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1 Supplementary Methods Measurement details and instrumentation MT data were recorded using five, GPS-synchronized, 24-bit data-acquisition systems and broadband induction coils manufactured by Phoenix Geophysics Ltd. Electric fields were measured using m long grounded-dipoles with Pb-PbCl 2 electrodes. Data were collected at 85 locations during August-September 2005 and July-September Acquisition times ranged from hours, including at least two nights. One MT system, kept at a fixed location, acted as the noise reference 31 for data processing and recorded continuously during each field campaign. Time-series data were processed in hour-long windows using remote referencing and robust signal processing techniques 32 as implemented by Phoenix Geophysics Ltd. The resulting apparent resistivity and phase data were then edited manually to remove bad data segments. The survey area around Mount St Helens is sparsely populated with very low levels of manmade electromagnetic noise and good quality MT data were obtained at almost all sites between 384 and Hz. Examples of sounding curves from the region between Mounts St. Helens, Adams and Rainer are shown in Fig. S1. The small jumps that can be seen in the sounding curves at s (12 Hz) are a result of a small mismatch between the position of the frequency determined by the processing software and the pass-band of the medium frequency range filter in the instrumentation. Data at this period were not included in the 2-D or 3-D inverse modelling. nature geoscience 1

2 Figure S1a. Sounding curve for site 617 located on the 2-D profile between Mounts St. Helens and Adams directly south of site 633 (Fig. 1). The red curves show the xy polarisation (i.e. electric field in the x-direction and magnetic field in the y-direction) apparent resistivity and phase, with the blue curves corresponding to the yx polarisation (electric field in the y-direction and magnetic field in the x-direction) in a Cartesian coordinate system with x increasing northwards and y eastwards. The x direction is approximately parallel to the trend of conductivity structure. 2/23 2 nature geoscience

3 Figure S1b. Sounding curve for site 621 (Fig. 1), located on the eastern margin of the SWCC. As in Fig. S1a, the red and blue curves show the xy polarisation and yx polarisation apparent resistivity and phase, respectively. nature geoscience 3

4 Figure S1c. Sounding curve for site 633 (Fig. 1), located south of Mount Rainier in the centre of the SWCC. As in Fig. S1a, the red and blue curves show the xy polarisation and yx polarisation apparent resistivity and phase, respectively. 4 nature geoscience

5 2-D inversion details The 2-D inversion 16 implemented in WinGLink includes the effects of topography and was started from an initial model consisting of a 100 Ωm resistivity half-space with a (fixed) 0.33 Ωm resistivity 2 km thick block representing the conductance of the ocean located 100 km from the western end of the E-W profile onto which the data was projected. The objective function used for the inversion minimises the sum of the total misfit and model roughness represented by the magnitude squared of the spatial gradient (Laplacian) of log(ρ model ). Model smoothing in the horizontal and vertical directions was the same, however, the effective degree of smoothing increases downwards as the vertical size of the blocks increase. This smoothing scheme acts to suppress short-scale lateral resistivity changes at deeper levels. The model discretisation used for the 2-D modelling is shown in Fig S2. Previous studies 14,15 show that 2-D inversions of the transverse magnetic (TM) mode or yx polarisation data (corresponding to current flow in the direction of the profile) from a quasi 2-D structure produce better approximations to the resistivity structure beneath the measurement profile line if the TM mode phase data has a larger weight than the corresponding transverse electric (TE) mode data. We also weight the TM phase data more strongly than the apparent resistivity data to reduce the effect of near surface distortion on the MT amplitudes (apparent resistivities). The error floors for the TM phase and apparent resistivity were set to 5% and 10%, respectively and 10% for the corresponding TE mode data. Thus the fit required for the TM phase component is twice that for the orthogonal (TE mode) phase and both apparent resistivities. An error floor of 0.1 was used for the component of the (dimensionless) induction vector in the profile direction. The emphasis on the TM mode in the inversion will also compensate to some degree for the effect of shallower structures, allowing the resistivities and geometry of larger-scale deeper features to be determined more accurately The smoothing parameters needed to stabilize the inversion were chosen after numerous trial inversions. The smoothing values used were τ = 2, α = 1, and β = 1; where τ represents the trade-off between fitting the model and adhering to model constraints, α is the horizontal smoothing factor, and β is a multiplier which relates the horizontal nature geoscience 5

6 smoothing to the vertical smoothing. When β = 1 the horizontal smoothing increases at the same rate as the vertical smoothing. For the model shown in Fig. 4, the inversion converged after ~300 iterations with a normalised RMS misfit of 2.3. Examples of the model fit at 5 representative stations are shown in Fig. S3. Although the 2-D modeling could potentially resolve structure at depths greater than the 40 km depth shown in Fig.4, the deep resistivity structure will be less well constrained due to the limited length (~85 km) of the measurement profile. For this reason we only show the top 40 km of the resistivity model. Results of hypothesis testing carried out to test the robustness of the 2-D are shown in Figs. S4 & S5. In Fig. S4, the results of a 2-D inversion for data from a SW-NE line running through Mount St. Helens are shown. These results demonstrate the robustness of the 2-D inversion to changes in the choice of profile direction. To test the sensitivity of the model to a localised conductive zone associated with the crater, an inversion was carried for the western a portion of the W-E line (Fig. 4a) with and without the station in the crater included. As expected, the results (Fig. S5) show that this station constrains only the upper part of the resistivity structure beneath the crater and its removal does not affect the deeper parts of the resistivity model beneath Mount St Helens. 6 nature geoscience

7 Figure S2. Mesh discretisation used for 2-D inverse modelling. The corner points of each cell within the mesh are marked by blue dots. The area of data coverage (station locations) lies in the central part of the mesh between 545 and 635 km. In the central region, containing the measurement points, the cell width is 200 m except where the projected station separation is less than 200 m in which the cell width was decreased to 100 m. Cell thickness increases exponentially downwards at a rate of 1.1 times starting at 60 m. nature geoscience 7

8 Figure S3a. Map showing the location of the measurement sites. Sites for which the 2- D model fit is shown in Figs S3b-f are shown by the red dots outlined in black. Other features as in Fig nature geoscience

9 Figure S3b. 2-D inverse model fit and data points for site MSH-611 (Fig. S3a). The inversion preferentially fits the (nominal) TM mode phase. nature geoscience 9

10 Figure S3c. 2-D inverse model fit and data points for site MSH-617 (Fig. S3a). The inversion preferentially fits the (nominal) TM mode phase. 10 nature geoscience

11 Figure S3d. 2-D inverse model fit and data points for site MSH-622 (Fig. S3a). The inversion preferentially fits the (nominal) TM mode phase. nature geoscience 11

12 Figure S3e. 2-D inverse model fit and data points for site MSH-626 (Fig. S3a). The inversion preferentially fits the (nominal) TM mode phase. 12 nature geoscience

13 Figure S3f. 2-D inverse model fit and data points for site MSH-647 (Fig. S3a). The inversion preferentially fits the (nominal) TM mode phase. nature geoscience 13

14 a) b) Figure S4. a) Location of the 40 km SW-NE data profile (dashed red line) through Mount St Helens used for the inverse 2-D model (b) superimposed on a phase tensor and induction vector map similar to Fig. 2 at T = 85.3 s. (The ellipse colour in (a) shows the minimum phase Φ min rather than Φ 2 used in Fig. 2). Triangles show the measurement locations used in the inversion with parameters and vertical discretisation the same as used for the model shown in Fig. 4. The normalised RMS error for this model (b) was nature geoscience

15 Figure S5. 2-D model inversion models used to test the sensitivity of the 2-D inversion to the data from the measurement station in the crater. The data used in these inversions was restricted to the short (35 km) E-W profile shown by the solid red line in Fig. S4. Triangles show the measurement locations used in the two inversions with the models in (a) and (b) showing respectively, the inverse models including and excluding the data from the site within the crater. Inversion parameters and vertical model discretisation are the same in both cases and are the same as used for the 2-D model shown in Fig. 4 for the long profile between Mounts St Helens and Adams. Both inversions produce a vertical conductive zone beneath the volcano that extends downwards to join a large region of high conductance east of the volcano at ~10 km depth. nature geoscience 15

16 3-D inversion details The 3-D inversion model of the MT data was calculated using WSINV3DMT 17. Input data consisted of impedance tensor values at 20 frequencies from the 67 sites contained in the 35 x 35-km 2 shown in Fig. 4. A constant 5% error was assumed for the impedances. The model mesh consisted of 42 cells in the x- and y-directions and 35 cells in z- direction. Cell size increases outside the 35 x 35-km 2 survey area and downwards as shown by the pixel size in Fig. 4. The starting model consisted of a 100 Ωm half-space with a 0.33 Ωm block on the western most side of the model mesh representing the ocean. The spatial smoothing parameters 17,36 (τ and δ x, δ y, δ z ), needed to stabilize the inversion were chosen after numerous trial inversions of a subset of the data. The values finally chosen: τ = 6, δ x = δ y = δ z = 0.2, are such that the degree of smoothing in the x, y and z directions is the same. The other parameters used by WSINV3DMT control the Lagrange multiplier, which trades off the data misfit with the so called model covariance containing the spatial smoothing and the desired level of misfit (X * ) which theoretically should be one. The values of the parameters controlling the Lagrange multiplier were left at the default values recommended by Siripunvaraporn et al 17. For real data, X * is greater than one. After further trials a value of 1.4 was chosen for X *. The inversion reached a normalised RMS of 1.8 after 8 iterations. A comparison between sounding curves calculated from the final model and corresponding observed soundings is shown in Figs. S6. Finally, the veracity of the 3-D inverse model was tested using an independent forward model 18 calculated from a simplified version of the 3-D inverse model that retains only the major features of the inverse model. Phase tensors for the inverse and forward calculation are compared to the observed tensors in Fig. S7. 16 nature geoscience

17 Figure S6. Response curves showing the fit of inverse results, the sounding curves for both the data inverted (dots) and the inverse response (lines) with xy component plotted in red where x is north. The resistivity response and original data are plotted for every station used in the inversion. nature geoscience 17

18 Figure S7. Resistivity depth slices from the 3-D forward (a-c) and inverse (m-o) models at 2.5, 7.0, and 20.0 km depth. Measurement locations are shown by black dots. Phase tensor ellipse maps for the forward (d-f) and inverse (j-l) model response and the observed data (g-i) (1.3, 13, 85 s period, respectively). The ellipses colour shows Φ2 and the contours show the phase tensor skew angle (β) and are shown for the periods ~ corresponding to the depth slices shown. Background topographic contour interval is 100 m. 18 nature geoscience

19 Supplementary Discussion In MT studies the ability to resolve deep structural features is hindered by the distorting effects of shallow resistivity heterogeneities. Since the phase tensor is free of these distortions we can use the phase tensor to identify major features of the resistivity structure at depth directly from the observed data 12. For example, in the period range that detects the deep conductor shown by the grey background in Fig. 3, the tensor ellipse axes are aligned approximately W-E outside the region of high phase but are nearly circular within the region. This behaviour of the tensor ellipses is that expected for a quasi 2-D situation for an elongated block of conductive material embedded in a more resistive region 12, 30. The most striking feature of the modeling (both 2-D and 3-D) is the connection between the vertical conduit and the regional zone of high conductivity in the mid crust that we identify with the SWCC. The necessity for this connection is demonstrated by the sensitivity of the phase tensor skew to the connection as illustrated by the forward models in Fig. S8. The SWCC was interpreted Stanley et al. 4 as: a marine forearc basin/accretionary prism complex, with the high probability that some of the shallower units consist of post accretion marine sedimentary rocks and possibly carbon-rich continental sediments. The lithologies considered by Stanley et al. 4 ranked in order of preference were: (1) marine sedimentary rocks of pre-eocene and Eocene age, mostly shale facies, (2) Tertiary continental sedimentary rocks equivalent to the Puget Group, (3) thick sequences of highly altered tuffs, and (4) graphitic and/or pyretic slates, schists, carbonates or argillites of pre-mesozoic age. The first three possibilities are consistent with the interpretation of the SWCC as a shallow 3-6 crustal feature but do not fit well with the depth (~15 km) that we infer for the SWCC from the 3-D model (Fig. 4). At shallow depth, sedimentary rocks are conductive due to interconnected pore fluids and the presence of high ion exchange capacity clays. However, at ~15 km depth the sediments would be expected to have been metamorphosed and the resulting meta- nature geoscience 19

20 sedimentary rocks are not usually associated with high conductivities unless they contain interconnected graphite or sulphides. While graphitic or pyretic meta-sediments could potentially explain the high conductivity in the SWCC, no non-igneous lithologies have been found as xenoliths in the eruptive products from Mount St Helens 22 and we consider this explanation of the high conductivity to be unlikely. Miller et al. 21 also argued against the interpretation of the SWCC as marine sediments using results from a wide-angle reflection/refraction seismic survey along a north-line running from south of Mount Rainer to the Canadian border crossing the northern half of the SWCC. According to these authors seismic velocities in the km depth range increase from about 6.0 to 7.2 km/s and do not support the presence of marine sedimentary rocks at depths of km as proposed by Stanley et al. 4. Another possible explanation for the high conductance in the SWCC is the presence aqueous fluid. The most abundant of xenoliths (gabbros) found in the 1980 and subsequent effusive eruption products at Mount St Helens show evidence of penetration by water rich fluids prior to their incorporation into the dacitic magma 22. According to Heliker 22, these xenoliths originate at shallower depths than the source region of the 1980 dacite; the availability of water making the gabbros (which contain up to 9% melt) susceptible to melting by the (relatively low temperature) dacitic magma 22. However, the presence of quenched residual melt in some xenoliths demonstrates that basaltic (higher temperature) melt resides in the lower reaches of the magma reservoir 22. This makes the existence of a separate aqueous phase at deeper levels unlikely as its presence would promote melting. Although we cannot entirely rule out the presence of a layer of aqueous fluid as being the cause of the high conductivity in the wider area of the SWCC away from Mount St Helens, the presence of silicic volcanoes at its margins suggest that the high conductivity is a consequence of the presence of a small volume of interconnected melt consistent with modern models of the formation of large magma reservoirs 23,37. Estimating the volume of melt in the SWCC from the resistivity model is fraught with uncertainty as the resistivity and distribution of the melt within the rock matrix is 20 nature geoscience

21 unknown. Within the conduit melt fraction in the moving magma must exceed ~50% 38 thus we can take the value of the resistivity in the conduit as a crude estimate of the melt resistivity. Values of the resistivity of the conduit in the 3-D resistivity model (Fig. 4) are ~0.1 Ωm, consistent with the value of melt resistivity suggested by Schilling et al 39. Away from the vicinity of the conduit, the resistivity of the SWCC in the 3-D model lies between ~1 and 10 Ωm. This is equivalent to a conductance of between ~2 and 20 ks for a 20 km thick conductive zone similar to Fig. 4 which is in good agreement with the conductance given by Egbert and Booker 7 (Fig. 1). Using 0.1 Ωm for the resistivity of the melt, a modified version of Archie s law derived by ten Grotenhius 2 for low melt fraction rocks and a resistivity of between 1-10 Ωm for the SWCC, implies a melt fraction in the SWCC of between 2 and 12%. At Mount St. Helens the compositional range of magmas present results from mixing of dacitic and basaltic end members rather than from simple fractional crystallization 8. Whereas basaltic magmas seem to be derived by partial melting of the mantle wedge 27, the source and location of dacitic magma production has been a matter of long debate. Earlier studies of Mount St. Helens suggested that the dacitic magmas were derived by partial melting of either the lower crust 25 or the down-going slab 26. Recent U-series isotope and thermal modelling investigations 40 place the silicic magma in the mid-upper crust below 10 km. Finally, recent B and Li isotopic studies 41 suggest that the subduction zone in the southern Washington Cascade is unusually hot and dry and they emphasize that melting in the region is primarily a result of the thermal structure of the arc rather than substantial amounts of fluids at depth. A model that invokes the presence of a large zone of partial melt (or crystal mush ) within the mid-crust provides a consistent and inclusive explanation for both the new geophysical evidence presented in this paper as well as the most recent geochemical and petrologic evidence available at this time. nature geoscience 21

22 Figure S8. Simple 3-D block models 19 (a and b) used to investigate the cause of the observed β response (Fig. 2). Phase tensor skew angle response (c and d) of models (a) and (b), respectively. The contours and ellipse colour show the skew angle β. Significant β values are produced only in the case where the two bodies are connected. Although this geometry does not reproduce the shape of the observed β response (Fig. S4), by adding a structure similar to the dyke like projection in the forward and inverse models (Fig. S7) the negative lobe of the β response can be suppressed. 22 nature geoscience

23 Supplementary References: 31. Gamble, T., Goubau, W., & Clarke, J. Magnetotellurics with a remote reference. Geophys. 44, (1979). 32. Jones, A.G., Chave, A.D., Egbert, G., Auld, D., & Bahr, K. A comparison of techniques for magnetotelluric response function estimation. J. Geophys. Res. 94, (1989). 33. Torres-Verdin, C., & Bostick, F. X., Jr. Principles of spatial surface electric field filtering in magnetotellurics: electro-magnetic array profiling (EMAP). Geophys. 57, (1992). 34. Wannamaker, P. E. Affordable magnetotellurics: interpretation in natural environments. in Three-dimensional electromagnetics (ed Oristaglio, M., & Spies, B.) (Geophys. Devel. Ser., 7, Soc. Explor. Geophys., Tulsa, 1999). 35. Wannamaker, P.E., Caldwell, T.G., Jiracek, G.R., Maris, V., Hill, G.J., Ogawa, Y., Bibby, H.M., Bennie, S.L., & Heise, W. Fluid and deformation regime of an advancing subduction system at Marlborough, New Zealand. Nature 460, (2009). 36. Siripunvaraporn, W., & Egbert, G.D. An efficient data-subspace inversion method for two-dimensional magnetotelluric data. Geophys. 65, (2000). 37. Miller, C.F., & Wark, D.A. Supervolcanoes and their explosive supereruptions. Elements. V4, (2008). 38. Marsh, B.D. On the cyrstallinity, probability of occurrence, and rheology of lava and magma. Contrib. Min. Pet. 78, (1981). 39. Schilling, F.R., Partzsch, G.M., Brasse, H., & SchwarzG. Partial melthing below the magmatic arc in the central Andes deduced from geoelectromagnetic field experiments and laboratory data. Phys Earth Planet. Int. 103, (1997). 40. Dosseto, A., Turner, S.P., Sandiford, M., & Davidson, J. Uranum-series isotope and thermal constraints on the rate and depth of silicic magma genesis. From: Annen, C., & Zellmer, G.F. (eds). Dynamics of Crustal Magma Transfer, Storage and Differentiation. Geological Society, London, Special Publications. 304, (2008). 41. Leeman, W.P., Tonarini, S., Chan, L.H., & Borg, L.E. Boron and lithium isotopic variations in a hot subduction zone the southern Washington Cascades. Chem. Geol. 212, (2004). nature geoscience 23