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Home , Geophysics, Seismology, S wave

Observational

Lecture 3 Seismic Rays and Structure

GNH7/GG09/GEOL4002 SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology

First seismologists were just interested in earthquake themselves. Modern seismology starts in 1883 when proposed that could be recorded at teleseismic stations 1889 von Rebeur Paschwitz recorded Tokyo earthquake at Potsdam

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology 2

1897 First breakthrough in determining when Oldham identified: Large waves Preliminary tremor

Secondary tremor

T Large Milne realised the significance and used travel time difference to locate Preliminary earthquakes → global earthquakes ∆

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology 3 1900 Oldham – P & S tremors travelled through the interior of the Earth while large waves propagated close of the surface 1906 Oldham – made the big leap forward and supplied the seismological evidence that the Earth has a central core 1909 Mohorovicic use the same argument of a discontinuity in the travel time curve to identify the To do better required a method of calculating wave velocity from travel time curve more accurately: 1907 & 1910 Herglotz, Wiechert Bateman inversion

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology 4

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology 5

1914 Gutenberg calculated depth of as 2900km or 0.545R

Solid 103 outer core

Shear wave

Present estimates of core depth are within a few km

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology 6

1936 Lehman discovered the Earth’s inner core

103 Found reflected 143 from inner core in P wave “shadow zone” Lehman used a geometric argument, but both Gutenberg and Jeffreys within 2 years had independently calculations of PKP rays to verify hypothesis

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology 7

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Jeffreys-Bullen Travel-Time Diagrams

Plots of travel times of teleseismic rays against epicentral distance ∆ provides the basic observational data base: Jeffreys-Bullen travel-time diagram for earthquake phases (1940). Direct P LQ Direct S LR

Travel time – from source to station, but depends on , refraction and diffraction.

Surface wave plots of T vs ∆ are straight lines due to constant velocity along path. Body wave plots of T vs ∆ are curves because velocity changes with depth.

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Jeffreys-Bullen Travel-Time Diagrams

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Ray Parameter Definition r sin i / v = constant = p Ray Parameter Constant, irrespective of local wave speed Definition: The ray parameter is the geometric property of a seismic ray that remains constant throughout its path. It is invariant in transmission, reflection, refraction and transformation. It is equal to r sin i / v. If the ray parameter is different we are talking about a different ray. The consequence of Snell’s Law (i), that the refracted ray lies in the plane containing the incident ray and the normal to the plane tangent to the interface, implies, in spherically symmetric media, that it lies in a diametral plane (one that contains the centre of the sphere).

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Wave transformation

Wave transformation is unique to seismology. Nothing like it occurs to sound, light or water waves. It is a consequence of elastic waves crossing boundaries in solid media. Refracted S Hitting a boundary with an incident P will cause the at the point of incidence to be not only compressed but also sheared. Refracted P

Likewise when SV hits a boundary obliquely get reflected and refracted P and Reflected P SV. When SH hits boundary obliquely only get reflected and refracted SH. When P is Incident P normal incident only get reflected and Reflected S refracted P. Several transformations can occur on one path leading to a complicated picture. This complexity can actually be turned to our advantage.

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic Rays in the Earth

PKP Refracted PcP Reflected off through the core core

dif P PcP PcS

PP pP Reflected off surface

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Deep earthquakes

Deeper earthquakes > 100km observed

Benioff zones

x Earthquakes cluster on plane x dipping away from axis x x xx

Obtain accurate depths from surface reflection of seismic waves Deep: phase pP separation seen at x sP teleseismic station P Shallow

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic Rays in the Earth 2

PPrimary wave S Secondary wave K P wave through outer core I P wave through inner core J through inner core P’ Abbreviation for PKP PP Reflected P wave with 2 legs SSS Reflected S wave with 3 legs pP P wave with leg from focus to sS S wave with leg from focus surface to surface SP S wave reflected as P wave PS P wave reflected as S wave

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic Rays in the Earth 3 c Wave reflected at outside boundary of outer core (e.g., ScS) i Wave reflected at outside boundary of inner core (e.g., PKiKP) m No. of reflections inside the outer boundary of outer core is m-1 d Depth in km from which a seismic ray is reflected h Wave that may be reflected from a discontinuity around inner core dif P,S Diffracted P or S waves around outer core LQ Love waves LR Rayleigh waves

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic Rays in the Earth 4

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Jeffreys-Bullen Travel-Time Diagrams

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD How do we determine Earth structure from seismology?

Our basic observational data are travel times for epicentral distance

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD P & S velocities from Travel Times

Jeffreys & Gutenberg PREM

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Rock

Once we have velocity profile we can deduce other physical properties.

P wave velocity (from rock physics)

1/ 2 K adiabatic bulk modulus α ⎛ 4 ⎞ S K S + µ. = ⎜ 3 ⎟ µ ⎜ ρ ⎟ ⎝ ⎠ ρ density of materials

For mathematical convenience we define the Lamé parameters λ, µ:

λ = KS –2/3. µ so, α λ 1/ 2 ⎛ + 2µ ⎞ = ⎜ ⎟ ⎝ ρ ⎠

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Rock physics 2

S wave velocity 1/ 2 β ⎛µ ⎞ = ⎜ ⎟ ⎝ ρ ⎠

For a Poisson solidα λ = µ by definition (actually a good approximation), then λ β (( + 2µ )/ )1/ 2 = ρ ()µ / ρ 1/ 2 i.e., α / β = √3 = 1.73 for Poisson solid P waves are just over 1½ times as fast as S waves a useful guide

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Rock physics 3 have no µ = 0 so β = √(µ/ρ) = 0

Solid rocks have undergone compaction due to overburden & therefore have greater densities, bulk modulus and shear modulus.

As KS & µ increase more rapidly with depth than ρ, so generally α, β generally increase with depth (i.e., KS/ρ & µ/ρ both increase with depth)

Example KS µ Granite 2.7x1010 N/m2 1.6x1010 N/m2 surface 3.0x1010 N/m2 at 10km Water 0.2x1010 N/m2 0 Granite α ~ 5.5 km/s Water α ~ 1.5 km/s β ~ 3 km/s β ~ 0 km/s

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Earth Models (Bullen)

From seismology we know α, β so we know K/ρ & µ/ρ What we don’t know is how Earth density varies with depth. This we can be found by an iterative process using the Adams- Williamson equation, derived from Newton’s Law of Gravitation. Must satisfy known Earth’s mass and moment of . Input from experimental rock physics/, computer simulations, known composition of universe/meteorites.

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Earth Models 3 (Bullen)

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Earth Models 4

Bullen shells

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Review

What makes seismology difficult? 1) Have to deal with P & S waves, Rayleigh and Love waves. (Other phases: Stoneley waves and T phases would be covered in advanced seismology.) 2) Earth is spherical, so have to introduce radius into ray parameter. 3) Earth is a complex structure – velocity varies with depth; discontinuities. 4) Physics of waves in solid media is complicated by transformations, e.g., P → P + SV. However this very complexity necessitates the use of seismology in determining Earth structure. Seismology has the highest resolution of any of our geophysical probes in mapping out Earth structure and composition.

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Review 2

Seismology has had the biggest impact of any discipline on the Earth and is predominant in . • Because of these complexities seismology is difficult. • Jeffreys: “If geophysics requires mathematics for its treatment it is the Earth that is responsible, not the geophysicist” [1924]. • The maths is horrendous, but the physics is accessible (lectures 3 & 4): 1) The physics of waves – particle motion, reflection, refraction and transformation. 2) Their ray paths and what that means in terms of Earth structure. GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD