3 Seismic Rays Earth Structure - ucl.ac.uk Seismic Rays Earth Structure.pdfGNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology 3 1900 Oldham – P

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

Observational Seismology

Lecture 3Seismic Rays and Earth Structure


History of Seismology

First seismologists were just interested in earthquake themselves.

Modern seismology starts in 1883 when John Milne proposed that earthquakes could be recorded at teleseismic stations

1889 von Rebeur Paschwitz recorded Tokyo earthquake at Potsdam


History of Seismology 2

1897 First breakthrough in determining Earth structure when Oldham identified:

Preliminary tremor

Secondary tremor

Large waves

T

∆

Preliminary

LargeMilne realised the significance and used travel time difference to locate earthquakes → global earthquakes


History of Seismology 31900 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 crust

To do better required a method of calculating wave velocity from travel time curve more accurately:

1907 & 1910 Herglotz, Wiechert Bateman inversion





Shear wave shadow zone

Solid mantle

Liquid outer core

1914 Gutenberg calculated depth of the core as 2900km or 0.545R

Present estimates of core depth are within a few km

103



1936 Lehman discovered the Earth’s inner core

Lehman used a geometric argument, but both Gutenberg and Jeffreys within 2 years had independently calculations of PKP rays to verify hypothesis

103

143Found P wave reflected from inner core in P wave “shadow zone”




Jeffreys-Bullen Travel-Time Diagrams

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

Direct P LQ Love wave

Direct S LR Rayleigh wave

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).

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.




Ray Parameter Definition

r sin i / v = constant = p Ray ParameterConstant, 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).


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 P

Incident P

Hitting a boundary with an incident P will cause the rock at the point of incidence to be not only compressed but also sheared.

Reflected P

Reflected S

Refracted S

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


Seismic Rays in the Earth

PKP Refracted through the core

PcP Reflected off core

dif P PcPPcS

pPPP

Reflected off surface


Deep earthquakes

Deeper earthquakes > 100km observed

Benioff zones

Earthquakes cluster on plane dipping away from trench axis

xx x xxx

Obtain accurate depths from surface reflection of seismic waves

x sPpP

P

Deep: phase separation seen at teleseismic station

Shallow


Seismic Rays in the Earth 2

P Primary wave

K P wave through outer core

I P wave through inner core

P’ Abbreviation for PKP

PP Reflected P wave with 2 legs

pP P wave with leg from focus to surface

SP S wave reflected as P wave

S Secondary wave

J S wave through inner core

SSS Reflected S wave with 3 legs

sS S wave with leg from focus to surface

PS P wave reflected as S wave



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






How do we determine Earth structure from seismology?

Our basic observational data are travel times for epicentral distance


P & S velocities from Travel Times

PREMJeffreys & Gutenberg


Rock physicsOnce we have velocity profile we can deduce other physical properties.

P wave velocity (from rock physics)

2/1.3

4

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ +=

ρ

µα

SKKS adiabatic bulk modulus

µ shear modulus

ρ density of materials

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

λ = KS – 2/3. µ so,2/1

2⎟⎟⎠

⎞⎜⎜⎝

⎛ +=

ρµλα


Rock physics 2S wave velocity

2/1

⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρµβ

For a Poisson solid λ = µ by definition (actually a good approximation), then

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

( )( )( ) 2/1

2/1

//2

ρµρµλ

βα +=


Rock physics 3Liquids have no shear strength

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, βgenerally increase with depth (i.e., KS/ρ & µ/ρ both increase with depth)

00.2x1010 N/m2Waterat 10km3.0x1010 N/m2

surface1.6x1010 N/m22.7x1010 N/m2GraniteµKSExample

Granite α ~ 5.5 km/s Water α ~ 1.5 km/s β ~ 3 km/s β ~ 0 km/s


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 inertia.

Input from experimental rock physics/mineral physics, computer simulations, known composition of universe/meteorites.


Earth Models 3(Bullen)


Earth Models 4

Bullen shells


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 advancedseismology.)

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 seismologyin determining Earth structure. Seismology has the highest resolution of any of our geophysical probes in mapping out Earth structure and composition.


Review 2

Seismology has had the biggest impact of any discipline on the Earth sciences and is predominant in geophysics.• 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.

Documents

3 Seismic Rays Earth Structure - ucl.ac.uk Seismic Rays Earth Structure.pdfGNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD History of Seismology 3 1900 Oldham – P