Mantle flow and multistage melting beneath the Galápagos hotspot revealed by seismic imaging

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1 Mantle flow and multistage melting beneath the Galápagos hotspot revealed by seismic imaging Darwin R. Villagómez, Douglas R. Toomey, Dennis J. Geist, Emilie E. E. Hooft, & Sean C. Solomon Joint Inversion Method Synthetic Inversions and Resolution Tests Body Wave Delay Times and Phase Velocity Measurements Results of Tomographic Inversions for S- wave Velocity Perturbations Depth Resolution of S- wave Velocity Anomalies Estimates of Melting Conditions, Volatile Concentrations, and Helium Partitioning References Supplemental Table S1. Misfit and variance reduction with a variety of inversion parameters Supplemental Table S2. Bulk distribution coefficients used in silicate melting model Supplementary Figure S1. Synthetic inversions of S- wave slowness perturbations Supplementary Figure S2. Synthetic inversions of a tilted velocity anomaly Supplementary Figure S3. Examples of S- wave data Supplementary Figure S4. S- wave delay times versus source location and wave path Supplementary Figure S5. Two- dimensional maps of phase velocity anomalies Supplementary Figure S6. Results of tomographic inversions of body and surface wave observations Supplementary Figure S7. Results of tomographic inversion for S- wave velocity structure using subsets of the S wave data NATURE GEOSCIENCE 1

2 Supplementary Figure S8. Results of tomographic inversion of body and surface wave observations using finite- frequency sensitivity kernels for body waves Supplementary Figure S9. Vertical cross- sections through S- wave perturbation model Supplementary Figure S10. Effect of squeezing depth on inferred heterogeneity and model misfit Joint Inversion Method We utilize a tomographic method that allows for the simultaneous inversion of body wave delay times and Rayleigh wave phase velocity anomalies to solve for three- dimensional (3- D) isotropic P and S wave velocities. The algorithm, which is a modification of our previous efforts 1,2, is non- linear and includes three- dimensional ray tracing, variable weighting of body and surface wave data, and coupling of P and S wave structures. The forward problem for body waves consists of the determination of the ray geometry and travel time for each source and seismic station 1. We calculate P and S wave paths and travel times through three- dimensional seismic slowness models using a shortest- path algorithm derived from graph theory 3,4. The teleseismic delay time, Δt, from a perturbational slowness model, Δu, is calculated according to Δ t = Δ u ds (1) path where the integral is evaluated along the ray path and ds is the incremental path length. The perturbational slowness model is defined on a grid of nodes. The forward problem for surface waves consists of computing the Rayleigh wave phase velocity c(ω) at particular frequencies ω for a given one- dimensional (1- D) P and S slowness model. For each set of vertical nodes in the perturbational grid, we estimate the Rayleigh wave phase velocity dispersion curve using DISPER80 5, which calculates normal modes for a laterally homogeneous model. We solve the non- linear joint tomographic inverse problem # % % $ C 1/2 dδt G λ C C 1/2 dδc A &# (% ( ' $ % Δu P Δu S & # ( '( = % C dδt % $ λ C C dδc 1/2 Δt 1/2 Δc & ( ( ' (2) 2 NATURE GEOSCIENCE

3 for changes Δu P and Δu S to the P and S slowness model, where Δt is the n d x 1 vector of body wave delay data, Δc is an n c x 1 vector containing the observed phase velocity anomalies, and n c is equal to the number of nodes on the horizontal plane for which there are phase velocity observations multiplied by the number of frequencies. C dδt and C dδc are the data covariance matrices, which contain variances along the diagonal and zero off- diagonal terms (because the observations are assumed to be independent) estimated for the body wave delay times and phase velocities, respectively. Δu P and Δu S are vectors of perturbational model parameters. G is the Fréchet matrix of partial derivatives of delay times with respect to model perturbations t i / u j (i =1,n d ). A is the matrix of partial derivatives of phase velocity perturbations with respect to model perturbations c k / u j (k = 1,n c ). λ C is a weight parameter that controls the amount of influence of the phase velocity data in the inversion and accounts for the relative uncertainty of delay times and phase velocity measurements. The problem is non- linear because the partial derivative matrices G and A are themselves functions of the model parameters Δu. The solution requires an iterative process whereby the partial derivatives are calculated at each iteration until the inversion converges to a solution. We use LSQR 6 to solve equation (2). We introduce two types of correction parameters to the inversion: (1) we add station corrections to account for the effect of shallow seismic structure beneath individual stations, and (2) we allow for shifts to the teleseismic event locations and origin times to reduce the influence of seismic structure outside of the model region. The inverse problem is ill conditioned, and thus we stabilize the inversion by applying additional constraints. We minimize the model norm using damping constraints and impose spatial smoothing by averaging slowness perturbations with those at adjacent nodes. We control the amount of damping and spatial smoothing with weighting parameters, and we explore their effects by conducting many tens of inversions. Synthetic Inversions and Resolution Tests To validate our method and to assess the resolution of the surface and body wave observations, we performed a series of synthetic inversions. We first created a 3- D synthetic model of slowness perturbations (Δu S ) and then predicted delay times and phase velocity anomalies, to which we added random noise. We then tomographically inverted these synthetic data and compared the resulting model with the original synthetic model. NATURE GEOSCIENCE 3

4 Results of tests for the depth resolution of surface and body waves are shown in Fig. S1. We tested three scenarios: surface wave data only, body wave delay times only, and joint inversion of surface and body waves. The results of the inversion of only surface wave data (Fig. S1b and S1f) show that the resolution of surface waves decreases rapidly with depth. Surface waves can resolve seismic structure relatively well at depths less than 100 km, but resolution is limited between 100 and 200 km depth, and surface waves cannot resolve seismic structure at depths greater than 200 km. On the other hand, body wave data show relatively good resolution between ~100 and ~300 km depth (Fig. S1c and S1g), but resolution is poor in the shallower and deeper parts of the model where there are not enough crossing seismic wave paths. Results of a joint inversion show that at depths between 100 and 200 km, the resolution of body and surface waves is complementary. Through the combination of surface and body wave data we are able to reliably recover seismic structure above ~300 km depth (Fig. S1d and S1h). Results of synthetic inversions that test the ability of the data and method to resolve different amounts of tilting of a velocity anomaly are shown in Fig. S2. We tested five different cases for a - 3% V S anomaly: no tilt (Fig. S2a and S2d), an anomaly tilted ~8 eastward from the upward vertical (0.5 in longitude over 400 km depth, Fig. S2b), an anomaly tilted ~16 eastward from the upward vertical (1 in longitude over 400 km depth, Fig. S2c), an anomaly tilted ~8 northward from the upward vertical (0.5 in latitude over 400 km depth, Fig. S2e), and an anomaly tilted ~16 northward from the upward vertical (1 in latitude over 400 km depth, Fig. S2f). The results of the inversions show that the shape and the amplitude of the anomaly are recovered well between ~100 and ~300 km depth for four of the five cases, whereas the tilt of the recovered anomaly is underestimated for a small tilt in the north south direction (Fig. S2e). These results suggest that the ray set and the inversion procedure can detect relatively small amounts of tilting of a velocity anomaly, particularly the component of tilt in the east west direction. Body Wave Delay Times and Phase Velocity Measurements Examples of S- wave arrivals are shown in Fig. S3. We measured 1769 S- wave relative delay times from 161 teleseismic events (m b > 5.5) with epicentral distances varying from 35 to 140 (Fig. S4a). S- wave delay times were estimated from records on horizontal channels rotated to the radial or transverse directions with respect to the station- to- event azimuth; 1046 and 723 measurements were made on the transverse and radial channels, respectively. Prior to measuring delay times, waveforms were corrected for instrument response and filtered using a third- order Butterworth filter run forward and backward to provide a zero phase response. Depending on data quality, we measured delays in the following filter 4 NATURE GEOSCIENCE

5 bands: Hz, Hz, and Hz. We measured relative delay times with respect to the IASP91 one- dimensional (1- D) seismic Earth model 7, using a cross correlation of up to three cycles of the waveform 8, though the great majority of our measurements used 1 to 1.5 cycles. Fig. S4b shows an east west projection of the S- wave ray paths that were used in the inversion. S wave delays tend to be consistently late (positive delays, red lines) for upper mantle paths between 91 and 92 W, suggesting that S waves are slowed when traversing the upper mantle beneath the island of Isabela. We estimated the uncertainty in the measurement of the delay times by performing the cross- correlation multiple times with the addition of noise with a randomized phase. The noise was taken from a time window immediately before the measured waveform. The error in the delay time was taken as the standard deviation of the multiple measurements. For surface waves, we used the two- dimensional (2- D) Rayleigh- wave isotropic phase velocity maps for the Galápagos region from Villagomez et al 9. The maps were obtained at periods between 20 s to 125 s (frequency between Hz and 0.05 Hz) from the inversion of measurements of phase and amplitude of Rayleigh waves. These frequency- dependent measurements of phase and amplitude of Rayleigh waves were inverted for 1- D and 2- D phase velocity structures separately for each frequency. 2- D phase velocity anomalies (Δc) were obtained by subtracting the 1- D phase velocities (regional average) from the 2- D phase velocities. Maps of Δc at 20 s, 40 s, and 80 s periods are shown in Fig. S5. At a period of 20 s the low Rayleigh phase velocity anomaly is centered between southern Isabela and Fernandina (Fig. S5a). For this period, changes in phase velocity are most sensitive to changes in V S between ~10 km and ~50 km depth (Fig. S5d). At a period of 80 s the low Rayleigh phase velocity anomaly is located toward the center of the archipelago (Fig. S5c). For this period, changes in phase velocity are most sensitive to changes in V S between ~50 km and ~150 km depth (Fig. S5d). Results of Tomographic Inversions for S- wave Velocity Perturbations We conducted a series of joint inversions using different inversion parameters (Table S1). We systematically varied the amounts of vertical and horizontal smoothing, the damping of the model norm, and the weighting of the Rayleigh wave phase velocity observations relative to the body wave data. Overall, the variance in observed delay times was reduced between 37% and 50% for a range of inversion parameters. For our preferred inversion we obtained a total variance reduction of 45% and a root mean square (RMS) misfit of shear wave delay times of s. NATURE GEOSCIENCE 5

6 In addition to the joint inversions of body and Rayleigh wave observations, we performed inversions using only body wave delay times or only Rayleigh phase velocities (Fig. S6). Inversions of only phase velocities are shown in Fig. S6a, b. Phase velocities are able to recover structure at depths less than ~100 km. At depths between 100 and 200 km, phase velocities perform a relatively good job at detecting the shape and location of the V S anomaly, but they greatly underestimate its amplitude. In contrast, inversions of only body wave delay times are able to recover structure at depths greater than 100 km (Fig. S6c, d). There is good agreement in the location of the V S anomaly recovered independently by the body and surface wave observations at depths between 100 and 200 km. Joint inversions (Fig. S6e, f) show that the body and surface wave observations are complementary and enhance resolution of the anomaly at depths between ~50 and ~150 km, when compared with independent inversions of only body wave or surface wave observations. We also conducted inversions for a subset of the S- wave delays measured only on the transverse channel (~60% of the total data set). Fig. S7 shows that these results closely resemble those obtained using delay times measured on both the radial and transverse channels. On the basis of this result we conclude that our delay time data set is not compromised by S- to- P conversions that reverberate in the water column near an ocean island station. Tomographic results obtained with ray theory and finite- frequency sensitivity kernels for body waves are effectively identical. The results of a joint inversion of body wave and surface wave observations conducted with frequency- dependent sensitivity kernels for the body waves following the methods of Schmandt and Humphreys 10 are shown in Fig. S8. (Note that all inversions of data sets that include surface wave observations use frequency- dependent sensitivity kernels for surface waves, as discussed by Villagómez et al. 9 ) Of particular interest is the location and shape of the low- velocity anomaly in the upper mantle in Fig. S8. A north south section at 91 W shows the low- velocity anomaly to be continuous (Fig. S8e), and between 300 and 100 km it tilts northward at an angle of ~45 as it shoals. An east west section through the low- velocity anomaly at 0 45 S (Fig. S8d) reveals a columnar feature that is ~100 km wide and continuous from ~100 to 300 km depth. From these results we conclude that our tomographic images are robust with respect to methodology and that the deflection of the Galápagos plume toward the spreading center is a feature that is supported by the data provided. Vertical cross- sections along lines of longitude (Fig. S9a- e) and latitude (Fig. S9f- j) highlight several characteristics of the low- velocity anomaly. East west cross- sections at 0.75 S and 0.5 S (Fig. S9b- c) show a V S anomaly with no tilt in the direction of plate motion. Cross- sections at 0.25 S and 0 S (Fig. 6 NATURE GEOSCIENCE

7 S9d- e) show that at latitudes north of Fernandina, the velocity anomaly is confined to depths shallower than ~150 km. All north south cross- sections (Fig. S9f- j) show that the low- velocity anomaly is tilted northward as it shoals. Depth Resolution of S- wave Velocity Anomalies To quantify the depth extent of the resolution of the joint tomography we performed inversions in which the lateral variations were confined to depths shallower than a squeezing depth that varied among solutions. This was implemented by having the damping constraint increase 100 times for depths greater than the selected squeezing depth. Results of the inversions with squeezing depths of 100, 200, 300 and 400 km are shown in Fig. S10a- d. The RMS misfit of the delay times and variance reduction as a function of squeezing depth are shown in Fig. S10e- f. The misfit (variance) decreases (increases) almost linearly with increasing squeezing depth, suggesting that the inversions may be detecting seismic structure throughout the entire depth range of the model. The decrease in misfit achieved when the squeezing depth increases from 300 to 400 km is approximately the same as that when the squeezing depth is increased from 100 to 200 km, which indicates that the decrease in model error (misfit) due to seismic structure between 300 and 400 km depth could be significant to the same level as that due to structure between 100 and 200 km depth. However, on the basis of the results of the synthetic inversions we conservatively estimate that the depth range of best resolution is from ~20 to ~300 km depth. Estimates of Melting Conditions, Volatile Concentrations, and Helium Partitioning Melt inclusions in basalts from the Galápagos Islands (Fernandina volcano) contain up to 6000 ppm CO Fernandina basalts are substantially fractionated from compositions that are in equilibrium with the mantle, perhaps by as much as 50% 12. Geochemical models of basalts from the western Galápagos show that they can be produced by ~5% partial melting 13. Correction for this amount of crystal fractionation and partial melting implies a CO 2 concentration of 150 ppm in the Galápagos mantle plume, under the assumption that C behaves as a perfectly incompatible element. An alternative estimate of the CO 2 concentration of the Galapagos mantle may be obtained through an estimate of the mantle s CO 2 /Nb ratio of 240 (Saal et al. 14 ). Fernandina basalts are notably rich in Nb (average 25 ppm). If we assume 50% crystallization and 5% melting, as above, then the CO 2 concentration implied by the Nb concentration is also 150 ppm. We note, however, that because it is NATURE GEOSCIENCE 7

8 likely that carbonate- rich melt is transported separately from silicate melt, the assumption of constant CO 2 /Nb and the use of melt inclusion CO 2 concentrations are invalid. Given 150 ppm CO 2 in the mantle source (see above), 0.03% carbonatite melt is produced near the solidus. For a potential temperature that is 100 C higher than that of MORB- producing mantle, the temperature exceeds the solidus at 250 km, and the melt is a silicate liquid with 22% CO 2 (Dasgupta et al. 15 ). Rock with 150 ppm CO 2 would therefore produce 0.14% melt at 250 km. As noted by Hofmann et al. 16, helium partitioning between mantle minerals and either silicate or carbonatite melt is far from understood. Burnard et al. 17 found that helium solubility in carbonatite melt is comparable to that in silicate melt. The distribution coefficient for helium between peridotite and silicate melt may be as low as 10-4 ( 18 ), compared with > 10-3 for the heavier radiogenic isotopes. This difference in distribution coefficients is crucial when the degree of melting is comparably small (e.g., 10-3 in our model). The bulk distribution coefficients for our model involving silicate melt (Fig. 5) are compiled from the literature and are listed in Table S2. References 1. Toomey, D. R., Solomon, S. C. & Purdy, G. M. Tomographic imaging of the shallow crustal structure of the East Pacific Rise at 9 30'N. J. Geophys. Res. 99, (1994). 2. Hammond, W. C. & Toomey, D. R. Seismic velocity anisotropy and heterogeneity beneath the Mantle Electromagnetic and Tomography Experiment (MELT) region of the East Pacific Rise from analysis of P and S body waves. J. Geophys. Res. 108, 2176 (2003). 3. Dijkstra, E. W. A note on two problems in connetion with graphs. Numer. Math. 1, (1959). 4. Moser, T. Shortest path calculation of seismic rays. Geophysics 56, (1991). 5. Saito, M. DISPER80: A subroutine package for calculation of seismic normal mode solutions (Academic Press, San Diego, Calif., 1988). 6. Paige, C. C. & Saunders, M. A. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Softw. 8, (1982). 7. Kennett, B. L. N. & Engdahl, E. R. Traveltimes for global earthquake location and phase identification. Geophys. J. Int. 105, (1991). 8. VanDecar, J. C. & Crosson, R. S. Determination of teleseismic relative phase arrival times using multi- channel cross- correlation and least squares. Bull. Seismol. Soc. Am. 80, (1990). 9. Villagómez, D., Toomey, D. R., Hooft, E. E. E. & Solomon, S. C. Upper mantle structure beneath the Galápagos Archipelago from surface wave tomography. J. Geophys. Res. 112, B07303 (2007). 10. Schmandt, B. & Humphreys, E. Seismic heterogeneity and small- scale convection in the southern California upper mantle. Geochem. Geophys. Geosyst. 11, Q05004 (2010). 11. Koleszar, A. M. et al. The volatile contents of the Galapagos plume; evidence for H 2 O and F open 8 NATURE GEOSCIENCE

9 system behavior in melt inclusions. Earth Planet. Sci. Lett. 287, (2009). 12. Geist, D. J. et al. Submarine Fernandina: Magmatism at the leading edge of the Galápagos hot spot. Geochem. Geophys. Geosyst. 7, Q12007 (2006). 13. Geist, D. J. et al. Wolf Volcano, Galapagos Archipelago: Melting and magmatic evolution at the margins of a mantle plume. J. Petrol. 46, (2005). 14. Saal, A. E., Hauri, E. H., Langmuir, C. H. & Perfit, M. R. Vapour undersaturation in primitive mid- ocean- ridge basalt and the volatile content of Earth's upper mantle. Nature 419, (2002). 15. Dasgupta, R. et al. Carbon- dioxide- rich silicate melt in the Earth s upper mantle. Nature 493, (2013). 16. Hofmann, A. W., Farnetani, C. G., Spiegelman, M. & Class, C. Displaced helium and carbon in the Hawaiian plume. Earth Planet. Sci. Lett. 312, (2011). 17. Burnard, P., Toplis, M. J. & Medynski, S. Low solubility of He and Ar in carbonatitic liquids: Implications for decoupling noble gas and lithophile isotope systems. Geochim. Cosmochim. Acta 74, (2010). 18. Heber, V. S., Brooker, R. A., Kelley, S. P. & Wood, B. J. Crystal melt partitioning of noble gases (helium, neon, argon, krypton, and xenon) for olivine and clinopyroxene. Geochim. Cosmochim. Acta 71, (2007). NATURE GEOSCIENCE 9

10 Table S1. RMS misfit of delay times and Rayleigh phase velocities and reduction of variance in delay times for selected joint inversions with different inversion parameters. Horizontal smoothing Vertical smoothing Weight damping constraint Phase velocity influence RMS misfit of delay times (s) Variance reduction RMS misfit of phase velocity (km/s) % % % % % % % % % % % % % % Notes: Rows are ordered by increasing RMS misfit of delay times and decreasing values of variance reduction. The parameters for the joint inversion selected for our final results are shown in boldface. 10 NATURE GEOSCIENCE

11 Table S2. Bulk distribution coefficients used in silicate melting model. Cs Rb Ba Nb La Pb Sr Nd Zr Sm Yb Y NATURE GEOSCIENCE 11

12 Fig. S1. Synthetic inversions of S- wave slowness perturbations. Color scale represents calculated shear- wave velocity perturbations. Panels are north south cross- sections at 91 W. (a- d) Synthetic model A. (e- h) Synthetic model B. (a and e) Synthetic perturbation model. (b and f) Results of inversions using only phase velocity data. (c and g) Results of inversions using only body wave delay times. (d and h) Results of joint inversions of phase velocities and body waves delay times. 12 NATURE GEOSCIENCE

13 Fig. S2. Synthetic inversions of a tilted velocity anomaly. Calculated S- wave velocity perturbations from synthetic inversions conducted to test the resolution of different degrees of plume tilt. Black box denotes the location of the synthetic velocity anomaly. Panels a c are east west cross- sections, and panels d f are north south cross- sections. (a and d) Synthetic plume with no tilt. (b) Synthetic anomaly tilted ~8 eastward from the upward vertical. (c) Synthetic anomaly tilted ~16 eastward from the upward vertical. (e) Synthetic anomaly tilted ~8 northward from the upward vertical. (f) Synthetic anomaly tilted ~16 northward from the upward vertical. NATURE GEOSCIENCE 13

14 PAYG PAYG Fig. S3. Examples of S- wave Data. S- wave arrivals filtered at Hz and aligned by cross correlation of waveform data within the black vertical lines. Station names (see Fig. 1) are indicated to left of each figure. (a) Back azimuth, epicentral distance, and focal depth of 139, 37, and 609 km, respectively. Data are from the transverse channel. (b) Back azimuth, epicentral distance, and focal depth of 241, 89, and 178 km, respectively. Data are from the radial channel. 14 NATURE GEOSCIENCE

15 Fig. S4. S- wave delay times versus source location and wave path. (a) Distribution of the 161 events (m b > 5.5) for which S- wave delay times were analyzed in this study. Red triangles indicate the locations of seismic events. Azimuthal equidistant projection centered at 0 N, 90 W. (b) East west projection of ray paths of teleseismically observed S waves for all seismic stations (white triangles). Red and blue lines indicate positive (late) and negative (early) delays with respect to a standard Earth model. Delay times have been adjusted by adding station corrections. NATURE GEOSCIENCE 15

16 Fig. S5. Two- dimensional maps of phase velocity anomalies. Phase velocity anomalies, Δc, for Rayleigh waves at (a) 20 s, (b) 40 s, and (c) 80 s period, from Villagómez et al 9. (d) Sensitivity kernels for Rayleigh waves as functions of depth for periods of 20, 40, 80, and 125 s. 16 NATURE GEOSCIENCE

17 Fig. S6. Results of tomographic inversions of body and surface wave observations. Color scale indicates percent deviation from the starting model. (a, c, and e) East west cross- section at 0.75 S. (b, d, and f) North south cross- sections at 91 W. (a- b) Results of inversions of only surface wave data (Rayleigh phase velocity anomalies). (c- d) Results of inversions of only body wave data (S- wave relative delay times). (e- f) Results of joint inversions of body and surface wave data NATURE GEOSCIENCE 17

18 0 a 0 b Depth (km) 0 0 Latitude 0 Latitude Fig. S7 Results of tomographic inversion for S- wave velocity structure using subsets of the S wave data. Color scale is fractional deviation from starting model (see Fig. 11 of Villagómez et al.). Cross- sections are north south at 91 W. a) 1769 observations derived from radial and transverse channels. b) 1046 observations using data from only the transverse channel. The anomaly patterns recovered by inversions of the two data sets are in substantial agreement. The amplitude of the reconstruction decreases in b because less data were used; nevertheless, the interpretation of the results would be identical. 18 NATURE GEOSCIENCE

19 1 N Depth 40 km a Latitude 0.75 S d 0 1 S Depth (km) 2 S 92 W 91 W 90 W 89 W 1 N 0 Depth 80 km b 92 W 91 W 90 W Longitude 91 W e 89 W 1 S 2 S 92 W 91 W 90 W 89 W Depth (km) 1 N Depth 200 km c 2 S 1 S 0 1 N 0 ln V S 1 S -2% 0 2% 2 S 92 W 91 W 90 W 89 W Fig. S8 Results of tomographic inversion of body and surface wave observations using finite- frequency sensitivity kernels for body waves. Color scale is percent deviation from the starting model (see Fig. 11 of Villagomez et al. 22 ). Map- view horizontal section at a) 40 km depth, b) 80 km depth, and c) 200 km depth. d) East west cross- section at 0 45 S. e) North south cross- section at 91 W. Dashed lines in (a- c) indicate locations of cross- sections d and e. NATURE GEOSCIENCE 19

20 Fig. S9. Vertical cross- sections through S- wave velocity perturbation model. (a- e) East west cross- sections. (f- j) North south cross- sections. Colors scale denotes percent deviation from the starting model. (k) Locations of the cross- sections (dashed lines) depicted in a j on a map view of the Galápagos Archipelago. 20 NATURE GEOSCIENCE

21 Fig. S10. Effect of squeezing depth on inferred heterogeneity and model misfit. (a- d) East west cross sections at 0.75 S of S- wave velocity perturbations obtained from inversions constrained by a variable squeezing depth indicated by the dashed horizontal lines (100, 200, 300, and 400 km). Color scale is the same as in Fig. S5. (e) RMS misfit as a function of squeezing depth. (f) Variance reduction as a function of squeezing depth. NATURE GEOSCIENCE 21