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Tracing rays through the Earth • Ray parameter p: receiv er source i1 sin i1 = sin i2= …= sin in = const. = p V1 V2 Vn ⇒ p is constant for a given ray V1 i2 V2 i3 V3 i4 V4 i c ritical • If V increases continuously with depth ⇒ the ray flattens and eventually bends upwards until critical refraction is reached critical ref raction receiv er source Velocity increases continuously with depth 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 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 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. Wave propagation in the Earth P S K I J c i a P-wave in the mantle an S-wave in the mantle a P-wave through the outer core a P-wave through the inner core an S-wave through the inner core a reflection from the CMB a reflection from the OCB-ICB • A classic black and white picture…. 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, http://www.geol.binghamton.edu/faculty/jones/ ) 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 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. 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 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 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 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 Continental Crust • Continental crust – stable continents average thickness 3540 km – under young mountains, 50-60 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 The Mantle • • • Upper limit = Moho Lower limit = CMB (core-mantle boundary) Layers: – – – – – – – rigid upper lid low-velocity layer (LVL) transition zone – 220-410 km transition zone – 410-670 km transition zone – 670-770 km D’ D’’ Upper Mantle • Upper mantle: – spherical symmetry does not hold well due to lateral variations – peridotites with olivine as dominant mineral – Moho to 80-120 km – rigid lid • paired with lower crust ⇒ lithosphere – layer that participates in plate tectonics – 120-220 (+/- 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) – 400-660 km: phase change, β-spinel → γ-spinel – 650-670 km: discontinuity, velocity increase (γ-spinel → perovskite) Lower Mantle • Lower mantle – Everything below 670 km – Composition poorly known • oxides of Fe, Mg, Fe-Mg silicates with perovskite structure – 670-770 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 • 150-200 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? The Core • Gutenberg, 1914: – Shadow zone for P-waves (105143 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 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) 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 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)