# Tracing rays through the Earth

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1 Tracing rays through the Earth Ray parameter p: source receiv er i 1 V 1 sin i 1 = sin i 2 = = sin i n = const. = p V 1 V 2 V n p is constant for a given ray i 2 i 3 i 4 V 2 V 3 V 4 i critical If V increases continuously with depth the ray flattens and eventually bends upwards until critical refraction is reached source Velocity increases continuously with depth critical ref raction receiv er

2 Tracing rays through the Earth If we know the variation in seismic velocity with depth, given the ray parameter p, we can: Determine the ray trajectory Determine the ray travel time Repeating this for all possible take-off angles graph of travel time versus distance

3 Velocity-depth structure In general: We do not know the velocity variation with depth We measure the travel time (from epicenter to seismic station) Inverse problem to get velocity at deepest point on the ray path (using a large number of travel time observations) sin i = Vdt R sin i = dt RdΔ V dδ

4 Velocity-depth structure Applied to the Earth: Major discontinuities in the seismic structure of the Earth discontinuities in mineralogy/petrology Moho, 410 km, 660 km, D, CMB IASP91 model (below), PREM (Preliminary Reference Earth Model) These models assume perfect spherical symmetry.

5 Wave propagation in the Earth P a P-wave in the mantle S an S-wave in the mantle K a P-wave through the outer core I a P-wave through the inner core J an S-wave through the inner core c a reflection from the CMB i a reflection from the OCB-ICB A classic black and white picture.

6 Wave propagation in the Earth The travel-time of waves to a given epicentral distance is affected by the focal depth of the earthquake, up to several hundred kilometers. Most t vs. Δ curves assume: - a perfectly spherical Earth - same vertical structure underneath each location Works fairly well, but lateral velocity variations exist leads to seismic tomography A more dynamic view of wave propagation in the Earth :seismic wave animation (seiswave.exe, )

7 Seismic tomography Spherical symmetry not perfectly valid: There are lateral variations of seismic velocities Travel time deviations in comparison to theoretical calculated values Travel-time residuals or anomalies Causes for anomalies: - focal depth of earthquake not zero - local velocity-depth distribution under a particular network - spherical symmetry not perfectly valid due to Earth s ellipticity Travel times can be classified as early or late depending on whether the wave passes through a slow or fast region On global scale, anomalies interpreted in terms of temperature and rigidity slow or warm regions above average temperature and lower rigidity fast or cold regions below average temperature and higher rigidity

8 Tomographic Imaging Using travel time information from many stations reconstruction of 2D and 3D velocity structures Various scales: Global Regional Local 3D view of the mantle, with orange surfaces surrounding warm blobs of mantle, assumed to be rising plumes.

9 Tomographic Imaging Can be done using body waves or surface waves Inversion of body-waves data only method to view lateral variations in velocity in deep interior Velocities in lithosphere correspond to plate movement, lower mantle corresponds to long wavelength features

10 Crust and crust-mantle boundary Mohorovicic, 1909: Close to epicenter: single P-wave arrival (Pg) Beyond ~200 km from epicenter: Pg was overtaken by another P-wave arrival (Pn) which traveled faster Pg = direct wave, propagates in the crust (5.6 km/s) Pn = refracted wave (head wave), propagates through the upper mantle (7.9 km/s) Estimated there was an increase in velocity at 54 km depth Mohorovicic discontinuity = Moho

11 Earth s Crust Strong lateral variations in crust, can t use inversion of body wave travel-times to get velocities (why?) can use seismic refraction profiles and deep crustal reflection sounding On a global scale, crustal thickness is variable Continental vs. oceanic crust global average is 33 km Variation of velocity with depth depends on location ancient continental crust very different than young continental or oceanic crust

12 Oceanic Crust Oceanic crust averages 5-10 km under average water depth of 4.5 km Layers oceanic sediments increase in thickness away from ridges igneous basement thin upper layer of basaltic lava flows over a complex of basaltic intrusions gabbroic rocks Oceanic crust

13 Continental Crust Continental crust stable continents average thickness km under young mountains, km thick much more complicated than oceanic Layers crustal sediments upper crust basement (granitic) seismic discontinuity (not everywhere) sialic low velocity layer laccolithic intrusions? middle crust (migmatites) lower crust (amphibolites/granulites) has a high velocity upper layer Continental crust

14 The Mantle Upper limit = Moho Lower limit = CMB (core-mantle boundary) Layers: rigid upper lid low-velocity layer (LVL) transition zone km transition zone km transition zone km D D

15 Upper Mantle Upper mantle: spherical symmetry does not hold well due to lateral variations peridotites with olivine as dominant mineral Moho to km rigid lid paired with lower crust lithosphere layer that participates in plate tectonics (+/- 30) km = low velocity zone attenuation (viscosity) = asthenosphere body waves do not bottom out in LVZ, must use long-period surface waves layer is not sharply defined 400 km: discontinuity, velocity increase (petrological change, olivine spinel phase transition) km: phase change, β-spinel γ-spinel km: discontinuity, velocity increase (γ-spinel perovskite)

16 Lower Mantle Lower mantle Everything below 670 km Composition poorly known oxides of Fe, Mg, Fe-Mg silicates with perovskite structure km: high, positive velocity gradient D layer: most of the lower, normal mantle smooth velocity gradients no seismic discontinuities D layer: thin layer just above core-mantle boundary km thick lateral variations of velocity (positive and negative): fast regions below subductions (positive) slow regions below ocean, i.e. Pacific Basin (small or negative) Source of mantle plumes?

17 The Core Gutenberg, 1914: Shadow zone for P-waves ( degrees) Core-mantle boundary = 2900 km Gutenberg discontinuity Mostly iron, + up to 10% nickel Lehman, 1936: Weak P-wave arrivals within shadow zone Inner core with higher velocities solid Liquid-inner core boundary = 5000 km Core Outer = liquid Viscosity ~ water Source of the Earth s magnetic field Inner = solid

18 Seismic anisotropy Definition - dependence of seismic velocity on direction a seismic wave travels through a crystal seismic waves traveling parallel to the a-axis of an olivine crystal travel faster than waves traveling perpendicular to the a-axis Mantle flow aligns the olivine crystals with the a axes parallel to the flow measuring anisotropy will tell flow direction: horizontal flow (shields) or vertical flow (MOR) Lower mantle mostly isotropic but D layer locally anisotropic (currently under investigation)

19 Anisotropy of the Core Inner core is anisotropic may be due to inner core flow aligning the iron crystals like olivine in the mantle velocities 2-4% higher than expected symmetry about the axis that is approx. aligned with Earth s N-S spin axis can measure this by travel times of body waves paths parallel to spin axis are fastest Repeated measurements of P-waves through inner and outer core position of inner core s fast axis has moved w.r.t. to crust and mantle over last 3 decades Core movement is a rotation inner core rotating faster than rest of the Earth several tenths of a degree/year complete revolution would take centuries

20 What have we learned? As waves propagate, they can undergo: Reflection Refraction (special case of critical refraction) Snell s law applies ray-tracing Using the propagation of seismic waves in the Earth, one can show that: The structure of the Earth has a spherical symmetry There are major discontinuities in seismic velocities in vertical direction, lateral variations give rise to seismic anisotropy and direction of flow These discontinuities separate layers (shells) of ~homogeneous petrological composition Crust (granite basalts/dolerite/gabbros) Mantle, with LVZ = asthenosphere (peridotite) Liquid outer core (Earth s magnetic field), iron (+ nickel) Solid inner core, iron (+ nickel)

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