Geology 5640/6640Introduction to Seismology

12 Jan 2015

© A.R. Lowry 2015Read for Wed 14 Jan: S&W 29-52 (§2.1-2.3)

Last time: Course overview

Seismology is used as a tool to investigate:

• Seismic sources: Earthquake physics, magma transfer in volcanic systems, “icequakes”, storms, nuclear test verification, …

• Seismic velocity & impedance structure: Seismic reflection imaging (oil & gas industry), site investigation (construction, environmental, hydro resources), virtually all fundamental research into processes in the Earth’s interior

SourcePulse

Seismogram

Source

Medium

Receiver

Origintime

Traveltime

Arrivaltime

A seismogram is a time-record of motion of an inertial mass…

… that contains information about the source, Earth response, and seismometer response.

(After S&WFig. 1.1-1)

11 km/s

8-10 km/s

8-14 km/s

Most of what we know about the Earth’s interior comes from seismology.

And not justEarth!Apollo-eraseismic datademonstratethe lunar interior has similaritiesto Earth’s…

How to use these powerpoints:

• Review them often: Before each class, while doing exercises, and in preparing your projects

• The most important points of each lecture (in my opinion) are summarized on the first slide of the next lecture

• Note the notation! Arial Black, italic means Important, pay attention… Arial Black, italic, red font means Critically Important concept or terminology that I expect you to understand intimately for exercises and projects Times New Roman, italic, black font means this is an equation or an algebraic variable

A Red Box with Grey Background means this is an especially important concept or equation

Seismology (A brief review ofthings you “already know”)

Four Types of Seismic Waves:

(1) P (primary) wave (Velocity Vp = 4 to 14 km/s)

(2) S (secondary) wave (Vs = 2/5 to 3/5 Vp, or 0)

(3) Surface Waves (Love, Rayleigh) V slightly < Vs

(4) Normal Modes (Resonant “Tones”, like a bell…) continue for months after largest earthquakes periods of hours or days “standing waves”

Body Waves}

P

S

Surface (Love)

Surface (Rayleigh)

Seismic waves are strain wavesthat propagate in a medium…

Common analogies use ripples in a pond, or light. There aresimilarities in that all three are described by the wave equation.Ripples & seismic waves similarly involve stress & displacements that propagate as individual particles in themedium oscillate between potential and kinetic energy states…

But, a major difference is rheology. Stress, displacement &strain in a solid continuum are governed by Hooke’s Law.

Despite differences, similarities inherent in the wave equation many important principles can be borrowed from optics.

One of these is Huygen’s Principle:

Every point on a wavefront can be treated as a point source for the next generation of wavelets. The wavefront at a timet later is a surfacetangent to thefurthest point oneach of thesewavelets. This isbecause extremalpoints of propagationhave the greatest constructiveinterference…

Another is Fermat’s Principle (or the principle ofleast time):

The propagation path (or raypath) between any two pointsis that for which travel-time is the least of all possible paths.

(Here a ray is the normal to a wavefront at any given time):

A key principle because most of our applications will involvea localized source and observation at a point (seismometer).

•

•

V = fast V = slow

least time in slow

least time in fast

Fermat’s principle leads to Snell’s Law:

Travel-time is minimized whenwhen the ratio of sines of theangle of incidence (anglefrom the normal) to a velocity boundary is equal to the ratio of the velocities, i.e.,

straight line

least time

€

sinθ1

sinθ2

=V1

V2

Aboriginal spear-fishers understand Snell’s law intuitively, after learning to always aim below the visual location of the fish!

Important terminology: Refractions are transmitted rays that bend at a change in medium; Reflections are bounces off an interface that remain within the original medium.

Refraction

Reflection

Reflections & Refractions:

Consider that when a seismic wave meets a layer boundarybetween solid media with different velocities V (= f = /T),• Energy E must be conserved• Stress must be continuous (i.e. the same on both sides)• Displacement u must be continuousThis is achieved by “partitioning” the energy between reflections & refractions, and in most cases by convertingpart of the energy from one type of wave to the other!

incoming P

reflected Preflected Srefracted P

refracted S