Whats seismology about Seismology is the study of

What’s seismology about? • Seismology is the study of the generation, propagation and recording of elastic waves in the Earth (and other celestial bodies) and of the sources that produce them.

Elastic Moduli • • • Young’s Modulus Poisson Ratio Bulk Modulus Shear Modulus Lamb’s constants Vp, Vs.

s = tensile stress = (F /A) e = tensional strain = (DL /L) … for uniaxial tension or compression Young’s modulus s E= e

s = tensile stress = (F /A) e = tensional strain = (DL /L) … for uniaxial tension or compression Young’s modulus s E= e

Under a stress (sxx) along the x-axis, DL longitudinal strain = exx = L and transverse strain = eyy = Then, DW W Poisson’s ratio = - (eyy / exx)

Bulk Modulus = (DP/Q) … where and Q = dilatation = DV/V P = pressure

A L shear stress = (DF /A) shear strain = (Dl /L) shear modulus m shear stress = shear strain

Elastic Moduli and Densities of Some Common Materials From Lay & Wallace (1995)

From Lay & Wallace (1995)

Vp = a = Vs = b = K + (4/3)m = r l + 2 m r Where m, l are the Lamé coefficients and l is l = k - 2 m 3 E = (1+n n ) ( 1 - 2 n )

Body Waves compressions P-wave dilatations S-wavelength am plit ude

Body wave Amp ~ 1/x Surface wave Amp ~ x-1/2

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Body Waves compressions P-wave dilatations S-wavelength am plit ude

Seismic Rays & Geometric Ray Theory • • Rays are defined as the normal to the wave fronts and thus point in the direction of propagation. Connecting these successive directions forms a ray paths. In the case of plane wave, rays are a family of straight lines; in the case of spherical wave, rays are spokes radiating out from the seismic source. They provide a convenient means of tracking an expanding wave front. The seismic rays corresponding to P and S waves behave very much as light does in traveling through materials of varying indices of refraction. This leads to many parallels with optics: rays bend, focus, and defocus depending on the velocity distribution. Although geometric ray theory is an approximation, it, however, simplifies the analysis and yet gives the correct answer or a good approximation.

Fermat’s Principle • Ray paths between two points are those for which travel time is an extremum, either a minimum or maximum, with respect to the nearby possible paths.

Snell’s Law and Fermat Principle Snell’s Law Fermat Principle: T(x) is either minimum or maximum

Reynolds (1997)

Spherical Ray Parameter R sin i V = constant = p

What control reflection and transmission? • Continuity of stress • Continuity of displacement

I 1 = I 2 = Reynolds (1997)