction of fast anisotropic velocity and the length of the travel path inside the anisotropic region. The angle $Φ$ is defined as the angle between the direction of fast shear wave polarisation and north. In the case of two or more anisotropic layers, $δt$ and $Φ$ become backazimuth and frequency dependent and only apparent $δt$ and $Φ$ can be measured.

The method by Silver and Chan (1991) determines the two splitting parameters $δt$ and $Φ$ by correcting for the effect of anisotropy. The aim is to find those $δt$ and $Φ$ values which minimise the SKS or SKKS amplitude on the transverse component (short: transverse component minimisation). Using a cross-correlation and a grid search in the $δt-Φ$ domain (Fig. 4d), synthetic seismograms are calculated and the energy (squared amplitude) of the anisotropy-corrected T seismogram ($Tc)^2$ is determined (Fig. 4b). ($Tc)^2$ is plotted in a $δt-Φ$ diagram which should reach a minimum for the correct $δt$ and $Φ$ parameters (Fig. 4d). We chose 3 s as upper limit for $δt$ because greater values are unrealistic. As control, the polarisation in the R–$Tc$ plane should become linear in radial direction for the corrected $Tc$ waveform (Fig. 4b). We considered only those splitting measurements as useful results which show a clear linear particle motion in the R–T plane after correction and a well-determined minimum in the grid search. Based on the correct $δt$ and $Φ$ anisotropy parameters, a synthetic split T component seismogram can be computed and compared to the measured T recording (Fig. 4c). This method was used in numerous studies (Savage 1999) and is quite robust as long as the SNR at the T component is larger than 2. For a comparison with other methods, see Long and van der Hilst (2005) or Vecsey et al. (2008).
<table><caption>**Table 2** Event list with SKS/SKKS splitting results at 5–15-s dominant period. *M*<sub>w</sub> is the moment magnitude; event details are taken from the International Seismological Centre</caption><thead><tr><th>Date (day month year)</th><th>Time (hh:mm:ss)</th><th>Latitude (°)</th><th>Longitude (°)</th><th>Depth (km)</th><th>M<sub>w</sub></th><th>Region</th></tr></thead><tbody><tr><td>23 06 1991</td><td>21:22:29</td><td>-26.80</td><td>-63.35</td><td>558</td><td>7.1</td><td>Argentina</td></tr><tr><td>06 07 1991</td><td>12:19:49</td><td>-13.11</td><td>-72.19</td><td>104</td><td>7.0</td><td>Peru</td></tr><tr><td>10 05 1994</td><td>06:36:28</td><td>-28.50</td><td>-63.10</td><td>600</td><td>6.9</td><td>Argentina</td></tr><tr><td>09 06 1994</td><td>00:33:16</td><td>-13.84</td><td>-67.55</td><td>631</td><td>8.2</td><td>Bolivia</td></tr><tr><td>19 08 1994</td><td>10:02:52</td><td>-26.64</td><td>-63.42</td><td>563</td><td>6.5</td><td>Argentina</td></tr><tr><td>28 11 1997</td><td>22:53:42</td><td>-13.74</td><td>-68.79</td><td>586</td><td>6.7</td><td>Peru-Bolivia border</td></tr><tr><td>28 09 1998</td><td>13:34:30</td><td>-8.19</td><td>112.41</td><td>151</td><td>6.6</td><td>Java</td></tr><tr><td>23 04 2000</td><td>09:27:23</td><td>-28.31</td><td>-62.99</td><td>608</td><td>7.0</td><td>Argentina</td></tr><tr><td>27 07 2003</td><td>11:41:27</td><td>-20.13</td><td>-65.18</td><td>345</td><td>6.0</td><td>Bolivia</td></tr><tr><td>25 07 2004</td><td>14:35:19</td><td>-2.43</td><td>103.98</td><td>582</td><td>7.3</td><td>Sumatra</td></tr><tr><td>13 06 2005</td><td>22:44:34</td><td>-19.99</td><td>-69.20</td><td>115</td><td>7.8</td><td>Chile</td></tr><tr><td>17 11 2005</td><td>19:26:54</td><td>-22.37</td><td>-67.93</td><td>154</td><td>6.8</td><td>Chile-Bolivia border</td></tr><tr><td>25 08 2006</td><td>00:44:46</td><td>-24.40</td><td>-67.03</td><td>184</td><td>6.6</td><td>Chile-Argentina border</td></tr><tr><td>15 10 2006</td><td>17:14:12</td><td>20.12</td><td>-156.16</td><td>20</td><td>6.0</td><td>Hawaii</td></tr><tr><td>17 10 2006</td><td>01:25:12</td><td>-5.91</td><td>151.03</td><td>32</td><td>6.6</td><td>New Britain region</td></tr><tr><td>30 01 2007</td><td>21:37:44</td><td>21.07</td><td>144.86</td><td>20</td><td>6.6</td><td>Mariana Islands</td></tr><tr><td>26 07 2007</td><td>05:40:16</td><td>2.85</td><td>127.51</td><td>25</td><td>6.9</td><td>Halmahera</td></tr><tr><td>28 09 2007</td><td>13:38:59</td><td>21.99</td><td>142.71</td><td>275</td><td>7.5</td><td>Volcano Islands</td></tr><tr><td>16 11 2007</td><td>03:13:00</td><td>-2.36</td><td>-77.84</td><td>123</td><td>6.7</td><td>Peru-Ecuador border</td></tr><tr><td>09 12 2007</td><td>07:28:20</td><td>-26.16</td><td>-177.34</td><td>152</td><td>7.7</td><td>South Fiji Islands</td></tr><tr><td>09 05 2008</td><td>21:51:30</td><td>12.51</td><td>143.18</td><td>76</td><td>6.6</td><td>Mariana Islands</td></tr><tr><td>08 07 2008</td><td>09:13:07</td><td>-15.99</td><td>-71.75</td><td>123</td><td>6.2</td><td>Peru</td></tr><tr><td>26 08 2008</td><td>21:00:37</td><td>-7.64</td><td>-74.38</td><td>154</td><td>6.4</td><td>Peru-Brazil border</td></tr><tr><td>30 08 2008</td><td>06:54:08</td><td>-6.15</td><td>147.26</td><td>75</td><td>6.3</td><td>E New Guinea region</td></tr><tr><td>11 09 2008</td><td>00:00:00</td><td>1.88</td><td>127.36</td><td>96</td><td>6.5</td><td>Halmahera</td></tr><tr><td>12 07 2009</td><td>06:12:47</td><td>-15.04</td><td>-70.44</td><td>198</td><td>6.1</td><td>Peru</td></tr></tbody></table>

## 4.2 Frequency dependence

Our splitting results partly vary at single stations for different backazimuths as well as between nearby stations in the Southern Scandes. Such variations may be related to frequency-dependent effects: small-scale heterogeneity (Grechka and McMechan 1995) or depth-dependent anisotropy (Rümpker et al. 1999). Synthetic finite frequency studies show that the sensitivity region for anisotropic structure increases with SKS wave length and hence SKS period (Sieminski et al. 2008). Therefore, we determine splitting parameters by varying the frequency bandwidth of the SKS waveforms. This analysis can be done best at station KONO which provides most recordings with a good SNR. The tested

period band 5–50 s corresponds to wavelengths of about 20–200 km in the upper mantle.

At first, the frequency or period content of the SKS recordings is tested by looking at the waveforms of the split phase of the T component (Fig. 5). In the unfiltered recording, the split SKS phase can be clearly identified (Fig. 5a), including a long period noise phase (about 80 s) and numerous short period arrivals (<5 s). The short period range of 5–10 s is displayed in Fig. 5b which has a clear transverse energy on the SKS waveform. At shorter periods, the amplitude of the SKS phase is too small for a splitting analysis. At periods of 5–15 s, the SKS phase is best observed in this example as well as for most other events and stations (Roy 2010). Therefore, the 5–15-s period band is selected for standard analysis in this paper.

<figure><img src="image_119.png" /></figure>
**Fig. 3** Record section from the MAGNUS network. Shear wavefronts of the Mariana Islands region earthquake, 28th September 2007 (275 km in depth, $m_b=6.7$, $M_w=7.7$), are shown in the period band 5–15 s with trace normalisation: **a** radial component with four main phases, **b** transverse component with split transverse SKS and SKKS waves

<figure><img src="image_120.png" /></figure>

SKS is still visible in the 10–50-s period range (Fig. 5d); however, for periods longer than 15 s, SKS has a small amplitude (Fig. 5e), especially for periods exceeding 20 s (Fig. 5f). Splitting parameters were determined for 5–10, 5–15 and 15–50 s recordings (Fig. 6). For KONO, we find that the apparent fast polarisation direction $\Phi$ changes systematically anti-clockwise from +9° (Fig. 6a) to +5° (Fig. 6b) and –9° (Fig. 6c). These changes in $\Phi$ are smaller than the error bars of about 3–4° and much smaller than the variation that we find among neighbouring stations (see Fig. 8). The delay time $\delta t$ increases systematically with increasing period from 1.2 s (Fig. 6a) to 1.5 s (Fig. 6b) and 2.5 s (Fig. 6c). This measured $\delta t$ increase with

period is significant and also known from other SKS analyses in New Zealand (Marson-Pidgeon and Savage 1997), Japan (Long and van der Hilst 2005; Wirth and Long 2010) or the Gulf of California (Long 2010); further results and interpretation are given in “Section 6”.

## 4.3 Array processing

Array methods are used to measure the backazimuth and slowness of a wavefield. Based on these parameters, stacking of individual waveforms from neighbouring seismic stations can be done in order to improve the SNR of small coherent amplitude phases (Rost et al. 2006). Here we try such a data processing approach to
<figure><img src="image_121.png" /><figcaption>**Fig. 4** Determination of splitting parameters at station KONO using waveforms of an earthquake underneath Argentina on 23rd June 1991 (556 km in depth, $m_b=6.1$). **a** Measured waveforms, **b** corrected waveforms using determined splitting parameters, **c**</figcaption></figure>

comparison between observed and calculated transverse component, **d** minimisation function for the transverse component; the minimum is found at $\delta t=1.2 \pm 0.3$ s and $\Phi=19 \pm 4^\circ$ (red line indicates 95 % confidence region)

SKS splitting in a similar way as that of Gledhill and Gubbins (1996). Waveform stacking before the splitting analysis requires that very similar waveforms are observed at neighbouring stations and that the anisotropic structure does not vary below these stations in order to avoid waveform blurring or even deterioration of the splitting parameters.

The SCANLIPS1 station line across Northern Norway and Sweden (Fig. 1) is ideal to apply array processing for SKS phases because the stations are close together (about 15–20 km in distance; Figs. 1 and 9a) which is less than the dominant wavelength of 20–60 km of the analysed SKS and SKKS recordings. Across the SCANLIPS1 line, the few splitting results at single-station measurements do not change much between neighbouring stations (Fig. 9a; Table 3); however, due to low SNR, these results must be interpreted with caution. In order to derive more stable splitting measurements, we improve the SNR of the SKS and SKKS

signals by stacking the R and T seismograms of neighbouring stations.

Figure 7 displays the SKS and SKKS waveforms across the SCANLIPS1 line for an event underneath the Chile–Argentina border region (25 August 2006, 00:44:47 UT). The recordings in Fig. 7a, **d** display the single (unstacked) seismograms of the R and T components, respectively. In Fig. 7b, **c**, we show the R component of the SKS and SKKS phases after stacking and alignment to the SKS and SKKS phases for better visibility.

Stacking was performed in the following way: first, we corrected the move-out of the recordings with the theoretical slowness values, which are 4.3 s/° for SKS and 6.9 s/° for SKKS, and the backazimuth of 249°. Then, the recordings of three neighbouring stations were stacked along the recording line in a gliding manner. Stations N6005, N6030 and N6032 were not used for this stacking method because the recordings
<figure><img src="image_122.png" /><figcaption>**Fig. 5** SKS waveform on the tangential component of a 200-km-deep earthquake underneath Peru (12 July 2009, 06:12 UT, $m_b=5.7$, $M_w=6.1$) at station KONO.

**a** Unfiltered recording, **b** bandpass-filtered 5–10 s, **c** 5–15 s, **d** 10–50 s, **e** 15–50 s, **f** 20–50 s</figcaption></figure>

of N6005 were corrupt and the other two stations are not in line with the others. The station names given in Fig. 7b, c refer to the middle station of the three stacked recordings.

These stacked transverse waveforms are displayed in Fig. 7e, f. The stacked seismograms indicate that there is a clear SKS signal on the T recordings and hence we can expect anisotropy below the Central Scandes as well. The stacked seismograms gain more clear split SKS and even SKKS measurements due to the better SNR compared to the single measurements (Fig. 7a, d). Thus, stacking SKS or SKKS waveforms can allow a more detailed study of anisotropy compared to single recordings if suitable nearby stations are available.

## 5 Results

Our splitting analysis provides 154 results ($\Phi$–$\delta t$ pairs) from clearly split SKS or SKKS waveforms (Table 3; Figs. 8 and 9). We removed noisy data as well as possible null splits because the latter could not be clearly distinguished from noisy waveforms. In general, the presented $\Phi$ values are well resolved mostly within $\pm 20^\circ$ ($2-\sigma$ level), while $\delta t$ has quite large error limits of about $\pm 1$ s.

### 5.1 Station KONO

Station KONO in Southern Norway provides the most useful waveforms for our splitting analysis (Table 3). The apparent $\Phi$ is oriented N–S with a slight change toward NNW/SSE for increasing wave period (Fig. 6). The apparent split time $\delta t$ increases with period: it is mostly below 1.4 s for periods of less than 10 s and reaches ~3 s for periods above 15 s (Fig. 6). The splitting analyses with the 12 SKS recordings from events below South America provide very reproducible results (blue arrows in Fig. 8). Splitting results based on one event below Java (red arrow, $\Phi$~19°) and one event below Fiji (black arrow, $\Phi$~37°) have a NE–SW tendency. The splitting results in the database of the International Seismological Centre (http://www.isc.ac.uk/SKS/; accessed 1 July 2012) have a NNE–SSW direction of $\Phi$ which coincides with our measurements.

### 5.2 Southern Norway

At the MAGNUS network in Southern Norway, the measured $\Phi$ directions appear quite variable at first sight (Fig. 8). Splitting results for events from the
—thus, it is inferred that the splitting measurements are stable and reproducible. At some stations, $\Phi$ varies with backazimuth (e.g. stations NWG01, 03, 04, 19, 22, 27, 29, 31 and NORSAR) and at a few stations $\Phi$ is less dependent on the backazimuth (NWG04, 18, 21, 30 and KONO). However, better backazimuthal coverage is needed to confirm the latter cases.

In the north of the MAGNUS network, station NWG01 has three different apparent $\Phi$ for three different backazimuths and station NWG03 has at least two different $\Phi$, indicating a complex anisotropic underground. The apparent split time $\delta t$ is above 1 s at most stations, but there is no systematic trend in the spatial distribution of $\delta t$ in Southern Norway. The value of $\delta t$ is mostly similar for different SKS phases from the same epicentre backazimuth but varies between different stations.

## 5.3 Central Scandes and Sweden

In the transitional region between the Southern and Northern Scandes, the splitting results are relatively homogeneous across the SCANLIPS1 line (Fig. 9a, b). We were able to determine nine splitting results from single-station measurements and 26 additional results after the gliding station stack (see “Section 4.3”). In the western part of SCANLIPS1, close to the coast, apparent $\Phi$ is oriented N–S (stations N6002-N6004). Just to the east, $\Phi$ is directed NE–SW at stations N6006–N6009. To the east of 11°E, $\Phi$ is uniform in NW–SE direction across the low mountains and their eastern foreland in Sweden. Only one SKKS splitting measurement at N6025 has $\Phi$ with NE–SW direction. Along the SCANLIPS1 line, $\Phi$ does not vary much between SKS (dark blue) and SKKS (light blue) measurements, indicating a possible common birefringence origin in the upper mantle and/or crust. The apparent split time $\delta t$ is generally high, with many values exceeding 2 s. Although $\delta t$ is not determined very precisely (typical uncertainties of up to 1 s), these high $\delta t$ values are very uniform for a South American event (blue in Fig. 9a, b). The SKS and SKKS splitting results from the event under the New Britain region (red and orange) are more E–W-oriented with a smaller $\delta t$, indicating complex anisotropic layer geometry. The smooth results may become more complex when observations from more backazimuths can be obtained as in Southern Norway.

same backazimuth region are displayed with the same colour coding as the epicentre distribution in Fig. 2. $\Phi$ values measured for events with a similar epicentre backazimuth are mostly consistent at the same station

<figure><img src="image_123.png" /></figure>

<figure><img src="image_124.png" /></figure>

<figure><img src="image_125.png" /><figcaption>Fig. 6 Splitting results at KONO for different period bands: a 5–10 s, b 5–15 s, c 10–50 s</figcaption></figure>
<table><caption>**Table 3** SKS/SKKS splitting results from this study. The results for station KONO were measured at 5–15-s period as for the other stations</caption><thead><tr><th>Station code</th><th>Event date</th><th>δt (s)</th><th>Error δt (s)</th><th>Φ (°)</th><th>Error Φ (°)</th><th>Phase</th></tr></thead><tbody><tr><td colspan="7"><strong>Permanent</strong></td></tr><tr><td>BER</td><td>09052008</td><td>1.1</td><td>0.7</td><td>20</td><td>12</td><td>SKS</td></tr><tr><td>HFC2</td><td>28092007</td><td>1.0</td><td>1.3</td><td>18</td><td>18</td><td>SKS</td></tr><tr><td>KONO</td><td>09122007</td><td>1.9</td><td>0.9</td><td>37</td><td>13</td><td>SKKS</td></tr><tr><td></td><td>15102006</td><td>1.8</td><td>1.1</td><td>2</td><td>10</td><td>SKS</td></tr><tr><td></td><td>12072009</td><td>1.9</td><td>0.7</td><td>2</td><td>8</td><td>SKS</td></tr><tr><td></td><td>17112005</td><td>1.6</td><td>1.0</td><td>4</td><td>15</td><td>SKS</td></tr><tr><td></td><td>23042000</td><td>1.5</td><td>0.7</td><td>172</td><td>13</td><td>SKS</td></tr><tr><td></td><td>27072003</td><td>1.3</td><td>0.4</td><td>15</td><td>18</td><td>SKS</td></tr><tr><td></td><td>28111997</td><td>1.1</td><td>0.7</td><td>4</td><td>15</td><td>SKS</td></tr><tr><td></td><td>28091998</td><td>1.4</td><td>0.6</td><td>19</td><td>10</td><td>SKS</td></tr><tr><td></td><td>08072008</td><td>1.8</td><td>1.8</td><td>2</td><td>10</td><td>SKS</td></tr><tr><td></td><td>23061991</td><td>1.2</td><td>0.3</td><td>19</td><td>3</td><td>SKS</td></tr><tr><td></td><td>19081994</td><td>1.4</td><td>0.4</td><td>8</td><td>15</td><td>SKS</td></tr><tr><td></td><td>09061994</td><td>1.7</td><td>1.0</td><td>179</td><td>10</td><td>SKS</td></tr><tr><td></td><td>10051994</td><td>1.2</td><td>0.5</td><td>175</td><td>13</td><td>SKS</td></tr><tr><td></td><td>13062005</td><td>2.2</td><td>1.0</td><td>177</td><td>13</td><td>SKS</td></tr><tr><td colspan="7"><strong>NORSAR</strong></td></tr><tr><td>NAO01</td><td>09122007</td><td>2.1</td><td>0.7</td><td>27</td><td>4</td><td>SKKS</td></tr><tr><td></td><td>28091998</td><td>1.6</td><td>1.0</td><td>90</td><td>0.4</td><td>SKS</td></tr><tr><td></td><td>13062005</td><td>1.8</td><td>1.3</td><td>170</td><td>7</td><td>SKS</td></tr><tr><td></td><td>23061991</td><td>2.6</td><td>1.0</td><td>162</td><td>2</td><td>SKS</td></tr><tr><td>NB201</td><td>28092007</td><td>0.9</td><td>1.5</td><td>2</td><td>20</td><td>SKS</td></tr><tr><td></td><td>28091998</td><td>0.8</td><td>1.0</td><td>106</td><td>39</td><td>SKS</td></tr><tr><td></td><td>13062005</td><td>2.7</td><td>1.4</td><td>166</td><td>2</td><td>SKS</td></tr><tr><td>NBO00</td><td>28092007</td><td>1.6</td><td>1.5</td><td>32</td><td>20</td><td>SKS</td></tr><tr><td></td><td>28091998</td><td>0.9</td><td>0.5</td><td>154</td><td>12</td><td>SKS</td></tr><tr><td></td><td>30082008</td><td>1.1</td><td>1.0</td><td>118</td><td>31</td><td>SKS</td></tr><tr><td>NC204</td><td>16112007</td><td>1.4</td><td>0.9</td><td>110</td><td>15</td><td>SKS</td></tr><tr><td></td><td>28092007</td><td>1.4</td><td>1.5</td><td>152</td><td>20</td><td>SKS</td></tr><tr><td></td><td>28091998</td><td>0.6</td><td>0.5</td><td>118</td><td>34</td><td>SKS</td></tr><tr><td></td><td>12092009</td><td>2.5</td><td>0.8</td><td>85</td><td>2</td><td>SKS</td></tr><tr><td></td><td>27072003</td><td>2.8</td><td>1.4</td><td>75</td><td>4</td><td>SKS</td></tr><tr><td>NC303</td><td>28092007</td><td>0.9</td><td>1.5</td><td>2</td><td>20</td><td>SKS</td></tr><tr><td></td><td>28111997</td><td>1.1</td><td>1.5</td><td>89</td><td>42</td><td>SKS</td></tr><tr><td></td><td>28091998</td><td>0.7</td><td>0.7</td><td>116</td><td>15</td><td>SKS</td></tr><tr><td></td><td>25072004</td><td>1.7</td><td>1.2</td><td>157</td><td>25</td><td>SKS</td></tr><tr><td></td><td>08072008</td><td>1.4</td><td>1.1</td><td>86</td><td>15</td><td>SKS</td></tr><tr><td></td><td>06061991</td><td>1.2</td><td>1.5</td><td>96</td><td>43</td><td>SKS</td></tr><tr><td>NC405</td><td>28092007</td><td>1.7</td><td>1.4</td><td>28</td><td>20</td><td>SKS</td></tr><tr><td></td><td>26082008</td><td>0.8</td><td>0.5</td><td>112</td><td>20</td><td>SKS</td></tr><tr><td>NC602</td><td>09052008</td><td>3.0</td><td>1.1</td><td>145</td><td>5</td><td>SKS</td></tr><tr><td></td><td>16112007</td><td>2.2</td><td>1.4</td><td>8</td><td>11</td><td>SKS</td></tr><tr><td></td><td>28092007</td><td>1.7</td><td>1.2</td><td>148</td><td>12</td><td>SKS</td></tr></tbody></table>
<table><caption>**Table 3 (continued)**</caption><thead><tr><th>Station code</th><th>Event date</th><th>δt (s)</th><th>Error δt (s)</th><th>Φ (°)</th><th>Error Φ (°)</th><th>Phase</th></tr></thead><tbody><tr><td rowspan="5">MAGNUS mobile</td><td>30012007</td><td>2.8</td><td>1.4</td><td>143</td><td>6</td><td>SKS</td></tr><tr><td>28111997</td><td>1.4</td><td>1.0</td><td>9</td><td>17</td><td>SKS</td></tr><tr><td>08072008</td><td>2.5</td><td>2.1</td><td>176</td><td>18</td><td>SKS</td></tr><tr><td>12092009</td><td>1.9</td><td>1.3</td><td>179</td><td>20</td><td>SKS</td></tr><tr><td>27072003</td><td>0.8</td><td>1.4</td><td>1</td><td>35</td><td>SKS</td></tr><tr><td>NWG01</td><td>09052008</td><td>3.0</td><td>1.5</td><td>36</td><td>5</td><td>SKS</td></tr><tr><td rowspan="5">NWG03</td><td>09122007</td><td>1.0</td><td>0.7</td><td>87</td><td>13</td><td>SKKS</td></tr><tr><td>15102006</td><td>1.4</td><td>0.5</td><td>1</td><td>5</td><td>SKS</td></tr><tr><td>09052008</td><td>1.1</td><td>0.9</td><td>32</td><td>5</td><td>SKS</td></tr><tr><td>15102006</td><td>0.9</td><td>0.8</td><td>12</td><td>15</td><td>SKS</td></tr><tr><td>17102006</td><td>1.3</td><td>1.2</td><td>143</td><td>18</td><td>SKS</td></tr><tr><td rowspan="5">NWG04</td><td>26072007</td><td>1.4</td><td>1.4</td><td>163</td><td>15</td><td>SKS</td></tr><tr><td>28092007</td><td>1.6</td><td>1.4</td><td>29</td><td>20</td><td>SKS</td></tr><tr><td>09122007</td><td>2.4</td><td>0.6</td><td>26</td><td>3</td><td>SKKS</td></tr><tr><td>28092007</td><td>0.9</td><td>1.5</td><td>0</td><td>20</td><td>SKS</td></tr><tr><td>15102006</td><td>2.2</td><td>1.1</td><td>3</td><td>17</td><td>SKS</td></tr><tr><td>NWG05</td><td>09052008</td><td>2.5</td><td>1.8</td><td>142</td><td>10</td><td>SKS</td></tr><tr><td>NWG07</td><td>28092007</td><td>1.7</td><td>0.6</td><td>78</td><td>4</td><td>SKS</td></tr><tr><td>NWG08</td><td>17102006</td><td>0.8</td><td>1.0</td><td>63</td><td>20</td><td>SKS</td></tr><tr><td>NWG09</td><td>09052008</td><td>1.7</td><td>1.3</td><td>142</td><td>10</td><td>SKS</td></tr><tr><td>NWG11</td><td>09052008</td><td>1.0</td><td>1.4</td><td>150</td><td>20</td><td>SKS</td></tr><tr><td rowspan="5">NWG12</td><td>28092007</td><td>1.2</td><td>0.8</td><td>5</td><td>15</td><td>SKS</td></tr><tr><td>30012007</td><td>1.6</td><td>1.1</td><td>154</td><td>15</td><td>SKS</td></tr><tr><td>26072007</td><td>2.9</td><td>2.7</td><td>146</td><td>20</td><td>SKS</td></tr><tr><td>09052008</td><td>2.4</td><td>1.0</td><td>37</td><td>2</td><td>SKS</td></tr><tr><td>09052008</td><td>3.0</td><td>0.8</td><td>31</td><td>3</td><td>SKS</td></tr><tr><td>NWG13</td><td>09052008</td><td>0.9</td><td>0.6</td><td>30</td><td>13</td><td>SKS</td></tr><tr><td>NWG15</td><td>09052008</td><td>0.9</td><td>0.6</td><td>57</td><td>3</td><td>SKS</td></tr><tr><td>NWG16</td><td>26072007</td><td>3.0</td><td>2.0</td><td>32</td><td>12</td><td>SKS</td></tr><tr><td>NWG17</td><td>17102006</td><td>2.3</td><td>2.2</td><td>37</td><td>10</td><td>SKS</td></tr><tr><td>NWG18</td><td>09052008</td><td>1.2</td><td>1.5</td><td>42</td><td>6</td><td>SKS</td></tr><tr><td>NWG19</td><td>28092007</td><td>1.9</td><td>1.6</td><td>31</td><td>19</td><td>SKS</td></tr><tr><td rowspan="5">NWG20</td><td>09122007</td><td>1.2</td><td>0.6</td><td>79</td><td>13</td><td>SKKS</td></tr><tr><td>15102006</td><td>2.4</td><td>1.0</td><td>66</td><td>4</td><td>SKS</td></tr><tr><td>17102006</td><td>2.2</td><td>0.7</td><td>127</td><td>9</td><td>SKS</td></tr><tr><td>28092007</td><td>0.5</td><td>1.1</td><td>169</td><td>20</td><td>SKS</td></tr><tr><td>09052008</td><td>1.9</td><td>0.6</td><td>23</td><td>7</td><td>SKS</td></tr><tr><td>NWG21</td><td>17102006</td><td>1.2</td><td>0.6</td><td>20</td><td>13</td><td>SKS</td></tr><tr><td>NWG22</td><td>28092007</td><td>1.3</td><td>0.6</td><td>14</td><td>11</td><td>SKS</td></tr><tr><td rowspan="3">NWG22</td><td>30012007</td><td>1.8</td><td>0.6</td><td>1</td><td>5</td><td>SKS</td></tr><tr><td>06112007</td><td>2.6</td><td>0.8</td><td>163</td><td>7</td><td>SKS</td></tr><tr><td>28092007</td><td>2.6</td><td>0.6</td><td>27</td><td>4</td><td>SKS</td></tr><tr><td>NWG22</td><td>30012007</td><td>2.3</td><td>0.3</td><td>21</td><td>1</td><td>SKS</td></tr></tbody></table>

<figure><img src="image_126.png" /></figure>
<table><caption>**Table 3 (continued)**</caption><thead><tr><th>Station code</th><th>Event date</th><th>δt (s)</th><th>Error δt (s)</th><th>Φ (°)</th><th>Error Φ (°)</th><th>Phase</th></tr></thead><tbody><tr><td rowspan="3">NWG23</td><td>17102006</td><td>1.5</td><td>0.7</td><td>155</td><td>13</td><td>SKS</td></tr><tr><td>26072007</td><td>1.5</td><td>1.3</td><td>170</td><td>23</td><td>SKS</td></tr><tr><td>28092007</td><td>1.2</td><td>0.5</td><td>149</td><td>7</td><td>SKS</td></tr><tr><td>NWG24</td><td>17102006</td><td>1.1</td><td>1.4</td><td>152</td><td>20</td><td>SKS</td></tr><tr><td>NWG25</td><td>15102006</td><td>1.7</td><td>1.0</td><td>61</td><td>10</td><td>SKS</td></tr><tr><td rowspan="2">NWG27</td><td>09052008</td><td>1.2</td><td>1.1</td><td>147</td><td>16</td><td>SKS</td></tr><tr><td>09122007</td><td>2.6</td><td>0.6</td><td>23</td><td>4</td><td>SKKS</td></tr><tr><td rowspan="2">NWG28</td><td>09052008</td><td>3.0</td><td>1.2</td><td>152</td><td>8</td><td>SKS</td></tr><tr><td>30012007</td><td>2.0</td><td>0.5</td><td>159</td><td>7</td><td>SKS</td></tr><tr><td rowspan="3">NWG29</td><td>09052008</td><td>2.7</td><td>1.4</td><td>138</td><td>3</td><td>SKS</td></tr><tr><td>16112007</td><td>1.9</td><td>1.9</td><td>93</td><td>20</td><td>SKS</td></tr><tr><td>17102006</td><td>2.5</td><td>0.5</td><td>155</td><td>4</td><td>SKS</td></tr><tr><td rowspan="3">NWG30</td><td>09052008</td><td>1.1</td><td>0.2</td><td>167.19</td><td>12</td><td>SKS</td></tr><tr><td>17102006</td><td>0.9</td><td>0.4</td><td>0.5</td><td>17</td><td>SKS</td></tr><tr><td>28092007</td><td>3.0</td><td>0.5</td><td>138.1</td><td>3</td><td>SKS</td></tr><tr><td rowspan="3">NWG31</td><td>09122007</td><td>1.3</td><td>1.8</td><td>4</td><td>28</td><td>SKKS</td></tr><tr><td>16112007</td><td>2.7</td><td>1.0</td><td>149</td><td>9</td><td>SKS</td></tr><tr><td>30012007</td><td>3.0</td><td>1.5</td><td>30</td><td>5</td><td>SKS</td></tr><tr><td>NWG34</td><td>09122007</td><td>0.9</td><td>0.6</td><td>57</td><td>18</td><td>SKKS</td></tr><tr><td>NWG35</td><td>09052008</td><td>1.7</td><td>1.0</td><td>152</td><td>14</td><td>SKS</td></tr><tr><td colspan="7">SCANLIPS1 unstacked</td></tr><tr><td>N6002</td><td>25082006</td><td>1.9</td><td>1.2</td><td>167</td><td>9</td><td>SKS</td></tr><tr><td>N6003</td><td>25082006</td><td>1.3</td><td>0.5</td><td>5</td><td>12</td><td>SKS</td></tr><tr><td>N6008</td><td>17102006</td><td>3.0</td><td>1.5</td><td>35</td><td>5</td><td>SKKS</td></tr><tr><td>N6010</td><td>17102006</td><td>0.8</td><td>1.1</td><td>106</td><td>38</td><td>SKS</td></tr><tr><td rowspan="3">N6014</td><td>25082006</td><td>1.5</td><td>1.3</td><td>148</td><td>13</td><td>SKS</td></tr><tr><td>25082006</td><td>2.7</td><td>1.6</td><td>154</td><td>4</td><td>SKKS</td></tr><tr><td>17102006</td><td>2.7</td><td>1.1</td><td>123</td><td>14</td><td>SKS</td></tr><tr><td>N6017</td><td>25082006</td><td>3.0</td><td>1.5</td><td>153</td><td>4</td><td>SKS</td></tr><tr><td>N6026</td><td>25082006</td><td>3.0</td><td>1.4</td><td>157</td><td>3</td><td>SKS</td></tr><tr><td colspan="7">SCANLIPS1 stacked</td></tr><tr><td rowspan="2">N6002</td><td>25082006</td><td>1.3</td><td>0.7</td><td>173</td><td>10</td><td>SKS</td></tr><tr><td>25082006</td><td>0.8</td><td>1.4</td><td>1</td><td>20</td><td>SKKS</td></tr><tr><td rowspan="2">N6003</td><td>25082006</td><td>1.6</td><td>0.9</td><td>173</td><td>7</td><td>SKS</td></tr><tr><td>25082006</td><td>1.6</td><td>1.1</td><td>175</td><td>20</td><td>SKKS</td></tr><tr><td rowspan="2">N6004</td><td>25082006</td><td>1.0</td><td>0.8</td><td>175</td><td>15</td><td>SKS</td></tr><tr><td>25082006</td><td>1.1</td><td>0.6</td><td>25</td><td>15</td><td>SKKS</td></tr><tr><td>N6006</td><td>25082006</td><td>1.5</td><td>1.3</td><td>49</td><td>15</td><td>SKKS</td></tr><tr><td>N6007</td><td>25082006</td><td>3.0</td><td>0.4</td><td>60</td><td>3</td><td>SKKS</td></tr><tr><td rowspan="2">N6008</td><td>25082006</td><td>1.8</td><td>1.4</td><td>150</td><td>15</td><td>SKS</td></tr><tr><td>17102006</td><td>0.6</td><td>1.1</td><td>87</td><td>30</td><td>SKS</td></tr><tr><td>N6009</td><td>25082006</td><td>1.8</td><td>0.9</td><td>150</td><td>3</td><td>SKS</td></tr><tr><td>N6010</td><td>17102006</td><td>1.2</td><td>0.5</td><td>119</td><td>8</td><td>SKS</td></tr><tr><td>N6011</td><td>25082006</td><td>1.8</td><td>0.6</td><td>149</td><td>4</td><td>SKKS</td></tr></tbody></table>
<table><caption>**Table 3 (continued)**</caption><thead><tr><th>Station code</th><th>Event date</th><th>δt (s)</th><th>Error δt (s)</th><th>Φ (°)</th><th>Error Φ (°)</th><th>Phase</th></tr></thead><tbody><tr><td rowspan="3">N6013</td><td>17102006</td><td>1.3</td><td>1.4</td><td>122</td><td>30</td><td>SKS</td></tr><tr><td>25082006</td><td>2.5</td><td>0.5</td><td>153</td><td>2</td><td>SKS</td></tr><tr><td>17102006</td><td>1.2</td><td>1.2</td><td>118</td><td>33</td><td>SKS</td></tr><tr><td rowspan="2">N6014</td><td>25082006</td><td>2.3</td><td>0.9</td><td>152</td><td>2</td><td>SKS</td></tr><tr><td>17102006</td><td>1.0</td><td>1.3</td><td>119</td><td>35</td><td>SKS</td></tr><tr><td>N6016</td><td>25082006</td><td>2.8</td><td>0.9</td><td>152</td><td>5</td><td>SKS</td></tr><tr><td>N6017</td><td>17102006</td><td>0.6</td><td>0.7</td><td>83</td><td>38</td><td>SKS</td></tr><tr><td rowspan="2">N6018</td><td>25082006</td><td>2.3</td><td>1.5</td><td>153</td><td>5</td><td>SKS</td></tr><tr><td>25082006</td><td>2.9</td><td>0.7</td><td>153</td><td>14</td><td>SKKS</td></tr><tr><td>N6019</td><td>25082006</td><td>2.7</td><td>1.5</td><td>153</td><td>5</td><td>SKS</td></tr><tr><td>N6020</td><td>25082006</td><td>2.2</td><td>1.3</td><td>151</td><td>5</td><td>SKS</td></tr><tr><td>N6021</td><td>25082006</td><td>2.3</td><td>1.4</td><td>154</td><td>10</td><td>SKS</td></tr><tr><td>N6025</td><td>25082006</td><td>2.0</td><td>0.6</td><td>53</td><td>8</td><td>SKKS</td></tr><tr><td colspan="7">SCANLIPS2</td></tr><tr><td>N7001</td><td>11092008</td><td>1.2</td><td>0.9</td><td>53</td><td>15</td><td>SKS</td></tr><tr><td>N7003</td><td>11092008</td><td>2.0</td><td>1.4</td><td>56</td><td>14</td><td>SKS</td></tr><tr><td rowspan="2">N7005</td><td>30082008</td><td>1.4</td><td>0.8</td><td>27</td><td>14</td><td>SKS</td></tr><tr><td>11092008</td><td>0.8</td><td>0.3</td><td>3</td><td>10</td><td>SKS</td></tr><tr><td rowspan="2">N7014</td><td>30082008</td><td>3.0</td><td>1.9</td><td>156</td><td>8</td><td>SKKS</td></tr><tr><td>11092008</td><td>2.4</td><td>1.0</td><td>63</td><td>4</td><td>SKS</td></tr><tr><td rowspan="2">N7020</td><td>30082008</td><td>1.3</td><td>0.8</td><td>44</td><td>15</td><td>SKKS</td></tr><tr><td>11092008</td><td>1.1</td><td>0.6</td><td>3</td><td>10</td><td>SKS</td></tr><tr><td rowspan="3">N7023</td><td>26082008</td><td>3.0</td><td>1.3</td><td>11</td><td>3</td><td>SKS</td></tr><tr><td>11092008</td><td>1.0</td><td>0.2</td><td>50</td><td>9</td><td>SKS</td></tr><tr><td>26082008</td><td>1.8</td><td>1.0</td><td>83</td><td>8</td><td>SKS</td></tr><tr><td rowspan="2">N7025</td><td>08072008</td><td>2.5</td><td>0.7</td><td>79</td><td>2</td><td>SKS</td></tr><tr><td>11092008</td><td>1.1</td><td>0.4</td><td>54</td><td>9</td><td>SKS</td></tr><tr><td>N7027</td><td>11092008</td><td>1.2</td><td>0.6</td><td>179</td><td>8</td><td>SKS</td></tr></tbody></table>

## 5.4 Northern Scandes and Sweden

Fourteen splitting results obtained from four earthquakes could be determined with the SCANLIPS2 dataset. Along the SCANLIPS2 line, $\Phi$ is mainly in NE-SW direction (Fig. 9c). This $\Phi$ direction is found close to the coast (N7001, N7003) and in Sweden on the eastern part of the line. There is one significant anomaly at station N7005 with $\Phi$~NW-SE and a long $\delta t$ of 3 s from an SKKS phase of an event under New Guinea. It is unclear whether this splitting result is due to a local feature underneath station N7005 because another SKS splitting measurement (Halmahera event) has N-S orientation with a much shorter $\delta t$ of just 0.8 s. Both measurements have a similar SNR on the

T component. The observed splitting results in the north may become more complex when observations from more backazimuths can be included as in Southern Norway.

# 6 Discussion and interpretation

Our observations of split SKS and SKKS waves and their derived apparent splitting parameters are strong indicators for seismic anisotropy below the Scandes in Norway and parts of Sweden. However, the splitting parameters $\Phi$ and $\delta t$ vary for different epicentre backazimuths at some stations as well as between station clusters. Such variations indicate a complex
a

<figure><img src="image_127.png" /></figure>

b

<figure><img src="image_128.png" /></figure>

c

<figure><img src="image_129.png" /></figure>

d

<figure><img src="image_130.png" /></figure>

e

<figure><img src="image_131.png" /></figure>

f

<figure><img src="image_132.png" /></figure>

**Fig. 7** SKS and SKKS waveforms at SCANLIPS1 stations of an event under the Chile–Argentina border region (25 Aug. 2006, 00:44:47 UT at 184 km in depth, *M*<sub>w</sub>=6.6): **a** radial component, filtered at 5–15 Hz and amplitude normalisation, **b** stacked radial waveforms from three neighbouring stations

anisotropic structure at depth. The observed *Φ* and *δt* variations do not allow an interpretation with a simple

aligned along the slowness of 4.3 s/° of the SKS phase, **c** stacked and aligned radial SKKS phase (along 6.9 s/° slowness), **d** filtered and unstacked transverse component, **e** stacked transverse SKS phase, **f** stacked transverse SKKS phase

model such as *one* anisotropic layer with transverse anisotropy and *one* horizontal fast polarisation axis.
<figure><img src="image_133.png" /><figcaption>**Fig. 8** Splitting results at the MAGNUS network in Southern Norway. The *colour coding* corresponds to the backazimuthal regions in Fig. 2. The main tectonic units are given after Ramberg et al. (2008). *MTFC Møre-Trøndelag Fault Complex*. Note that only the last two digits of the station names are given</figcaption></figure>

More complex models are required, including lateral variation of anisotropy or isotropic crustal domains, multiple anisotropic layers, dipping fast axes, variable layer depths as well as variable layer thicknesses. However, complex anisotropic models cannot be determined uniquely with our dataset. Such complex models predict apparent *Φ* and *δt* values with strong backazimuth dependence, e.g. often including a characteristic 90° pattern (see Silver and Savage (1994) or Rümpker and Silver (1998)) and with frequency dependence (Rümpker et al. 1999). Our epicentre distribution (Fig. 2) limits such a backazimuth-dependent analysis. Even worse, most epicentres are in the NW Pacific and South America regions (Fig. 2), which have a backazimuth difference of about 180° at our stations. Such oppositely propagating shear waves should split to similar apparent *Φ* and *δt* values in horizontally transverse

anisotropic structures and cannot resolve complex structures in many cases. Further constraints on seismic anisotropy are not available for our study region. Our dataset is presently the only one to describe seismic anisotropy below the Scandes.

There are several indications that our observations are mainly caused by deep-seated anisotropy in the upper mantle underneath the Scandes. First, the observed split times ($\delta t>1$ s) are too large to be explained solely with crustal anisotropy. Barruol and Mainprice (1993) argue that only as much as $\delta t \sim 0.3$ s can be explained with reasonable and known crustal rock fabrics. Second, new, high-quality seismic refraction models (Stratford et al. 2009; Stratford and Thybo 2011) and ambient noise Rayleigh wave tomography models (Köhler et al. 2011) do not indicate that there is widespread crustal seismic anisotropy in Southern Norway. Third, the frequency bandwidth of the observed SKS splitting at station KONO indicates that wavelengths exceeding the crustal thickness are affected by splitting and that very large regions have an impact on the splitting of the SKS/SKKS wavefields. We also infer that small-scale heterogeneity does not influence much the splitting parameters at KONO because short-period (5–15 s) and long-period (10–50 s) splitting results have very similar *Φ* angles (Fig. 6). Fourth, there is mostly no obvious difference between SKS and SKKS splitting results from the same event at the SCANLIPS experiments (Table 3; Fig. 9). Thus, we assume that the shear wave splitting is generated along a common ray path for SKS and SKKS phases, which means that anisotropy is located within the upper mantle and the crust (Niu and Perez 2004).

## 6.1 Southern Norway

In the Southern Scandes, there is an obvious spatial correlation between similar splitting results and the major tectonic units at the surface (Fig. 8). The apparent directions of *Φ* are nearly NW-SE on the Proterozoic outcrop regions and NE-SW on the Caledonian nappes. At the boundaries between these units, the *Φ* pattern is more variable, for example, at the NORSAR array and at the northern stations (NWG01 and NWG03) of the MAGNUS network. This observation is an indication for laterally varying anisotropy. As argued before, crustal anisotropy alone cannot explain our observations. The backazimuthal variation of *Φ* indicates that two or more layers with different anisotropic fabrics or an inclined fast axis contribute to shear wave splitting. Thus, it

<figure><img src="image_134.png" /></figure>
**Fig. 9** Splitting results in Central and Northern Norway and Sweden. Colours correspond to the backazimuthal regions in Fig. 2. Arrows in *dark blue* (South American events) and *red* (Pacific events) are SKS results; arrows in *light blue* and *orange* (with *black boundaries*) are SKKS results from these epicentral regions. **a** Splitting results at SCANLIPS1 obtained from single-station measurements, **b** splitting results after gliding station stack, **c** results at SCANLIPS2 obtained from single-station measurements. Note that only the last two digits of the station names are given for clarity

<figure><img src="image_135.png" /></figure>

<figure><img src="image_136.png" /></figure>

<figure><img src="image_137.png" /></figure>
seems that a near-surface anisotropic layer causes the
finally measured direction of $\Phi$. Such a layer could be
inherited from a local tectonic event which left behind a
local anisotropic rock fabric. Kaviani et al. (2011) dem-
onstrate that even a thin isotropic layer, which changes
laterally, can have a significant influence on the splitting
parameters. Our observations can also indicate a multi-
layer model similar to the synthetic modelling scenarios
by Rümpker et al. (1999). They study depth-dependent
anisotropy and demonstrate that in the upper layer the
fast axis orientation controls the apparent orientation of
$\Phi$ (possibly crustal fabrics in our case), whereas in the
lower layer the angle between the fast axis orientation
and the epicentre backazimuth control the split time $\delta t$.

Our frequency-dependent splitting parameters for
station KONO (Fig. 6) are similar to the synthetic
waveform modelling and splitting results for models
M3 and M4 in Rümpker et al. (1999). These synthetic
examples contain a change in the fast axis orientation
of about 50° and 60° between an upper and a lower
anisotropic layer. This configuration leads to a change
in apparent $\Phi$ of up to 40° relative to the true fast axis
orientation in the upper layer and up to 60° (mostly
<20°) between short-period (5 s) and long-period
(20 s) SKS phases. However, in such cases, $\Phi$ depends
on the backazimuth which we cannot resolve properly.
The frequency-dependent apparent delay time $\delta t$
increases with increasing period by up to 2–3 s in
Rümpker et al. (1999), which is also observed in our
data; this parameter is also backazimuth dependent.
Our high $\delta t$ of up to 3 s at KONO for events with back-
azimuths of 240–260° (South American epicentres) may
be a hint that this propagation direction is favourable for
strong shear wave splitting in a deep layer below the
Southern Scandes. A unique model of anisotropy cannot
be determined with the limited observed backazimuths.
In the following text, only regions with different splitting
characteristics are discussed.

At the stations on the Caledonian nappes in Southern
Scandes (Fig. 8), the NE–SW orientation of $\Phi$ is inter-
preted as evidence for a considerable change of the rock
fabric in the lithosphere compared to the neighbouring
Proterozoic blocks where $\Phi$ is preferably NW–SE-orient-
ed. The same Proterozoic lithosphere, and possibly trend
in rock fabric, may be present below the Caledonian
nappes, but the upper part of the lithosphere there was
heavily deformed during the collisional processes as well
as during the postcollisional collapse which again de-
formed it (Andersen 1998; Torsvik and Cocks 2005;

Ramberg et al. 2008). These deformational processes
produced rock fabrics that may now control the NE–
SW orientation of $\Phi$ which is different to the surrounding
older lithosphere units. The Caledonian nappes originate
from an eastward nappe translation, whereas the postcol-
lisional collapse had a top-westerly directed sense of
shear (Andersen 1998). Thus, mostly NW–SE-oriented
rock fabrics are found in the Caledonian mountains,
which do not correlate with our fast polarisation direc-
tions. Also, some NE–SW striking extensional structures
have been identified in the area of the Faltungsgraben
(Andersen 1998) where our stations BER, NWG13, 15,
16, 21 and 22 were situated and which measured a NE–
SW-oriented $\Phi$ (Fig. 8). The NE–SW trends postdate the
more dominant top-west reactivated faults (Andersen
1998) and also other tectonic structures at depth may
contribute to the splitting pattern in the Caledonian
mountains. There is an uncertainty on how deep the
surface tectonics and its related rock fabric reach down
to depth. However, we infer that the crustal structure,
such as the Caledonian nappes, has an influence on the
observed SKS/SKKS splitting similar to the influence of
even isotropic sediment layers (Kaviani et al. 2011). Due
to the large $\delta t$ values, it is obvious that shear wave
splitting has an additional lower lithospheric or even
asthenospheric origin, but the fast polarisation direction
cannot be resolved at this depth range. Our findings are
similar to the results of Bastow et al. (2007) who analyse
SKS splitting in the Caledonian mountains in Northern
Scotland and its surroundings. They also find variation of
$\Phi$ across short station distances, which is interpreted as
fossil anisotropic signature of lithospheric blocks.

The surface projection of the ray paths in the an-
isotropic medium are outlined in Fig. 10. For this
projection, we assume a uniform 3 % anisotropy at
depth to determine an estimate for the length of the
SKS/SKKS ray path which is calculated with an aver-
age shear wave velocity of 4.5 km/s and the average $\delta t$
value for a backazimuth region at a station site. The
surface projection is then determined based on the
average incidence angle of the rays. The colour coding
in Fig. 10 corresponds to the apparent $\Phi$ and the map
visualises the spatial distribution of $\Phi$ and $\delta t$. There
are several domains with similar splitting parameters
indicating small-scale coherence of anisotropy, e.g. in
the area of the Caledonian nappes and the Proterozoic
basement region in the south.

In the northwestern part of the MAGNUS network,
the Møre–Trøndelag fault complex (MTFC; Fig. 8)

<figure><img src="image_138.png" /></figure>
<figure><img src="image_139.png" /><figcaption>**Fig. 10** Surface projection of split ray paths with fast anisotropic direction in colour. These ray path segments point into the backazimuth direction and they indicate the data coverage at depth. The segments are based on average ray paths for SKS phases from the main source regions (see Fig. 2 and text)</figcaption></figure>

may play an additional role concerning deformation and generation of rock fabrics (Gilotti and Hull 1993; Redfield et al. 2005; Olsen et al. 2007). The NE–SW striking MTFC is about 50 km in width, about 300 km in length and consists partly of penetratively deformed rock masses. However, seismic anisotropy related to the MTFC has not yet been studied in detail. Our varying splitting results at stations NWG01, 03 and 04 indicate that anisotropy is complex in the vicinity of the MTFC and should be studied in more detail.

Around the Oslo Graben in southernmost Norway, the splitting results are also not unique. The ray path distribution in Fig. 10 shows that the split SKS/SKKS waves did not propagate directly underneath the Oslo Graben; however, the whole region is characterised by small-scale variations in geology, including faults and

shear zones related to the rifting processes (Neumann et al. 1995). Our $\Phi$ and $\delta t$ results vary at stations NWG19, 25, 27 and 34 (Fig. 8) with mainly apparent $\Phi$ in ENE–WSW direction. At other nearby stations, $\Phi$ has a more NW–SE trend in the Proterozoic lithospheric domain (Figs. 8 and 10) which belongs to the Sveconorwegina in this region. This variability in $\Phi$ may be due to locally changing dominant rock fabrics related to the rifting processes of the Oslo Graben. The $\Phi$ pattern gets even more complex at the NORSAR stations (Figs. 8 and 10) which are just at the northern end of the Oslo Graben and extend into the Caledonian nappes (named Eocambrian rocks; see Bungum et al. (1971)). At the southern stations at NORSAR, $\Phi$ is oriented mainly N–S with backazimuth-dependent deviations, whereas at the northern station at NORSAR $\Phi$ prevails in E–W direction (Fig. 8). This change possibly reflects the transition from the Caledonian nappes in the north with rock fabrics due to E–W postcollisional extension relative to the rifted Sveconorwegian lithosphere in the south. Anyhow, we interpret the small-scale variability as a significant influence of near-surface, crustal structure on the shear wave splitting results.

In southern Sweden, at station HFC2, we find a NNE–SSW-oriented $\Phi$ which is the same result as at the nearby station UDD in Eken et al. (2010). They interpret their splitting measurements in this region (58–62° N) as scattered compared to more uniform splitting results in the north and south of Sweden.

## 6.2 Central Scandes and Sweden

Across the SCANLIPS1 line at about 63° N, three domains with similar splitting parameters can be distinguished (Fig. 9a, b). To the west of 10° E longitude, close to the Atlantic coast, $\Phi$ is N–S-oriented for SKS and SKKS splits from South America. At about 10° to 11.5° E longitude, $\Phi$ varies for different backazimuths as well as SKS and SKKS. There seems to be a complex anisotropic structure at depth which may be related to the northern end of the MTFC as observed further south. The rock fabric of this fault zone is characterised by laterally varying directions in foliation and lineations (Gilotti and Hull 1993). In the Caledonian nappes, mainly NW–SE-oriented foliation is found, indicating top-to-the-NW transport, whereas NE–SW structures including deformed rock matrixes dominate close to the shear faults (Gilotti and Hull 1993). This deformation causes locally significant and
variable seismic anisotropy. Below this crustal zone,
in the mantle, there may be another direction of the
fast polarisation axis; however, due to few observed
backazimuths, this cannot be resolved with the presently
available datasets.

Along the eastern part of SCANLIPS1 (east of
11.5° E) up to the coast of the Baltic Sea in Sweden,
the apparent Φ is very stable in NW-SE direction for
the analysed South American event. SKS and SKKS
measurements of this event are nearly the same, with
the exception of one SW-NE Φ result at station
N0025. Measurements at SKS phases from Pacific
events (red arrows in Fig. 9) have a more E-W trend,
indicating that a single layer model of anisotropy
cannot explain the measurements. Splitting results at
the permanent Swedish stations (NOR, SOL and
HEM) also retrieved a WNW-ESE apparent Φ which
is attributed to the anisotropic signature of the Central
Svecofennian province (Eken et al. 2010). Structural
maps indicate a NW-SE orientation of ductile shear
zone and tectonic foliation at about 15° to 16° E.
Further east, this structural trend changes to NE-SW
foliation (Högdahl et al. 2009), coinciding with Φ at
station N0025. This coincidence is a strong hint that
upper crustal rock fabrics can influence the fast polar-
isation direction of SKS waves. At present, we cannot
determine the fast polarisation direction at deeper lev-
els in the crust or mantle. The δt values in this region
are high with an average δt of 1.7 s and many single
measurements exceeding 2 s (Table 3), which may be
due to either a long travel path in the mantle with
uniform moderate anisotropy (<3 %) or a short travel
path with a highly anisotropic rock fabric.

6.3 Northern Scandes and Sweden

The Φ results across SCANLIPS2 line (66° to 68°N)
clearly differ from SCANLIPS1 (~63.5° N). In the
Northern Scandes and across its eastern foreland in
Northern Sweden, the prevailing direction of Φ is NE-
SW. Only at station N7005 inside the Northern
Scandes is Φ oriented N–S (SKS) to NW–SE (SKKS).
In Sweden, at the permanent network, apparent Φ is also
NE–SW (Eken et al. 2010), which is interpreted to be
due to a North Scevofennian–Karelian domain. Our Φ
results show a clear difference in anisotropic signature
between the Central and Northern Scecofennian
domains as was also found by Eken et al. (2010). The
δt values in the northern part are similar on average

(~1.7 s) to the average δt in the central part of the
Scandes and Sweden.

7 Summary

We present SKS/SKKS splitting results from broadband
stations in Norway and Sweden which cover the Scan-
dinavian Mountains as well as their eastern foreland. The
splitting parameters Φ and δt can be determined well and
are stable at most stations and lead to reproducible results
for similar epicentre regions. The splitting results are not
consistent with a simple one-layer model of anisotropy.
We find frequency-dependent splitting parameters at
KONO, which indicate depth-dependent anisotropy. At
many stations, the splitting parameters depend on the
backazimuth of the events which also indicates multiple-
layer anisotropy or inclined fast axis alignment. The split
times are mostly well above 1 s, indicating a mantle
contribution. However, a correlation of the apparent fast
direction Φ with mantle fabric in the lower lithosphere or
flow in the asthenosphere cannot be deduced yet. There-
fore, the non-uniqueness of the splitting results from
different backazimuths still impedes an interpretation
towards the origin of the uplift processes of the Scandi-
navian Mountains.

The recovered complicated pattern of Φ and δt cannot
be explained with a unique model of the anisotropic
structure at depth because splitting is observed from
few backazimuths. However, characteristic signatures
of Φ can be observed for different tectonic domains and
partly correlate with preferred mineral orientations of
rocks at the surface. In the south of Norway, Φ is mainly
NW-SE-oriented in the Sveconorwegian Proterozoic
domain. On the Caledonian nappes, Φ is NE-SW-orient-
ed and Φ appears to vary significantly around the Oslo
Graben and Møre-Trøndelag fault complex. In these two
regions, the lithosphere is deeply faulted and deformed,
which may lead to a small-scale pattern of rock fabrics
and hence varying splitting results. In Central Sweden,
on the Central Svecofennian lithosphere, Φ is preferably
in NW-SE direction, clearly different from the NE-SW
orientation of Φ in the Northern Svecofennian province
further north.

The determination of the splitting results was partly
improved by stacking the SKS/SKKS waveforms us-
ing array techniques. This approach should be pursued
in the future to achieve more splitting parameters,
especially from backazimuth regions without present
observations. Such improved backazimuth coverage is
necessary to better interpret the observed splitting
parameters in terms of anisotropic structure at depth.

**Acknowledgments** We thank especially Dr. Richard England, Dr. Johannes Schweitzer, and Dipl.-Geophys. Britta Wawerzinek for providing SCANLIPS, NORSAR, and MAGNUS waveforms, respectively. Two anonymous reviewers provided helpful and critical comments. MAGNUS waveforms were recorded with the mobile KArolsruhe BroadBand Array of the Universität Karlsruhe (TH) (now KIT), Germany, as well as with permanent stations of the NORSAR array and the Norwegian National Seismological Network. Financial support for the MAGNUS experiment was provided by the University of Aarhus, University of Copenhagen, University of Karlsruhe, and University of Oslo as well as NOR-SAR. SCANLIPS was conducted using seismic stations from the NERC Geophysical Equipment Facility (SEIS-UK) and NERC funding. This work has been done in association with the partners of the ESF EUROCORES TOPO-EUROPE Programme 07-TOPO-EUROPE-FP-014 “The Scandinavian mountain chain: deep processes (TopoScandiaDeep)”. It was supported by the Deutsche Forschungsgemeinschaft through grant RI1133/8-1. SeismicHandler (Stammler 1993) was used for seismic waveform processing and GMT software (Wessel and Smith 1998) was used for plotting maps.

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# Appendix C

Article: Effect of ray and speed perturbations on Ionospheric Tomography by Over-the-horizon radar: A new method
<figure><img src="image_140.png" /></figure>
# Journal of Geophysical Research: Space Physics

## RESEARCH ARTICLE

10.1002/2014JA020137

**Key Points:**

* A new 3-D ionospheric tomography method for monostatic OTH radar

* The raypath deflection effect is not negligible

* Three-dimensional reconstruction of the electron density over Europe is possible

**Correspondence to:**

C. Roy,
roy@ipgp.fr

**Citation:**

Roy, C., G. Occhipinti, L. Boschi, J.-P. Moliné, and M. Wieczorek (2014), Effect of ray and speed perturbations on ionospheric tomography by over-the-horizon radar: A new method, *J. Geophys. Res. Space Physics*, 119, doi:10.1002/2014JA020137.

Received 28 APR 2014
Accepted 18 AUG 2014
Accepted article online 22 AUG 2014

## Effect of ray and speed perturbations on ionospheric tomography by over-the-horizon radar: A new method

Corinna Roy¹,², Giovanni Occhipinti¹, Lapo Boschi³, Jean-Philippe Moliné², and Mark Wieczorek¹

¹Institut de Physique du Globe de Paris, Université Paris Diderot, Paris, France, ²Office National d'études et de recherches aérospatiales, Palaiseau, France, ³Laboratoire iSTeP, Université Pierre et Marie Curie, Paris, France

**Abstract** Most recent methods in ionospheric tomography are based on the inversion of the total electron content measured by ground-based GPS receivers. As a consequence of the high frequency of the GPS signal and the absence of horizontal raypaths, the electron density structure is mainly reconstructed in the F2 region (300 km), where the ionosphere reaches the maximum of ionization, and is not sensitive to the lower ionospheric structure. We propose here a new tomographic method of the lower ionosphere, based on the full inversion of over-the-horizon (OTH) radar data. Previous studies using OTH radar for ionospheric tomography inverted only the leading edge echo curve of backscatter ionograms. The major advantage of our methodology is taking into account, numerically and jointly, the effect that the electron density perturbations induce not only in the speed of electromagnetic waves but also on the raypath geometry. This last point is extremely critical for OTH radar inversions as the emitted signal propagates through the ionosphere between a fixed starting point (the radar) and an unknown end point on the Earth surface where the signal is backscattered. We detail our ionospheric tomography method with the aid of benchmark tests. Having proved the necessity to take into account both effects simultaneously, we apply our method to real data. This is the first time that the effect of the raypath deflection has been quantified and that the ionospheric plasma density has been estimated over the entirety of Europe with an OTH radar.

## 1. Introduction

Most recent methods in ionospheric tomography are based on the inversion of the total electron content (TEC) derived from dual-frequency receivers of the Global Navigation Satellites System (GNSS), mainly the American Global Positioning System (GPS). The TEC is the integral of electron density along the raypath between the satellite and the receiver, computed from the phase difference between two signals emitted by the GPS satellite and measured at the receiver [Mannucci et al., 1993]. TEC is usually visualized as global or regional two-dimensional maps to show the state of the ionosphere [Mannucci et al., 1998]. The measurement of TEC on the raypath between satellites and receivers, jointly with some priori information about the background ionospheric model, allows additionally to estimate the local electron density of the ionosphere using the inverse problem theory, [e.g., Tarantola, 2005].

GNSS ionospheric tomography was first tested in simulations by Austen et al. [1988], showing that numerical tomography techniques can be used to produce two-dimensional vertical cross sections of the electron density in the ionosphere. Andreeva et al. [1990] published the first experimental result using TEC data collected at three receivers in Russia and reconstructed a two-dimensional vertical cross section of the ionosphere by satellite radio tomography for the first time.

The installation of global (e.g., the International GNSS Service) and regional (e.g., GNSS Earth Observation Network (GEONET) in Japan) ground-based GPS networks greatly increased the amount of available data and raypath coverage, making three-dimensional reconstruction of the ionosphere with time evolution (3-D + 1) possible. Since then, GPS-based computerized ionospheric tomography has been widely used to investigate the temporal and spatial variations of ionospheric structures [Hansen et al., 1997; Hajj et al., 1994; Hernández-Pajares et al., 1998; Bust et al., 2004; Garcia et al., 2005; Ma et al., 2005; Yizengaw et al., 2005; Wen et al., 2007].

Although GPS is a powerful tool for studying the ionosphere, theoretical limitations of ionospheric tomography using GNSS satellite-to-Earth configuration have been discussed in detail in the literature [Yeh and
Raymund, 1991; Na and Sutton, 1994]. Apart from the spatial and temporal limitations associated with the experimental arrangements, the data sets are often incomplete because of the finite sampling interval and the limited angle of view of each receiver. Additionally, most of the tomographic methods make the assumption of an invariant ionosphere during the time of measurement.

Notwithstanding those previous limitations, the major problems of ionospheric tomography using GPS are the following. First, the absence of horizontal raypaths, resulting in a low vertical resolution. Second, the high frequency of the GPS signal limits the sensitivity of the electromagnetic waves to the maximum of electron density in the ionosphere, nominally the *F* region at around 300 km altitude.

To overcome the major limitations of low vertical resolution, three approaches are possible. The first approach is to incorporate, in the reconstruction, extra information from other instruments, for instance ionosonde data, which allow for the determination of electron density in the lower ionospheric layers, such as the *E* (~100 km) and *F*1 region (~250 km). Heaton et al. [1995] tested the incorporation of scaled ionograms into the imaging and found improvement in the vertical profiles. Kersley et al. [1993] showed promising results with the incorporation of ionosonde data into the reconstruction algorithm and better agreement with the EISCAT (European Incoherent Scatter Scientific Association) measurements in the vicinity of the layer maximum. Markkanen et al. [1995] applied a Bayesian approach to simulated results and incorporated peak heights as a priori information in the reconstruction algorithm for calculating the *F* region electron density, which are compared with the EISCAT radar observations.

The second approach is to use general knowledge of the shape of ionospheric profiles to constrain the reconstruction results and to fill the information gap: The most widely used solution is the one proposed by Fremouw et al. [1992], who used a set of vertical orthonormal functions, created from ionospheric models, to model the vertical profile. Unfortunately, existing ionospheric models are partially incorrect, because they fail to predict the strong day-to-day variations, consequently the reconstructions constrained with vertical profiles from ionospheric models are often inaccurate. Consequently, Fehmers et al. [1998] proposed a model-independent algorithm that compensates for the lack of horizontal raypaths with information that is not related to some specific model: basically, they impose that the electron density cannot be negative at high and low altitudes and is additionally smooth and vertically stratified. Their tests show moderate success with an error in the layer-height estimation on the order of 90 km.

Another recently developed method uses occultation data. The technique is based on using the radio signals continuously broadcast by the GNSS satellites (GPS/Global Navigation Satellite System/Galileo) that are measured by a receiver on a low Earth orbit satellite. Along its way through the ionosphere the signal has been refracted due to free electrons that modify the refraction index. Since both satellites move over time, this technique allows a vertical scanning of successive layers of the atmosphere. Rius et al. [1997] showed that the combined measurement of GPS TEC by ground stations and occultations improved the vertical resolution. Additionally, the authors proved that the use of ground stations alone is insufficient for vertical reconstruction of the electron density.

To deal with the instabilities of the solution, introduced by noise and the ill conditioning of the problem, different reconstruction algorithms have been tested for ionospheric tomography. Several works [Kersley et al., 1993; Heaton et al., 1995; Mitchell et al., 1995; Pryse et al., 1995; Vasicek and Kronschnabl, 1995] applied the iterative multiplicative algebraic reconstruction technique [Gordon et al., 1970] that attempts to minimize the difference between measured and calculated TEC values by modifying the background ionosphere until the differences are acceptably small. Kunitsyn et al. [1994a, 1994b] tried an iterative algebraic reconstruction technique algorithm that incorporates some prior information into each pixel in the ionospheric grid that they wish to solve. The solution obtained with this algorithm, however, is severely limited because it is very sensitive to the initial ionospheric model. To cope with this problem, Wen et al. [2010] recently proposed the constrained algebraic reconstruction technique, where cells not hit by any ray extract information from neighbor cells.

The purpose of our work is to present a new tomographic method of the lower ionosphere (≤300 km) based on the full inversion of over-the-horizon (OTH) radar data. Our method can integrate easily GPS TEC observations of ground-based or onboard receivers (occultation), as well as ionosonde measurements when such data are available.
<figure><img src="image_141.png" /><figcaption>**Figure 1.** Schematic representation of our parametrization of *j* rays with elevation angle *φ* and *i* cells with the raypath deflection induced by a localized perturbation (e.g., gray cell) producing a perturbed ray (red) compared to the unperturbed ray (black).</figcaption></figure>

OTH radar takes advantage of the refraction properties of the ionosphere, where the presence of free electrons causes the electromagnetic (EM) wave deflection in the ionosphere. Consequently, the emitted signal, after deflection in the ionosphere, can reach the ground beyond the horizon, typically up to thousands of kilometers away from the transmitter. There, the signal is backscattered and goes back to the receiver following the same raypath (Figure 1). The received signal contains all information about the propagating medium. We emphasize

that the point where the signal is backscattered is not fixed and changes with the ionization of the propagating medium.

Previous studies in ionospheric tomography by OTH radar are all based on the inversion of the leading edge echo curve, which contains, for each frequency, only the information of the ray with minimal group delay (measured from the emitter to a point of first contact with the Earth). To estimate the three major ionospheric parameters (the critical frequency $f_c$, the peak height, and the semithickness for each layer), two approaches to solve the inverse problem are possible. Either fitting the observed leading edge with a quasi-parabolic ionospheric layer [Rao, 1974; Bertel and Cole, 1988; Ruelle and Landeau, 1994; Landeau et al., 1997]; or using ray tracing to numerically simulate the leading edge [Coleman, 1998; Fridman and Fridman, 1994; Fridman, 1998].

A major drawback of using only the leading edge is that valuable information present in the data is neglected. To overcome this limitation, we set up an inverse problem taking into account the complete radar data set. We use the ray-tracing tool TDR (Tracé de Rayon) [Occhipinti, 2006] to calculate the synthetic propagation time. This code traces rays in an a priori heterogenic 3-D ionospheric model NeQuick [Radicella and Leitinger, 2001] and in the elliptical WGS84 coordinate system [National Imagery and Mapping Agency, 2000], solving numerically the Eikonal equation, describing the propagation of rays in a medium, by a fourth-order Runge-Kutta method. It neglects the Earth's magnetic field, in order to apply the method to all OTH radars that are not able to determine the wave polarization and consequently cannot discriminate between the ordinary and extraordinary mode, induced by the geomagnetic field. In section 4, the calculated propagation time is compared with the propagation time measured by the OTH radar. In our inverse problem, the electron density in the ionosphere is directly estimated from the difference between the calculated and measured propagation time (section 4 and Figure 10).

As a consequence of the measurement characteristics and geometry of OTH radar, the major challenge of this methodology is imposed by the measurement geometry. EM waves emitted by OTH radars are reflected in the ionosphere then arrive at the ground where they are backscattered to the receiver following the same raypath. Though we treat only the monostatic case in this work, the method could be easily generalized to bistatic cases, where the receiver and emitter are not at the same location.

We present here a new ionospheric tomography method that takes into account, jointly, the velocity variation of electromagnetic waves induced by the electron density variation, as well as the induced perturbation in the raypath (section 2). The developed methodology will be tested using a set of synthetic benchmark tests (section 3) and will be applied to real data from the OTH radar Nostradamus (New Transhorizon Decametric System Applying Studio Methods) [Bazin et al., 2006] in section 4.

## 2. Theory

### 2.1. The Forward Problem

The propagation of high-frequency (HF) radio waves in the ionosphere can be described using ray theory. Assuming an isotropic ionospheric medium, neglecting the Earth magnetic field
<figure><img src="image_142.png" /><figcaption>**Figure 2.** (left) Propagation time calculated without approximation (first line of equation (3)) versus (middle) linearized propagation time (calculated with the second line of equation (3)), and the (right) difference between them in percent. Computation for 1071 rays traced with elevation angle 10°–60° and frequency 6–16 MHz.</figcaption></figure>

and losses in the ionosphere, the propagation time along the raypath $s(\vec{r})$ is given by Fermat's principle:

$$T_{\text{phase}} = \frac{1}{c} \int_{s(n)} n(\vec{r}) \, ds, \qquad (1)$$

where c is the speed of light, $n(\vec{r})$ the refractive index of the medium, and $\vec{r}$ position.

Assuming the ionosphere is a stationary, isotropic, and horizontal stratified medium, the unmagnetized refractive index depends only on the frequency $f_e$ of the emitted EM wave and the electron density $N_e(\vec{r})$,

$$n(\vec{r}) = \sqrt{1 - \frac{e^2 N_e(\vec{r})}{4\pi^2 \epsilon_0 m_e f_e^2}} \approx \sqrt{1 - \frac{80.6 N_e(\vec{r})}{f_e^2}}, \qquad (2)$$

where $\epsilon_0$ is the vacuum permittivity and $e$ and $m_e$ are the charge and the mass of the electron, respectively. The layered structure of the ionosphere produces a change of the refractive index as a function of altitude and bends EM waves emitted at high frequency (HF) toward the ground to locations beyond the horizon, typically up to thousands of kilometers away from the transmitter. By replacing the refractive index (2) in equation (1) and linearizing by a first-order Taylor series expansion, the propagation time of an EM wave can be separated into two parts:

$$T_{\text{phase}} = \frac{1}{c} \int_{s(n)} \sqrt{1 - \frac{80.6 N_e(\vec{r})}{f_e^2}} ds \\ \approx \frac{1}{c} \int_{s(n)} ds - \frac{40.3}{c f_e^2} \int_{s(n)} N_e(\vec{r}) ds, \qquad (3)$$

where the first integral of the second line describes the propagation in the vacuum and the second one the delay introduced by the ionosphere. Figure 2 shows the limit of the linearization comparing the first and second line of equation (3). The difference between the exact and linearized propagation time is always smaller than 3.5% when elevation angle is less than 60°.
Equation (3) allows to calculate, using the ray-tracing code TDR described by *Occhipinti* [2006], the propagation time $T_{phase}^{synth}$ of any EM wave with a given frequency $f_e$ in any given ionospheric model with electron density $N_e^0(\vec{r})$.

$$T_{phase}^{synth} = \frac{1}{c} \int_{s(n)} ds - \frac{40.3}{cf_e^2} \int_{s(n)} N_e^0(\vec{r}) ds.$$

We introduce an electron density perturbation $\delta N_e(\vec{r})$ of the a priori model $Ne^0(\vec{r})$ to describe the real ionosphere $Ne^0(\vec{r}) + \delta N_e(\vec{r})$. Then the propagation time in the real ionosphere is given by

$$T_{phase}^{real} = \frac{1}{c} \int_{s(n)} ds - \frac{40.3}{cf_e^2} \int_{s(n)} (N_e^0(\vec{r}) + \delta N_e(\vec{r})) ds \\ = T_{phase}^{synth} - \frac{40.3}{cf_e^2} \int_{s(n)} \delta N_e(\vec{r}) ds.$$

We then obtain a travel time perturbation $\delta T_{phase}$ that is the difference between propagation times in the real ionosphere and in the a priori model (e.g., Figure 10):

$$\delta T_{phase} = T_{phase}^{real} - T_{phase}^{synth} = -\frac{40.3}{cf_e^2} \int_{s(n)} \delta N_e(\vec{r}) ds \quad (4)$$

This solution allows us to compute the travel time perturbation $\delta T_{phase}$ as a function of an electron density perturbation $\delta N_e$ of the a priori model $Ne^0$. The difference between the propagation time measured by the OTH radar and the one computed by TDR is directly linked to the electron density perturbation $\delta N_e$.

We emphasize that this approach is based on the hypothesis that the raypath $s(n)$ in the real ionosphere and in the a priori model is the same. That means that we are supposing that the electron density variation $\delta N_e$ only introduces variations in the speed of the EM waves and not in the raypath. Consequently, we call this approach the v method.

## 2.2. The Inverse Problem

In order to solve numerically our problem, we choose a parametrization of N homogeneous, nonoverlapping blocks, indexed i, where the electron density perturbation $\delta N_e(\vec{r})$ can be expressed as

$$\delta N_e(\vec{r}) = \sum_{i=1}^{N} \delta m_i \cdot B_i(\vec{r}), \quad (5)$$

where the electron density perturbation in the block i is $\delta m_i$ and N known basis functions $B_i(\vec{r})$ are

$$B_i(\vec{r}) = \begin{cases} 1 & \text{if } \vec{r} \text{ in block } i, \\ 0 & \text{otherwise} \end{cases}$$

Consequently, equation (4) for the jth measurement of travel time perturbation takes the following form:

$$\delta T_j = -\frac{40.3}{f_{ej}^2 c} \sum_{i=1}^{N} \delta m_i ds_{ij}. \quad (6)$$

where $ds_{ij}$ is the length of raypath segments within block i of ray j.

Introducing the matrix A of size M × N, where M is the number of travel time measurements and N is the number of basis functions (i.e., the number of blocks in the parametrization of our ionospheric model), equation (6) can be rewritten as

$$\delta T_j = \sum_{i=1}^{N} \delta m_i A_{ji}. \quad (7)$$

In tensor notation equation (7) takes the form

$$\delta \mathbf{T} = \mathbf{A} \cdot \delta \mathbf{m}, \quad (8)$$

where $\delta \mathbf{m}$ is the vector of model parameters with N unknown electron density perturbations $\delta m_i$, $\delta \mathbf{T}$ is the vector containing the M observed travel time perturbations $\delta T_j$, and A is the geometric
matrix containing the M × N raypath segments $ds_{ij}$ of the jth ray in block ith, as well as the ray coefficient,

$$A_{ji} = - \frac{40.3}{f_e^2 c} ds_{ij}.$$

## 2.3. Solution of the Inverse Problem Regularization

Following Menke [1989] we solve equation (8) seeking the model that minimizes the $L_2$ norm for both data and model, namely, $|| \delta \mathbf{T} - \mathbf{A} \cdot \delta \mathbf{m} ||^2 = \min$ and $|| \delta \mathbf{m} ||^2 = \min$. The first condition imposes the best fit to the data, and the second condition minimizes the discrepancy from the a priori model. These two conditions are equivalent to solving the following two equations:

$$\delta \mathbf{m} = (\mathbf{A}^T \cdot \mathbf{A})^{-1} \cdot \mathbf{A}^T \cdot \delta \mathbf{T} \Leftrightarrow || \delta \mathbf{T} - \mathbf{A} \cdot \delta \mathbf{m} ||^2 = \min$$

$$\delta \mathbf{m} = \mathbf{A}^T \cdot (\mathbf{A} \cdot \mathbf{A}^T)^{-1} \cdot \delta \mathbf{T} \Leftrightarrow || \delta \mathbf{m} ||^2 = \min$$

It is known that inverse problems in geophysics generally present a number N of parameters (here the vector $\delta \mathbf{m}$) larger than the number M of observations (here the vector $\delta \mathbf{T}$). Consequently, the problem is underdetermined, and the matrices $\mathbf{A}^T \cdot \mathbf{A}$ and $\mathbf{A} \cdot \mathbf{A}^T$ cannot be inverted. The matrices are close to singular, and even if the inverse matrices formally exist, they are often ill conditioned; that is, small changes in the data vector ($\delta \mathbf{T}$) lead to large changes in the model estimation ($\delta \mathbf{m}$).

To find a more stable solution ($\delta \mathbf{m}$) balancing the sensitivity to the data, as well as the coherence with the a priori model, Menke [1989] suggests the following damped least squares solution

$$\delta \mathbf{m} = (\mathbf{A}^T \cdot \mathbf{A} + \lambda \cdot \mathbf{I})^{-1} \cdot \mathbf{A}^T \cdot \delta \mathbf{T}, \quad (9)$$

which minimizes the cost function $|| \delta \mathbf{T} - \mathbf{A} \cdot \delta \mathbf{m} ||^2 + \lambda || \delta \mathbf{m} ||^2$, where $\lambda$ is a regularization parameter and $\mathbf{I}$ the identity matrix.

It is not possible to minimize both terms simultaneously, but the parameter $\lambda$ controls the emphasis that we put on the conflicting requirements. In the section 3.2, we highlight the way how to select the best value of $\lambda$ satisfying our problem.

## 2.4. Taking the Raypath Deflection Into Account

In monostatic OTH radars, the end points of the rays (where the signal is backscattered by the ground) are not known. Consequently, the location of the scattering point can change for a constant elevation angle and depends on the electron density variation $\delta N_e(\vec{r})$ in the ionosphere (Figure 1). As a result, the raypath deviation, introduced by the variation of the scattering point, can introduce an additional shift $\delta T_{phase}^{ray}$ in the propagation time. We extend the theory described above, in order to take into account jointly not only the speed variation (v method) but also the raypath deflection induced by the variation of the scattering point, what we call the v and r method. Snieder and Spencer [1993] showed that both effects can be combined in the perturbation approach, and the two effects are simply additive to first order. Based on equation (31a) of Snieder and Spencer [1993] we can write the total observed time delay as

$$\delta T_{phase} = - \frac{40.3}{c f_e^2} \int_{s(n)} \delta N_e(\vec{r}) ds + \delta T_{phase}^{ray} \quad (10)$$

If $s(n)$ is the raypath in the a priori model $N_e^0(\vec{r})$ and $s^*(n)$ is the raypath in the perturbed model $N_e^0(\vec{r}) + \delta N_e(\vec{r})$, $\delta T_{phase}^{ray}$ is described by

$$\delta T_{phase}^{ray} = \frac{1}{c} \int_{s^*(n)} ds^* - \frac{1}{c} \int_{s(n)} ds \\ + \frac{40.3}{c f_e^2} \left[ \int_{s(n)} N_e^0(\vec{r}) ds - \int_{s^*(n)} N_e^0(\vec{r}) ds^* \right. \\ \left. + \int_{s(n)} \delta N_e(\vec{r}) ds - \int_{s^*(n)} \delta N_e(\vec{r}) ds^* \right]. \quad (11)$$

Figure 3 compares the values of $\delta T_{phase}^{velocity}$ and $\delta T_{phase}^{ray}$ for a selected set of rays and shows that the raypath deflection is not negligible. This is discussed in more detail in section 3.1.
<figure><img src="image_143.png" /><figcaption>**Figure 3.** The ratio of $\delta T_{\text{ray}}$ (equation (11)) to $\delta T_{\text{speed}}$ (equation (4)) computed for the localized perturbation (Figure 4) and checkerboard (Figure 5) target models. The number of raypath are arranged in such a way that for one frequency (6–16 MHz), the elevation angle has been varied between 10° and 60°. The peaks correspond to low elevation angles between 10° and 30° for each frequency.</figcaption></figure>

In this section, we extend the theory described above, in order to take into account jointly, not only the speed variation (v method) but also the raypath deflection induced by the variation of the scattering point (v and r method).

$\delta T_{\text{phase}}^{\text{ray}}$ depends on $\delta N_e$, since raypath deflections are caused by electron density perturbations. To set up an inverse problem, allowing us to determine $\delta N_e$ based on observations of $\delta T_{\text{phase}}$, we therefore write $\delta T_{\text{phase}}$ as a linear function of $\delta N_e$. The study of Snieder and Spencer [1993] also indicates that sensitivity kernels $k(\vec{r})$ can be defined such that

$$ \delta T_{\text{phase}}^{\text{ray}} = \int_{s(n)} k(\vec{r}) \cdot \delta N e(\vec{r}) \quad (12) $$

where $k(\vec{r})$ is the data kernel [Menke, 1989], which in the v method described above is just a delta function along the unperturbed ray $s(n)$. Here the kernel contains the Fréchet derivatives $\partial T/\partial m$, where $\partial T$ is a perturbation in the propagation time caused by a perturbation in the model $m$. If the relation between the model $m$ and the propagation time $T$ is linear, the sensitivity function $k(\vec{r})$ can be computed numerically. In practice, using the parametrization described above, we impose a localized electron density perturbation of arbitrary amplitude $\delta Ne_i^*$ at only the $i$th cell; consequently, we can compute by ray tracing the partial time perturbation $\delta T_j^*$ along the $j$th ray induced by $\delta Ne_i^*$ in the $i$th cell:

$$ \delta T_j^* = k_{ij} \cdot \delta Ne_i^* \quad (13) $$

This allows us to create our base function

$$ k_{ij} = \frac{\delta T_j^*}{\delta Ne_i^*} $$

that, following our linear hypothesis, is valid for a general case. We emphasize for additional clarity that the perturbed propagation time $\delta T_j^*$ is computed following equation (11), where the perturbed raypath $s^*(n)$ is traced in the a priori model plus the perturbation $\delta Ne_i^*$ only in the $i$th cell. We can finally express equation (10) as

$$ \delta T_j = -\frac{40.3}{f_{ej}^2 c} \sum_{i=1}^{N} \delta m_i \, ds_{ij} + \sum_{i=1}^{N} k_{ij} \delta m_i, \quad (14) $$

or, in a tensor formalism as

$$ \delta \mathbf{T} = (\mathbf{A} + \mathbf{A}') \cdot \delta \mathbf{m}, \quad (15) $$

where $A'_{ij} = k_{ij}$. The general inverse method solution described in the section 2.3 is applied to the matrix $\mathbf{A}$ in the case of v method, and to the matrix $\mathbf{A} + \mathbf{A}'$ in the case of v and r method.

### 3. Inversion Results for Synthetics

In order to validate and compare the two methods described in the previous sections, we generate synthetic data by the ray-tracing TDR in a known a priori ionospheric model, NeQuick [Radicella and Leitinger, 2001] that we call $Ne^{a priori}$, plus an additional perturbation that we call $\delta Ne^{\text{target}}$. The $\delta \mathbf{T}$ is calculated as a difference of propagation time in $Ne^{a priori} + \delta Ne^{\text{target}}$ minus the propagation time in $Ne^{a priori}$. We emphasize that the ray geometry is different in the two models as the perturbation $\delta Ne^{\text{target}}$ introduces variation of the raypath.
<figure><img src="image_144.png" /><figcaption>**Figure 4.** (a) Inversion results for the localized electron density perturbation benchmark with three different methods and for three different values of $\lambda$. Inversions for the best regularization parameter $\lambda_{best}$ (middle row) for each method: frozen rays (left column), v method (middle column), and v and r method (right column). (b) Target model. (c) Ratio between plasma frequency and emission frequency along the raypath quantifying the sensitivity of each ray to the propagating medium. Rays are most sensitive to the medium where the ratio is approximately 1. (d) L curves for the frozen rays, v method, and v and r method. Diamonds correspond to the best values of regularization $\lambda$, i.e., $5.62 \cdot 10^{-5}$, 0.2, and 0.63 respectively.</figcaption></figure>

Additionally, we compute the vector of travel time perturbations $\delta T^{frozen}$ satisfying exactly the hypothesis that the electron density perturbation $\delta N_{\text{target}}$ modifies only the speed of EM waves (equation (4)); rays are frozen in the a priori model configuration. This data set represents the idealized case of no raypath perturbation, as if the ray end points were known; we shall invert it to separate the effects of poor data coverage and unknown raypath deflection or model resolution.

Independent of the method used ($v$ or $v$ and $r$), as well as for the synthetic data set ($\delta T$ or $\delta T^{frozen}$), the solution of our inverse problem $\delta m$ has to correspond to $\delta N_{\text{target}}$. We emphasize that all synthetic data are computed numerically by TDR in electron density continuous models ($N_e^{\text{a priori}}$ and $\delta N_{\text{target}}$) and not in discretized models following our parametrization. This is equivalent to introduce a noise in the synthetics in the order of 12%. The target model $\delta N_{\text{target}}$ is parametrized using the above described parametrization for comparison with the solution $\delta m$.

Quantitatively, we simulate rays with elevation angles between 10° and 60° and in the frequency range 6–16 MHz, as this is the operating capacity of the Nostradamus OTH radar [Bazin et al., 2006]. The background ionosphere $N_e^{\text{a priori}}$ was generated for October at 12:00 UT with a solar flux of 198.1 solar flux units. The model is parametrized by a grid starting from the geographical coordinates of the Nostradamus radar
<figure><img src="image_145.png" /><figcaption>**Figure 5.** Same as Figure 4 but for a checkerboard perturbation. Diamonds of the *L* curves correspond to the best values of regularization *λ*, i.e., 3.6 · 10⁻⁵, 0.28, and 0.5, respectively, for the frozen ray, *v* method, and *v* and *r* method.</figcaption></figure>

covering an area of 2500 km in distance and reaching up to 400 km altitude. Each pixel of the grid has a dimension of 25 km in distance and 20 km in altitude. We traced here 1071 rays, using $\delta\phi = 1^\circ$ in the elevation angle and $\delta f = 0.5$ MHz for the emission frequency, in accord with the capability of the radar Nostradamus.

We apply here the described methods to two different $\delta Ne^{\text{target}}$. The first is an ionospheric perturbation of a localized electron density perturbation of 0.1% of the background model $Ne^{\text{a priori}}$ (Figure 4), and the second is a checkerboard perturbation with the same order of amplitude (Figure 5). In the next section we comment in detail on the results of our synthetic tests.

The synthetic data set inverted in this section includes ~10³ rays. Ray tracing for the entire synthetic data set in parallel on eight processors takes around 2 min on a grid with spatial resolution of 25 × 20 km and 2000 cells. The 2-D inversion result for the *v* method is obtained after 5 min for the first iteration. The performance of the *v* and *r* method is grid dependent, because of the number of cells to perturb. For a grid with spatial resolution of 25 × 20 km and ~10³ rays, it takes around 40 min. For comparison with GPS ionospheric tomography we note that *Seemala et al.* [2014] can construct the 3-D electron density over Japan within 55 min on a grid with spatial resolution of 1° in latitude/longitude using data of 748 GEONET stations. Reducing the horizontal resolution of their grid to 2°, they obtain a 3-D image within 15 min.

**3.1. The v Method Versus v & r Method**

The inversion results for $\delta m$ of our first test are summarized in Figure 4, where the solutions obtained with the *v* method and the *v* and *r* method are directly compared with the idealized frozen rays solution
<figure><img src="image_146.png" /><figcaption>**Figure 6.** L curves for different $\lambda$ ranges indicated in the top left for the (a) localized and the (b) checkerboard benchmark test using the v and r method for inversion. (c and d) Corresponding error curves for the explored range of regularization parameters. The red point represents the minimum error, and the red line is the sum over the target models, i.e., $\sum_{i=1}^{\text{cells}} \left( \frac{dNe}{Ne} \right)_i^2$. The errors converge to the red line when the solution is totally damped.</figcaption></figure>

(subsection 3). Figure 4a shows the results for three different regularization parameters $\lambda$ where the inversion results for the best regularization parameter (section 3.2) are shown in the middle of each column. The best $\lambda$ is obtained by performing the inversion changing the regularization parameter and plotting the data misfit against the model misfit (i.e., L curve). The best regularization parameter lies at the maximum curvature of this curve, as this represents a compromise between small misfit and small solution norm (section 3.2).

As a consequence of the strong variation of the ionospheric background (electron density equal to zero at around 80 km, and of the order of $10^{11} - 10^{12}e/m^3$ at around 300 km) and the emission frequency dependence of the refraction index, EM waves emitted by the radar are particularly sensitive to the zone where the rays are reflected, where the plasma frequency $f_p$ is approximately equal to the emission frequency $f_e$ (Figure 5c). This defines the area of good coverage (independent of inversion method), as illustrated by Figure 5c with comparison with the frozen-ray inversion.

As is to be expected, solution models depend significantly on the regularization parameter. This effect is less severe in the idealized frozen-ray case that resembles GPS ionospheric tomography (both end points of the ray are known). As soon as raypath deflections (end point perturbations) are taken into account in our synthetic data, the resolution deteriorates and the choice of $\lambda$ (equation (9)) affects more profoundly our results. The correct location (500 km distance, 200 km altitude) of the maximum anomaly in the target model is only reconstructed by the v and r method provided that an adequate value is assigned to $\lambda$. Furthermore, the v method identifies a high $dNe/Ne$ anomaly in the general area of 200–500 km in horizontal distance and 100–200 km in altitude but slightly mislocates it and does not reproduce its shape. The better performance of the v and r method compared to v method is confirmed by Figure 4d, where the v and r L curve [Tikhonov, 1963] has a more pronounced corner than the L curve obtained with the v method.
<figure><img src="image_147.png" /><figcaption>**Figure 7.** Inversion results using the *v* and *r* method with the best value of regularization chosen from the *L* curves in Figure 6a for the localized perturbation in order to explore the sensitivity to the *λ* range. The bottom row shows the target model.</figcaption></figure>

Compared to the result obtained with the ideal frozen rays, both the *v* and *v* and *r* methods occasionally introduce large-scale low *dNe/Ne* anomalies that do not correspond to any feature of the target model, where the sign of perturbation is always positive. We ascribe these artifacts to the nonlinear effects of ray-path deflections, which (end points not being fixed) can in principle result in a faster propagation time even if the velocity perturbation is negative.

The inferences made from Figure 4 are confirmed by results illustrated in Figure 5, where the same set of inversions is conducted after replacing the target model (and associated synthetic data) with a checkerboard. General comparison from Figures 4a and 5a, with Figures 4c and 5c, clearly show that the model is mainly reproduced in the zone of sensitivity where the emission frequency *f*<sub>e</sub> is close to the plasma frequency *f*<sub>p</sub>. This clearly emphasize the role of the coverage in our solution.

The selection of the value of λ in order to choose the best solution is detailed in the next section. The
following discussions are only applied to the *v* and *r* method.

**3.2. Solution Dependence on Regularization**

To quantify the robustness of our solutions obtained with both the *v* and *v* and *r* methods, we explore
their dependence on our choice of regularization parameter *λ*. This analysis is limited to the synthetic data
discussed in section 3.1 so that obtained solution can be compared to a target model.

We first observe that while the *L* curve method (Figures 4d and 5d) is useful to monitor qualitatively the trade-off between data misfit and model quality, it is not guaranteed to provide the “best” solution, i.e., the one closest to the real world. This is confirmed by Figures 6a and 6b, where we show how the choice of model-norm normalization results in a different curvature of the *L*-curve and thus a different choice of preferred model. Each plot of Figures 7 and 8 illustrates the result for *λ*<sub>best</sub> obtained from the corresponding *L* curve in Figures 6a and 6b. Figures 6c and 6d show the discrepancy between solution and target model for the same set of inversions and confirms that the model quality can be significantly affected by a inadequate choice of *λ*. Inspection of Figures 6c and 6d allows to identify the value of *λ* corresponding to the minimum error (discrepancy between solution and target model).

The corresponding λ<sub>best</sub> are 0.63 and 0.5, respectively, and the inversion results corresponding to these
regularization parameters are shown in Figures 4 and 5 in the middle of the right columns. The differ-
ence between target and model is less than 40% for the localized and less than 57% for the checkerboard
perturbation, using the v and r method.

**3.3. Iterative Approach**

Since the results presented before are obtained after only one inversion, we attempt to improve the solu-
tion by iterating the synthetic inverse problem. That means that the solution models δ*m* found in section 3.1
can be used as starting models of new inversions. Raypaths are traced, the tomography matrix accordingly
recomputed, and the differences between observed (or, in the present case, synthetic) and computed (in
the new model) travel times replace the data to be inverted. In the interest of computational speed, we do
<figure><img src="image_148.png" /><figcaption>**Figure 8.** Inversion results using the *v* and *r* method with the best value of regularization chosen from the *L* curves in Figure 6b for a checkerboard perturbation in order to explore the sensitivity to the *λ* range. The bottom row shows the target model.</figcaption></figure>

not conduct a separate *L* curve analysis (which would involve several inversions) at each iteration, but we fix *λ* to the trace of **A**^T · **A** divided by 10 (*v* method) or the trace of (**A** + **A'**) divided by 100 (*v* and *r* method) [Press et al., 1992, chapter 18]. These values were determined with a few preliminary tests to properly tune convergence speed. The trace of the matrix is equal to the sum of eigenvalues and allows for a quick estimation of the eigenvalues that are well determined. Based on them, the regularization can be adjusted. The inspection of eigenvalues of the matrices showed that the *λ* selected by the *L* curve is too large in the case of the *v* method and too small for the *v* and *r* method compared to the largest eigenvalues. In the first case this is imposing large restriction to the solution, in the second case it is adding too much noise to the solution.

The results of this exercise are summarized in Figure 9. The difference between target and solution is less than 30% for the *v* and *r* at iteration 13 and less than 40% for the *v* method at iteration 5. Nevertheless, after a critical number of iterations, the discrepancy between solution and target model starts growing for both the *v* and *v* and *r* inversions. We interpret this as an effect of the mentioned trade-off between velocity heterogeneity and raypath deflection (section 3.1). Entries of the tomography matrix can be either negative or positive. Any given observation can be explained by a combination of both negative and positive

<figure><img src="image_149.png" /><figcaption>**Figure 9.** Data misfit $\sum_{j=1}^{\text{rays}} (\frac{dT}{T})_j$ and model misfit as function of the number of iterations for the (top) *v* method and the (bottom) *v* and *r* method. The inversion results for the minimum (red point) of the model misfit (iteration 5 for *v* method and iteration 13 for *v* and *r* method) are shown on the right column.</figcaption></figure>
<figure><img src="image_150.png" /><figcaption>**Figure 10.** Propagation time of the real data and synthetic data simulated by ray tracing as (a) function of frequency and elevation angle, and the (b) difference (%).</figcaption></figure>

heterogeneity whose amplitude might grow indefinitely as further iterations are performed. This problem is similar to that of selecting $\lambda$, and we suggest that the synthetic tests presented here can serve to determine adequate values for such parameters, to be used in real inversions with the same data coverage. This approach rests on the assumption that the effect of limitations in data coverage is more important to model resolution than that of data noise.

## 4. OTH Radar Nostradamus and Real Data Inversion

In the following section we apply the developed *v* and *r* method to real data of the OTH radar Nostradamus exploring the regularization parameter range with a $\lambda_{min} = 10^{-3}$ in accord with the results of the previous

<figure><img src="image_151.png" /><figcaption>**Figure 11.** Inversion of real data collected 14 March 2006, at 18:55 UT with azimuth 247°, and for two different grids: (left) pixel size 50 × 20 km and (right) pixel size 25 × 20 km in distance and altitude. The middle row shows the result for the best regularization parameter $\lambda_{best}$.</figcaption></figure>
<figure><img src="image_152.png" /><figcaption>**Figure 12.** Vertical profiles of electron density at (a) 500 km distance and (b) 1000 km distance from the radar. The red line shows the ionospheric a priori model NeQuick, and the black line is the solution obtained by the v and r method (the a priori model plus the perturbation).</figcaption></figure>

synthetic tests. Nostradamus is a monostatic radar that consists of 288 biconical antenna elements distributed over the arms of a three-branch star. The choice of this antenna arrangement allows beam forming with a coverage of 360° in azimuth and elevation control with a resolution of approximately 2.35° in azimuth and 5.43° in elevation for a frequency of 11 MHz. The central part of the array (96 antennas) is dedicated to transmission and reception, and the entire array is used for reception allowing a greater capability in receiving beam forming. The Nostradamus configuration allows to investigate a very large area of more than thousands of kilometer in range all around Europe.

We use here data that were collected on 14 March 2006, at 18:55 UT, for a frequency range 6–16 MHz and scanning in elevation from 10° to 60°. We traced rays with frequency and elevation angle corresponding to
<figure><img src="image_153.png" /><figcaption>**Figure 13.** Electron density perturbation obtained by real data inversion measured by the OTH radar Nostradamus the 14 March 2006, at 18:55 UT in four azimuth directions, nominally 67°, 157°, 247°, and 337°.</figcaption></figure>

the radar measurements in the a priori ionospheric model NeQuick given for this day and time. Figure 10 shows the comparison between data and the synthetics used to compute the vector $\delta\mathbf{T}$ of travel time perturbations for an azimuth of 247°. The difference is around 30% for rays with low frequency of 7–9 MHz, and around 20% for the highest frequencies of 16 MHz.

Figure 11 shows an example of the inversion of the real data in one selected azimuth (247°) for different values of regularization for the *v* and *r* method for two different grid sizes, i.e., (50 × 20 km and 25 × 20 km distance and altitude). There is no significant difference in the inversion results for this range of parameters, and the resolved perturbation is mainly located at 200 km altitude with a maximum of 50%. It is not surprising that the perturbation is located around 200 km altitude, since at this time (18:55 UT) the *E* layer has nearly disappeared and only the *F* layer remains strongly visible. The *v* and *r* method shows stable results for all regularization parameters, validating the reliability of the solution.

To further explore the inversion results, we calculated vertical profiles of electron density from the inversion with the best regularization parameter for two different distances from the radar (500 km and 1000 km), and we compare them with the electron density from the a priori model NeQuick. The resulting vertical profiles (Figure 12) show a sensitivity to variations located between 120 km and 260 km of altitude in accord with the sensitivity of the EM waves emitted by the radar. Indeed, the plasma frequency below 120 km altitude is too small to affect the emitted signal, and the maximum altitude of reflection is located around 260 km. The recovered electron density perturbation is of the order of 10%.

In order to show the potential applications of the OTH radar Nostradamus in ionospheric tomography, we inverted here the data for the same day and time measured for different azimuths: 67°, 157°, and 337°. The obtained tomographic images are plotted in Figure 13 over Europe, in the corresponding azimuthal directions. The electron density perturbation observed at 247° azimuth at 200 km altitude is visible in all azimuthal directions.

We highlight that the developed methodology could easily include other kinds of ionospheric data, in particular TEC measurements by ground-located or onboard GPS receivers. Consequently, we note the possibility of creating regional and/or global ionospheric tomography based on joint inversions of various ionospheric monitoring data.
## 5. Conclusions

We developed a new linear ionospheric tomography method for over-the-horizon radar (OTH) that takes into account not only the effect of the electron density perturbation on the velocity of electromagnetic waves (v method) but also the effect on the raypath deflection (v and r method). The characteristic uncertainty of end points of the raypath followed by EM waves emitted by OTH radar makes this second effect comparable to the first. Based on synthetic tests, we showed the necessity of taking into account the raypath deflection for tomographic inversions of the ionosphere. This is the first time that this problem is explored and emphasized in the OTH radar ionospheric tomography. Notwithstanding the methodological advance, the quality of the solution depends on the ray coverage, as well as, on the sensitivity of the rays to the medium that is the zone where the plasma frequency is close to the emission frequency of the propagating signal. This zone is strongly reduced at night, where only the high-frequency rays are reflected. The difference between target and solution for the localized perturbation is about 40% and 59% for the v and r and v methods, respectively, but can be reduced to 30% and 40% with iterations. For comparison we note that *Seemala et al.* [2014] archived a difference between target and solution of less than 10% with their GPS tomography over Japan during night.

Since the problem is underdetermined, meaning that the number of parameters to estimate is larger than the number of observations, our inversions have to be regularized. In order to find the best regularization parameter $\lambda$, we calculate a trade-off curve that quantifies the conflicting requirements between satisfying the data and the coherence with the a priori model. We highlight that the best regularization parameter $\lambda_{best}$ is strongly dependent of the explored $\lambda$ range. Consequently, we define a synthetic protocol to determine the $\lambda$ range to explore, in order to minimize the solution error. The selected $\lambda$ range can be applied to real data inversion in order to maximize the quality of the solution.

Application of the developed methodology on real data gives stable solutions, showing the quality of the inversion method and the reliability of the solution. A 3-D ionospheric tomography over Europe, based on the inversion of the OTH radar Nostradamus data, has been presented here in order to show the potential application of the developed method. Although our method has been developed for OTH radar, the number of these radars worldwide is limited to France (Nostradamus), United States (relocatable over-the-horizon radar), Australia (Jindalee), and North Pole (Super Dual Auroral Radar Network); consequently, we emphasize that this method can be developed further by including other ionospheric sounding techniques, in particular TEC measured by GPS, both measured at the ground with dense GPS array or by occultation with onboard GPS receivers. The latter is an interesting idea, because the two methods complement each other, where our method is sensitive to the lower ionosphere (up to 300 km altitude) during daytime, and the GPS because of its high frequency is sensitive to the region of maximum ionization (~300 km). Additionally, GPS data can compensate for the lack of reflected high-frequency (HF) rays during night.

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## Acknowledgments

This project is supported by the Programme National de Télédétection Spatiale (PNTS), grant PNTS-2014-07 and by the CNES grant SI-EuroTOMO. The Nostradamus data used in this work were supplied by ONERA. We thank the Aeronomy and Radiopropagation Laboratory of the Abdus Salam International Centre for Theoretical Physics (ICTP) for providing NeQuick model. The authors thank P. Lognonné for helpful theoretical discussions, as well as V. Rannou for discussions about real data inversions. We thank the reviewers for their constructive remarks.

Michael Balikhin thanks the reviewers for their assistance in evaluating the paper.
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# Acronyms

* $NO^+$ ionized nitric oxide. 23

* $N_2$ molecular nitrogen. 21

* $O^+$ ionized oxygen. 23

* $O_2$ dioxygen. 21

* $O_2^+$ ionized molecular oxygen. 23

* **3D** 3 Dimensions. 39, 42, 50–52, 56–59, 152, 159

* **AEROS** Aeronomy Satellite. 29

* **AGW** Acoustic Gravity Waves. 50

* **ART** The Algebraic Reconstruction Technique. 54

* **ARTIST** Automatic Real-Time Ionogram Scaler with True height. 36

* **CART** constrained algebraic reconstruction technique. 54

* **CCIR** Comité Consultatif International pour la Radio. 30

* **CGM** Conjugate Gradient Method. 83–87, 159

* **CHAMP** CHallenging Minisatellite Payload. 41, 56

* **CME** Coronal Mass Ejections. 26

* **COSMIC** Constellation Observing System for Meteorology Ionosphere and Climate. 41

* **COSPAR** Committee on Space Research. 29

* **DIAS** European Digital upper Atmosphere Server. 145

* **Digisonde** Digital Ionospheric Goniometric Ionosonde. 35–37

* **EISCAT** European Incoherent Scatter. 29, 54, 57

* **EM** electromagnetic. 19, 25, 26, 33–36, 43, 52, 55, 58–60, 63, 68, 71, 74, 86, 104, 139, 155
EPN EUREF Permanent Network. 42

EUV extreme ultraviolet. 23, 25, 29

GAIM Global Assimilation of Ionospheric Measurements. 28

GEONET GPS Earth Observation Network. 42

GLONASS Global'naya Navigatsionnaya Sputnikovaya Sistema. 41

GNSS Global Navigation Satellite System. 27, 41, 42

GPS Global Positioning System. 26, 28, 35, 40–42, 52–58, 142, 149–153, 155, 158, 159, 164

HF High Frequency. 22, 24, 25, 36, 43, 46, 50, 58, 159

ICTP International Centre for Theoretical Physics. 30

IGS International GNSS Service. 42, 53

IGW Internal Gravity Wave. 50

IMF Interplanetary Magnetic Field. 26

IRI International Reference Ionosphere. 28–30, 60

IRNSS Indian Regional Navigation Satellite System. 41

ISIS International Satellites for Ionospheric Studies. 29

ISR Incoherent Scatter Radar. 28

ITU-R International Telecommunication Union-Radiocommunication. 29, 30

JORN Jindalee Operational Radar Network. 45, 47, 158

LEO Low Earth Orbit. 41, 42, 55, 56

LOS Line Of Sight. 41

MADRE Magnetic-Drum Radar Equipment. 44, 45

MAGNUS MAntle investiGations of Norwegian Uplift Structures. 171

MART Multiplicative Algebraic Reconstruction Technique. 54

MIDAS Multi-Instrument Data Analysis System. 55

MQP Multi-Quasi-Parabolic. 145, 146

NIMS Navy Ionospheric Monitoring System. 40
**NO** nitric oxide. 22

**NOAA** National Oceanic and Atmospheric Administration. 37, 38, 138, 163

**Nostradamus** NOveau Système TRAnshorizon Décamétrique Appliquant les Méthodes Utilisées en Studio. iii, 15–17, 45, 47, 48, 59, 75, 131, 137, 140–143, 145, 146, 151, 153, 157–159

**NRL** Naval Research Laboratory. 44

**ONERA** Office National d'Etudes et de Recherche Aérospatiale. 47

**OpenMP** Open Multi-Processing. 108

**OTH** Over-the-horizon. 15, 26, 34, 38–40, 43–45, 47, 49, 50, 52, 56, 58, 59, 68, 103, 131, 140–142, 146, 148–151, 153, 155, 157–159, 163, 166, 167

**OTH-B** Over-the-horizon-Backscatter. 45

**PIM** Parametrized Ionosphere Model. 28

**POLAN** POLynomial AAnalysis. 36

**QC** quasi-cubic. 58

**QP** quasi-parabolic. 39, 58

**QVI** quasi-vertical-incident. 39

**QZSS** Quasi-Zenith Satellite System. 41

**ROTHR** Relocatable Over The Horizon Radar. 45, 47, 158

**SAMI2** Sami2 is Another Model of the Ionosphere. 28

**SFU** solar flux units. 60, 71, 85, 107, 138, 142

**SID** sudden ionospheric disturbance. 27

**SIRT** simultaneous iterative reconstruction technique. 53, 54

**STEC** Slant Total Electron Content. 52, 53

**SuperDARN** Super Dual Auroral Radar Network. 46, 47, 50, 153, 158, 163

**TDR** Tracé De Rayons. 69, 71, 85, 108

**TEC** Total Electron Content. 25, 26, 28, 40, 41, 52–54, 56, 57, 149, 150, 159

**TID** Traveling Ionospheric Disturbances. 19, 57

**URSI** Union Radio-Scientifique Internationale. 29
**USA** United States of America. 44, 158

**UV** Ultraviolet. 20, 22, 27

**VHF** Very High Frequency. 46

**WARF** Wide-Aperture Research Facility. 45