ALBERT

Description: We have used the iterative spectral fitting method to measure both the elastic and anelastic splitting functions of 20 inner core sensitive normal modes. These modes show significant improvement in spectral fit when anelastic splitting function coefficients d st are introduced in addition to the elastic splitting function coefficients c st . We employ two separate anelastic treatments: (i) fully anelastic measurement, in which a complete set of anelastic splitting function coefficients is measured in addition to the elastic coefficients, and (ii) zonal anelastic measurement, in which anelasticity is only allowed in zonal splitting function coefficients. Together, these two approaches confirm that normal modes sensitive to the Earth’s inner core resolve zonally dominant elastic and anelastic structures. The zonal dominance of anelasticity suggests that the inner core exhibit cylindrical attenuation anisotropy in addition to cylindrical velocity anisotropy. In particular, the zonally dominant anelasticity correlates with zonal elastic structure, that is, directions of higher velocity in the inner core also appear more attenuating.

Description: The splitting of the Earth's free-oscillation spectra places important constraints on the wave speed and density structure of the Earth's mantle and core. We present a new set of 164 self-coupled and 32 cross-coupled splitting functions. They are derived from modal spectra up to 10 mHz for 91 events with M w  ≥ 7.4 from the last 34 yr (1976–2010). Our data include the 2001 June 23 Peru event ( M w  = 8.4), the Sumatra events of 2004 ( M w  = 9.0) and 2005 ( M w  = 8.6), the 2008 Wenchuan, China event ( M w  = 7.9) and the 2010 Chile event ( M w  = 8.8). The new events provide significant improvement of data coverage particularly in continental areas. Almost half of the splitting functions have never been measured before. In particular, we measured 33 new modes sensitive to mantle compressional wave velocity, 10 new inner-core sensitive modes and 22 new cross-coupled splitting functions. These provide new constraints on the large-scale compressional structure of the mantle and the odd-degree structure of the mantle and inner core and can be used in future inversions of heterogeneous Earth structure. Our new splitting function coefficient data set will be available online.

Description: Reconciling the hemispherical structure of Earth’s inner core with its super-rotation Nature Geoscience 4, 264 (2011). doi:10.1038/ngeo1083 Authors: Lauren Waszek, Jessica Irving & Arwen Deuss Earth’s solid inner core grows through solidification of material from the fluid outer core onto its surface at rates of about 1 mm per year, freezing in core properties over time and generating an age–depth relation for the inner core. A hemispherical structure of the inner core is well-documented: an isotropic eastern hemisphere with fast seismic velocities contrasts with a slower, anisotropic western hemisphere. Independently, the inner core is reported to super-rotate at rates of up to 1° per year. Considering the slow growth, steady rotation rates of this magnitude would erase ’frozen-in’ regional variation and cannot coexist with hemispherical structure. Here, we exploit the age–depth relation, using the largest available PKIKP–PKiKP seismic travel time data set, to confirm hemispherical structure in the uppermost inner core, and to constrain the locations of the hemisphere boundaries. We find consistent eastward displacement of these boundaries with depth, from which we infer extremely slow steady inner core super-rotation of 0.1°–1° per million years. Our estimate of long-term super-rotation reconciles inner core rotation with hemispherical structure, two properties previously thought incompatible. It is in excellent agreement with geodynamo simulations, while not excluding the possibility that the much larger rotation rates inferred earlier correspond to fluctuations in inner core rotation on shorter timescales.

Description: SUMMARY Normal mode observations play an important role in studying broad-scale lateral variations in the Earth. Such studies require the calculation of accurate synthetic spectra in realistic earth models, and this remains a computationally challenging problem. Here, we describe a new implementation of the direct solution method for calculating normal mode spectra in laterally heterogeneous earth models. In this iterative direct solution method , the mode-coupling equations are solved in the frequency-domain using the preconditioned biconjugate gradient algorithm, and the time-domain solution is recovered using a numerical inverse Fourier transform. A number of example calculations are presented to demonstrate the accuracy and efficiency of the method for performing large ‘full coupling’ calculations as compared to methods based on matrix diagonalization and the traditional direct solution method.

Description: SUMMARY Normal mode observations play an important role in studying broad-scale lateral variations in the Earth. Such studies require the calculation of accurate synthetic spectra in realistic earth models, and this remains a computationally challenging problem. Here, we describe a new implementation of the direct solution method for calculating normal mode spectra in laterally heterogeneous earth models. In this iterative direct solution method , the mode-coupling equations are solved in the frequency-domain using the preconditioned biconjugate gradient algorithm, and the time-domain solution is recovered using a numerical inverse Fourier transform. A number of example calculations are presented to demonstrate the accuracy and efficiency of the method for performing large ‘full coupling’ calculations as compared to methods based on matrix diagonalization and the traditional direct solution method.

Description: One of the most powerful approaches for understanding the 3-D thermo-chemical structure of the lower mantle is to link tomographic models with mineral physics data. This is not straightforward because of strong trade-offs between thermal and chemical structures and their influence on seismic structures. They can be reduced by mapping simultaneously perturbations of wave speeds and density anomalies and by the quantitative assessment of the accuracy and uniqueness of seismic and mineralogical data. Here, we present new tomographic maps of low order even-degree seismic structures which are an improvement on earlier models. They satisfy constraints from body wave, surface wave and normal mode data simultaneously, thereby enhancing the spatial resolution. Furthermore, the seismic structure at a given location is represented by a probability density function (pdf) which takes into account the uncertainty and non-uniqueness of the solution due to modeling and data restrictions. Following a robust statistical procedure, we fit heterogeneity of wave speeds and density from hypothetical thermo-chemical models to those of our tomographic maps. We thereby constrain lateral variations of temperature as well as iron, silica and post-perovskite concentration in terms of pdfs. Our work shows that large scale chemical variations are likely everywhere in the lower mantle. In most of the D″ region post-perovskite is most abundant in the Circum-Pacific belt, but near the core its lateral variation is more complex. Furthermore, post-perovskite concentration trades off with the amplitudes of temperature and silicate variations, but not with their lateral distribution. This might be the reason why temperature and silicate variations appear not constrained by our data in the lowermost few hundred km of the mantle.

Description: Recent megathrust earthquakes, such as the 23 June 2001 Peru event, the Sumatra events of 2004 and 2005 and the 27 February 2010 Chile event, have given us the opportunity to measure splitting of the longest period normal modes. We use wave spectra to make robust measurements for modes 0S2, 0S3, 0S4, 2S1 and 1S2. Singlet frequencies of these modes have been measured previously using gravimeters, but here we use seismic records to observe splitting functions for 0S2 and 2S1 for the first time. Cross-coupling with nearby modes is included to account for ellipticity and rotation of the Earth and results in significantly improved splitting function measurements for 0S3, 0S4 and 1S2 compared with previous studies. The new splitting function measurements can easily be implemented in future tomographic modelling of aspherical velocity and, particularly, density structure.

Description: We investigate the hemispherical pattern in inner core velocity anisotropy using a new and independent high-quality data set of PKPbc-PKPdf and PKPab-PKPdf body wave observations. Our data show no evidence for a tilted anisotropy axis with respect to the Earth's rotation axis and is significantly better fit by a model with 4.4% anisotropy in the western hemisphere and only 1.0% in the eastern hemisphere than by a model of uniform anisotropy. We carry out variance minimization and find the boundaries between the hemispheres at lines of constant longitude at 14°E and 151°W. Variance minimization enables us to extract the imprint of hemispherical structure from all of the data, and not just polar paths, resulting in boundaries which are nearly 30° from the results of previous studies. The high quality of the data allows us to provide robust evidence that the isotropic velocity in the eastern hemisphere is 0.2% lower than in the western hemisphere in the top 660 km of the inner core. Our data set also suggests an increase in inner core anisotropy in the eastern hemisphere from 1% to around 6% at depths deeper than 660 km, indicating that the hemispherical pattern in anisotropy may disappear at greater depths. The presence of hemispherical structure rules out mechanisms for creating anisotropy which are unable to sustain longitudinal variations in the inner core. Furthermore, steady inner core superrotation of the order of 0.1°/year would eradicate the hemispherical differences, though inner core oscillation would still be permissible.

Description: SUMMARY Differential rotation of the Earth's inner core has been predicted in some geodynamo models, and seismic studies over the past 15 yr have resolved rotation rates up to 1° yr −1 . Most previous seismic body-wave studies have focussed on South Sandwich Islands events recorded at station COL in Alaska. Here, we present a globally extended study into temporal variations in the inner core over some 25 yr, using PKPbc-PKPdf traveltime residuals. To test for differential rotation of the inner core, displacement of inner-core heterogeneities over time is sought. We introduce a new method of space-flattening to remove the effect of spatial variations on the time variations; this allows for the use of both polar, semi-equatorial and equatorial geometries. First, we reanalyse polar paths from South Sandwich Islands events to stations COL and INK in North America. These stations yield a differential rotation of the inner core at a rate of 0.12–0.38° yr −1 in an eastward direction, in agreement with previous studies. However, station DAWY, which has a very similar path through the inner core as COL, yields at best a westward differential rotation of the inner core. Thus DAWY results are incompatible with the COL/INK inferred rotation. Secondly, earthquakes in the Aleutian Islands region, observed at BOSA and LBTB in southern Africa, exhibit temporal variations that are incompatible with the South Sandwich Islands-COL/INK inferred rotation rate. Thirdly, Kuril Islands events, recorded in South America at station BDF, yield inconclusive results. Finally, our final piece of evidence for the irreconcilability of differential inner-core rotation with global data comes from using earthquakes in the Vanuatu region, recorded at BCAO/BGCA in Central Africa, an equatorial geometry. These residuals resolve a westward inner-core rotation at a rate of 0.14° yr −1 , over the same time period that South Sandwich Islands events indicate an eastward rotation. As any rigid-body rotation should yield the same direction and rate independent of where the inner core is sampled, our results allow us to reject previously reported inner-core differential rotation rates of up to 0.1–0.5° yr −1 . Instead, our results suggest that structure in either the inner or the outer core is varying with time, over relatively short timescales and in ways that cannot be explained by, and do not support, a differentially rotating inner core.

Description: The existence of hemispherical variation in the Earth's inner core is well-documented, but consensus has not yet been reached on its detailed structure. The uppermost layers are a region of particular importance, as they are directly linked to the growth processes and post-solidification mechanisms of the inner core. Here, we use a large PKIKP-PKiKP differential travel time residual data set to derive a model for the upper inner core, providing new constraints on its isotropic and anisotropic velocity, and the amount of scattering. We find that the eastern and western hemisphere are separated by sharp boundaries. This is incompatible with the recently proposed inner core translation model, but might be explained by differences in outer core convection and inner core solidification rates. The eastern hemisphere displays weak anisotropy of 0.5%–1.0%. The western hemisphere, on the other hand, is characterized by the presence of an isotropic upper layer with a thickness of 57.5 km, with anisotropy of 2.8% appearing at deeper depths. The boundary between the isotropic layer and the deeper anisotropy appears sharp. We also detect, for the first time, a high velocity layer at the top of the eastern hemisphere with a thickness of 30 km, which we interpret as being due to an increased amount of light elements. There appears to be no relationship between the layered structure in the two hemispheres, with abrupt changes in velocity with depth in one hemisphere without any significant change at the same depth in the other hemisphere. Our results indicate that there is a difference in composition and mineral structure between the hemispheres, resulting in differing responses to external processes.