Seismic imaging of the Reunion mantle plume

doi:10.21203/rs.3.rs-4844057/v1

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Seismic imaging of the Reunion mantle plume

https://doi.org/10.21203/rs.3.rs-4844057/v1

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Since the mantle plume concept was proposed, the plume morphology has been debated in the past decades regarding its size, shape and origin. Reunion Island has been considered as the surface manifestation of a plume rising from the lower mantle. However, there has been few direct evidence from the deep mantle supporting this hypothesis until recent passive seismic observations. Here we use P-wave travel-time data recorded at many portable seismic stations to image the deep structure beneath Reunion Island, aiming to reveal the plume morphology and find evidence for off-axis interaction between the Reunion plume and the central Indian ridge (CIR). Our 3-D tomographic results show a mushroom-shaped low-velocity anomaly with a broad head and a thin, nearly vertical tail down to at least 1000 km depth, which exhibits an archetype plume and indicates weak mantle wind under Reunion Island. In the upper mantle, a low-velocity channel connects the Reunion plume and CIR along the Rodrigues ridge, indicating plume-related thermal and material exchanges from the Reunion plume to CIR. Slight ponding occurs around 660 km depth, which may reflect density stratification resulting from a phase change at the 660-km discontinuity.

Volcanic activities far from plate boundaries are associated with deep convection plumes¹. Many previous studies have suggested that a mantle plume has a broad head, followed by a long and thin plume conduit anchored on the core-mantle boundary^2,3 (CMB). Hot materials rising from the CMB take away heat from the core, cooling our planet⁴. These features are primary conceptions of an archetypal plume. However, with successive investigations by geophysical observations and dynamical modelling in the last decades, the hypothesis has withstood controversies regarding its mechanism, shape and origin depth^5–8. The shape of plumes varies in single and multiple branches, which may have vertical neckings, horizontal pondings and tilting conduits^9–12. The morphological structure of a plume has not yet reached a common consensus^13,14. The size and shape of a plume exist in great variety with a fat or thin tail¹³. In addition, its depth origin is still hotly debated. Only seven plumes (including the Reunion hotspot) are rising from the lower mantle in a classification of 49 hotspots worldwide based on their depth origins⁸. Active intraplate volcanoes are not always caused by deep mantle plumes. For example, intraplate volcanoes in East Asia are caused by hot and wet upwelling flows in the big mantle wedge above the subducted Pacific slab that is stagnant in the mantle transition zone^15–17 (MTZ). Furthermore, a study of converted waves at the MTZ discontinuities found no clear evidence for a thinning MTZ beneath 26 hotspots¹⁸, including the Reunion hotspot. This result suggests that abnormally high temperature of mantle plumes may not affect the MTZ, raising doubts on the origin depth of mantle plumes (i.e., most plumes may be originating in the upper mantle).

Plate reconstruction shows that the Deccan Traps (Fig. 1b), formed by volcanic activities of the Reunion hotspot in the Late Cretaceous^19,20, are considered as the earliest plume head. The Chagos-Laccadive Ridge and the Mascarene Plateau (Fig. 1b) are believed to be seafloor volcanic chains formed by actions of successive construction of the Reunion plume^8,21. Continuous and progressive dating features^22,23 (see white triangles and orange circles in Fig. 1b) strongly suggest that the volcanic chains are traces left by hotspot activities. Therefore, Reunion Island and its age-progressive linear tracks imply a fixed rise of hot and buoyant mantle plume lasting for 65.5 Ma^1,8,24. The most active basaltic volcanism worldwide on the island exhibits typical enrichments in geochemical characteristics²⁵. A high isotopic ³He/⁴He ratio indicates that the source of the Reunion plume is much deeper than mid-ocean ridges and reaches the lowermost mantle^8,15 (may be at a depth of ~ 1900 km or deeper; see ref. ²⁴). Sufficient buoyancy flux ascends through the entire mantle to feed active volcanism on the surface^8,26. Geodynamic modelling and geochemical and geophysical observations support this view from different aspects^27–32.

Global and regional tomographic results suggest that the Reunion hotspot sources from the D” layer and is related to the African large low-shear-velocity province^11,15,24,33 (LLSVP). The Reunion plume was considered to be one branch of a plume tree originating from the African LLSVP¹¹. Anisotropic tomography using Rayleigh waves recorded at stations of the RHUM-RUM experiment³⁴ revealed a low shear-velocity zone beneath the Reunion hotspot in the upper mantle³⁵. Their results constrained the geometry of the plume head, but the deep structure is still unknown due to the depth limitation of the Rayleigh-wave tomography³⁵. Hemispherical-scale waveform tomography³³ and finite-frequency tomography¹¹ illuminate the whole-mantle structure of the Reunion plume from the CMB to the surface. However, cut-off frequencies of the data used in the waveform inversion are 400 and 40 s, so the lack of high frequencies leads to a low lateral resolution of 2° (see ref. ³³). In contrast, checkerboard resolution tests of the finite-frequency tomography¹¹ show that the lateral resolution of their model is ~ 500 km. These previous seismic imaging efforts depict morphologies of the Reunion hotspot, but the size of the plume conduit, whether fat or thin, is uncertain in detail according to their resolution.

We present a new three-dimensional (3-D) P-wave velocity (Vp) model derived from 2380 arrival times of 156 local earthquakes (Fig. 1a) and 6052 relative arrival-time residuals of 296 teleseismic events (Fig. 1c). Our Vp model unveils an archetypal mantle plume beneath the Reunion Island with a broad head in the upper mantle and a narrow conduit down to 1000 km depth. In our study region, most places with good station coverage have a horizontal resolution of 1° in the final Vp model, much higher than the previous tomographic results, leading to a more reliable mantle plume image.

Distribution of teleseismic travel-time residuals

To obtain a robust 3-D tomographic model imaging the fine structure of the mantle plume below Reunion Island, we carefully compute relative travel-time residuals of teleseismic direct P waves with many quality criteria (see method section for details). Meticulous processing steps ensure that our Vp model is able to capture reliable details of the mantle plume. Crustal corrections are made to the teleseismic relative travel-time residuals so as to reduce the influence of crustal heterogeneity on Vp tomography. After the crustal corrections, average relative travel-time residuals of all teleseismic events provide valuable insights into the mantle heterogeneity (Fig. 2), indicating significant lateral Vp variations. The pattern of mean relative residuals shows that most early arrivals are located in the sea basin and southeast of Madagascar (Fig. 2a). Delayed arrivals appear in north and southwest Madagascar, Reunion Island and at four stations along Rodrigues Island. Most stations along the mid-ocean ridges show early arrivals and only one station at the Central Indian Ridge (CIR) shows a weakly delayed arrival. We focus on the region in and around Reunion Island, where early arrivals appear near the margins of the plume swell and delayed arrivals appear on the swell (Fig. 2). This distribution pattern of teleseismic travel-time residuals offers crucial information on the structure and dynamics of the mantle plume in this region, shedding light on complex geological processes at play.

P-wave tomographic images

The final 3-D high-resolution Vp model is obtained by a joint inversion of the local and teleseismic travel-time data, which involves the application of a 3-D ray tracing technique and the LSQR algorithm under damping and smoothing regularizations (see Method section for details). Our Vp tomographic results show that high-velocity (high-V) anomalies (< 300 km depth) are mainly distributed in the sea basin, only a few of them scattered in the domain of Madagascar (Fig. 3 and Extended Data Fig. 1). However, low-velocity (low-V) anomalies (< 300 km depth) are mainly located in the vicinity of Madagascar, Reunion Island, Mauritius Island and Rodrigues Island in the lithosphere and upper mantle (Fig. 3 and Extended Data Fig. 1). Here, we focus on the deep mantle structure of the Reunion plume (see the yellow box in Fig. 1c). Figure 3 presents Vp tomographic images down to 1000 km depth beneath Reunion Island, chiefly showing a mushroom-shaped anomaly with the lowest Vp perturbations of -2% in the lithosphere and low-V perturbations of -1% in the mantle. The top of this anomaly exhibits a low-V zone of ~ 450 km wide in the lithosphere and upper mantle (Figs. 3b and 3c), connecting an approximately vertical narrow low-V anomaly in the mantle (~ 220 km width), which is slightly bent toward southeast of Reunion Island at a depth of ~ 500 km. The plume center at 1000 km depth is shifted ~ 100 km southeast relative to the center of Reunion Island. In Fig. 3a, the top slice at 50 km depth shows a SW-NE trending low-V zone below Reunion Island and Mauritius Island, linking to the Rodrigues Ridge. However, this low-V zone is divided into two parts at 100 km depth (see the second top slice in Fig. 3a).

Interaction of the Reunion plume with central Indian ridge

Interaction between a mantle plume and mid-ocean ridge is quite common in the Indian Ocean, as revealed by geophysical and geochemical observations^31,36,37. Interactions of the southwest Indian ridge (SWIR) with the Marion and Bouvet hotspots were suggested by geoid and gravity data^31,36. Variations of Na₈ indicating a higher mantle temperature of the ridge section between the Indomed and Gallieni fracture zones may be impacted by the Crozet hotspot³⁶. The isotopically enriched geochemical signature and extremely thick crust at SWIR are strong evidence for the off-axis interaction between the Crozet hotspot and SWIR^37,38. Although the Reunion and Crozet hotspots are located in the Indian Ocean and close to the ultra-slow and slow-spreading ridges³⁹, the interaction of the Reunion hotspot with CIR is somewhat different from that of the Crozet hotspot and SWIR. There is a seafloor volcanic ridge between the Reunion hotspot and CIR (see the Rodrigues Ridge in Fig. 1). Basalts along the Rodrigues Ridge have ages of 8–10 Ma⁴⁰ and enriched geochemical signatures⁴¹. The seafloor relief of the Rodrigues Ridge was suggested as a result of material and heat exchanges from the Reunion hotspot to CIR^35,42. Meanwhile, the geochemical features of basalts at CIR (18–21°S latitude) are the same as those of the Reunion hotspot^41,43–45. However, there are no such characteristics between the Crozet hotspot and SWIR.

Focusing on the teleseismic relative residuals in the area between the Reunion hotspot and CIR, four stations along the Rodrigues Ridge and one station located at CIR present weakly delayed arrivals (Fig. 2a). Corresponding to the teleseismic relative residuals, our Vp tomography shows a low-V anomaly at 50 km depth, which may indicate a relatively hotter magma channel connecting the Reunion plume and CIR (Fig. 3a). Recent studies of surface-wave tomography and anisotropy proposed the same inference^35,42. Their results show a low-V channel and a west-east azimuthal anisotropy from the Reunion plume to CIR, which are interpreted as an asthenospheric flow driven by the plume⁴². A vertical mantle plume reaching the lithosphere could be deflected by the plume-plate interaction⁴⁶. The decompression environment at the divergent plate boundary supports a way to drive accumulated materials and heat from the Reunion plume to CIR. The plume materials and heat may laterally migrate and ultimately reach the melting region, giving a specific ocean island basalt signature to the erupted basalts at CIR. The low-V zone between Reunion Island and CIR may reflect such materials and heat transfer, leading to the interaction between the Reunion hotspot and CIR.

Plume morphology and implications

A plume originating from the CMB is relatively hotter and more buoyant than the ambient mantle¹⁰. The temperature excess is estimated to be ~ 100–400℃ in the upper mantle^47,48 and may reach 500℃ in the lower mantle⁴⁹. Buoyant mantle flow arriving at the bottom of the lithosphere leads to 1–2 km uplifts^50–52. The lithosphere is subsequently cracked due to the buoyant upwelling and decompression expansion, and magma resulting from decompression melting erupts along fractures in the lithosphere to form intraplate volcanoes^53–55. The uplifted Reunion Island and its volcanoes reflect the surface manifestations of the Reunion plume^11,35,42.

The mean residual pattern after the crustal corrections shows early arrivals near the margins of the plume swell and delayed arrivals on the swell (Fig. 2), indicating relatively lower Vp beneath Reunion Island and higher Vp around the swell. The early arrivals in the sea basin around the delayed arrivals at Reunion Island indicate that the upper mantle structure beneath the vicinity of Reunion Island is very inhomogeneous. Our high-resolution Vp tomography down to 1000 km depth presents a mushroom-shaped low-V anomaly with a very broad head up to ~ 450 km in diameter and a narrow tail of ~ 220 km (Figs. 3 and 4), which shows a classic “primary” plume proposed by Courtillot et al.⁸. Due to the limitation of teleseismic travel-time tomography at the shallow depths, the plume head may be broader than that in our images (Figs. 3 and 4). In terms of the shape of the plume conduit, its width is narrower than that in previous results beneath the MTZ^11,33,56, and there is slightly horizontal ponding around 660 km depth (Figs. 3 and 4) rather than broad ponding at depths of 660–1000 km imaged by full waveform inversion^33,56 (FWI). The differences may result from the ray-based tomographic techniques, which are high-frequency assumptions that simplify the full elastic wave Eq. 5⁷. Due to the computational cost of FWI, waveforms are usually filtered with relatively low frequencies, e.g., cut-off frequencies are 400 and 40 s in the FWI study of Wamba et al.³³. However, lateral pondings of the lower mantle plume are still debated^8,10. Numerical modelling reveals that lateral pondings may result from density layering induced by mantle composition, whereas viscosity stratification results in necking without ponding⁹. The slight ponding around 660 km depth beneath the Reunion hotspot may infer that the phase change from ringwoodite to bridgmanite and periclase may form density stratification. The thin plume tail is similar to the Yellowstone hotspot revealed by teleseismic core waves⁵⁸. However, the Yellowstone plume tail is tilted, which is interpreted as the influence of a stronger lower-mantle wind^15,58. However, our Vp tomography shows that an approximately vertical thin conduit exists in the lower mantle from 1000 km depth with slight ponding, then vertically impinges the lithosphere beneath Reunion Island. There is only ~ 100 km horizontal shift according to the plume center at 1000 km depth and the surface (see Fig. 3). The plume tilting angle is estimated to be ~ 6˚, suggesting that the whole mantle wind below Reunion Island is much weaker than that under Yellowstone, Hawaii and Iceland (e.g., ref. ¹⁵). But the NW-SE oriented bending tail of the Reunion plume at ~ 500 km depth (Fig. 3) may be caused by a slightly stronger mantle flow at that depth.

In summary, our high-resolution Vp tomography reveals a mantle plume originating at 1000 km or greater depth beneath Reunion Island, which has a broad plume head and vertically thin conduit, presenting a classic mushroom-shaped plume (Fig. 4). The approximately vertical plume conduit suggests that the strength of the mantle flow (or mantle wind) is weak below Reunion Island. The low Vp anomaly in the upper mantle towards CIR suggests that mantle materials and heat are driven from the Reunion plume to CIR, which is evidence for the off-axis interaction of the plume-ridge system.

Seismic data

To image the mantle plume down to 1000 km depth, we use data recorded at seismic stations on Reunion Island and in a wide area around the island (Fig. 1a). The seismic stations far away from Reunion Island can provide a denser ray coverage for imaging the deep part of the plume (in and below the MTZ; see Extended Data Fig. 2). Waveforms of local and teleseismic events recorded at 243 stations (57 permanent stations and 186 temporary stations in Fig. 1a) are retrieved from the Incorporated Research Institutions for Seismology Data Management Centre (including one station of AF network, four stations of G network, one station of II network, one station of MR network and 28 stations of XV network), the French RESIF Data Centre (including 46 stations of PF network, two stations of RA network, 15 stations of YA network, 74 stations of YV network and ten stations of ZF network) and the GEOFON Data Centre (including ten stations of 3E network, two stations of GE network and 49 stations of ZE network). Among these stations, 83 and 11 stations are/were deployed on Reunion Island and Mauritius Island, respectively. Waveform data recorded at 57 broadband Ocean Bottom Seismographs of YV network deployed by the RHUM-RUM experiment³⁴ are also used in this study (see purple squares in Fig. 1a). Supplementary Table 1 in Supporting Information shows more detailed information on the above-mentioned networks.

To collect arrival-time data of local earthquakes, we select 783 well-constrained events from the ISC-EHB catalogue⁵⁹, which occurred inside our tomographic inversion volume from January 2000 to December 2018. Based on origin times of the selected local earthquakes, waveforms are retrieved from all available stations, and a bandpass filter with corner frequencies of 0.1 and 5.0 Hz is applied to all downloaded waveforms. Arrival times of the local earthquakes are automatically detected by the PickNet package⁶⁰, which uses a deep-learning approach to pick precise phase arrival times close to that by manual work efficiently and automatically. All detected arrival times are inspected visually to ensure their picking accuracy (Supplementary Fig. 1). Events with less than four arrivals are removed from our dataset. Finally, the remaining 2380 high-quality arrival times of 156 local earthquakes (Fig. 1a) are used in the tomographic inversion.

We also select 26,111 teleseismic events (M > 5.0) falling in epicentral distances between 27° and 97° to each station to determine P-wave relative travel-time residuals in the same period of the local earthquakes. The predicted P-wave arrival time at each station is computed for the ak135 Earth model⁶¹, and then waveforms at 120 s before and after the predicted arrival time are retrieved. After removing the response, mean and linear trend, a bandpass filter with corner frequencies of 0.01 and 2.0 Hz is applied to all the retrieved seismograms. The signal-to-noise ratio (SNR) of each trace is calculated following Hu et al.⁶² and Pilia et al.⁶³. To obtain high-quality relative travel-time residuals, only seismograms with SNRs greater than 1.5 remain for subsequent processing. All the remaining traces are visually inspected to ensure the SNR quality of waveforms. The adaptive stacking approach⁶⁴ is used to calculate patterns of relative travel-time residuals of teleseismic events (Supplementary Fig. 2). As a result, 296 events with 6052 high-quality P-wave arrivals are extracted by repeating alignment for all traces of the same earthquake until achieving the best time shifts. Time shifts are rigorously constrained in ± 2.0 s to prevent cycle skipping.

Crustal corrections

Due to the uneven distribution of local earthquakes (Fig. 1a) and limited crust sampling power of teleseismic events, datasets of the remaining local and teleseismic events cannot constrain the crustal structure well. Consequently, crustal corrections are implemented to mitigate the influence of crustal heterogeneity on teleseismic travel-time residuals. The 3-D crustal model utilized in the corrections is constructed using P-wave velocities derived from the CRUST1.0 model⁶⁵. The correction for each event-station pair is estimated by the following Eq. (1):

$$\:\delta\:{t}_{crust}={t}_{3D}-{t}_{ak135}\:\left(1\right)$$

where $\:{t}_{3D}$ represents the crustal travel-time of each event-station pair calculated for the above 3-D velocity model; $\:{t}_{ak135}$ is the crustal travel-time computed for 1-D crustal velocities from the ak135 Earth model⁶¹; $\:\delta\:{t}_{crust}$ indicates the difference resulting from the 3-D inhomogeneous crust. Thereby, the corrected relative travel-time residual is represented as:

$$\:{t}_{cc}={t}_{res}-\delta\:{t}_{crust}\:\left(2\right)$$

where $\:{t}_{cc}$ and $\:{t}_{res}$ indicate the relative travel-time residuals after and before the crustal correction, respectively. After the crustal corrections are made, the distribution of early and delayed arrivals of teleseismic events becomes more compatible with the surface tectonic features (Fig. 2).

Tomographic inversion

To derive a 3-D Vp model down to 1000 km depth from the relative travel-time residuals of teleseismic events and arrival times of local earthquakes, we apply a tomographic method^66,67 that includes a 3-D ray-tracing technique⁶⁶ to compute theoretical travel times and ray paths, and the LSQR algorithm⁶⁸ to conduct tomographic inversion with damping and smoothing regularizations^66,67. The 3-D Vp model of the study area is parameterized into 45,540 regular grid nodes with a horizontal interval of 0.75˚ and a vertical interval of 100 km (Supplementary Fig. 4). Vp perturbation (dVp) at each grid node is taken as an unknown parameter. The dVp at any point in the model is calculated by linearly interpolating the dVp values at eight nodes surrounding that point. To obtain a reliable result, extensive tomographic inversions are conducted to find the optimal horizontal smoothing (0.003), vertical smoothing (0.001) and damping (1.0) values (Supplementary Figs. 5 and 6). The optimal bottom depth (1000 km) of our 3-D Vp model is obtained by changing the bottom depth to make the model best fit the data (Supplementary Fig. 7). Under the above-mentioned constraints, the optimal Vp model is obtained that reduces the total root-mean-square travel-time residual from 1.244 s to 0.179 s (85.6% decrease).

Resolution analysis

To investigate the spatial resolution of the final 3-D Vp model, we performed three checkerboard resolution tests (CRTs) with different lateral grid intervals (1.0°, 1.5° and 2°) based on the same event-station pairs as those in the real observational system (Supplementary Figs. 8–13). Firstly, multiple checkerboard models are constructed with alternately positive and negative Vp perturbations of 4% at the grid nodes to calculate synthetic travel times using the same coordinates of hypocenters and receivers as those in the observed dataset. Secondly, before inversion, Gaussian noise distributed between − 0.3 and 0.3 s with a standard deviation of 0.1 s is added to the synthetic travel times to simulate picking uncertainties of the real data. Finally, the noise-added synthetic travel times are inverted to obtain an output model. The test results show that the coarse grids with a lateral interval of 2° are precisely recovered (Supplementary Figs. 8 and 9). The intermediately and finely spaced checkerboards (1.5° and 1.0°) beneath Reunion Island and Madagascar are also recovered well (Supplementary Figs. 10–13).

Furthermore, extensive structural tests are performed to evaluate the resolving power of our dataset for the mantle plume using the same routines as the CRT. In the input models of the tests, different plume widths of 200 km, 250 km and 300 km are set below Reunion Island down to 660 km, 900 km and 1400 km depths. Here, we test the plume down to 1400 km depth denoting that our data can constrain the Vp structure below the maximum bottom depth of 1000 km. In these tests, the plume is presumed to have a low-V perturbation of -4%. The test results show that a part of the plume in the MTZ is hard to image with a plume width of 200 km (Supplementary Fig. 14). In contrast, our dataset is able to partially recover the plume in the area of MTZ with a plume width of 250 km (Extended Data Fig. 3). When the plume width is 300 km, the mantle plume is well constrained by our dataset (Supplementary Fig. 15). These synthetic resolution tests indicate that our Vp tomographic model is robust and reliable to image the mantle plume down to 1000 km depth.

Acknowledgements

We appreciate helpful discussions with Drs. Yiming Luo and Caicai Zha. We thank the data centers of Incorporated Research Institutions for Seismology (IRIS), GEOFON Data Center and International Seismological Center (ISC) for providing the high-quality data used in this work. This study was supported by the National Natural Science Foundation of China (No. 42106068 and 42376052), the China Postdoctoral Science Foundation (No. 2021M691412), Japan Society for the Promotion of Science (No. 19H01996), and the Earthquake and Volcano Hazard Reduction Research project of the MEXT, Japan.

Data availability

Waveforms used in this study are available at the Incorporated Research Institutions for Seismology (https://ds.iris.edu/ds/), French RESIF Data Center (https://seismology.resif.fr/) and GEOFON Data Center (http://eida.gfz-potsdam.de/webdc3/). Hypocentral parameters are obtained from the ISC-EHB bulletin (http://www.isc.ac.uk/isc-ehb/) and ISC bulletin (https://www.isc.ac.uk/iscbulletin/).

Code availability

The adaptive stacking⁶⁴ code is used to compute the relative travel-time residuals of teleseismic events, which is available at http://rses.anu.edu.au/seismology/soft/astack/index.html. A deep-learning method (PickNET⁶⁰) is used to determine arrival times of local earthquakes automatically, the trained models are available at https://www.researchgate.net/profile/Jian-Wang-2. The open-source package ObsPy⁶⁹ is used for data preprocessing and is available at https://github.com/obspy/obspy. The free software GMT⁷⁰ is used for data visualization and is available at https://www.generic-mapping-tools.org/.

Author information

Affiliations

School of Geomatics and Municipal Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou, China

Hao Hu

Department of Ocean Science and Engineering, Southern University of Science and Technology, Shenzhen, China

Hao Hu, Jian Lin

Department of Geophysics, Graduate School of Science, Tohoku University, Sendai, Japan

Dapeng Zhao

Key Laboratory of Submarine Geosciences, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou, China

Aiguo Ruan

Contributions

H.H. designed this work and wrote the first draft of the manuscript. D.Z. provided the tomographic inversion codes and improved the manuscript. All coauthors contributed to interpretation of the results and preparation of the manuscript.

Corresponding author

Correspondence to H. Hu and D. Zhao.

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Seismic imaging of the Reunion mantle plume

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Abstract

Figures

Main

Distribution of teleseismic travel-time residuals

P-wave tomographic images

Interaction of the Reunion plume with central Indian ridge

Plume morphology and implications

Methods

Seismic data

Crustal corrections

Tomographic inversion

Resolution analysis

Declarations

References

Additional Declarations

Supplementary Files

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