George Helffrich

Outer-core compositional stratification from observed core wave speed profiles

Light elements must be present in the nearly pure iron core of the Earth to match the remotely observed properties of the outer and inner cores. Crystallization of the inner core excludes light elements from the solid, concentrating them in liquid near the inner-core boundary that potentially rises and collects at the top of the core, and this may have a seismically observable signal. Here we present array-based observations of seismic waves sensitive to this part of the core whose wave speeds require there to be radial compositional variation in the topmost 300u2009km of the outer core. The velocity profile significantly departs from that of compression of a homogeneous liquid. Total light-element enrichment is up to five weight per cent at the top of the core if modelled in the Fe–O–S system. The stratification suggests the existence of a subadiabatic temperature gradient at the top of the outer core.

Hydrous upwelling across the mantle transition zone beneath the Afar Triple Junction

The mechanisms that drive the upwelling of chemical heterogeneity from the lower to upper mantle (e.g., thermal versus compositional buoyancy) are key to our understanding of whole mantle convective processes. We address these issues through a receiver function study on new seismic data from recent deployments located on the Afar Triple Junction, a location associated with deep mantle upwelling. The detailed images of upper mantle and mantle transition zone structure illuminate features that give insights into the nature of upwelling from the deep Earth. A seismic low-velocity layer directly above the mantle transition zone, interpreted as a stable melt layer, along with a prominent 520 km discontinuity suggest the presence of a hydrous upwelling. A relatively uniform transition zone thickness across the region suggests a weak thermal anomaly (<100 K) may be present and that upwelling must be at least partly driven by compositional buoyancy. The results suggest that the lower mantle is a source of volatile rich, chemically distinct upwellings that influence the structure of the upper mantle, and potentially the chemistry of surface lavas.

The Seismic Analysis Code: Spectral estimation in SAC

SPECTRAL ESTIMATION Spectral estimation is the task of taking a time series and decomposing it into its component frequencies. The total length of the time series and, if it has been sampled at a fixed time interval, the inter-sample spacing control the minimum and maximum frequencies that the time series contains. Different methodologies may be used to estimate the power at each frequency at constant intervals between these bounds. This so-called power spectrum provides a way to quantitatively characterize the frequency content of the time series. The information is usually presented in the form of a graph of power versus frequency. The power spectrum informs further processing avenues for the time series. Usually this involves discrimination of any signal in the spectrum from noise. If the signal is of high quality, the signals power will dominate the noise. Thus the power spectrum will be peaked in a frequency band containing the signal. If the goal is to design a filtering strategy to minimize the noise, this analysis will suggest the type of filter and the corner frequency to use. Another application might be to seek tidal resonances at a coastal site based on repeated sea level measurements, or a marigram. In this case, the frequencies of the spectral peaks are the desired information, and perhaps their widths or positional uncertainties. Spectral estimation is technically complex due to the characteristics of the signal under study.

Accessing SAC functionality and data from external programs

Despite the broad range of utility that SAC provides, at times it may be necessary to use external applications to augment its capabilities. In addition, it is sometimes desirable to access the functionality of SAC without interacting manually with the program, for example to include it in a longer processing workflow. In this chapter we will describe techniques and give examples of how to achieve both these ends. Note that details of the languages and applications for which examples are shown are beyond the scope of this book. The reader should seek more specialized books for that material. AUTOMATING SAC EXECUTION Running SAC from the shell Executing SAC While a decent amount of batch processing is possible within SAC using its built-in macro language (see Chapter 5), it is often useful (for example, to access functionality built into the operating system) to run SAC using scripting languages provided by the shell (under UNIX-like environments, examples include bash and tcsh ). One way is by using startup files (see Section 4.10). After the commands in it are executed, SAC then enters interactive mode. Because (usually) there is no need for an interactive phase when scripting, it is helpful to make the last line a QUIT command to terminate SAC and allow control to return to the shell.

Basic SAC commands

COMMAND STYLE SAC commands are typed from the command line or read from a file. After each command is processed, SAC reads another command from its input source until it is told to stop or the input is exhausted. Commands are single verbs (e.g., READ, WRITE), or a compound phrase (e.g., FILTER-DESIGN). Abbreviations exist for the longer or commonly used command names. A series of options that control the commands actions follow the command name. Command names or options may be typed in upper or lower case. However, when file names appear in commands, case does matter, and SAC preserves it. White space separates options and the command name, and can even precede the command name. This is useful for indenting groups of commands for documentation purposes. Multiple commands may be placed on the same line separated by the “;” (semicolon) character and will be processed left-to-right as they appear on the command line. Any command whose first character is * is a comment and is ignored. Thus the string ; * introduces a comment in the command listings that follow. SAC supplies default command options if they are not specified. Command options, once set, stay in force for future uses of the same command. This provides a way to tailor personal command defaults. SAC can read a file of commands setting your personal defaults before it reads the input. They will be described in detail in Section 4.10.