Forsyth, 1998, Phase Velocities of Rayleigh Waves in the MELT Experiment on the East Pacific Rise， Science

• The peak sensitivity of Rayleigh waves to shear velocity is at a depth of about one-third of a wavelength, or 30 to 35 km for a 25-s period wave, for example (The phase velocity at 25 s is an integrated measure of the shear velocity structure in the upper 100 km of the mantle).

• The Mantle Electromagnetic and Tomography (MELT) Experiment was designed to provide spatial resolution that is limited primarily by the physical averaging associated with finite wavelength waves, not by station or event geometry.

• Some teleseismic studies have found that Rayleigh waves propagate faster perpendicular to the East Pacific Rise (EPR) (5, 6). This azimuthal anisotropy is attributed to a pattern of flow in the mantle that aligns the a axis of olivine crystals perpendicular to the ridge axis. The conclusion that anisotropy is required has been controversial, because there are trade-offs between a simple pattern of anisotropy and a more complicated pattern of heterogeneous, isotropic velocities.

• To account for nonplanar wavefields (10), we represented the incoming wavefield from each earthquake as the sum of two plane waves, each with initially unknown amplitude, phase, and propagation direction.

• The addition of wavefield parameters and the use of amplitude information (11) make the tomographic inversion nonlinear, so we iterated to a solution using a linearized approach with the wavefield parameters
  damped to prevent large changes in parameter values in any one step.

• The pattern of azimuthal anisotropy is consistent with predictions that there will be little azimuthal anisotropy where the crystallographic a axis of olivine is preferentially aligned vertically in upwelling flow and that anisotropy will increase with rotation to a more horizontal orientation aligned with plate motion as the flow diverges away from the spreading center (22).

• Lattice-preferred orientation (LPO) of olivine crystals is generated through dislocation creep, but diffusion creep produces no substantial LPO (24).

notes

• Rayleigh waves have a dilatational or volumetric component that can be detected on differential pressure
  gauges (DPGs) in addition to the vertical and horizontal seismometers. We used vertical records whenever possible. An empirical transfer function was derived to convert pressure records into the equivalent vertical record. Transfer functions were also used to convert the responses of instruments from different OBS groups into the equivalent of a single type of vertical seismometer.

• Weighting function is a Gaussian function of distance to the node, with characteristic falloff distance about equal to the wavelength of the wave.

• Ray paths for surface waves deviate from great circle paths because of refraction by lateral heterogeneities. It is therefore customary in array analysis to solve for the azimuth and slowness of the best fitting plane wave. A more serious problem is multipathing or scattering or the effects of a complex wavefront, which produce interference between packets of energy of the same frequency arriving at a station along different paths. This interference causes characteristic amplitude variations across the array and phase shifts that can seriously distort apparent phase velocities measured with the assumption of planar waves (25).

• Because amplitudes carry information about the wavefield interference, at each frequency, we modeled
  the real and imaginary components for each record, rather than just the phase. Amplitudes are corrected for geometrical spreading on a uniform sphere, instrument-site response, and attenuation.