ATENUACIÓN ATENUACIÓN INTRÍNSECA ¿Qué es atenuación? ¿Cómo describimos la atenuación? ¿Cuáles son las causas de la atenuación? ¿Cómo podemos estimar la atenuación? ¿Dónde en la tierra vemos la atenuación? CAMBIOS EN LA AMPLITUD DE ONDAS CAUSADOS POR: • Difusión geométrica (geometric spreading) - el frente de onda se expande y la energía se extiende sobre una área más grande (o más pequeña) y la amplitud de la onda se disminuye (aumenta). • Esparcimiento (scattering) • - la onda interactúa con cuerpos más pequeños de la longitud de onda, con velocidad de onda diferente que el medio circundante y se esparce. • Atenuación intrínseca (intrinsic attenuation) • - el movimiento de la onda activa procesos que convierten la energía de la onda a otras formas de energía (calor), por fricción interna (internal friction). • En este clase nos enfocamos en la atenuación intrínseca. DESCRIPCIÓN DE ATENUACIÓN OSCILADOR ARMÓNICO AMORTIGUADO OAA (DAMPED HARMONIC OSCILLATOR) • Para analizar el comportamiento de un sistema amortiguado mecánico, simple, estudiamos el OAA. La ecuación de movimiento (balance de fuerzas) γ - factor de amortiguamiento k ↓ u(t) Vamos a ver que es útil usar las siguientes variables m Q - factor de calidad DESCRIPCIÓN DE ATENUACIÓN OSCILADOR ARMÓNICO AMORTIGUADO OAA (DAMPED HARMONIC OSCILLATOR) • Supongo una solución en la forma k ↓ u(t) • Solución: m término oscilatorio término decaimiento • Los dos términos contienen Q!! Stein & Wysession ATENUACIÓN - FACTOR DE CALIDAD, Q (QUALITY FACTOR) Usamos el factor de calidad para describir el decaimiento de la amplitud de un movimiento oscilatorio ¿Cómo entender Q? Q-1 describe la relación entre la parte imaginaria y real de la frecuencia (1) (2) (3) e-folding time Q es proporcional al tiempo necesario para bajar la amplitud al valor 1/e de la amplitud original número de ciclos para bajar la amplitud a 4% de la amplitud original ATENUACIÓN - FACTOR DE CALIDAD EN SISMOLOGÍA, Q (QUALITY FACTOR) CUIDADO! En sismología usamos Q para describir el decaimiento de las ondas, pero también para describir el medio, Qα y Qβ o QK y Qμ El factor de calidad de corte Qμ es mucho menor que el factor de calidad volumétrico QK. Los factores de calidad de ondas P y de ondas S ambos dependen del factor de calidad de corte. El factor de calidad de ondas P es más de dos veces el factor de calidad de ondas S. Q-1K << Q-1μ OPERADOR DE ATENUACIÓN - T* Para simular atenuación para ondas de cuerpo podemos convolucionar sínteticos calculados sin atenuación con la función en la figura a la derecha. Esta función se llama operador de atenuación. Parametrizado con t* = t/Q, t = tiempo de viaje En la Tierra, para ondas de cuerpo de periodos más de 1 segundo: tα* = 1 seg y tβ* = 4 seg. ATENUACIÓN LA DEPENDENCIA DE FRECUENCIA (FREQUENCY DEPENDENCE) OBSERVACIÓN: Q casi constante sobre un rango grande de frecuencias. ¿Cómo puede ser? Misterio!! ¿el factor de amortiguamiento depende de frecuencia? ATENUACIÓN - DISPERSIÓN FÍSICA (PHYSICAL DISPERSION) Dispersión física - significa que la velocidad de ondas depende de la frecuencia Ejemplo: Una función delta viajando en un medio con velocidad de onda c. En el dominio de frecuencia: Sin dispersión, la amplitud disminuye con distancia y con constante Q la atenuación depende fuertemente de la frecuencia. El cambio de amplitud con distancia es A(w): con t=x/c Solución: ? non-causal ATENUACIÓN - DISPERSIÓN FÍSICA (PHYSICAL DISPERSION) ¡Dispersión física es necesaria para conservar causalidad! Una solución (La ley de atenuación de Azimi): Para una onda vertical de ScS, el tiempo de viaje es 5 segundos más para T = 40 segundos que de T = 1 segundo. Causa discrepancia entre modelos de ondas de cuerpo y los de modos normales, si no es tomado en cuenta. REPASO: OSCILADOR ARMÓNICO AMORTIGUADO FORZADO (Forced damped harmonic oscillator) Oscilador forzado con frecuencia ω Solución de prueba: Solución: CAUSAS DE LA ATENUACIÓN MODELOS FÍSICOS DE ANELASTICIDAD Banda de absorción: Respuesta del “standard linear solid” de una deformación armónica, con frecuencia w La atenuación: La velocidad: τ = η/k2 “Relaxation time constant” “Standard linear solid” CAUSAS DE LA ATENUACIÓN MODELOS FÍSICOS DE ANELASTICIDAD Q casi constante sobre un rango grande de frecuencias. ¿Cómo puede ser? Por la superposición de bandas de absorción de diferentes mecanismos. (?) CAUSAS DE ATENUACIÓN PROCESOS MICROSCÓPICOS • Thermally Activated Processes: Processes that are more effective with increasing temperature and follow (τ - relaxation time, E* - activation energy, R - Gas constant): τ=τ0 eE*/RT • Diffusion creep: Deformation of crystalline solids by the diffusion of vacancies through their crystal lattice • Dislocation creep: Involves the movement of dislocations through the crystal lattice • Grain boundary mobility: se mueve la frontera entre granos • Partial melting: very effective in lowering Q, even for small melt fractions • Grain boundary friction: if the material is not completely glued together, the motion can cause grains sliding against each other, resulting in friction. Rango sísmico IMPACTO DE ALGUNOS VARIABLES EN LA ATENUACIÓN Y LA VELOCIDAD DE ONDA • Temperatura: La temperatura más alta aumenta la atenuación y disminuye las velocidades de onda. • Composición: La atenuación no tiene mucha sensibilidad, pero las velocidades de onda sí. • Fusión parcial: Fusión parcial aumenta la atenuación de corte (Q-1β) y disminuyen las velocidades. • Contenido de agua: Contenido de agua aumenta mucho la atenuación pero no tiene un gran impacto en las velocidades de onda. • Tamaño de granos: Algunos procesos de atenuación son más eficientes en las fronteras entre granos, y por eso la atenuación disminuye cuando el tamaño de granos aumenta. e to thoseto in displacement (Figure 2). Signal-to-noise erted bally [Eiler et 2.1. Calculating t* h-temperature tios (SNRs) were determined using the noise [ ] The spectra of P and S waveforms from local ght occur in events recorded by theaTUCAN array were anapectra calculated from 3-s window before each . Thus, taken lyzed using the vertical and transverse components, geophysical, the signals. COMO EVALUAMOS ATENUACIÓN respectively, following the method of Stachnik et reater hydra- nd magmas. 13 al. [2004]. P and S arrivals were picked on waveform time series [Syracuse et al., 2008], then multitaper spectra [Park et al., 1987] were calculated in 3-s windows, starting 0.5 s before the arrival, corrected for instrument gain, and converted to displacement (Figure 2). Signal-to-noise ratios (SNRs) were determined using the noise spectra calculated from a 3-s window before each of the signals. 3 ONDAS DE CUERPO - T* Geochemistry Geophysics Geosystems Geochemistry Geophysics Geosystems G3 4an ] along-arc Path-averaged attenuation was parameterized G rychert et al.: attenuation beneath nicaragua and costa rica rychert et al.: attenuation beneath nicaragua and costa rica 10.1029/2008GC002040 10.1029/2008GC002040 terms of an attenuation operator, t* = t/Q, for avel time t assuming a displacement spectrum (f ) as follows: rc changes in ay also play a esses. Preving-arc varia1990, 2003, ket al., i 1994; , 2005]. In port of mand [Herrstrom 1; Hoernle et dge material has a longer plate and a [14] Path-averaged attenuation was parameterized * in terms of an attenuation operator, t* = t/Q, for2 jk =ð1 þ Ajktravel ðfi Þ time ¼ Ctjkassuming M0k e$pfa i tdisplacement ðfspectrum i =fck Þ Þ Ajk(fi) as follows: ð1Þ .g., Anderson and Hough,* =ð11984] for the kth event A ðf Þ ¼ C M e þ ðf =f Þ Þ ð1Þ corded at[e.g., theAnderson jth station for each frequency (fi), and Hough, 1984] for the kth event for greater at the jth station for each frequency (f ),frequencyis a constant accounting for here wedge,C the jk(r)recorded where C (r) is a constant accounting for frequencyd magmatic dependent effectseffects of ofeach path, independent each path, such assuch geome- as geomevariations in trical spreading, free surface interaction, and the ith a greater ical spreading, free ofsurface and the spherical average the radiation interaction, pattern [Aki and n Costa Rica, Richards, 1980]. M /(1 + (f /f ) ) is a simple pressures of average pherical of the radiation pattern [Aki and source spectrum [Brune, 1970] where M and f gua as well 2 are the seismic moment and (f corner frequency, /(1 + /f ) )corner is a simple ichards, M muir et al., 1980]. 0k i ck allowing a different seismic moment and t al., 2008]. ource spectrum [Brune, 1970] where M0k and fck 5 of 26 e the seismic moment and corner frequency, lowing a different seismic and corner Rychert moment et al 2008 jk i jk 0k $pfi tjk i ck 2 i jk 0k i ck 2 0k ck Figure 2. Waveform and spectrum examples. (a, b, e, f) Waveforms and (c, d, g, h) corresponding spectra of both the P wave 2a– 2d)spectrum and the examples. S wave (Figures 2h) are compared station in the forespectra arc, MANS Figure 2. (Figures Waveform and (a, b, e, 2e– f) Waveforms and (c, d,at g,a h) corresponding of both (Figures 2a, 2c, 2e, and2a 2g), andand a station the back arc, B4 2d, 2f, and The hypocenter theMANS event the P wave (Figures – 2d) the Sinwave (Figures 2e (Figures – 2h) are2b, compared at a2h). station in the fore of arc, was at 1092a,km i.e., the arc, slab,B4 beneath the2b, arc2d, near Rica line of theofTUCAN (Figures 2c,depth, 2e, and10.6!N, 2g), and$84.8!W, a station in theinback (Figures 2f, the andCosta 2h). The hypocenter the event array. In 109 the waveform the $84.8!W, blue lines represent signal, and the redthe lines are Rica the picks on the the TUCAN signals. was at km depth, plots 10.6!N, i.e., in thetheslab, beneath thedashed arc near Costa line of Inarray. the spectrum plots, blue lines spectra,the redsignal, lines represent noise, red andlines cyanare lines fitting In the waveform plots therepresent blue linesthe represent and the dashed theshow picksthe on best the signals. spectra from the t* inversions. Green vertical delimit the frequencies that are the inversion In the spectrum plots, blue lines represent thelines spectra, red lines represent noise, andused cyaninlines show the for bestt*. fitting spectra from the t* inversions. Green vertical lines delimit the frequencies that are used in the inversion for t*. frequency for the P and S wave of each earthquake. The equation wasPrearranged the earthquake. following frequency for the and S waveinto of each [Stachnik et al., 2004]. Equation (2) was then solved for aetsingle corner frequency and was moment [Stachnik al., 2004]. Equation (2) then the source and receiver. We argue in the Appendix that integrating along the great circle path instead of the true ray path is valid for the length scales in which we are interested. [10] The perturbation in phase velocity, dc/c0(w), is expanded in spherical harmonics, she stud And COMO EVALUAMOS ATENUACIÓN X X dc ðw; q; fÞ ¼ C ðwÞY ðq; fÞ; ONDAS DE cSUPERFICIE wh ð4Þ k(r lm lm sen 0 l¼0 m¼&l B05317 DALTON AND EKSTRÖM: SURFACE (Fig where Ylm(q, f) are the fully normalized surface spherical obt the effect maximum harmonics degree l 2000]. and order Selby and of Woodhouse, Here,m,weLtreat on c is this freq are the resu degree of the phase expansion, and Cray amplitude using an velocity expression from linearized theory, lm(w) coefficients to be determined. The focusing depends linearly [1 dcj0 dcj 1 onlnthe AF ðwphase Þ ¼ velocity, ðwÞ þ Dand ðwÞ we þ write cosec D ith 2c0 2c0 2 Z D sim ! dc Lc • Se l usa que las ondas de superficie disminuyen su X& cosðD & 2fÞ' ðwÞdf; ð3Þ sinðD & fÞX sin f@ % ln A ðwÞ ¼ C ðwÞF ; c ð5Þ amplitud con distancia, where D is the epicentral distance, f is the along-path coordinate, q is the path-perpendicular coordinate, dc/c is debido a la atenuación. where F represents theinimplementation of equation the relative perturbation surface wave phase velocity, (3) andin 0 i;j F Lc l2 q lm i;j lm 0 l¼0 m¼&l i,j lm • • A(ω) = AS(ω) AI(ω) AF(ω) AQ(ω) 0 spherical pathvelocity connecting the ithatearthdcjD indicatefor thethe phase perturbation the dcj0 and harmonics quake and the jth receiver. source and receiver, respectively [Dahlen and Tromp, 11] The effect of attenuation on the modified wave amplitude, AQ, [1998]. This expression is slightly from the is original expressed oneasprovided by Woodhouse and Wong [1986], as wh ave var it includes a term "with sensitivity to the phase velocity# at the Z w receiver. The wave amplitude due&1 to focusing depends A dQ ðw; q; fÞdsðq; fÞ ; ð6Þ Q ðwÞ ¼ exp & primarily on the second 2U ðderivative wÞ path of velocity perpendicular to the ray path. Waves traveling through a low-velocity wh trough are focused and amplified, and therespectively, opposite is true where q and f are latitude and longitude, U(w) dQ& l for propagation along a channel of fast velocity. Implicit in is group velocity, and dQ&1(w, q, f) is the perturbation in [1 equation (3) is the assumption of an infinite frequency wave Figur surface wave attenuation away from the value predicted by atte Dalton al 2006 that does not deviate from the et great circle path connecting &1 funda (w, q, f) is related to PREM. Surface wave attenuation Q qua the source and receiver. We argue in the Appendix &1 that shear (r, ray q, f) tion theintegrating Earth’s intrinsic bulk attenuation, Qm true along theshear greatand circle path instead of the &1 study. (S - source, I - receiver, F- geometric spreading, Q - attenuation) plane. Figure 1, from Geller and Stein (1977), shows the spectra of the spheroidal 400 ' r'l' ' _oS: '1' 300 COMO EVALUAMOS ATENUACIÓN MODOS NORMALES 14_ ÷2 200 I I c o7 o -2 0+2 IO0 I i J i i 00180 00185 00190 Frequency, cycles/rain 200 ' ' ' ' _oS3 o +a I00 - 5 ~ • • Se usa que los modos normales disminuyen su amplitud con tiempo, debido a la atenuación. Para modos radiales podemos ajustar (“fit”) el logaritmo de la amplitud, A(t), a una línea recta. • Difícil porque la división de los modos causa pulsación, menos para los modos radiales que no tienen división (“splitting”). • Q para el modo fundamental radial 0S0 es 5700 (!), 1S0 - 2000, 1S0 - 1200 ] ' ' ' -5. ' I ' ' I /I +i 0 A II +5 I llll -2 0+2 - ATTENUATION M E A S U R E M E N T S - - C H I L E A N AND ALASKAN EARTHQUAKES C i i i i I I i i i i i 1597 i The solution for the modes and Geller, 1977) is obtained 0 0 2amplitudes 75 0 0of 2 8split 0 0 0 2(Stein 85 by transforming the spherical expansion F r eharmonic quency, c y c l e s / r a m of the excitation from the frame of reference of the source into geographic singlet amplitudes FIG. 1. Split spheroidal mode spectra for 0S2coordinates. (top) and 0SaThe (bottom) excited by the are Chilean earthquake, written so there are separate factors for source (latitude separation and longitude), as observed onthat a strainmeter at Isabella, California. Thelocation Eigenfrequency is taken from Dahlen source fault frequency geometry has (strike, and slip direction), location, and peaks. Synthetic (1968), but depth, the central beendip, chosen to yield a best receiver fit with the observed relative spectra for the finite of Kanamori and Cipar (1974) are given for each mode. The the normalized energy of fault each geometry mode. amplitudes normalized and plotted with regular spacing. For a are spheroidal or torsional multiplet and for a step function dislocation with multiplets 0,92 and by the Chilean earthquake, as observed on a strain0S2 0Ss excited T=53.8 min, meter (strike 38.4 W of N) at Isabella, California by Benioff et al. (1961). The singlet pair with m = _+1 has much larger amplitudes than the rest of the o,92multiplet and, similarly, 0S3-+2 stands out from its multiplet. We also show synthetic relative spectral amplitudes computed for the finite fault and long-period precursor determined by Kanamori and Cipar (1974} from long-period surface waves. The spectral amplitudes do not depend on the precise frequency separation, so for convenience the theoretical amplitudes are plotted with regular spacing. L 0 L , L , i 50 L L hr i , I I00 , i i , I 150 FIG. 2. Data and synthetics for 0S2. The top trace is filtered (tide-removed) data from the first 150 hr of Isabella strain record of the Chilean earthquake. The lower trace is the synthetic seismogram, including the effects of splitting. The synthetic was tapered and filtered in the same way as the data. unit moment, the displacement or strain component, summing over modes with angular order 1 and azimuthal order m, is given to zeroeth order by MODELOS GLOBALES DE ATENUACIÓN PREM •Q en un modelo esférico: • alto en la corteza • bajo en el manto superior • bajo en el núcleo interno MODELOS GLOBALES DE ATENUACIÓN (DE ONDAS SUPERFICIALES) • Una 162 correlación entre anomalías en atenuación (1/Q) y velocidad. B09303 C.A. Dalton, U.H. Faul / Lithos 120 (2010) 160–172 QRFSI12 S362ANI 100 km -0.010 -0.005 DALTON ET AL.: GLOBAL UPPER-MANTLE ATTENUATION 0.000 0.005 dQ-1 B09303 0.010 -6 -4 -2 0 2 4 6 dv/v (%) 400 km -0.005 0.000 0.005 dQ-1 -2 0 2 dv/v (%) Fig. 1. Comparison global andGTR1 shear-velocity (right) models at 100-km and 400-km depth. The attenuation model QRFSI12 is plotted as the deviation awa Figure 5. Regionally averaged attenuation profiles forof the sixshear-attenuation tectonic regions (left) of the −1 1 regionalization scheme. (a) Results correspond to the reference model 1 ofat Figure 4. (b)1-D Results from the globally averaged Q value each depth; Q− is 0.0126 and 0.00577 at 100 and 400 km, respectively. Isotropic velocity from model S362ANI (Kustowski et al., 2008 μ μ correspond to reference model 2 of Figure 4. is shown here expanded in spherical harmonics up to degree 12. decrease in attenuation down to !450 km. Strong radial two regions, although the absolute Q"1 values of our study gradients in attenuation are penalized by the regularization slightly lower than in the earlier At 150 km,arethe old-continental pointswork. maintain a shallower-than- sufficient for oceanic regions at 100-km depth and continenta glob (sph from 0.05 be a the 0.04 poin loca 0.03 and A 0.02 exp than 0.01 regi resp 0 of t 800 900 1000 1100 1200 1300 1400 1500 1600 C.A. Dalton, U.H. Faul / Lithos 120 (2010) 160–172 con oC) Temperature ( gen (a) 5 poin (c) 0.08anomalously high-velocity points are generally associated oceanic crust older than 70 Myr and old-continental areas. adjo At 150 km (Fig. 5), almost all of the oceanic points fall withi con 0.07 loca experimental range, with only ∼25% of the young-oceanic p 4.8 characterized by lower-than-experimental velocities and/orocea lo 0.06 loca than-experimental attenuation. In contrast, 72% of the old-contin equ 4.6 points have larger velocity and/or higher attenuation than cenw 0.05 experimental range. This trend persists at 200-km depth, tion ∼50% of old-continental points fall to the right of the experim 4.4 A 0.04 range while nearly all of the oceanic points are located within beca experimental range. At 250 km, a handful of old-continental p you 0.03 (15%) are located to the right of the range, but the vast majority 4.2 200 points agree with the mineral-physics model. Paci 0.02 At 100 km, outliers located to the left of the experimental rang Ridg almost all located along the global mid-ocean-ridge system. Th 4 exp 0.01 especially true for the East Pacific Rise, the Pacific Antarctic Ridge, an Southeast Indian Ridge. Areas of the Mid-Atlantic Ridge near the A 0 hotspot and centered on the equator also exhibit anomalously 3.8 3.8 4 4.2 4.4 4.6 4.8 800 900 1000 1100 1200 1300 1400 1500 1600 velocity and/or low attenuation. Small clusters of5 these points ca C.A. Dalton, U.H. Faul / Lithos 120 (2010) 160–172 o Fig. 2 Velocity (km/s) Temperature ( C) found in the northeastern Pacific and centered on the Red Sea.100Ben the oceans, outliers located to the right of the experimental betw 100 km (b) 150 km (b)(a) 0.08 comprise much of the western Atlantic, offshore Africa, and the and nor 0.025 0.025 value data central Pacific. Some of the anomalously high-velocity/high-attenu curv 1mm, V=12 points that are adjacent to continental areas could result from sme 0.07 1cm, V=12 the e 5cm, V=12 of the continental properties into the oceanic regions, given tha 0.02 0.02 1mm, V=20 global models used for this analysis have a relatively coarse resol 0.06 1cm, V=20 (spherical-harmonic degree 12). However, many of the outliers a 5cm, V=20 oceans < 70 my from any continental region (e.g., the central Pacific) and are not lik 0.05 oceans > 70 my 0.015 0.015 be artefacts. Within the old continents, 84% of the points are locat old continents the right of the experimental range. The remaining 16% of old-contin 0.04 points that fall within or to the left of the experiments are gen located adjacent to tectonically younger provinces, as is the case for E 0.01 0.01 0.03 and Sudan, which are adjacent to the Red Sea, and for southeast Ch At 150 km, almost all outliers located to the right of 0.02 experimental range (i.e., higher velocity and/or higher attenu 0.005 0.005 than the mineral-physics model) are found within old-contin 0.01 regions: only 1.3% and 8.1% of young and old oceanic reg respectively, fall to the right of the experimental trend, whereas 0 0 0 the old-continental points do. As is the case for 100 km, the of 4.2 4.3 4.4 4.5 4.6 4.7 4.8 800 900 4.210004.311004.412004.513004.614004.715004.81600 continental pointsVelocity that fall within the experimental range oC) Velocity ((km/s) (km/s) Temperature generally adjacent to tectonically younger areas. The few oc points 200 km (d) 250 kmwith values to the right of the experimental range almo (c)(c) 0.08 0.025 0.025 adjoin an old continent, perhaps indicating some smearing o continental seismic properties into the nearby ocean basins. Ou 0.07 located to the left of the experimental trends are found most oceanic regions b70 Myr. As with 100 km, many of these point 0.02 0.02 0.06 located near the East Pacific Rise, Pacific Antarctic Ridge, equatorial Mid-Atlantic Ridge. Iceland, the eastern Pacific, and Attenuation (1/Q) 0.06 • Hay diferencia entre océanos jóvenes, océanos viejos y continentes viejos. Attenuation (1/Q) (a) comparación entre los experimentos y los modelos globales. 164 Attenuation (1/Q) • Velocity (km/s) Experimentos con olivino seco en un rango de frecuencias, temperaturas y tamaño de granos (a-c) Attenuation (1/Q) • Attenuation (1/Q) MODELOS GLOBALES DE ATENUACIÓN Dalton & Faul 2010 MODELOS GLOBALES DE ATENUACIÓN C.A. Dalton, U.H. Faul / Lithos 120 (2010) 160–172 (b) after dispersion correction • Océanos: “melt squirt”, no “grain boundary sliding”. • Continentes: composición diferente, empobrecido hasta 200km de profundidad. 0.025 0.025 0.02 0.02 Attenuation (1/Q) Los puntos afuera del rango de los experimentos están en las dorsales oceánicas jóvenes y en las partes más viejos de la litósfera. Attenuation (1/Q) (a) 100 km • 0.015 0.01 0.005 0 165 0.015 0.01 0.005 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Velocity (km/s) 0 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Velocity (km/s) Fig. 4. (a) Identifying seismological shear velocity and attenuation points that fall inside and outside of the range defined by the mineral-physics model of Faul and Jackson (2005). The experimental range is shown by the green polygon and includes the velocity and attenuation values predicted for a range of grain sizes and activation volumes (see Fig. 3). Grey points are located within the experimental range, red points fall to the left of the range and blue points to the right. The map shows the geographical location of all points. Triangles indicate old-continental points, squares indicate oceanic regions b 70 Myr, and circles show oceanic regions N70 Myr. For a depth of 100 km. (b) Estimated changes in velocity as a result of corrections for laterally variable anelastic dispersion. Coloring of points and position of polygon are same as in a. Period = 75 s assumed for the calculations. discussion of the northeastern and central Pacific and old oceanic seafloor to a subsequent publication. We recognize that the mineral-physics model may not be appropriate for the upper mantle, given the conditions of the experiments from which it was derived (e.g., Jackson et al., 2002). For example, experimental grain size and pressure are too small, requiring extrap- could be studied. Also, the experiments were performed only on samples of pure olivine; effects related to the coexistence of olivine with other mineral phases (e.g., Sundberg and Cooper, 2007) and majorelement compositional variations were not considered. However, these experiments represent the best quantitative laboratory constraints currently available and offer an opportunity for direct comparison with Dalton & Faul 2010 MODELOS REGIONALES DE ATENUACIÓN UNA ZONA DE SUBDUCCIÓN G Geochemistry Geophysics Geosystems • Xenolitos muestran un manto con más agua, y más fusión. • Restringido - Q-1 no negativo. • No toman en cuenta multitrayectoria. 3 rychert et al.: attenuation beneath nicaragua and costa rica 10.1029/2008GC002040 Figure 1. Map of the study region. Shading indicates topography. The black line with triangles marks the trench. Red triangles mark volcanoes. Yellow circles mark the Tomography Under Costa Rica and Nicaragua (TUCAN) broadband seismic array. White and black inverted triangles mark permanent stations. White circles mark Seismogenic Zone Experiment (SEIZE) array. Slab contours are shown with blue line. Black dashed line traces the Quesada Sharp Contortion (QSC) [Protti et al., 1995]. Purple arrow denotes direction of increases in geochemical indicators of water content and degree and depth of melting [Plank and Langmuir, 1988; 1993; Leeman et al., 1994; Reagan et al., 1994; Roggensack et al., 1997; Patino et al., 2000; Carr et al., 2003; Kelley et al., 2006; Sadofsky et al., 2008]. Rychert et al 2008 MODELOS REGIONALES DE ATENUACIÓN UNA ZONA DE SUBDUCCIÓN • Más atenuación en Nicaragua. • La fusión en Nicaragua ocurre en condiciones más hidratadas, y en un área más grande y a profundidades más grandes. • Después de corregir los valores de atenuación por contenido de agua, obtienen temperaturas similares entre las dos regiones, o, la atenuación abajo de Nicaragua es dominada por el contenido de agua, no por la temperatura. Figure 5. Attenuation results. Results of (a – b) unconstrained inversion of P wave data for P attenuation, (c – d) unconstrained inversion of S data for shear attenuation, (e –f) unconstrained joint inversion of P and S wave data for bulk and shear attenuation (shear attenuation is shown), (g– h) constrained inversion of P and S wave data for shear and bulk attenuation (shear attenuation is shown), and (i– j) unconstrained inversion of P and S wave data for shear and bulk attenuation where damping parameters permit bulk attenuation in the crust and mantle (bulk attenuation is shown). Constrained inversions enforce nonnegativity in QS!1. Green line represents resolution = 0.4. Yellow circles indicate seismicity. Red inverted triangles mark station locations. Green triangles mark volcanoes. The projection width is 50 km on either side of the cross-section line. Figure 5. Attenuation 11 results. of 26 Results of (a – b) unconstrained inversion of P wave data for P attenuation, (c – d) unconstrained inversion of S data for shear attenuation, (e –f) unconstrained joint inversion of P and S wave data for ATENUACIÓN INTRÍNSECA ¿Qué es atenuación? ¿Cómo describimos la atenuación? ¿Cuáles son las causas de la atenuación? ¿Cómo podemos estimar la atenuación? ¿Dónde en la tierra vemos la atenuación?