To the lowest order, the seismic structure of the Earth's interior can be simply divided into several layered spherical shells, including an outer solid crust, a highly viscous upper mantle, a solid mid and lower mantle, a liquid outer core that is much less viscous than the upper mantle, and a solid inner core.
It has been widely accepted that the Earth's solid inner core consists mainly of heavy minerals Fe (~85%) and Ni (~6%) with a significant fraction of light elements such as O, S and Si (e.g. Jephcoat & Olson, 1987; Stixrude et al., 1997). As the temperature cools with time, Fe and Ni solidify and the inner core grows in radius. In the process, the light elements O, S and Si are expelled from the inner core into the outer core.
The outer core is composed of the same heavy materials Fe and Ni as the inner core but in a liquid state. There has been much less interest in studying the seismic structure of the outer core in comparison to the other regions. One reason is that the liquid outer core has only compressional wave which puts a stronger limitation on our ability to resolve its structural details. The other reason is that the outer core has always been considered to be more or less chemically homogenized by vigorous internal convection (Masters, 1979). Any variation in the structure of the outer core is thought of purely due to the depth gradient of pressure and temperature. This consideration is also the basis in establishing the outer core structure in the global average one-dimensional (1D) models such as PREM (Dziewonski & Anderson, 1981).
However, the light elements O, S and Si expelled from the inner core may alter this situation. Because of gravitational buoyancy, these lighter materials rise up through the Fe/Ni filled outer core and become trapped beneath the core-mantle boundary (CMB), a
solid thermal-chemical barrier, as illustrated in Fig.1.1. Such a scenario implies that there are light materials (in comparison to the expected heavy elements Fe and Ni), and therefore a chemical stratification may exist at the top of the outer core (e.g. Lister &
Buffett, 1998; Buffett & Seagle, 2010; Frost et al, 2010), but the validity of this scenario needs to be confirmed by evidence gathered from geophysical (especially seismology) observations, laboratory experiments, and numerical modelings.
Fig. 1.1 Cartoon illustrating the schematic model of an outer core with light materials on its top. The light blue curvy arc indicates the CMB with possible topography. The inner core consists mainly heavy elements Fe and Ni, and a fraction of light materials O, S and Si (red dots), which are expelled from the inner core during its formation, rise up through the outer core, and are eventually trapped beneath the CMB.
The seismic waves propagating through the outer core, such as SKS and its core multiples SmKS, provide us the direct means to estimate the wave speed in the outer core and to infer the structure there. The effect of lighter materials on wave speed seems to be straightforward. In the liquid outer core, the speed of the compressional K wave is
,
(1.1) where and are the bulk modulus and density, respectively. Therefore, intuitively a density decrease associated with the existence of lighter elements would result in an increase in wave speed. However, Helffrich (2012) demonstrated that the elastic
property of a multi-component liquid behaves non-linearly if the mixture has not reached an ideal state, and may offset the effect of density change on the wave speed.
Therefore, chemical stratification at the top of the outer core due to the existence of lighter materials there could lead to the non-intuitive outcome of wave speed decrease.
The rapid increase in global deployments of permanent and temporary networks has provided more and more opportunities of obtaining high-quality records of SmKS waveforms which make the detailed investigation of the outer core feasible. Various seismic observations have been reported. Based on a limited dataset using earthquakes in Indonesia and stations in Africa, Tanaka (2004) reported possible low P-wave speed in a 50-km layer below the CMB. Eaton & Kendall (2006) found that a 12-km thick high-speed/low-density layer below the CMB best explained their SmKS traveltimes obtained from broadband seismograms at stations in Canada from a few earthquakes in Indonesia and Fiji. Tanaka (2007) analyzed a series of global records of SmKS, and proposed a model with a 1.4% lower speed than PREM in the top of 90 km of the outer core. More recently, a pair of studies by two independent groups reported very different findings. Alexandrakis & Eaton (2010) carefully analyzed SmKS traveltimes from 44 teleseismic earthquakes with a variety of source depths and in epicentral distance range 124°-140°, and concluded that there is no evidence for outer core stratification. In contrast, Helffrich & Kaneshima (2010) modeled the SmKS traveltimes along the two paths from South America to Japan and from Fiji to Europe, and suggested that the wave speed in the 300-km layer below the CMB can be up to 0.3% lower than PREM.
The validity of the previous studies on the outer core structure using the SmKS traveltimes may be limited by three aspects. First, all these authors have used relatively few earthquakes and stations, and their data are limited in both quantity and geographical coverage. Secondly, most of them have used the traveltimes of SmKS up
to S5KS, which are often weak and have low signal-to-noise ratios, which reduced the measurement quality. Finally, the long traveling distances of the SmKS waves lead to attenuation of high-frequency contents and in the recorded signals. Therefore, these waves are usually best observed at frequencies below 0.2 Hz, which makes measurement of the onset times of arrivals very difficult. However, all the previous studies have been using ray theory to model the SmKS traveltimes, but the bias introduced by finite-frequency effect are not addressed.
The purpose of this study is to conduct a careful and thorough investigation of the seismic structure at the top of the outer core by establishing a larger and higher-quality dataset of SmKS traveltimes from globally distributed earthquakes and stations, and a more accurate modeling of these traveltimes. We focus on the differential traveltimes between SKKS and S3KS waves to both ensure the quality of the measurements and eliminate the possible contributions from factors such as source location errors and lateral structural variations along the paths in the mantle. We measure the differential traveltimes by the cross correlation of SKKS and (Hilbert-transformed) S3KS waveforms, and we model the finite-frequency differential traveltimes by the cross correlation of waveforms calculated by the direct-solution method (DSM).
The outline of this thesis is as follows. In Chapter 2, we describe the process for measuring the S3KS-SKKS differential traveltimes, and the DSM method used in modeling these data. Then we present the observed S3KS-SKKS differential traveltimes as well as predictions by PREM and several PREM-like models in Chapter 3. In Chapter 4, we carry out inversion method to search more models to understand the velocity structure below CMB 550 km. Finally we discuss and summarize our results in Chapter 5.