Fig1 withtransect andinset

Anant Hariharan

and 2 more

 Abstract Shear-wave splitting measured across Ethiopia, combined with prior anisotropy results, indicate that lithospheric anisotropy is consistently ~N25E within both the rift and up to 550 km away. Delay times away from the rift are ~0.75 sec lower. The broad subparallel anisotropy, with higher delay times within the rift, suggest that melt within the rift is aligned with and superimposed upon a broader pattern, likely fossil anisotropy within Precambrian lithosphere. Azimuths beneath the Ethiopian Highlands near the source of Miocene flood basalts rotate to ~N45E parallel to rift border faults. Back-azimuthal variation in this region requires two layers of anisotropy, fit using a deeper N25E layer overlain by a layer of ENE-oriented anisotropy. Dikes emplaced in the crust and uppermost mantle during flood basalt eruption, now frozen, may control the shallow anisotropy. We suggest that extension had initiated subparallel to the Miocene rift direction during the eruption of the flood basalts.  IntroductionWithin the MER, rifting followed irregular spatial and temporal development, involving linkage of discrete rift segments. The controls on rift propagation have been linked to pre-existing lithospheric sutures, such as a Neoproterozoic Pan-African suture  \citep{Keranen_2008}. Recently, a vast array of of geophysical studies have explored the nature of the rift's evolution, as well and crustal and upper-mantle structure. Results from teleseismic P-wave tomography indicate a broad low-velocity anomaly underneath the rift \citep{Bastow_2005} wider than the rift valley itself. However, the length scale and number of these associated mantle upwellings is still an active topic of research, with recent tomographic models indicating a number of small-scale upwellings \citep{Civiero_2016}. Constraints on low shear-wave velocities from tomographic studies and results from receiver functions suggest elevated upper mantle temperatures beneath the region and penetrating into the surrounding Precambrian craton \citep{Keranen_2009}. Within the rift, active-source tomography results image localized magmatic, cooled gabbroic bodies as regions of high P-wave velocity \citep{Keranen_2004}. Extension is localized around these segments, accounting for the fact that geodetic measurements of strain across the rift valley are less than predicted from Nubia-Somalia separation rates \citep{Bendick_2006}.  Measurements of conductivity \citep{Whaler_2006} offer constraints on the melt presence, suggesting between 0.4% and 20% melt in the lower crust, where strain is broadly distributed \citep{Keranen_2009}. Recognition of the role of broad deformation has led focus to shift towards understanding the lithospheric state around the region.  However, limited seismic apertures have prevented researchers from doing so in a conclusive and high-resolution fashion. Seismic anisotropy has long since been recognized as a powerful tool to probe the nature of upper-mantle structure and mantle flow and better understand surface tectonics and geophysical processes taking place at the near surface \citep{Long_2009}.  In particular, mantle anisotropy, which is often linked to mantle flow and the alignment of the a axis of olivine crystals, is often quantified using shear-wave splitting analyses of XKS wave arrivals.  The presence of anisotropy results in this phase being split into a fast and slow shear wave upon entering and exiting an anisotropic region. By measuring the delay time between this phases, as well as the axis along which the wave is polarized, one can quantify this effect. We use the parameters δt and φ to do so, where δt is the time delay between the phases and φ represents the orientation of the fast axis.  Other mechanisms that may cause seismic anisotropy include the presence of melt-aligned cracks or pockets, as well as layering \citep{Holtzman_2010}. Multiple studies employing seismic anisotropy have thus taken place at a range of tectonic settings, including other rifting regions \citep{Eilon_2014}, \citep{Reed_2017}. In the Main Ethiopian Rift, seismic anisotropy from SKS phase splitting results measured within the rift valley has been attributed to the presence of melt and linked to lithospheric magma injection \citep{Kendall_2005}, supporting the regional model of magma-assisted rifting. S-wave Splitting results from local earthquakes also indicate upper crustal anisotropy is strong within quaternary magmatic segments, and is linked to melt pocket alignment even in the upper crust \citep{Keir_2005}.  `Overall, we lack a strong understanding of how deformation penetrates into the flanks of the Main Ethiopian Rift, and anisotropy is a powerful physical parameter that can yield insight into this problem. Our study thus applies a new dataset collected by seismometers deployed on the flanks of the Main Ethiopian Rift to understand how broad deformation is taken up away from the structural rift valley and to constrain the origin and extent of this deformation.

Anant Hariharan

and 2 more

PURPOSE The suite of functions associated with loris5 reads in a tomographic model, expands the model in a wavelet basis onto the cubed sphere, and explores instructive features of this expansion- for instance, how do the scaling coefficients used vary with depth? This can help characterize earth structure using a new and applicable measure and elucidate both the scale (wavelength) and depth-dependence of seismic heterogeneity. This document describes how the codes that conduct the analysis do so, and helps elucidate the inner workings of the individual functions involved, with the end goal of making future analyses easily reproducible and allowing readers to easily experiment with the relevant codes. BACKGROUND Wavelet analysis makes use of basis functions that are localized pulses in wavenumber/wavelength space. A PRIMER ON KEY ASPECTS OF THE CODES Important Inputs: What you need at hand to start the Analysis - Model: The loris5 codes implement this specification with the gnorjr value. If set to 1, this reads the Montelli et al. model. Stick with this for our implementation. For more on this, see the section beneath. - You need a list of model depths, as in the GNDepths_txt file. This will correspond to the depths at which your model is interpolated to. - Wavelet construction: Which set of basis functions will you use: D2, D4, or D6? - N - how fine is the grid you subdivide your intervals on the sphere into? - J - what is the limit on the scale you use for your wavelets? - d - a vector of depths. What depths do you want to read the model at? - note that if there is more than 1 here, the function re-runs itself, picking only a single one of the depths out of this vector. These depths must be in the main model file. - Preconditioning- If done, this allows for wavelet cancellation in the interior of the grid.  Generating an Tomographic Model Interpolated onto a Cubed Sphere We include additional scripts that can interpolate models from within .epix files onto specific regions. Reading in a Velocity Model A given depth is input iteratively by reading from a velocity perturbation file, which contains dv anomalies mapped to lat/lon values on the cubed sphere. For the readGNmodel framework, which does not assume spherical harmonics, we assume the model has been setup in a cubed-sphere framework. This might require interpolation, and can be done with the script written by Ved  The script that reads files iteratively reads 6N² lines, assuming that there will be this many lines that correspond to a given depth. The readGNmodel script checks that there is only one depth within this group of lines, then reshapes it, grouping by each Kappa value over the sphere. FEATURES OF THE PARAMETRIZATION The cubed sphere The wavelet codes are run on the cubed sphere. This construct divides the Earth into 6 different chunks, the position of which can be rotated using different Euler Angles. Each of these chunks are gridded into 62N points. In the wavelet domain, the cubed sphere is parametrized into concentric squares of length 2N − j where j is the scale of interest. THE ORIGINAL LORIS5 WORKFLOW Brief Sequence of Steps 1. lines (1-60)sets up default values for the inputs.  2. lines (58-70) writes an output (.mat) file that will be filled eventually, named in accordance with input parameters 3. An if-loop is begun at line 73, and is executed if there’s more than one depth in the depth list 4. A nested if-loop checks if the wavelet transform calculations have been done for this depth yet,  5. If it hasn’t the calculation begins as follows: First, it assigns the thresholding percentile (typically 85). This is hardcoded into the script- we can probably modify this to change it! Sets up grids on the cubed sphere, depending on the “levels” variable. These grids are stored in vwlev and vwlevs. 6. Lines 91-102 initializes an empty structure array to store results.  7. Begin re-calling the function, this time depth by depth from the d vector containing the depths. IMPORTANT: In this case, (where there’s only a single depth) the code begins running from line 435 onward.  For this single depth, create an output .mat file. 8. Read the model at the given depth, with different scripts depending on which variable you use. Note: The model is only available at certain discrete depths, reading at depths that are not these will cause readGNmodel to break.  9. Temporary faking of the pixel center registration by changing number of points. 10. Take the norm of the the velocity vector, and get some other stats, save them to the vstats array. 11. Take the wavelet transforms using the angularD(?)WT function. This is stored in the vwt array.  12. Recalculate statistics.