Seismic Attenuation at the Equatorial Mid‐Atlantic Ridge Constrained by Local Rayleigh Wave Analysis From the PI‐LAB Experiment

The ocean lithosphere represents a simple realisation of the tectonic plate, offering a unique opportunity to better understand its physical and chemical properties in relationship to those of the underlying asthenosphere. While seismic velocity is frequently used to image the plate, seismic attenuation (Qμ−1) offers an important complimentary observation. We use fundamental mode Rayleigh waves from 17 local, M > 4.2 earthquakes recorded at stations located on 0–80 My old lithosphere near the equatorial Mid‐Atlantic Ridge. We determine the attenuation coefficient ( γ $\gamma $ ) for periods between 15 and 40 s and invert for 1‐D average shear wave quality factor values ( Qμ ${Q}_{\mu }$ ) and shear wave velocity (Vs). We find Qμ ${Q}_{\mu }$ values of 175 ± 16 at 50 km depth, decreasing to 90 ± 15 at greater than 60 km. Comparison of our Qμ ${Q}_{\mu }$ and Vs measurements to previous observations from oceanic settings shows agreement in terms of higher Qμ ${Q}_{\mu }$ and Vs in the lithosphere in comparison to the asthenosphere. The observations from oceanic settings are in general agreement with the laboratory predictions for Qμ ${Q}_{\mu }$ ‐Vs relationships for thermal models. However, a small amount of partial melt (1%) is required to explain several previous observations. Our result also compares favorably to previous observations of lithospheric and asthenospheric attenuation with respect to frequency. Melt is not required for the 1‐D average of our study area, consistent with previous electromagnetic and seismic imaging that suggested melt in punctuated and/or thin channel anomalies rather than over broad regions of the mantle.

Generally most studies find a slow shear wave (Vs) and compressional (Vp) velocity, low resistivity, and high shear wave attenuation (Q μ −1 ) zone directly beneath mid-oceanic ridges in the asthenosphere (Eilon & Abers, 2017;Evans et al., 2005;Johansen et al., 2019;Key et al., 2013;Nishimura & Forsyth, 1989;Shapiro & Ritzwoller, 2002). There has been a long debate about the causes of such anomalies beneath the ridge areas, in other words whether it is owing to high temperatures that occur in response to passive upwelling and/or buoyant and active upwelling or whether other factors are required. In general seismic velocities, resistivities, and quality factors (inverse attenuation values Q ) beneath ridges are too low to be explained by thermal processes alone (Eilon & Abers, 2017;Forsyth et al., 1998;Harmon et al., 2020;Johansen et al., 2019;Key et al., 2013;Saikia et al., 2021;Wang et al., 2020).
A host of sub-solidus conditions have been proposed to explain the low velocities, low resistivities, low and discontinuities at constant depth across variably aged lithosphere, and/or sharp discontinuities. These include grain size (Jackson & Faul, 2010), elastically accommodated grain boundary sliding owing to hydration (Karato & Park, 2019), enhanced effects of near melt conditions on seismic waves (Yamauchi & Takei, 2016), a change in anisotropy (Auer et al., 2014;Beghein et al., 2014;Burgos et al., 2020), and the oxidation state of the mantle (Cline et al., 2018). However, none of these possibilities explain all of observations with a range of sensitivities. Partial melt provides an attractive option, given that it is predicted to have a large influence on seismic waves and also magnetotelluric imaging (Clark & Lesher, 2017;Hammond & Humphreys, 2000;Ni et al., 2011) However, geochemical constraints (Albarède, 1998;Gale et al., 2013) and also theoretical permeability models suggest that melt should not persist in the mantle over time and length scales that would be seismically imageable (Mckenzie & Bickle, 1988;Turner & Hawkesworth, 1997). Therefore, the debate continues.
One challenge in determining the factors that explain the observations is that they are often from different methods with different sensitivities in different locations, and most observations are of seismic velocity. Q μ −1 observations are particularly valuable because they provide complementary sensitivity to the more commonly constrained seismic velocity, providing additional insight, especially when combined with velocity. Experimental studies suggest that Vs and Q μ −1 should have a unique relationship with increasing Q μ −1 and decreasing Vs as temperature increases (Havlin et al., 2021;Jackson & Faul, 2010;McCarthy et al., 2011;Yamauchi & Takei, 2016). This relationship is also likely different for other parameters such as variable grain size, hydration, or partial melt (Havlin et al., 2021;Jackson & Faul, 2010;Karato & Park, 2019;McCarthy et al., 2011;Yamauchi & Takei, 2016).
Experimental constraints also suggest that the frequency dependence of Q μ −1 may be different in the lithosphere in comparison to the asthenosphere possibly because of different properties such as the presence of partial melt (Faul et al., 2004;Jackson & Faul, 2010) or hydration (Karato & Park, 2019). Different frequency dependencies of Q μ −1 in the lithosphere and the asthenosphere have been observed by oceanic Q μ −1 studies using waveforms at different periods beneath very old (>100 Myr) Pacific seafloor and interpreted in terms of either partial melt and/ or pre-melt conditions (Takeuchi et al., 2017;Yamauchi & Takei, 2016). Less variability in frequency dependence has also been suggested beneath 70 Myr old Pacific lithosphere (Ma et al., 2020). 10.1029/2021GC010085 3 of 16 At a global scale, surface wave imaging finds low Q μ beneath most of the Earth's ridges and rifts and high Q μ beneath the ancient stable continental interiors, likely reflecting first order variations, such as higher and lower temperatures, respectively (Dalton et al., 2008). Global surface wave attenuation studies also distinguish high Q μ lithospheric lids overlying low Q μ asthenosphere beneath the oceans (Dalton et al., 2008). Attenuation anomaly observations in subduction zone mantle wedges have also been used to infer the locations of thermal anomalies, water, and partial melt (Eberhart Phillips et al., 2013Ko et al., 2012;Myers et al., 1998;Pozgay et al., 2009;Schurr et al., 2003;Stachnik et al., 2004;Takanami et al., 2000;Tsumura et al., 2000). The complimentary sensitivities of attenuation and velocity have also been used to further distinguish the locations and pathways of water and melt through the mantle wedge Syracuse et al., 2008;Wei et al., 2015;Wei & Wiens, 2018).
Consideration of Vs and Q μ observations together in oceanic settings is also particularly helpful in constraining the properties of the Earth. So far there have been a handful of high resolution in situ studies of Q μ , several of which also constrain Vs, and these have been primarily from the Pacific. Beneath young seafloor age (<10 Myr) at the ultra-fast spreading East Pacific Rise (EPR) at 17°S a study using Rayleigh waves and the two plane wave method and a minimum parameterization, found Q μ = 184 ± 20 and Vs = 4.27 ± 0.05 km/s for the lithosphere and Q μ = 79-98 and Vs = 4.11 ± 0.06 km/s for the asthenosphere (Yang et al., 2007). A study using the same method and a minimum parameterization on similar aged seafloor at the intermediate, but hotspot influenced Juan de Fuca Ridge found Q μ = 114 ± 40 and Vs = 4.29 ± 0.06 km/s in the lithosphere and Q μ = 46 ± 6 and Vs = 4.23 ± 0.03 km/s in the asthenosphere (Ruan et al., 2018). A higher frequency study using body waves in the same region found Q μ = 25 near the ridge and Q μ < 90 away from the ridge in the region (Eilon & Abers, 2017). A study on older seafloor, near the NoMelt experiment on 70 Myr old seafloor using Rayleigh waves found Q μ = 1,400 ± 14 and Vs = 4.54 ± 0.09 km/s in the lithosphere and Q μ = 110 ± 16and Vs = 4.28 ± 0.05 km/s in the asthenosphere (Ma et al., 2020). Finally, at high frequency on very old lithosphere >100 Myr old using Po/So, Takeuchi et al. (2017) found Q μ = 3,200 in the lithosphere and Q μ = 60 the asthenosphere.
Here, we present results from the Passive Imaging of the Lithosphere Asthenosphere Boundary (PI-LAB) experiment and the Experiment to Unearth the Rheological Oceanic Lithosphere-Asthenosphere Boundary (EURO-LAB) at the equatorial Mid Atlantic Agius et al., 2018Agius et al., , 2021Bogiatzis et al., 2020;Hicks et al., 2020;Leptokaropoulos et al., 2021;Rychert et al., 2021;Saikia et al., 2020Saikia et al., , 2021Wang et al., 2020), which was designed to image the base of the tectonic plate and determine what makes a plate, plate-like (Rychert et al., 2005(Rychert et al., , 2016(Rychert et al., , 2018a(Rychert et al., , 2018bRychert & Shearer, 2009). In this study, we image the upper mantle Q μ −1 beneath the equatorial Mid-Atlantic Ridge. First, we measure the attenuation coefficient (γ) parameter at the period range 15-40 s using Rayleigh wave amplitude data from surface waves. Then the attenuation coefficients are inverted to determine a 1-D model for the study region as a function of depth. We compare our result to previous and Vs studies of oceanic lithosphere and laboratory predictions to determine the physical state of upper mantle in our study area. We also compare our results to previous observations to determine the frequency dependence of Q μ −1 in the lithosphere and the asthenosphere.

Data and Methodology
We use data from the PI-LAB experiment, which includes 39, 3-component broadband Ocean Bottom Seismometers (OBS) each equipped with a differential pressure gauge (DPG), which was deployed from March 2016 to March 2017 ( Figure 1). We use vertical component Rayleigh wave seismograms for local earthquake events. We use 17 events having magnitudes greater than or equal to 4.2 (black stars in Figure 1). Although initially 39 stations were installed, two stations (I01D and I36D) were not recovered, and 2 stations had technical errors caused by a lack of recording of one or more channels. Some station records also exhibit tilt caused by strong motion in the near-field and are excluded from the analysis. The ray-paths and stations are shown in Figure 1. Example waveforms for two events are shown in Figure 2.
We use surface wave amplitude to estimate the attenuation coefficient in the period range of 15-40 s. In general, the surface wave attenuation can be described by − , where is the attenuation coefficient and r is distance, which is related to surface wave quality factor ( ) as = ∕ , where is the group velocity and f is frequency. The attenuation coefficient is estimated from the frequency domain seismogram, ( ) using the following formula: where is the amplitude of the event at a given frequency, 0 is the zero order Hankel function for frequency , and represents the phase velocity. The (2[ − ]) term of back azimuth θ and apparent earthquake radiation direction φ, account for the source radiation pattern of each earthquake at each period (Mitchell, 1995). We choose the Hankel function because our study is at a near-to-intermediate distance range of the earthquakes, and we cannot use the asymptotic plane wave approximation to match the amplitude. The Hankel function precisely captures the geometric spreading of surface waves, with its complex sinusoidally decaying amplitude with distance. Observe amplitude variations as a function of distance for two events is shown in Figure 3. We use the 1-D phase velocities for the region estimated from the vertical component Rayleigh wave observations of teleseismic events and ambient noise in this period range . The phase velocities at <18 s are not reported by Harmon et al. (2020) although they are consistent with the group velocity measurements reported by Saikia et al. (2021). Here, we show the average phase velocity variations at the period range of 15-111 s in Figure 4c. We use a grid search method to determine the amplitude (A) of the source spectra at the given frequency and the attenuation coefficient. We use a grid spacing 200 in A from 1,000 to 10,000 and γ from 0 to 7.5 × 10 −4 with a spacing of 0.0005. The focal mechanisms are known for the events used in this study, so we use initial values for φ based on the focal mechanism and perform a grid search over ±30° from the initial value in 1° steps.
We invert the 1-D phase velocity and attenuation coefficients for 1-D Vs and as a function of depth beneath the region assuming a fixed Vp/Vs ratio and density structure. We use a fixed Vp/Vs of 1.78 and assume an average water depth of 4,000 m for the region. To calculate the predicted phase velocity and attenuation coefficients from a given and Vs structure, we use the Computer Programs in Seismology code (Hermann & Ammon, 2004). The code incorporates attenuation effects and can explicitly include a water layer. The program generates the partial derivatives for Vs, and we use a finite difference approximation for the partial derivatives for attenuation coefficients with respect to Vs and . We also assume the compressional wave quality factor ( ) is approximately double , but find this ratio (+/− 50%) has little impact on the result. In the water layer, the code only considers the effect of on the attenuation coefficient and dispersion. We set to 900 in the water layer, which remains fixed during the inversion. Testing indicates that smaller values (down to 100) do not significantly alter the results of the inversion, and so we choose a high value as we do not expect water to be a lossy medium. We make no distinction between raypaths that cross the ridge and those that do not as we are only interested in a 1-D regional average for the purposes of this paper. We do not invert for anisotropy or account for its effects and instead assume isotropic velocities. Given the 1-D nature of our result and modeling, we cannot account for the effects of scattering caused by strong lateral velocity variations on the Q μ observation. Therefore, the apparent Q μ that we report reflects the effects of both scattering and intrinsic attenuation. We discuss below in greater detail the depths at which our Q μ model may be more strongly influenced by scattering.
We invert for the reference shear velocity, Vs (ω 0 ), which is corrected for the effects of attenuation to a frequency of 1 Hz. The reference velocity represents the frequency independent result, as opposed to the apparent Vs at the frequency range of observation if no attenuation is assumed. The code accounts for the effects of physical dispersion via a correction to the phase velocity dispersion that is calculated by integrating over depth the product of attenuation structure and the partial derivatives of phase velocity with respect to the shear and compressional velocity. However, we also present the apparent Vs for comparison to other studies and laboratory predictions that present the apparent Vs. The following relationship can be used to scale the reference Vs to apparent Vs at the frequency range of observation (Kolsky, 1956;Liu et al., 1976): where is angular frequency and 0 is the reference angular frequency. For the frequency range and values determined here, the correction between reference Vs and apparent Vs is 1%-2% and encapsulated in the error bars. We note that the apparent Vs is also very similar to the starting Vs model, that is, that reported by Harmon et al. (2020), which did not correct for attenuation (Figure 4).

Results
We first plot the seismograms (Figure 2) and the amplitude variations as a function of distance across the array (Figure 3). We also show amplitude variations corrected for geometrical spreading ( Figure S1). We find a pattern of decreasing amplitude with increasing distance, which likely results from the combined effects of geometric spreading, source radiation pattern, focusing/scattering, and intrinsic attenuation. Our inversion result and other global and regional results included in our comparisons typically account for geometric spreading and source radiation pattern. There is some scatter in the amplitude which may be related to velocity heterogeneity and associated focusing/scattering and local site effects. We proceed focusing primarily on intrinsic attenuation and considering potential effects from focusing/scattering in cases where the latter provides an explanation for divergent observations. We plot the estimated attenuation coefficients at the period of range from 15-40 s with their associated standard error bars (Figure 4d). The Vs sensitivity curves at different periods are shown in Figure 4a. One example of the grid search result for amplitude and attenuation coefficient for one event at period 18 s is shown in Figure 4b. The grid search result has a clearly defined minimum that provides an error estimate for the individual measurements, and these are propagated through to the error in the average result.

The inversion result for
for the region is shown in Figure 4f along with standard error of the linearized least squares inversion at the final iteration (gray) and the Vs result in Figure 4e again with standard error. In the shallow portion of the crust and upper mantle (4-10 km) is low 40 ± 17 and increases to 175 ± 16 at 10 km depth. At lithospheric depths varies more smoothly, 175 ± 16 at 10-50 km depth. At greater depths (>60 km), varies more uniformly within the range of 75-115. The apparent Vs 1-D profile, that is, the velocity observed for the frequency of interrogation, is similar to that from previous work Saikia et al., 2021). The reference Vs structure, that is, the velocity corrected to the frequency independent version at 1 Hz, is very similar to the apparent Vs structure, but slightly faster, by 1%-2%. The error values of both Vs structures are also the same (0.03-0.07 km/s), but error on the apparent Vs is not shown for clarity.
For comparison, apparent Vs and models for 10 and 30 My seafloor predicted for a thermal model by laboratory experiments are shown (Figures 4f and 4g) (Jackson & Faul, 2010). We also compared our results with the EPR (Yang et al., 2007), the Juan de Fuca Ridge (Ruan et al., 2018), old Pacific lithosphere (Ma et al., 2020), PREM (Dziewonski & Anderson, 1981), and a variety of oceanic ages from a global model (Dalton et al., 2008) ( Figure 5). We have also examined the and apparent Vs relationship of the present study and other studies of oceanic regions in comparison to four different experimental predictions (Jackson & Faul, 2010;McCarthy et al., 2011;Yamauchi & Takei, 2016) using the very broadband rheology calculator (Havlin et al., 2021) (Figure 6). The frequency dependence of shear attenuation in the lithosphere and asthenosphere from previously published results along with the results from the present study is shown in Figure 7

Discussion
Our 1-D Q μ model reflects the general expectations for an oceanic profile. The low in the shallowest sub-oceanic layers (4-10 km) is likely dominated by the combined effects of topography and pelagic sediments with low shear moduli and other scattering effects of a heterogeneous crust rather than reflecting intrinsic attenuation. The topography across the region is rough, varying by several km , and previous work has suggested that scattering of short period surface waves in the water is strong (Harmon et al., 2009). Therefore, we do not interpret the shallow result any further. The mantle lithosphere (10-50 km) is characterized by high Figure 5. Comparison of average 1-D observations. (a) The best fitting reference Vs (solid lines), reference Vs error (gray) and apparent shear velocity (dashed black) are compared to the other global and regional models (colored lines: solid for reference Vs and dashed for apparent Vs) (b) −1 (solid black) and −1 error (gray) from the present study are compared to other global and regional models (colored lines).
(175 ± 16) likely reflecting a cool and rigid plate, at least in comparison to the underlying asthenosphere, which is characterized by lower (90 ± 15) owing to higher temperatures and/or other factors which we will discuss further in subsequent paragraphs.
A comparison of our Vs and results to the laboratory based predictions provides a reference point for the control of temperature on the structure (Figure 4). Although we present both apparent Vs and reference Vs (Figures 4-6), apparent Vs values are best for comparisons to the laboratory experiments, given that those studies also report apparent Vs (Figures 4 and 6). The Vs predictions for the Jackson and Faul (2010)   , and X Fit Premelt following Yamauchi and Takei (2016). Since the PREM model is in terms of reference velocity, here it is adjusted to the average frequency used in this study (15-143 s) for comparison purpose. system (Figure 4f). One of the reasons for the discrepancy could be that the Jackson and Faul (2010) prediction is for the half-space cooling model, which does not account for lateral heat conduction. Geodynamic models that account for lateral heat conduction predict cooler temperatures which would likely be characterized by faster seismic velocities and higher beneath slow spreading ridges (Phipps Morgan et al., 1987). In addition, the Jackson and Faul (2010) parameterization is tuned for temperatures >1100°C, so comparisons at ∼>50 km are likely the only depths that are valid for comparison (Jackson & Faul, 2010). At depths >50 km our V s is larger and our is lower than predicted by experiments suggesting either that other factors besides temperature may be required or a slightly different parameterization of Vs/Q μ is needed (Figures 4e and 4f). Other parameterizations of Q μ −1 based on seismic observations of Goes et al. (2012) have been slightly more successful in matching sub-ridge observations in the Pacific. However, again these parameterizations have required additional mechanisms to completely explain the observations. We will explore other parameterizations in a global context below.
The comparison of our Vs result to other in situ studies and global results from oceanic lithosphere highlights the variability of Vs structures (Figure 5a). Near the ridge, spreading rate appears to have a strong effect Vs. The ultrafast spreading EPR at 17°S has the slowest profile overall with the slowest "fast lid" and asthenosphere (Yang et al., 2007). This is followed by the intermediate Juan De Fuca Ridge (Ruan et al., 2018). The global averages are the next fastest profiles, while our profile from the slow spreading Mid-Atlantic Ridge is the fastest overall with some overlap between our result and the mid-age ocean global profile (Dalton et al., 2008). This variation is predicted somewhat based on the relative age and spreading rate, because at slower spreading rates, lateral conductive cooling results in a ∼20 km thick lithosphere beneath young seafloor ages (Parmentier & Morgan, 1990). Our result is also similar to that from old Pacific lithosphere originally formed at the fast spreading EPR (Ma et al., 2020).
The comparisons of also demonstrate the variability of seismic properties as a function of seafloor age at lithospheric depths, but not necessarily spreading rate, and also not necessarily at asthenospheric depths (Figure 5). At lithospheric depths, even accounting for differences in lithospheric thickness, there is wide variation in (150-1,400) from young to very old seafloor. The highest (1,400) is associated with the oldest seafloor of NoMelt. The remainder of the lithospheric measurements from young seafloor are much smaller, but with no obvious trend in spreading rate. Specifically, our result from the slow spreading Mid-Atlantic Ridge is = 175 ± 16, the result beneath the intermediate spreading Juan de Fuca Ridge is = 500 (Ruan et al., 2018), while the result beneath the ultrafast spreading EPR is = 225 (Yang et al., 2007). Our result is within error of the ultra-fast spreading EPR. The variability in lithospheric beneath ridges, suggests some other process affects the apparent of the lithosphere, and it is not necessarily related to spreading rate. For example, lenses of cooled melt and patchy alteration of the lithosphere to greater depths could result in a heterogeneous lithospheric structure, which could cause scattering and a reduced apparent in our study area. Asthenospheric values for most of the regions are within error of our result at 80-140 km depth ( Figure 5).
There are some general trends visible when we compare our results to previously reported Rayleigh wave results for Vsin oceanic regions (Figures 5 and 6). For this comparison, we use the maximum value of Q μ from smooth inversions in the lithosphere (shown in Figure 5) given that the remainder of studies are also from smooth models. The from the smooth parameterisations also likely better reflects the lithospheric mantle since it avoids artifacts from the crust, which may be characterized by high attenuation owing to scattering. However, we expand the error bars in Figure 6 to include the smaller Q μ values reported from minimum parameterization models (Ruan et al., 2018;Yang et al., 2007). Asthenospheric Q μ for smooth and minimum parameterization models were within error of each other. Both the Vs and values are larger in the lithosphere in comparison to asthenosphere based on all the global observations. In the lithosphere, our result is close to within error Figure 7. Comparison of the frequency dependence of attenuation in the lithosphere (blue lines) and asthenosphere (red lines) between the present study and the other studies. We compare with the global PREM model and the QL6 model (Durek & Ekström, 1996), the oceanic part of the QRSDI12 model (Dalton et al., 2008), the regional model from the East Pacific Rise region (Yang et al., 2007), regional models from the Juan de Fuca Ridge from body waves (Eilon & Abers, 2017) and surface waves (Ruan et al., 2018), and the regional model beneath the northwestern Pacific region (Takeuchi et al., 2017). The star represents the results of the present study. The result from this study is highlighted in yellow. This figure is modified from Takeuchi et al. (2017). of the global attenuation models from Dalton et al. (2008). Ma et al. (2020) found a high (4.54 ± 0.09 km/s) lithospheric Vs that is similar to our results, with a much greater , which could be in the trend of our results and the global models. However, the Yang et al. (2007) result has a slow Vs (4.27 ± 0.05 km/s) relative to (225 ± 50), and this is similarly true for Ruan et al. (2018) (Vs = 4.29 ± 0.05 km/s with = 500 ± 400). The range of reported is larger in the lithosphere (125-1,400) in comparison to the asthenosphere (50-100), whereas the range of Vs reported in the lithosphere (4.3-4.6 km/s) is similar to that reported in the asthenosphere (4.1-4.5 km/s), respectively. The asthenospheric results from all studies form a near linear array, given the smaller variability in .
We further examine the relationships between the observed Vs and and the predictions from 4 different Vsrelationships based on laboratory experiments ( Figure 6). These include the Andrade and the extended Burghers models of Jackson and Faul (2010), the master curve based on Maxwell relaxation time approach of McCarthy et al. (2011), and the master curve modified for the effects of pre-melt of Yamauchi and Takei (2016). We choose two pressures, 1 GPa (about 32 km depth) and 2.5 GPa (about 82 km depth), to represent the lithosphere and the asthenosphere, respectively. We calculated the predicted and Vs for a range of temperatures between 1,200-1,800°C and for a frequency range from 0.01-0.05 Hz, using the Very Broadband Rheology calculator (Havlin et al., 2021) assuming elastic coefficients appropriate for an olivine mantle (Figure 6a). We use the default settings in the calculations, which utilize the same coefficients and assumptions from the original published works. We assume a 1.3 cm grain size in the Andrade, extended Burghers models, which is a free parameter. The grain sizes for the empirical fits from the Maxwell relaxation time master curve and master curve modified for the effects of premelt are fixed at 1 and 4 mm, that is, the values assumed in the original publications in fitting the master curves to seismic observations. The shapes of the master curves (X Fit MSW) are different from the other three predictions with a sharp kink visible near 4.55 km/s. The master curve corrected for pre-melt (X Fit Premelt) has higher at< 1,300°C than the other three predictions. We also calculate and Vs for the same temperature and pressures, but also allow 1% partial melt (Figure 6b). The effect on is minimal, but reduces the velocities by ∼2% based on the Takei (1998) wetting angle parameterization for melt and seismic velocity (Figure 6b).
The observations from the lithosphere generally fall within the range of predictions from laboratory experiments with some exceptions. The Yang et al., (2007) Vs is slower than predicted, and the Ruan et al. (2018), Ma et al. (2020) and PREM (Dziewonski & Anderson, 1981) models have high relative to the predictions. The high from Ruan et al. (2018) and Ma et al. (2020) might be explained by cooler temperatures than calculated here, but the slow Vs of Ruan et al. (2018) would still remain outside the predictions. The asthenospheric Vs and observations fall on top of the laboratory predictions for a thermal model and have a near linear trend, which generally agrees with the laboratory predictions. The -Vs observations are in best agreement with the master curve model (X Fit MSW) (Figure 6a). The observations for a given Vs are higher than the predictions from the other three parameterisations. However, to explain the observations with temperature variation alone would require a range that would span 1,300-1,800°C. This seems unlikely given that we are considering mid-ocean ridges and "normal" old oceanic lithosphere, that is, not hotspots. The average mantle potential temperature is thought to be 1,310-1,430°C (Sarafian et al., 2015), with only a variation of ±100°C expected in most tectonic environments except for hotspots (Hart et al., 2008;Putirka et al., 2007), although some petrologic/seismic ridge estimates give a range of 1,300-1,550°C (Dalton et al., 2014). In addition, given typical adiabats, mantle temperatures at the depths of these asthenospheric observations do not likely exceed the mantle potential temperature by much (∼< 30-50°C). The addition of 1% melt (Figure 6b), shifts all of the curves to lower velocities, although the mantle temperatures required by some observations are still quite high, up to 1,600-1,700°C. Therefore, partial melt percentages that exceed 1% may be required to explain some of the slow Vs observations while not exceeding expected mantle temperatures. Therefore, adding melt to the system, effectively lowering the Vs relative to the , could explain the observations in the asthenosphere. Overall, the master curve model provides the best fit to the observations in the lithosphere and asthenosphere, given the assumptions used here in general, as it does not under predict for a given Vs. Other models might be made to fit better by tuning the model parameter choices.
Our lithospheric and asthenospheric Q μ −1 results generally fit into the frequency dependent trends suggested by global comparisons. Our lithospheric Q μ −1 is similar to averages over the ocean basins from longer period global models QL7 and QRFSI12 (Durek & Ekström, 1996;Dalton et al., 2008) (Figure 7). It could be interpreted as following the trend of decreasing Q μ −1 with increasing frequency suggested for the lithosphere (Takeuchi et al., 2017). In other words our result could broadly be seen as connecting the longer period results (QL7, QRFSI12) to PREM, Juan de Fuca (Ruan et al., 2018) and the higher frequency result of Takeuchi et al. (2017). The NoMelt lithospheric Q μ −1 is smaller and has been interpreted as not necessarily following this trend (Ma et al., 2020). One possibility is that the low Q μ −1 is related to the older and likely cooler lithosphere of NoMelt. Our asthenospheric Q μ −1 broadly falls within the trend of frequency independent Q μ −1 in the asthenosphere. It has been suggested that this is the result of an absorption band peak that falls within the seismic frequency band as a result of a different mechanism (Takeuchi et al., 2017). The effect is likely caused by a different factor in the asthenosphere, such as the presence of partial melt and/or pre-melt conditions. At the same time, our asthenospheric Q μ −1 is slightly smaller than the other results, more similar to NoMelt. One possible explanation is that melt is only present in the asthenosphere over some sections of our study area. This has been suggested based on observations of punctuated anomalies in both shear wave velocities from surface waves , magnetotelluric imaging , seismic imaging guided by magnetotelluric imaging , and intermittent imaging of sharp discontinuities from receiver functions . Overall, the trends from the other studies suggest that no large difference in Q μ −1 in the lithosphere in comparison to the asthenosphere is predicted at the long periods of our study (Figure 7). Therefore, we do not have a strong interpretation of whether our result supports a different frequency dependence of Q μ −1 in the lithosphere in comparison to the asthenosphere. Finer lateral resolution of 3-D Q μ −1 in our study area is required to fully disambiguate if asthenospheric Q μ −1 requires the presence of partial melt in some regions. Similarly, additional attenuation measurements in a variety of locations and at higher frequencies are required to further investigate the attenuation-frequency trends in the lithosphere versus the asthenosphere.

Conclusions
We have estimated for 0-80 Myr old oceanic lithosphere and asthenosphere beneath and nearby the equatorial Mid-Atlantic Ridge using local Rayleigh waves from 15-40 s period. We find values of 175 ± 16 in the lithosphere and 90 ± 15 in the asthenosphere. Our result agrees with other observations from global models and in situ experiments from a variety of seafloor ages in the Pacific which find higher and Vs values in the lithosphere in comparison to the asthenosphere.
results from previous oceanic studies show a much wider spread in lithospheric (125-1,400) than asthenospheric (50-100). Comparisons of previous global and regional observations including our result to four different laboratory predictions of Vs and for thermal models shows generally good agreement; although, some disparity suggests that a small amount of partial melt is likely required to explain several observations. We find lithospheric Vs estimates are generally faster beneath slower spreading ridges, as expected owing to lateral conductive cooling. However, we find beneath ridges is not necessarily dependent on spreading rate and therefore additional factors, such as a component of scattering beneath our study area may be required to reduce . Our results could be considered consistent with different frequency dependencies of in the lithosphere in comparison to the asthenosphere, although according to the global trends the difference is not expected to be large at the longer periods of our result. Our 1-D average aligns with the predictions from laboratory experiments for a thermal model, and does not require the presence of partial melt, consistent with previous observations that required melt intermittently in our study area. Further investigation of regionally and globally in 3-dimensions is required to better constrain this possibility.

Data Availability Statement
All the figures were generated using Generic Mapping Tools v.