The analysis of seismic records depends on being able to disentangle the influence of the source and the structure of the Earth. Effective source characterisation thus becomes an important prerequisite for gaining new information on earth structure. Conversely, knowledge of the structure of the Earth is essential for providing estimates of the location of seismic events and the quantitative assessment of source mechanisms.

The need to know both the structure of the Earth and the properties of the source with only the information available from seismograms has dictated the development of seismology. Improved source locations have led to better Earth models, which in turn have been used to extract more information on all aspects of the source.

Seismic source estimation

The major part of the information used in the location of a seismic event is a set of arrival times of seismic phases which has been measured from displays of seismic waveforms by experienced analysts. For seismic arrays it is possible to provide additional information such as the apparent azimuth of the arriving energy and its velocity across the array.

For each seismic station the object is to provide arrival times (and array information) for a number of different seismic phases which have followed different propagation paths through the earth, together with an indication of the likely character of the arrival. Particular effort is made to try to extract information which is sensitive to the depth of the event, e.g., by recognising the phases pP, sP which are reflected back from the surface above the source.

The initial identifications of phase character may need to be modified when information from many stations are combined. One of the most difficult tasks has then to be faced. From the assemblage of arrival time picks, azimuth, and apparent velocity, those readings fromdifferent stations which should be grouped together have to be recognised and a preliminary location assigned. This location will then be refined by matching the patterns of observed and predicted arrival times.

Around the globe, many different seismic events can occur in a given time period so there is no guarantee that all readings correspond to the same event.

Much of the impact made in recent years by seismic tomography has come from global studies in which three-dimensional structure has been revealed throughout themantle, and even in the inner core.

Two very different styles of approach have been employed, based both on the nature of the data sets which have been used and also on the style of representation of heterogeneity. For studies in which seismic waveforms are calculated using modal summation or dispersion is used, spherical harmonics are a natural choice for the basis of representation of heterogeneity because they are closely related to the mode representation itself. On the other hand for ray information, although it is possible to project rays onto a spherical harmonic basis there is not the same direct relation as in modal methods.

Where information from modal and body wave times is combined, then a single representation in terms of spherical harmonics is commonly adopted (see, e.g., Su & Dziewonski, 1997). However, studies using just travel times have frequently used cellular representations (e.g., Grand, 1994; van der Hilst et al., 1997), but spherical harmonics can be useful where summary properties are desired as in the work of Robertson & Woodhouse (1995, 1996) on the relationship of P and S wavespeed heterogeneity.

A very important aspect of global studies arises from the distribution of earthquake sources across the globe (figure 32.1). As is well known, the occurrence of earthquakes is concentrated into zones associated with subduction processes. There is a modest level of activity along the mid-ocean ridges and scattered, infrequent events in stable continental and oceanic regions. The distribution of high quality seismic stations is also uneven because they also tend to concentrate in areas of significant seismicity. The efforts of Geoscope and IRIS in establishing global networks of broad-band seismometers have made a major difference to coverage, but still such regions as Africa have a very limited number of stations. The other major gap is represented by the world's oceans and this has been partly infilled by island stations notably by IRIS and the Ocean Hemisphere Project. Ocean bottom geophysical observatories, either attached to disused telephone cables or free-standing are planned, but will be expensive to establish and maintain.

As noted in volume I, the inspiration for this book came from the remarkable set of articles by Beno Gutenberg in the Handbuch der Geophysik, particularly vol. 4, 1932. Gutenburg provided a comprehensive summary of the current theory and accompanied this with a discussion of the nature of seismic observations.

This second volume of The Seismic Wavefield is primarily devoted to the interpretation of observed seismograms in terms of the physical processes which control their properties, with a strong link to the theoretical development in the first volume. References to sections in the first volume are indicated using a section marker (e.g., § I:3.1.2) and for equations from the earlier volume the volume number is represented explicitly as in (I:14.2.1). The emphasis throughout the book is on body waves and surface waves with frequencies above 10 mHz, rather than phenomena which are best treated through a normalmode development for the whole Earth, which are well covered in Theoretical Global Seismology by Dahlen & Tromp (1998).

The treatment starts with a discussion of near-source effects and strong ground motion. Then attention is directed to the wavefield as seen at progressively larger distances. For regional ranges, out to 1000 km from the source, the properties of the crust and uppermost mantle play an important role. In the far-regional range, for epicentral distances from 1000 km to 3000 km, the complex interactions with upper mantle discontinuities dictate the character of P and S arrivals. For larger epicentral distances a global perspective is appropriate, but surface multiples still carry relatively shallowly propagating waves to substantial distances.

The introduction to the discussion of seismic wave propagation across the globe was strongly influenced by the 2 m long wall chart From Earthquake to Seismogram prepared in 1962 under the direction of the late Professor S. Warren Carey at the University of Tasmania. In this chart the wavefronts of body waves and surface waves are carefully mapped through the Earth and across its surface, and these wavefronts are related to the features of a seismogram from an earthquake in the Kuriles recorded at the Hobart Observatory in Tasmania.

What is Vortex Sound?

Vortex sound is the sound produced as a by-product of unsteady fluid motions (Fig. 1.1.1). It is part of the more general subject of aerodynamic sound. The modern theory of aerodynamic sound was pioneered by James Lighthill in the early 1950s. Lighthill (1952) wanted to understand the mechanisms of noise generation by the jet engines of new passenger jet aircraft that were then about to enter service. However, it is now widely recognized that any mechanism that produces sound can actually be formulated as a problem of aerodynamic sound. Thus, apart from the high speed turbulent jet – which may be regarded as a distribution of intense turbulence velocity fluctuations that generate sound by converting a tiny fraction of the jet rotational kinetic energy into the longitudinal waves that constitute sound – colliding solid bodies, aeroengine rotor blades, vibrating surfaces, complex fluid–structure interactions in the larynx (responsible for speech), musical instruments, conventional loudspeakers, crackling paper, explosions, combustion and combustion instabilities in rockets, and so forth all fall within the theory of aerodynamic sound in its broadest sense.

In this book we shall consider principally the production of sound by unsteady motions of a fluid. Any fluid that possesses intrinsic kinetic energy, that is, energy not directly attributable to a moving boundary (which is largely withdrawn from the fluid when the boundary motion ceases), must possess vorticity. We shall see that in a certain sense and for a vast number of flows vorticity may be regarded as the ultimate source of the sound generated by the flow.

Vortex sound is the branch of fluid mechanics concerned with the conversion of hydrodynamic (rotational) kinetic energy into the longitudinal disturbances we call sound. The subject is itself a subsection of the theory of aerodynamic sound, which encompasses a much wider range of problems also involving, for example, combustion and ‘entropy’ sources of sound. The book is based on an introductory one-semester graduate level course given on several occasions at Boston University. Most students at this level possess an insufficient grasp of basic principles to appreciate the subtle coupling of the hydrodynamic and acoustic fields, and many are ill-equipped to deal with the novel analytical techniques that have been developed to investigate the coupling. Great care has therefore been taken to discuss underlying fluid mechanical and acoustic concepts, and to explain as fully as possible the steps in a complicated derivation.

A considerable number of practical problems occur at low Mach numbers (say, less than about 0.4). It seems reasonable, therefore, to confine an introductory discussion specifically to low Mach number flows. It is then possible to investigate a number of idealized hydrodynamic flows involving elementary distributions of vorticity adjacent to solid boundaries, and to analyze in detail the sound produced by these vortex–surface interactions. For a broad range of such problems, and a corresponding broad range of noise problems encountered in industrial applications, the effective acoustic sources turn out to be localized to one or more regions that are small compared to the acoustic wavelength.

The Acoustic Analogy

The sound generated by turbulence in an unbounded fluid is usually called aerodynamic sound. Most unsteady flows of technological interest are of high Reynolds number and turbulent, and the acoustic radiation is a very small byproduct of the motion. The turbulence is usually produced by fluid motion over a solid boundary or by flow instability. Lighthill (1952) transformed the Navier–Stokes and continuity equations to form an exact, inhomogeneous wave equation whose source terms are important only within the turbulent region. He argued that sound is a very small component of the whole motion and that, once generated, its back-reaction on the main flow can usually be ignored. The properties of the unsteady flow in the source region may then be determined by neglecting the production and propagation of the sound, a reasonable approximation if the Mach number M is small, and there are many important flows where the hypothesis is obviously correct, and where the theory leads to unambiguous predictions of the sound.

Lighthill was initially interested in solving the problem, illustrated in Fig. 2.1.1a, of the sound produced by a turbulent nozzle flow. However, his original theory actually applies to the simpler situation shown in Fig. 2.1.1b, in which the sound is imagined to be generated by a finite region of rotational flow in an unbounded fluid. This avoids complications caused by the presence of the nozzle.