Journal of Geophysical Research: Solid Earth

Journal of Geophysical Research: Solid Earth

Supporting Information for

Three-dimensional seismic structure of the Mid-Atlantic Ridge: An investigation of tectonic, magmatic, andhydrothermal processes in the Rainbow Area

Robert A. Dunn1, Ryuta Arai1, 2, Deborah E. Eason1, J. Pablo Canales3, Robert A. Sohn3

1. Department of Geology and Geophysics, School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, 1680 East-West Rd. Honolulu, HI 96822, USA

2. Research and Development Center for Earthquake and Tsunami, Japan Agency for Marine-Earth Science and Technology, 3173-25 Showa-machi Kanazawa-ku Yokohama Kanagawa 236-0001 Japan

3. Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02540, USA

Contents of this file

Figures S1 to S4

Introduction

This supporting information file contains text and figures which provide additionaldescriptions of the seismic modeling.Model resolution depends in large part on the distribution of seismic ray paths and how much information they impart to each model parameter (i.e., grid point) of the tomographic volume. There are roughly 152,000 data and rays and about 212,000 isotropic and anisotropic model parameters within the interior of the volume where rays sample (about 15% of the model parameters lie around the exterior edges and bottom of the model volume and are not sampled by rays). Of these interior points, the mean number of rays influencing a model parameter is 370. The regularization constraints on image smoothness added to the inverse problem serve to couple neighboring model parameters so that the inverse problem consists of solving for local averages of model parameters rather than the values of individual parameters. This reduces the effective number of unknowns to much less than the number of data. Regularization has the important added benefit of preventing statistical over fitting of the data.

Spatial resolution and variance of the final tomographic image is controlled by image smoothness constraints. A grid search was performed by varying the strength of separate horizontal and vertical smoothness constraints to determine an acceptable range of 3-D solutions that fit the data. With respect to the starting model, the travel time data have a normalized chi-square misfit of 27. The final model has a misfit of ~1. Fig. S1 shows histograms of the travel time residuals relative to the starting and final models.

/ Fig. S1. Histograms of travel time data residuals (observed minus calculated ray path travel time) relative to the starting model (red) and the final model (blue).

S1. Alternative Tomography Models

Two alternative solutions to the standard solution are presented in Figure S2. These solutions were created using different horizontal/vertical smoothing parameters (see Appendix) to show the trade-off between horizontal and vertical resolution for solutions that nevertheless equally fit the data. One is a vertically-smoother and horizontally-rougher solution with smoothing parameters of (40, 100) (alternate solution 1 in Figure S1), and the other is a vertically-rougher and horizontally-smoother model with (140, 40) (alternate solution 2 in Figure S2). These solutions otherwise have the same parameterization as for the standard solution. These solutions show small velocity differences with respect to the standard solution (less than 0.1 km/s in most parts of the model), indicating the robustness of the imaging to changes in parameterization. The differences that are apparent between these alternative solutions highlight the following trade-off: at the limit of resolution, features that are tall and narrow, or short and wide, are resolvable, but not both short and narrow.

We also examined the tradeoff of the tomographic solution with magnitude of anisotropy (Figure S3). For this test, we used two times larger and four times smaller damping values for anisotropy than that used to produce the standard solution. This test shows that there are slight differences in magnitude of velocity anomalies but the pattern of the anomalies did not significantly change with changes in anisotropy strength.

Fig.S2 These models show small velocity differences from the standard model (less than 0.1 km/s in most areas) due to differences in smooth strength (as indicated on the plot). Dashed gray lines outline the locations of the massifs. Ridge segments and spreading direction are indicated by dashed lines and arrows, respectively. A mask was applied to the images (areas blanked out) to remove areas with low ray density (low resolution).

Fig.S3. Map view slices of solutions with the same parameterization as for the standard solution except with relatively larger (0.04; first row) and smaller (0.005; second row) allowed variance of the anisotropy parameters; the standard solution has a variance parameter of 0.02. In the case for larger variance, the anisotropy component of the image has slightly larger magnitude features, but the isotropic part of the solution islike that of the standard solution (upper row). In the case for lower allowed variance, the anisotropy is almost completely “damped out” with almost no anisotropy, andthere is higher final data misfit; the isotropic part of the solution is like that of the standard solution (lower row). The results indicate that due to the strong azimuthal coverage of the data throughout the model volume, the presence of anisotropy has minimal impact on the isotropic components of the image. Dashed gray lines outline the locations of the massifs. Ridge segments and spreading direction are indicated by dashed lines and arrows, respectively. A mask was applied to the images (areas blanked out) to remove areas with low ray density (low resolution). Full results of the anisotropy will be published elsewhere.

S2. Additional Checkerboard Tests

The upper 750 m of the crust has been notoriously difficult to image in past studies due to widely-spaced stations and source lines. In this study, stations and shot lines are spaced at intervals smaller than most past studies of this nature. Fig. S4 shows the resultsof checkerboard reconstructions as in the Appendix, but with the initial checkerboard patterns restricted to depths of 0-300 m (left column) and 300-600 m (right column). From a map-view perspective, reconstructions are good throughout the central portions of the experiment, but vertical smoothing doubles or more the original 300 m height of each anomaly, depending on distance from the center of the study. Distinguishing thin (<500 m) features at these depths is therefore complicated by this smearing.

Figure S4. Checkerboard test imagesfor the upper crustal low-velocity layer. (a-b) Map view depth slices from two checkerboard solutions (depths noted on each plot). The input checkerboard anomalies were 2x2x0.3 km3 in size. The depth range of initial checkers is 0-0.3 km (a) and 0.3-0.6 km (b). (c-d) Vertical cross-sections taken across the center of each image volume, showing depth distribution of the recovered anomaly pattern.

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