dt dδ = r 0 sin i 0 V 0 = P
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Locating Local Earthquakes - Systematic change is S-P time is the basis to do so Distance ---->
AT LOCAL DISTANCES - FOR SINGLE STATION - the difference in the P arrival and the S arrival at the station can give you the distance the waves traveled. rearranges to t s t p = Dis tan ce β Distan ce α t s t p = Dis tan ce ( 1 β 1 α ) Distan ce = Assume µ = λ -> β= α/(sqrt3) α= sqrt3 *β and p-wave velocity is 5.km/s Distan ce = D = t s t p ( 1 β 1 α ) t s t p 3 1 α D(km) = (t s t p ) km / s P-wave S-wave α=sqrt(λ+2µ/ρ) β=sqrt(µ/ρ) Elastic moduli µ= measure of materials resistance to shear σij = 2µεij ν= measure of radial to axial strain ε 11 = ε 22/ ε 11 ν = λ 2(λ+µ) ν = ~.25 in earth slope
Local Earthquake - Determining WHEN (origin time) earthquake initiated -- WADATI DIAGRAMS 4 x β x α slope = x α slope = α β 1, S-P Time 3 2 1 Origin Time 0 47 4 4 50 51 52 P-Arrival Times (secs) Knowing origin time and arrival time and velocity at which wave travels, we can determine distance to the earthquake as well. ( P i OT) α = D i
Map View to illustrate epicenter determination With previous, triangulation can be used To determine EPICENTER And FOCAL DEPTH Radius = (P-OT) α Cross Section to illustrate focal depth determination Station STA 2 distance Δ STA 1 STA 3 Epicenter x Epicenter Di=(P-OT) α focal depth d Focal depth = sqrt (D 2 -Δ 2 ) X 1/2 focal depth = (D2+Δ 2) Hypocenter
Locating Earthquakes in a Spherical Earth 1. Observe P and S arrival times at many stations 2. Assume Preliminary epicenter, depth, and origin time 3. Then calculate predicted travel time t i and distance D i for each recording station for assumed location and origin time. 4. Now, using assumed origin time and actual arrival times with travel time curves to calculate separate estimate of distance to each station from the epicenter. 5. Because assumed epicenter is wrong - finite differences will exist and these differences will be function of azimuth 6. Similarly for origin time - the meanof errors will be offset from zero. 7. Iteratively adjusting location and origin time to reduce errors leads to best estimate of location and origin time. Actual Location Eo 30 20 10 0-10 -20 7 D-Di ^ 1 2 10 6 5 1 Az(E) 2 E, the 3 Assumed Location 7 Az(E) 0 10 270 6 360 3 5 4 4 10 1
Depth is best determined for teleseisms by examination of depth phases surface 2h cos I i 2h P-wave i h=depth pp wave i focus ΔT pp = 2hcosi P-wave
Depth is best determined for teleseisms by examination of depth phases
Magnitude - Local Distances - The Richter Scale Richter made the important observation
1 2 3
Bigger earthquake Smaller earthquake Reference earthquake
Amplitude of Reference Earthquake = -2.76 Log(Distance) + 2.4
Distance in kilometers Amplitude in microns D
Limitations on Richters magnitude scale Limited to use with particular short-period seismic instrument (Wood-Anderson) Radiation pattern not considered Site specific - same in LA as in New York? Today we refer to scale as Local Magnitude - or M L
Magnitude at Regional and Teleseismic Distances Body Wave magnitude m b Measured from peak amplitude of P-waves at regional and teleseismic distances Taken as peak ground motion of P-waveform recorded on short-period instruments with natural periods of T<3s and peak response at ~1s! m = log a b " T # $ +Q ( h, Δ )
! m = log a b " T # $ +Q ( h, Δ ) Earth Structure ------------> leads to need of correction factor 2 Depth 3 Distance Estimates of body wave magnitude will vary by ±.3 magnitude units between stations
Surface Wave Magnitude Ms Most prominent waves recorded on seismograms at teleseismic distances are long-period surface waves Body waves show lesser amplitude because they experience greater geometrical spreading Because of earth structure - attenuation is generally minimum for 20s period waves. M s = log a +1.66 log Δ + 2.0 * Valid only for events less than about 60km depth - because production of surface waves is a function of depth.
All magnitude scales are empirical. Usually a magnitude M is determined from and amplitude A and the period T of certain type of seismic waves through a formula which contains several constants. These constants are dtermined in such a way that the magnitudes on the new scale agree with those of an existing one, at least over a certain magnitude range. Historically, calibrations have commonly been done for best fits of Ms to ML were done around ML=6, but there is no a priori reason for the scales to agree completely over a large range. M 7 M L vs M s M L vs M s Gutenberg and Richter (156) Kanamori and Jennings (17) M vs M s x m B m b 6 5 M L m B 4 3 3 4 5 6 7 10 M s
Magnitude Saturation.. Earthquakes emanate a spectrum of many frequencies A Different frequencies characterized by different amplitudes Energy spectrum is generally flat at long periods and decays toward shorter periods/higher frequencies. Decay is result of finiteness of fault source and destructive interference of higher frequency waves. B It is this fact that results in the largest surface amplitudes recorded from surface waves to saturate at about 7.5 while the largest body wave magnitudes to saturate at about 5.5. C
Magnitude Saturation.. Earthquakes emanate a spectrum of many frequencies A Different frequencies characterized by different amplitudes Energy spectrum is generally flat at long periods and decays toward shorter periods/higher frequencies. Decay is result of finiteness of fault source and destructive interference of higher frequency waves. B It is this fact that results in the largest surface amplitudes recorded from surface waves to saturate at about 7.5 while the largest body wave magnitudes to saturate at about 5.5. C
Measures of magnitude are not measures of size not energy Measures of magnitude are not coupled to any physical parameter that describes the earthquake source (note - equations are not even dimensionally correct). Gutenberg and Richter considered the energy contained in a passing seismic wave to calculate a relationship between magnitude and energy log E = 5. + 2.4M b log E = 11. +1.5M s A one-unit increase in Ms results in 32-fold increase in energy release
IX. Earthquake Size - Intensity Isosesimal Distribution for Earthquake A 10 10 10 10 Isosesimal Distribution for Earthquake 5 10 General panic. Masonry D destroyed; masonry C heavily damaged, sometimes with complete collapse; masonry B seriously damaged. General damage to foundations. Frame Structurs, if not bolted shifted off foundatins. Frames racked. Serous damage to reservoirs. Underground pipes broken. Conspcuous cracks in ground. In alluviaed areas, sand and mud ejected, earthquake fountains, sand craters. X. Most masonry and frame structures destroyed with their fondatins. Some well-built wooden structures and bridges destroyed. Serious damage to dams, dikes, embankments. XI. XII. Large landslides. Water thrown on banks of cnals, rivers, lakes, etc. Sand and mud shifted horizontally on beaches and flat land. Rails bent slightly Rails bent greatly. Underground pipellines completely out of service Damage nearly total. Large rock masses displaced. Lines of sight and level distorted. Objects thrown into the air. 10 10 10 Modified Mercalli Intensity I. Not felt. Marginal and long-period effects of large earthquakes II. Felt by persons at rest, on upper floors, or favorably placed III. Felt indoors.hanging objects wing. Vibration like passing of light trucks. Duration estimated. May not be recognized as an earthquake IV. Hanging objects swing. Vibration like passing of heavy trucks; or sensation of a jolt like a heavby ball strikin the walls. Standing cars rock. Windows, dishes, doors rattle. Glassesclink. Crockery clashes. In the upper range of IV, wooden walls and frame creek. V. Felt outdoors; direction estimated. Sleepers asakened. Liquids disturbed, some spiled. Small unstable objects dispaced or upset. Doors swing, close, open. Shutter, pictures move. Pendulum clocks VI. VII. stop, start, change rate. Felt by all. Many frightened and run outdoors. Persons walk unsteadily. Windows, dishes, glassware broken. Knickknacks, books, etc., off shelves. Pictures off walls.furnituere moved or overtuned. Weak plaster and masonry D cracked. Small bells ring (church, school). Trees, bushes shaken visibly, or heard to rustle. Difficult to stand. Noticed by drivers. Hangin objects quiver.furniture broken. Damage to masonry D., including cracks. Weak chimneys broken at roof lin. Fall of plaster, loose bricks, stones, tiles, cornices, also unbraced parapets and architectural ornaments. Some cracks in masonry C. Waves on ponds, water turbid with mud. Small slides and caving in along sand or gravel banks. Large bells reing. Concrete irrigation ditches damaged. VIII. Steering of cars affected. Damage to masonry C; partial collapse. Some damage to masonry B; none to masonry A. Fall of stucco and some masonry walls. Twisting, fall of chimneys, factory stacks, monuments, towers, elevated tanks. Frame houses moved on foundation if not bolted down; loose panel walls thrown out. Decayed piling broken off. Branches broken from trees. Changes in flow or temperature of springs and wells.cracks in wet ground and on steep slopes.
Keep in mind Intensity is a convolution of ground shaking and types of construction. Construction practices vary widely leading to different intensity scales Ground shaking will be function of size or strength of earthquake however it is measured e.g. magnitude type of seismic wave generated radiation pattern depth of earthquake distance of earthquake local site response e.g. geology Observations synthesized by isoseismal maps.
Collecting intensity data for which the size has been determined from instrumental recording allows regressions to be made between earthquake size and felt area which can then be used to make estimates of the size of older historical earthquakes that occurred before seismic instruments were developed.
SEISMIC MOMENT A Like magnitude, it may be determined from the measurement of instrumentally recorded seismic waves. But, it it may also be related directly to physical parameters that describe the earthquake source. M o = µu A = shear modulus (rigidity) x average slip on fault x fault area (length x width) B Units of energy Does not saturate C
the displacement field due to a shear dislocation can be given by the displacement field due to a distribution of equivalent double couples that are placed in the medium without any dislocation ξ 3 (a) ξ 1 ξ 3 (b) ξ 1 U r = U θ = U φ = M 4πµr 2 F r(µ, λ )sin 2 θ sin 2φ M 4πµr 2 F θ (µ,λ)sin2θ sin2φ M 4πµr 2 F φ (µ,λ)sin θ cos2φ
U FP Far-field radiation pattern of P-wave and S-wave for shear dislocation 1 1 ( x,t) = 4πρα 3 r M 0 % t r ' & α ( sin2θ cosφ r ˆ U FS ( x, t) = 1 1 4πρβ 3 r M 0 %, t r ' & β( cos2θ cosφ ˆ θ cosθ sinφφ ˆ [ ] fault normal auxiliary plane Θ=0 fault plane slip vector 2-52 2-53
fault normal auxiliary plane Θ=0 fault plane slip vector 2-52 2-53