PLOT ANNOTATION

Seismograms

For SAC, the basic display element is a seismogram plotted with time along the horizontal axis and the sampled quantity along the vertical axis. SAC's basic plotting commands, PLOT, PLOT1 and PLOT2, supply axis tick marks numbered to show the relevant scales and connect data points with lines. SAC draws tick marks around all four sides of the plot to facilitate quantitative use of the data in the plot.

Tick marks, axes and borders

SAC uses a good default algorithm that chooses tick mark intervals and numbering based on the range of values to be plotted. If the result is unsatisfactory, tick mark intervals may be explicitly set using the XDIV and YDIV commands for the horizontal and vertical axes, respectively. The number or spacing of the tick marks may be specified using the keywords INCREMENT or NUMBER. To reset the default settings, use the NICE option.

The TICKS command selectively turns off the tick marks on each of plot's four sides using the keywords TOP, BOTTOM, LEFT and RIGHT, respectively. The omission of tick marks results in clearer plots, but they lose their quantitative clarity. TICKS is mostly used to make publication-quality plots for inclusion in a talk or a publication.

Grid lines across the plot (like graph paper) may be useful in some circumstances but are distracting due to the resulting clutter. To draw grid lines on plots, use the GRID, XGRID and YGRID commands; they are off by default.

Crust, mantle, lithosphere and asthenosphere

Traditionally, Earth scientists have divided the outer parts of the Earth into the crust and mantle. Broadly speaking these reflect a major change in chemical composition. Mantle rocks comprise a high proportion of minerals containing the elements iron and manganese, and have relatively high density (≥3300 kg m−3) and seismic P-wave velocity (≥8 km s−1); on the other hand crustal rocks, which are ultimately derived from melting (and associated fractionation) of the mantle, have lower proportions of iron and manganese, higher proportions of aluminium and silicon, and consequently lower densities and velocities. The oceanic crust is generally thinner (≤8 km) and slightly denser (~2800 kg m−3) than continental crust.

An alternative way of subdividing the Earth is based not on its composition but its mechanical properties. In this classification the outermost, relatively cool, layer is one where rocks behave in a strong, brittle or elastic manner, and is termed the lithosphere from the Greek lithos, ‘rocky’ (Dietz, 1961). Underlying this is a warmer, weak layer which, on geological timescales (~1Ma), behaves as a plastic medium, and is termed the asthenosphere (from the Greek asthenēs, ‘weak’). The viscosity of the asthenosphere is of the order of 1020 Pa s (Lowrie, 1997).

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 command's 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.

Introduction

The oceanic lithosphere is a mechanical boundary layer, defined by its rigid, elastic properties and distinguished from the underlying asthenosphere, which has a plastic rheology (Chapter 3). On the other hand, the crust reflects the chemical differentiation of the Earth, and comprises rocks that are generally less dense and have lower seismic velocities than the underlying mantle. The oceanic crust is up to about 7 km thick. It consists mainly of products formed by partial melting of the mantle: basaltic lavas and the gabbros and dolerites that form their deep-seated counterparts, with similar chemistry but larger mineral grains resulting from slower cooling and crystallisation. Our knowledge of the structure of oceanic crust comes mainly from a combination of seismological, gravity and sampling studies (Cann, 1970, 1974; Carbotte and Scheirer, 2004).

Crustal thickness

The Mohorovičić discontinuity, or Moho for short, marks the base of the crust. It was originally defined seismically (on continents) as a velocity discontinuity at which the P-wave velocity first exceeds 8.0 km s－1; sometimes this is called the ‘seismological Moho’. In contrast, the ‘petrological’ Moho is defined as the base of the geological crust, irrespective of seismic velocity (Section 5.3.4). The earliest oceanic seismic refraction experiments detected the seismological Moho at depths of some 6 – 8 km below the base of the sediments – much less than the thickness of the continental crust (Raitt, 1956; Hill, 1957; Raitt, 1963; Figure 2.12).

WHAT IS SAC?

SAC is an acronym for the Seismic Analysis Code, a command line tool for basic operations on time series data, especially seismic data. SAC includes a graphical interface for viewing and picking waveforms. It defines a standard type of file for storing and retrieving time series and also reads files written in other data formats (SEG-Y, MSEED, GCF) used during field collection of seismic data. SAC is self-contained and does not rely on network access for any of its capabilities, including documentation, which makes it useful for field data quality control.

SAC reads data formats (CSS and GSE formats) used by nuclear test monitoring agencies. It also contains programming language constructs that provide basic methods for developing elaborate, multi-step analysis methodologies. Collectively, these features make SAC a useful interactive platform upon which customized analytical methods may be built and prototypical procedures may be developed.

SAC is widely known. The IRIS Data Management Center (DMC), one of the largest whole-Earth seismological data repositories in existence, allows data to be requested in SAC form. The instrument response information provided by the DMC's SEED reading program, rseed, is usable by SAC in pole-zero or evalresp form. Owing to SAC's longevity, a rather large and well debugged software tool ecosystem has evolved around its file format. One such tool, jweed, searches for and retrieves data held by the DMC. SAC data and SAC-compatible instrument response information are among its output options.

THE CONCEPT OF 3D DATA

SAC has facilities for handling a basic type of three-dimensional (3D) data, which are function values evaluated on a regular grid of (X,Y) positions. This type of data can be viewed as evenly sampled in space and fits naturally into SAC file types. The file consists of the string of samples at each grid point, and file header information that flags it as 3D gives the X and Y dimensions of the grid. SAC calls data of this type XYZ.

The simplest visualization of 3D data is map elevation data. Imagine a section of land whose elevation is specified on a grid every 100 m eastwards and 100 m northwards. Over a plot of land 1 km by 1 km, the elevation could be described by a string of 121 values, the first 11 values along the westernmost traverse and the final 11 along the easternmost traverse.

Another type of data that can be represented in 3D is a spectrum as a function of time. If equal lengths of time are cut from a seismogram, the number of points in their FFTs will be the same. If the interval between spectral samples is constant, these values will also form agrid.

A final type of data inherently 3D is a misfit function evaluated over a two-dimensional (2D) grid of points. The misfit minimum within the sampled parameter space yields the optimum combination of parameters that best fit some observations, and the shape of the minimum provides a measure of the joint uncertainty of the parameter estimates.

Ridges and plate kinematics

An important aspect of MORs is their function as divergent boundaries between tectonic plates (Figure 4.1). Plate tectonics considers the lithosphere to be broken into a number of thin, rigid caps, whose relative motions across the Earth are described by plate kinematics (McKenzie and Parker, 1967; Le Pichon, 1968; Morgan, 1968). Plate motions are described in terms of pure geometry, utilising Euler's rotation theorem that any motion on a sphere can be represented as a single rotation about an axis passing through the sphere's centre. This axis cuts the surface at two points called the Euler poles, or ‘poles of rotation’. The relative motion between any two plates is completely described by the latitude and longitude of the relevant Euler pole and the rate of rotation. The most recent global description of plate motions is given by DeMets et al. (1990, 1994) .

The trace of an Euler rotation on the surface of the sphere is a ‘small circle’ centred on the pole (Figure 4.2). Such circles are analogous to lines of latitude, which are small circles about the geographic poles. Two plates sharing a common boundary aligned along such a small circle will move relative to one another by pure slip, so the azimuth of this small circle is the spreading direction. Geologically, such plate boundaries are transform faults (Wilson, 1965; Section 4.4). ‘Great circles’ (diameters of the sphere) that are normal to transform faults meet at the rotation pole (Figure 4.2). There are two other types of plate boundary: ‘trenches’ or subduction zones, where plates converge, and ‘ridges’, where they diverge. The ridges are spreading centres and are the main subject of this book. Since MOR axes represent divergent, or spreading, plate boundaries, they are often called ‘spreading centres’ or ‘spreading axes’.