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Structure of Earth as imaged by seismic waves crust upper mantle transition zone lower mantle core-mantle boundary D”, core-mantle boundary layer outer core inner core 2000 4000 km radius of earth = 6371 km 6000 8000 10,000 12,000 Seismic waves involve stress, strain, and density Two important types of stresses and strains: Pressure, P and volume change per unit volume, DV/V Shear stress and shear strain For linear elasticity, Hooke’s law applies: stress = elastic_constant x strain For elastic waves, two elastic constants are key: DP modulus of incompressibility DV / V shear stress modulus of rigidity shear strain density And density of the material, = mass/volume Two types of elastic waves Compressional or P waves involve volume change and shear Shear or S waves involve only shear Click on these links to see particle motions: P wave particle motions S wave particle motions Elastic wave velocities determined by material properties 4 3 P wave velocity V p S wave velocity Vs epicenter Earth surface expanding wavefront at some instant of time after earthquake occurrence ray perpendicular to wavefront seismograph station Earth center epicenter tt(D) = total travel time along ray from earthquake to station Earth surface ray D = epicentral distance in degrees D Earth center seismograph station Globally recorded earthquakes during the past 40 years earthquake depth 0-33 km 33-70 70-300 300-700 Partial map of modern global seismograph network time, minutes 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees click on link to P and S phases in the earth PKIKP ScS PcS PcP These lines represent plus or minus one minute errors in reading arrival times Nomenclature for seismic body phases P wave segments in blue S wave segments in red P or S mantle K outer core I or J inner core c = reflection at core mantle boundary i = reflection at inner core-outer core boundary Single path refracted through mantle S P seismic wave source Inner core Outer core Mantle time, minutes 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. S P These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees Single reflection at surface PP Inner core Outer core Mantle SS time, minutes 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees Single reflection at core-mantle boundary PcP reflection Single reflection at core-mantle boundary ScS Single reflection with conversion of P to S PcS time, minutes 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. ScS PcS PcP These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees P in mantle, refracting to P in the outer core (K) and out through the mantle as P P K P PKP P segments in mantle, P segments in outer core (K), and P segment in inner core (I) PKIKP P K I K P time, minutes 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. PKIKP These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees S in mantle, refracting and converting to P in outer core, then refracting back out and converting back to S in the mantle SKS S K S S in mantle, refracting and converting to P in outer core, P reflects once at inner side of core-mantle boundary, then refracting back out back with conversion to S in the mantle S reflection K K S SKKS time, minutes 2,538,185 travel time observations from International Seismological Centre (ISC), for earthquakes with depths between “0” and 60 km. These are the commonly reported phases as reported to the ISC from seismograph stations from around the world; see phase types on next page distance, degrees Compressional (P) and Shear (S) wave velocities, Vp and Vs depth 0 0 1 2 3 4 seismic wave velocity 5 6 7 8 9 10 km/sec upper mantle transition zone 1000 km lower mantle 2000 D’’ layer 3000 4000 outer core 5000 6000 7000 inner core 11 12 13 14 From Vp and Vs to seismic parameter Vp Vs 4 3 2 4 2 V p 3 Vs ( R ) DP modulus of incompressibility DV / V shear stress modulus of rigidity shear strain density (R) = "seismic parameter" derived from Vp(R) and Vs(R) For self compression of homogeneous material (R) = / = - dP/(dV/V) = dP/(d/) d/dR = -/g dP = - g dR where R = radius to a point in the earth, and g = gravitational acceleration at that radius g = GMR/R2 where MR = mass within sphere of radius R For self compression of homogeneous material d/dR = -/g This is the gradient in density determined by the seismic wave velocities. To obtain density, one must integrate by fixing the density, , and gravity, g, at the top of the layer and calculating both and g as one proceeds downwards. The calculation assumes a simple compression of material that does not change chemistry or phase. the compression as one goes deeper produces an adiabatic temperature increase. For self compression of homogeneous material d/dR = -/g The method is applied to the following layers: upper mantle lower mantle outer core inner core To determine the jumps in density between these layers, the following constraints are used: Mass of earth Moment of Inertia of Earth Periods of free oscillations of Earth Density, 0 0 2000 4000 6000 kg/m3 8000 10000 1000 km depth, km 2000 3000 4000 5000 6000 core-mantle boundary 12000 14000 Gravitational acceleration, g 0 2 4 m/s2 0 1000 km depth, km 2000 3000 4000 5000 6000 core-mantle boundary 6 8 10 12 Pressure, P 0 0 50 100 150 200 GPa. 250 300 1000 km depth, km 2000 3000 4000 5000 6000 core-mantle boundary 350 400 Density vrs pressure 14000 12000 kg/m3 10000 8000 6000 4000 2000 0 0 50 100 150 200 GPa. 250 300 350 400 Density vrs pressure Inner core/outer core boundary 14000 liquid to solid 12000 core-mantle boundary kg/m3 composition change 10000 phase changes 8000 6000 4000 mantle density 2000 crustal density 0 0 50 100 150 200 GPa. 250 300 350 400 chemical stratification and differentiation basaltic-granitic crust phase changes Mg(Fe) silicates fluid, 90% iron solidified iron 2000 4000 km 6000 8000 10,000 12,000 Earth’s convective systems cool, strong lithospheric boundary layer slowly convecting mantle: plate tectonic engine core-mantle thermo-chemical boundary layer rapidly convecting outer core: geomagnetic dynamo solid inner core 2000 4000 km 6000 8000 10,000 12,000 Temperature in mantle 0 Temperature, degrees C 2000 3000 4000 1000 5000 conductive heat flow upper mantle near surface thermal boundary layer = lithosphere transition zone mantle convection advective heat flow lower mantle D” CMB outer core conductive heat flow iron melting ? D” = Lower mantle thermo-chemical boundary layer Temperature profile through entire earth Mantle convection, hot spots and plumes Lowrie, Fundamentals of Geophysics, Fig. 6.26 abstract Average P-wave velocity perturbation in the lowermost 1000 km of the mantle Generation of Earth’s magnetic field in the outer core mantle outer core The geomagnetic dynamo: • turbulent fluid convection • electrically conducting fluid • fluid flow-electromagnetic interactions • effects of rotation of earth inner core Geomagnetic field