Observations of core‐mantle boundary Stoneley modes

Core‐mantle boundary (CMB) Stoneley modes represent a unique class of normal modes with extremely strong sensitivity to wave speed and density variations in the D” region. We measure splitting functions of eight CMB Stoneley modes using modal spectra from 93 events with M w > 7.4 between 1976 and 2011. The obtained splitting function maps correlate well with the predicted splitting calculated for S20RTS+Crust5.1 structure and the distribution of S diff and P diff travel time anomalies, suggesting that they are robust. We illustrate how our new CMB Stoneley mode splitting functions can be used to estimate density variations in the Earth's lowermost mantle. Key Points We present CMB Stoneley mode splitting function measurements The CMB Stoneley mode splitting correlates well with diffracted body wave data Our measurements allow to constrain density variations in the lowermost mantlePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/99080/1/figS2_plot_prem_freq_Q_stoneley_paperrotated.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/99080/2/grl50514.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/99080/3/figS1_plot_coef_stoneley_paper_deg2_newrotated.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/99080/4/README_suppl_mat_GRL.pd

Comparing ray-theoretical and finite-frequency teleseismic traveltimes:Implications for constraining the ratio of S-wave to P-wave velocity variations in the lower mantle

A number of seismological studies have indicated that the ratio R of S-wave and P-wave velocity perturbations increases to 3–4 in the lower mantle with the highest values in the large low-velocity provinces (LLVPs) beneath Africa and the central Pacific. Traveltime constraints on R are based primarily on ray-theoretical modelling of delay times of P waves (ΔTP) and S waves (ΔTS), even for measurements derived from long-period waveforms and core-diffracted waves for which ray theory (RT) is deemed inaccurate. Along with a published set of traveltime delays, we compare predicted values of ΔTP, ΔTS, and the ΔTS/ΔTP ratio for RT and finite-frequency (FF) theory to determine the resolvability of R in the lower mantle. We determine the FF predictions of ΔTP and ΔTS using cross-correlation methods applied to spectral-element method waveforms, analogous to the analysis of recorded waveforms, and by integration using FF sensitivity kernels. Our calculations indicate that RT and FF predict a similar variation of the ΔTS/ΔTP ratio when R increases linearly with depth in the mantle. However, variations of R in relatively thin layers ( 20 s). This is because FF predicts that ΔTP and ΔTS vary smoothly with epicentral distance even when vertical P-wave and S-wave gradients change abruptly. Our waveform simulations also show that the estimate of R for the Pacific LLVP is strongly affected by velocity structure shallower in the mantle. If R increases with depth in the mantle, which appears to be a robust inference, the acceleration of P waves in the lithosphere beneath eastern North America and the high-velocity Farallon anomaly negates the P-wave deceleration in the LLVP. This results in a ΔTP of about 0, whereas ΔTS is positive. Consequently, the recorded high ΔTS/ΔTP for events in the southwest Pacific and stations in North America may be misinterpreted as an anomalously high R for the Pacific LLVP

Robust estimates of the ratio between S- and P-wave velocity anomalies in the Earth's mantle using normal modes

Seismic tomography allows us to image the interior of the Earth. In general, to determine the nature of seismic anomalies, constraints on more than one seismic parameter are required. For example, the ratio R between perturbations in vs and vp (dlnvs and dlnvp, respectively) is studied extensively in the lowermost mantle and interpreted in terms of thermal and/or chemical anomalies. However, to jointly interpret tomographic models of variations in vs and vp or their ratio R, it is essential for them to share the same local resolution. Most existing models do not provide resolution information, and thus cannot guarantee to honour this condition. In addition, uncertainties are typically not provided, making it difficult to robustly interpret the ratio R = dlnvs / dlnvp. To overcome these issues, we utilise the recently developed SOLA tomographic method, a variant of the linear Backus–Gilbert inversion scheme. SOLA retrieves local-average model estimates, together with information on their uncertainties, whilst it also provides direct control on model resolution through target kernels. In this contribution, we apply SOLA to normal-mode data with sensitivity to both vs and vp, as well as density throughout the mantle. Specifically, we aim to develop models of both vs and vp with the same local resolution. We test our methodology and approach using synthetic tests for various noise cases (random noise, data noise or also additional 3D Earth noise due to variations in other physical parameters than the one of interest). We find that the addition of the 3D noise increases the uncertainties in our model estimates significantly, only allowing us to find model estimates in six or four layers for vs and vp, respectively. While the synthetic tests indicate that no satisfactory density models can be obtained, we easily manage to construct models of dlnvs and dlnvp with almost identical resolution, from which the ratio R can be robustly inferred. The obtained values of R in our synthetic experiments significantly depend on the noise case considered and the method used to calculate it, with the addition of 3D noise always leading to an overestimate of R. When applying our approach to real data, we obtain values of R in the range of 2.5–4.0 in the lowest 600 km of the mantle, which are consistent with previous studies. Our model estimates with related resolving kernels and uncertainties can be used to test geodynamic model predictions to provide further insights into the temperature and composition of the mantle

Distribution service : competition within and among retail formats

Distribution service provision is an important instrument for the creation of availability. The book addresses in five parts the role of distribution service in individual channel member decision making in a competitive retailing environment through theoretical and empirical modeling and analysis. The empirical applications all concern the Dutch domestic cut flower market. The book starts in part I with development of a new and integrative conceptualization for distribution service elaborating on views from logistics, economics, and psychology. The second part of the book addresses the theory underlying consumer evaluation of and choice from assortments. It provides a theoretical framework of consumption goals, situational, and contextual variables, including retailer distribution service provision, as determinants of consumer evaluation of and choice from assortments. Several hypotheses are tested in an empirical study. Extended multinomial logit modeling of the experimental choice data has been used as a tool for optimization of retail assortments. Part III investigates the role of retail distribution service provision in consumer post-purchase evaluation processes and extends existing research on consumer post-purchase evaluation. Part IV focuses on the role of distribution service in vertical and horizontal strategic interactions between channel members, particularly between manufacturers and retailers, and its consequences for the emergence of different channel structures and retail formats. A game-theoretic model has been developed for retail competition with respect to price and distribution service and its consequences for the emergence of differentiated retail formats. Finally, part V discusses research implications and future research challenges.</p