Ludovic Bréger

Anisotropy in the center of the inner core

We have assembled a collection of PKP data from broadband records of the Geoscope network. This collection is unique because, for the first time, it includes polar paths at epicentral distances between 172° and 177°, for which PKPDF samples the central part of the inner core. After Hilbert transforming the DF branch, the waveforms of PKPAB and PKPDF usually become very similar, and we measure differential travel times with an accuracy of a fraction of a second. The differential (AB-DF) times for equatorial paths are close to those predicted by PREM, whereas for the polar paths, they are larger by 3 to 6 sec. Absolute DF times confirm that the effect is primarily in the inner core. These observations are compatible with a model of cylindrical anisotropy in the inner core with the axis of symmetry aligned with the Earths spin axis and an amplitude of 3.5%. They require that the anisotropy extend to the central part of the inner core, confirming extrapolations made by Creager (1992) and ruling out models where anisotropy is confined to the outer 300 km of the inner core (Tromp, 1993).

The effect of D″ on PKP(AB−DF) travel time residuals and possible implications for inner core structure

Abstract The hypothesis that the deep inner core is anisotropic is based on PKP travel time observations at large distances and relies on a small number of very anomalous measurements for paths quasi-parallel to the Earth’s rotation axis. Here, we analyze a global dataset of PKP(AB−DF) travel times residuals, and discuss their significant dispersion (±2 s), and coherent large scale patterns. We show that the trends observed for quasi-equatorial paths are consistent with predictions from recent tomographic mantle models, when the latter are modified to account for strong heterogeneity at the base of the mantle under the Pacific Ocean and Africa, as documented in several recent studies. Likewise, for polar paths, we show that a large part of the signal could be explained by deep mantle structure. The effects of complex structure in the deep mantle on PKP(AB−DF) travel times should be carefully considered in order to reliably estimate the anisotropic structure of the central part of the inner core.

Anisotropic structures at the base of the Earth's mantle

The D″ shell at the base of the Earths mantle is thought to be a thermal and compositional boundary layer where vigorous dynamical processes are taking place. An important property of D″ is its seismic anisotropy, expressed as different velocities for horizontally and vertically polarized shear waves that have been diffracted or reflected at the core–mantle boundary,. The nature of this anisotropy has been the subject of debate. Here we present an analysis of various seismic phases, generated in the Kermadec–Fiji–Tonga zone and recorded at stations in North America, which reveal a region at the base of the mantle beneath the southwest Pacific Ocean where horizontally propagating vertically polarized waves are slower (by at least 10 per cent) than horizontally polarized waves. This observed anisotropy is an order of magnitude larger than that previously thought to exist in the lower mantle, and corresponds to lateral variations in horizontally polarized shear-wave velocity which are also of about 10 per cent. We speculate that this anisotropy may be the result of the mixing and shearing of strongly heterogeneous material in the boundary layer.

Anomalous splitting of free oscillations: A reevaluation of possible interpretations

The splitting of normal modes sensitive to structure in the inner core is larger than can be explained by three-dimensional heterogeneity confined to the earths mantle. A preferred interpretation of this anomalous splitting involves inner core anisotropy, providing a unified explanation of these data and of observed trends in the travel times of PKP waves that sample the inner core. We reexamine this interpretation, as well as a previously suggested alternative one in terms of outer core structure. Our motivation comes from recent results which indicate that simple, smooth models of inner core anisotropy are in disagreement with some PKP observations. We invert a recently assembled high quality dataset, comprising modes sensitive to mantle and outermost core structure, as well as modes sensitive to mantle, outer core and inner core structure. We compare models parametrized to include either inner core anisotropy or heterogeneity in the outer core. We show the following: (1) Outer core models, with fewer parameters, provide good overall fits to most modes with weak or strong sensitivity in the inner core, except for mode 3 S 2 , the inner core mode with the strongest splitting. (2) V s and p profiles obtained for models with outer core structure using mantle and core modes are in better agreement with those obtained using data sensitive to mantle structure alone, whereas the V p structure in D shows a stronger c 20 component when inner core anisotropy is considered. (3) Lateral heterogeneity restricted to the mantle, in particular strong heterogeneity in D, fails to account consistently for the splitting of all modes. Outer core models thus deserve further investigation and should be weighted against more complex models of inner core anisotropy to explain anomalous splitting of normal modes and PKP travel times. The outer core structure obtained, while arguably unrealistic, is consistent with concentration of light elements, either confined to the Taylor cylinder tangent to the inner core or in polar caps at the top and bottom of the outer core. A small amount of shear within such polar caps might account for the excess splitting of some core modes.

Modeling Credit Risk

Spreads for credit instruments denominated in euros, sterling, and U.S. dollars over their local swap curves are examined here. The findings indicate that monthly spread changes were strongly currency-dependent during the period May 1999–May 2001. Sector-by-rating factor returns are at best weakly correlated across currencies, and U.S. dollar spread returns are generally more volatile than the other two by a factor of two or three. This is contrary to what would be expected from covered interest arbitrage. The conclusion is that analysts should estimate credit factor risk models separately in each market, as risk forecasting models using a single set of spread factors for different markets will not be accurate.

Test of tomographic models of D″ using differential travel time data

We compare local measurements of SH-velocity in D under the Pacific Ocean with four recent S-velocity models derived with different techniques. From the local measurements, we find evidence for both strong fast and slow anomalies with an amplitude sometimes exceeding 10%, as well as strong lateral velocity gradients. The tomographic models underestimate the magnitude of the observed anomalies by roughly a factor of 3. The model that best matches both the sign and the localisation of the anomalous structures is exclusively an SH model. This indicates, in particular, that the presence of anisotropy in D may not be ignored and that it is important to separate SH and SV contributions in tomographic studies of the lowermost mantle.

New constraints on the structure of the inner core from P’P’

We measured absolute P’P’df as well as differential P’P’bc-P’P’df and P’P’ab-P’P’df travel time residuals for earthquakes in Alaska and the Aleutians recorded at NORSAR array (Norway). For such paths, P’P’df samples two regions of the inner core which have been identified as strongly anisotropic (∼3.5%), respectively beneath the Central Pacific and Africa, and should arrive some ∼6s earlier than predicted by a standard model. Absolute and differential travel times do not appear to be anomalous. A very complex texture and/or heterogeneity of the top ∼400km of the inner core, or a significant contribution from the strongly heterogeneous D”, is required to explain this discrepancy.

Agency Ratings in the Pfandbrief Market

Pfandbriefe are bond issues issued by German mortgage banks. Agency ratings do not play a significant role in the risk profile of jumbo Pfandbriefe, one type of Pfandbriefe, so it might be that the withdrawal of government guarantees and the prospect of agency rating downgrades do not mean more risk in the highly standardized jumbo market, with its many investor protections. Ratings do appear to have more relevance for the basic Pfandbriefe, where non-standardized issues, lower liquidity, and higher trading costs pose greater challenges for investors who wish to adjust their holdings quickly. There are systematic and sometimes large differences between Pfandbriefe and jumbo Pfandbriefe. Spread levels are clearly more homogeneous for jumbos than for Pfandbriefe. The higher liquidity and standardization of jumbo issues also results in a stronger benchmark where both issuer idiosyncrasies and risk are largely reduced. The risk modeling implications are clear; the two asset types should be treated separately.

Global Integration of Developed Credit Markets

Return correlations in the U.S. dollar and euro credit markets are systematically different on at least two dimensions: returns for normal day–to–day spread changes versus spread returns associated with extreme events; and spread returns for investment–grade versus speculative issuers. A large part of the return correlation is driven by extreme global events such as the 2001 terrorist attacks or the 2002 credit crisis ensuing on the Enron meltdown. Under more normal market conditions, euro and U.S. dollar credit markets are weakly linked, especially for highly rated debt. Returns on speculative debt issued by the same issuer in different markets tend to be highly correlated; this is less so for high–grade issuers. An immediate implication is that currency diversification is much more efficient than name diversification for high–grade debt. Conversely, high–yield portfolios benefit from name or even sector diversification more than they benefit from currency diversification. Risk models need to include currency–dependent factors, particularly for investment–grade instruments. The results provide some indication of the way to use global credit factors or factor return proxies to estimate credit risk in markets lacking much corporate bond data.