atenuaciÓnusuarios.geofisica.unam.mx/vala/cursos/sismologia...descripciÓn de atenuaciÓn -...

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)

γ - factor de amortiguamiento

↓ u(t)

k

m

⇒

• Para analizar el comportamiento de un sistema amortiguado mecánico, simple, estudiamos el OAA.

La ecuación de movimiento (balance de fuerzas)

Vamos a ver que es útil usar las siguientes variables

Q - factor de calidad

DESCRIPCIÓN DE ATENUACIÓN - OSCILADOR ARMÓNICO AMORTIGUADO OAA (DAMPED HARMONIC OSCILLATOR)

• Supongo una solución en la forma

Stein & Wysession

término oscilatoriotérmino decaimiento

• Solución:

↓ u(t)

k

m

• Los dos términos contienen Q!!

(3)

ATENUACIÓN - FACTOR DE CALIDAD, Q (QUALITY FACTOR)

Q es proporcional al tiempo necesario para bajar la amplitud al valor 1/e de la amplitud original

Q-1 describe la relación entre la parte imaginaria y real de la frecuencia

Usamos el factor de calidad para describir el decaimiento de la amplitud de un movimiento oscilatorio

e-folding time

¿Cómo entender Q?

(1)

(2)

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

⇒

Q-1K << Q-1μ

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.

⇒

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.

?non-causal

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):

En el dominio de frecuencia:

con t=x/cSolución:

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 “Standard linear solid”

“Relaxation time constant”

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.

COMO EVALUAMOS ATENUACIÓN -ONDAS DE CUERPO - T*

frequency for the P and S wave of each earthquake.The equation was rearranged into the followingform:

ln!Ajk!fi"" # ln!1# !fi=fck"2" $ ln!Cjk!r"" % ln!M0k" $ pfit*jk!2"

[Stachnik et al., 2004]. Equation (2) was thensolved for a single corner frequency and momentfor each event and an attenuation operator for eachevent-station pair, for both P and S waveforms.Since the problem is nonlinear, the equation was

Figure 2. Waveform and spectrum examples. (a, b, e, f) Waveforms and (c, d, g, h) corresponding spectra of boththe P wave (Figures 2a–2d) and the S wave (Figures 2e–2h) are compared at a station in the fore arc, MANS(Figures 2a, 2c, 2e, and 2g), and a station in the back arc, B4 (Figures 2b, 2d, 2f, and 2h). The hypocenter of the eventwas at 109 km depth, 10.6!N, $84.8!W, i.e., in the slab, beneath the arc near the Costa Rica line of the TUCANarray. In the waveform plots the blue lines represent the signal, and the dashed red lines are the picks on the signals.In the spectrum plots, blue lines represent the spectra, red lines represent noise, and cyan lines show the best fittingspectra from the t* inversions. Green vertical lines delimit the frequencies that are used in the inversion for t*.

GeochemistryGeophysicsGeosystems G3G3 rychert et al.: attenuation beneath nicaragua and costa rica 10.1029/2008GC002040

6 of 26

predicts higher water contents in the mantle onaverage beneath Nicaragua than beneath Costa Rica.

[9] While our understanding of the distribution ofwater in Central American magmas is still devel-oping, other evidence points to greater and/ordeeper hydration of the subducting plate beneathNicaragua. This includes deep normal faultsobserved in the Cocos plate before it subducts[Ranero et al., 2003], low crust and mantle veloc-ities in the subducting plate seaward of the trenchconsistent with 12–17% mantle serpentinization[Ivandic et al., 2008], an unusually thick lowvelocity layer sensed by body waves trapped nearthe slab-wedge interface [Abers et al., 2003], and amantle-penetrating low velocity layer indicative of10–20% serpentine constrained by body wavetomography with TUCAN array data [Syracuse etal., 2008]. Such geophysical evidence for deeperhydration of the Nicaraguan slab is also consistentwith the anomalously low d18O values that arefound in Nicaraguan olivines, relative to those inCosta Rica or any other arc olivine globally [Eiler etal., 2005]. Such low values require high-temperaturehydrothermal reactions such as might occur indeeper regions of the subducting plate. Thus, takentogether, the trace element, isotopic, geophysical,and preliminary H2O data point to a greater hydra-tion of the Nicaraguan slab, mantle, and magmas.

[10] In addition to what appears to be an along-arcvariation in water input, other along-arc changes inslab and wedge physical conditions may also play arole in dehydration and melting processes. Previ-ously considered factors include along-arc varia-tions in slab dip [e.g., Carr et al., 1990, 2003,2007] and temperature [e.g., Leeman et al., 1994;Chan et al., 1999; Peacock et al., 2005]. Inaddition, northwestern along-arc transport of man-tle wedge material has been proposed [Herrstromet al., 1995; Abratis and Woerner, 2001; Hoernle etal., 2008] which could produce wedge materialbeneath northwestern Nicaragua that has a longerhistory of interaction with the Cocos plate and astronger slab signature.

[11] Despite the preceding evidence for greaterhydration in the Nicaraguan mantle wedge, thelink between volatile abundance and magmaticproductivity is unclear. Along-arc variations inCa, Na, Fe, and Si are consistent with a greaterdegree of melting in Nicaragua than in Costa Rica,and some evidence exists for greater pressures ofmelt equilibration beneath Nicaragua as well[Plank and Langmuir, 1988; Langmuir et al.,1992; Carr et al., 2003; Sadofsky et al., 2008].

Such higher degrees of melting would be consis-tent with higher water contents driving melting[Kelley et al., 2006; Langmuir et al., 2006; Sadofskyet al., 2008]. However, estimates of extrusive vol-canic flux based on volcanic edifices are similarbetween Nicaragua and Costa Rica [Carr et al.,2007], although when tephra volumes are included,magma flux in Nicaragua may be somewhat higherthan in Costa Rica [Kutterolf et al., 2008]. Thus,while there may be a link between the H2O contentof the mantle and degree of melting, the link withmagma production is less clear.

[12] In order to provide new constraints on thesequestions that relate to the melting process in themantle, we use attenuation tomography to probethe structure of the slab and wedge and constrainthe distribution of water and temperature in thesubduction zone.

2. Methods

2.1. Calculating t*

[13] The spectra of P and S waveforms from localevents recorded by the TUCAN array were ana-lyzed using the vertical and transverse components,respectively, following the method of Stachnik etal. [2004]. P and S arrivals were picked on wave-form time series [Syracuse et al., 2008], thenmultitaper spectra [Park et al., 1987] were calcu-lated in 3-s windows, starting 0.5 s before thearrival, corrected for instrument gain, and con-verted to displacement (Figure 2). Signal-to-noiseratios (SNRs) were determined using the noisespectra calculated from a 3-s window before eachof the signals.

[14] Path-averaged attenuation was parameterizedin terms of an attenuation operator, t* = t/Q, fortravel time t assuming a displacement spectrumAjk(fi) as follows:

Ajk!fi" # CjkM0ke$pfi t*jk =!1% !fi=fck"2" !1"

[e.g., Anderson and Hough, 1984] for the kth eventrecorded at the jth station for each frequency (fi),where Cjk(r) is a constant accounting for frequency-independent effects of each path, such as geome-trical spreading, free surface interaction, and thespherical average of the radiation pattern [Aki andRichards, 1980]. M0k/(1 + (fi/fck)

2) is a simplesource spectrum [Brune, 1970] where M0k and fckare the seismic moment and corner frequency,allowing a different seismic moment and corner


5 of 26

predicts higher water contents in the mantle onaverage beneath Nicaragua than beneath Costa Rica.

[9] While our understanding of the distribution ofwater in Central American magmas is still devel-oping, other evidence points to greater and/ordeeper hydration of the subducting plate beneathNicaragua. This includes deep normal faultsobserved in the Cocos plate before it subducts[Ranero et al., 2003], low crust and mantle veloc-ities in the subducting plate seaward of the trenchconsistent with 12–17% mantle serpentinization[Ivandic et al., 2008], an unusually thick lowvelocity layer sensed by body waves trapped nearthe slab-wedge interface [Abers et al., 2003], and amantle-penetrating low velocity layer indicative of10–20% serpentine constrained by body wavetomography with TUCAN array data [Syracuse etal., 2008]. Such geophysical evidence for deeperhydration of the Nicaraguan slab is also consistentwith the anomalously low d18O values that arefound in Nicaraguan olivines, relative to those inCosta Rica or any other arc olivine globally [Eiler etal., 2005]. Such low values require high-temperaturehydrothermal reactions such as might occur indeeper regions of the subducting plate. Thus, takentogether, the trace element, isotopic, geophysical,and preliminary H2O data point to a greater hydra-tion of the Nicaraguan slab, mantle, and magmas.

[10] In addition to what appears to be an along-arcvariation in water input, other along-arc changes inslab and wedge physical conditions may also play arole in dehydration and melting processes. Previ-ously considered factors include along-arc varia-tions in slab dip [e.g., Carr et al., 1990, 2003,2007] and temperature [e.g., Leeman et al., 1994;Chan et al., 1999; Peacock et al., 2005]. Inaddition, northwestern along-arc transport of man-tle wedge material has been proposed [Herrstromet al., 1995; Abratis and Woerner, 2001; Hoernle etal., 2008] which could produce wedge materialbeneath northwestern Nicaragua that has a longerhistory of interaction with the Cocos plate and astronger slab signature.

[11] Despite the preceding evidence for greaterhydration in the Nicaraguan mantle wedge, thelink between volatile abundance and magmaticproductivity is unclear. Along-arc variations inCa, Na, Fe, and Si are consistent with a greaterdegree of melting in Nicaragua than in Costa Rica,and some evidence exists for greater pressures ofmelt equilibration beneath Nicaragua as well[Plank and Langmuir, 1988; Langmuir et al.,1992; Carr et al., 2003; Sadofsky et al., 2008].

Such higher degrees of melting would be consis-tent with higher water contents driving melting[Kelley et al., 2006; Langmuir et al., 2006; Sadofskyet al., 2008]. However, estimates of extrusive vol-canic flux based on volcanic edifices are similarbetween Nicaragua and Costa Rica [Carr et al.,2007], although when tephra volumes are included,magma flux in Nicaragua may be somewhat higherthan in Costa Rica [Kutterolf et al., 2008]. Thus,while there may be a link between the H2O contentof the mantle and degree of melting, the link withmagma production is less clear.

[12] In order to provide new constraints on thesequestions that relate to the melting process in themantle, we use attenuation tomography to probethe structure of the slab and wedge and constrainthe distribution of water and temperature in thesubduction zone.

2. Methods

2.1. Calculating t*

[13] The spectra of P and S waveforms from localevents recorded by the TUCAN array were ana-lyzed using the vertical and transverse components,respectively, following the method of Stachnik etal. [2004]. P and S arrivals were picked on wave-form time series [Syracuse et al., 2008], thenmultitaper spectra [Park et al., 1987] were calcu-lated in 3-s windows, starting 0.5 s before thearrival, corrected for instrument gain, and con-verted to displacement (Figure 2). Signal-to-noiseratios (SNRs) were determined using the noisespectra calculated from a 3-s window before eachof the signals.

[14] Path-averaged attenuation was parameterizedin terms of an attenuation operator, t* = t/Q, fortravel time t assuming a displacement spectrumAjk(fi) as follows:

Ajk!fi" # CjkM0ke$pfi t*jk =!1% !fi=fck"2" !1"

[e.g., Anderson and Hough, 1984] for the kth eventrecorded at the jth station for each frequency (fi),where Cjk(r) is a constant accounting for frequency-independent effects of each path, such as geome-trical spreading, free surface interaction, and thespherical average of the radiation pattern [Aki andRichards, 1980]. M0k/(1 + (fi/fck)

2) is a simplesource spectrum [Brune, 1970] where M0k and fckare the seismic moment and corner frequency,allowing a different seismic moment and corner


5 of 26

frequency for the P and S wave of each earthquake.The equation was rearranged into the followingform:

ln!Ajk!fi"" # ln!1# !fi=fck"2" $ ln!Cjk!r"" % ln!M0k" $ pfit*jk!2"

[Stachnik et al., 2004]. Equation (2) was thensolved for a single corner frequency and momentfor each event and an attenuation operator for eachevent-station pair, for both P and S waveforms.Since the problem is nonlinear, the equation was

Figure 2. Waveform and spectrum examples. (a, b, e, f) Waveforms and (c, d, g, h) corresponding spectra of boththe P wave (Figures 2a–2d) and the S wave (Figures 2e–2h) are compared at a station in the fore arc, MANS(Figures 2a, 2c, 2e, and 2g), and a station in the back arc, B4 (Figures 2b, 2d, 2f, and 2h). The hypocenter of the eventwas at 109 km depth, 10.6!N, $84.8!W, i.e., in the slab, beneath the arc near the Costa Rica line of the TUCANarray. In the waveform plots the blue lines represent the signal, and the dashed red lines are the picks on the signals.In the spectrum plots, blue lines represent the spectra, red lines represent noise, and cyan lines show the best fittingspectra from the t* inversions. Green vertical lines delimit the frequencies that are used in the inversion for t*.


6 of 26

Rychert et al 2008

COMO EVALUAMOS ATENUACIÓN -ONDAS DE SUPERFICIE

• Se usa que las ondas de superficie disminuyen su amplitud con distancia, debido a la atenuación.

• A(ω) = AS(ω) AI(ω) AF(ω) AQ(ω)

• (S - source, I - receiver, F- geometric spreading, Q - attenuation)

Selby and Woodhouse, 2000]. Here, we treat this effect onamplitude using an expression from linearized ray theory,

lnAF w! " # dcj02c0

w! " $ dcjD2c0

w! " $ 1

2cosecD

%Z D

0

sin D& f! " sinf@2q

!

& cos D& 2f! "' dcc0

w! "df; !3"

where D is the epicentral distance, f is the along-pathcoordinate, q is the path-perpendicular coordinate, dc/c0 isthe relative perturbation in surface wave phase velocity, anddcj0 and dcjD indicate the phase velocity perturbation at thesource and receiver, respectively [Dahlen and Tromp,1998]. This expression is slightly modified from theoriginal one provided by Woodhouse and Wong [1986], asit includes a term with sensitivity to the phase velocity at thereceiver. The wave amplitude due to focusing dependsprimarily on the second derivative of velocity perpendicularto the ray path. Waves traveling through a low-velocitytrough are focused and amplified, and the opposite is truefor propagation along a channel of fast velocity. Implicit inequation (3) is the assumption of an infinite frequency wavethat does not deviate from the great circle path connectingthe source and receiver. We argue in the Appendix thatintegrating along the great circle path instead of the true raypath is valid for the length scales in which we are interested.[10] The perturbation in phase velocity, dc/c0(w), is ex-

panded in spherical harmonics,

dcc0

w; q;f! " #X

Lc

l#0

X

l

m#&l

Clm w! "Ylm q;f! "; !4"

where Ylm(q, f) are the fully normalized surface sphericalharmonics of degree l and order m, Lc is the maximumdegree of the phase velocity expansion, and Clm(w) are thecoefficients to be determined. The focusing depends linearlyon the phase velocity, and we write

lnAi;jF w! " #

X

Lc

l#0

X

l

m#&l

Clm w! "Fi;jlm; !5"

where Flmi,j represents the implementation of equation (3) in

spherical harmonics for the path connecting the ith earth-quake and the jth receiver.[11] The effect of attenuation on the wave amplitude, AQ,

is expressed as

AQ w! " # exp & w2U w! "

Z

path

dQ&1 w; q;f! "ds q;f! "" #

; !6"

where q and f are latitude and longitude, respectively, U(w)is group velocity, and dQ&1(w, q, f) is the perturbation insurface wave attenuation away from the value predicted byPREM. Surface wave attenuation Q&1(w, q, f) is related tothe Earth’s intrinsic shear and bulk attenuation, Qm

&1(r, q, f)and Qk

&1(r, q, f), by

Q&1 w; q;f! " #Z a

0

M w; r! "m r! "Q&1m r; q;f! "r2dr

$Z a

0

K w; r! "k r! "Q&1k r; q;f! "r2dr; !7"

where integration is over the radius of the Earth, and K(w, r)k(r) and M(w, r)m(r) are the kernels that describe the radialsensitivity of Rayleigh waves to bulk and shear attenuation(Figure 1). In this paper, we focus on the method forobtaining maps of surface wave attenuation at discretefrequencies and delay a discussion of the implications of ourresults for the Earth’s intrinsic attenuation until a later paper.[12] For an amplitude observation corresponding to the

ith earthquake and the jth receiver, equation (6) can besimplified to

Ai;jQ w! " # exp & wXi;j

2U w! " dQ&1i;j w! "

" #

; !8"

where Xi,j is the length of the path and dQ&1i;j (w) is the

average perturbation in Q&1 along that path. The lateralvariations in dQ&1 are expanded with spherical harmonics,

dQ&1 w; q;f! " #X

LQ

l#0

X

l

m#&l

dQ&1lm w! "Ylm q;f! "; !9"

where LQ is the maximum degree of the Q&1 expansion, anddQlm

&1(w) are the coefficients to be determined.[13] In the inversion for our preferred surface wave

attenuation maps presented in section 4, we solve for fourquantities: ln AS, ln AI, Clm(w), and dQlm

&1(w). For observa-tions of amplitude anomalies ln Ai,j, we can then write

&2U

wXi;jlnAi

S $ lnAjI $

X

Lc

l#0

X

l

m#&l

Clm w! "Fi;jlm

" #

$X

LQ

l#0

X

l

m#&l

dQ&1lm w! "Y i;j

lm # &2U lnAi;j

wXi;j; !10"

Figure 1. Kernels that describe the radial sensitivity offundamental mode Rayleigh waves to the Earth’s intrinsicshear attenuation for the range of periods examined in thisstudy. The reference model is PREM [Dziewonski andAnderson, 1981].

B05317 DALTON AND EKSTROM: SURFACE WAVE ATTENUATION

3 of 19

B05317

Selby and Woodhouse, 2000]. Here, we treat this effect onamplitude using an expression from linearized ray theory,

lnAF w! " # dcj02c0

w! " $ dcjD2c0

w! " $ 1

2cosecD

%Z D

0

sin D& f! " sinf@2q

!

& cos D& 2f! "' dcc0

w! "df; !3"

where D is the epicentral distance, f is the along-pathcoordinate, q is the path-perpendicular coordinate, dc/c0 isthe relative perturbation in surface wave phase velocity, anddcj0 and dcjD indicate the phase velocity perturbation at thesource and receiver, respectively [Dahlen and Tromp,1998]. This expression is slightly modified from theoriginal one provided by Woodhouse and Wong [1986], asit includes a term with sensitivity to the phase velocity at thereceiver. The wave amplitude due to focusing dependsprimarily on the second derivative of velocity perpendicularto the ray path. Waves traveling through a low-velocitytrough are focused and amplified, and the opposite is truefor propagation along a channel of fast velocity. Implicit inequation (3) is the assumption of an infinite frequency wavethat does not deviate from the great circle path connectingthe source and receiver. We argue in the Appendix thatintegrating along the great circle path instead of the true raypath is valid for the length scales in which we are interested.[10] The perturbation in phase velocity, dc/c0(w), is ex-

panded in spherical harmonics,

dcc0

w; q;f! " #X

Lc

l#0

X

l

m#&l

Clm w! "Ylm q;f! "; !4"

where Ylm(q, f) are the fully normalized surface sphericalharmonics of degree l and order m, Lc is the maximumdegree of the phase velocity expansion, and Clm(w) are thecoefficients to be determined. The focusing depends linearlyon the phase velocity, and we write

lnAi;jF w! " #

X

Lc

l#0

X

l

m#&l

Clm w! "Fi;jlm; !5"

where Flmi,j represents the implementation of equation (3) in

spherical harmonics for the path connecting the ith earth-quake and the jth receiver.[11] The effect of attenuation on the wave amplitude, AQ,

is expressed as

AQ w! " # exp & w2U w! "

Z

path

dQ&1 w; q;f! "ds q;f! "" #

; !6"

where q and f are latitude and longitude, respectively, U(w)is group velocity, and dQ&1(w, q, f) is the perturbation insurface wave attenuation away from the value predicted byPREM. Surface wave attenuation Q&1(w, q, f) is related tothe Earth’s intrinsic shear and bulk attenuation, Qm

&1(r, q, f)and Qk

&1(r, q, f), by

Q&1 w; q;f! " #Z a

0

M w; r! "m r! "Q&1m r; q;f! "r2dr

$Z a

0

K w; r! "k r! "Q&1k r; q;f! "r2dr; !7"

where integration is over the radius of the Earth, and K(w, r)k(r) and M(w, r)m(r) are the kernels that describe the radialsensitivity of Rayleigh waves to bulk and shear attenuation(Figure 1). In this paper, we focus on the method forobtaining maps of surface wave attenuation at discretefrequencies and delay a discussion of the implications of ourresults for the Earth’s intrinsic attenuation until a later paper.[12] For an amplitude observation corresponding to the

ith earthquake and the jth receiver, equation (6) can besimplified to

Ai;jQ w! " # exp & wXi;j

2U w! " dQ&1i;j w! "

" #

; !8"

where Xi,j is the length of the path and dQ&1i;j (w) is the

average perturbation in Q&1 along that path. The lateralvariations in dQ&1 are expanded with spherical harmonics,

dQ&1 w; q;f! " #X

LQ

l#0

X

l

m#&l

dQ&1lm w! "Ylm q;f! "; !9"

where LQ is the maximum degree of the Q&1 expansion, anddQlm

&1(w) are the coefficients to be determined.[13] In the inversion for our preferred surface wave

attenuation maps presented in section 4, we solve for fourquantities: ln AS, ln AI, Clm(w), and dQlm

&1(w). For observa-tions of amplitude anomalies ln Ai,j, we can then write

&2U

wXi;jlnAi

S $ lnAjI $

X

Lc

l#0

X

l

m#&l

Clm w! "Fi;jlm

" #

$X

LQ

l#0

X

l

m#&l

dQ&1lm w! "Y i;j

lm # &2U lnAi;j

wXi;j; !10"

Figure 1. Kernels that describe the radial sensitivity offundamental mode Rayleigh waves to the Earth’s intrinsicshear attenuation for the range of periods examined in thisstudy. The reference model is PREM [Dziewonski andAnderson, 1981].

B05317 DALTON AND EKSTROM: SURFACE WAVE ATTENUATION

3 of 19

B05317

Dalton et al 2006

COMO EVALUAMOS ATENUACIÓN - MODOS NORMALES

• 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

ATTENUATION MEASUREMENTS--CHILEAN AND ALASKAN EARTHQUAKES 1597

The solution for the amplitudes of split modes (Stein and Geller, 1977) is obtained by transforming the spherical harmonic expansion of the excitation from the frame of reference of the source into geographic coordinates. The singlet amplitudes are written so that there are separate factors for source location (latitude and longitude), source depth, fault geometry (strike, dip, and slip direction), receiver location, and the normalized energy of each mode.

For a spheroidal or torsional multiplet and for a step function dislocation with

0S2 T=53.8 min,

L L , L , i L L i , I , i i , I 0 50 hr I00 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

l U(r , t) =

rn~--l [Elm ( ~')e i~l'~t + E?,~ ( ~')e-i~'~t]e -~'t/2Q~

where wzm is the eigenfrequency of the mode. The overtone number, n, will be suppressed for convenience throughout this section. The attenuation factor is assumed to be the same for the entire multiplet. The displacement or strain spectral density of the l m t h mode, Elm, is given explicity by Stein and Geller (1977). The only perturbations which are important at long periods, rotation and ellipticity, are both symmetric about the rotation axis. To find the displacement, we need the excitation coefficients, which are obtained from the excitation coefficients used for a nonrotating earth in a frame of reference centered on the earthquake source, from

1596 S E T H S T E I N A N D R O B E R T J. G E L L E R

However, for split modes, it is not possible to derive a simple expression for the interference, either in the time or frequency domains, which will isolate the terms involving Q. Thus, to measure Q, it is necessary to know the amplitude and phase of each singlet, and to combine them to form a time series including the interference effects. Alsop et al. (1961b) proposed conditions under which Q might successfully be measured, despite the splitting. The time-domain Q measurement technique used in this paper is valid without any such limiting assumptions. Also, in contrast to frequency-domain techniques, time-domain Q measurements allow us to reject data below the ambient noise level for each mode.

TIME DOMAIN SYNTHESIS METHOD Our attenuation measurement method is based on the results of Stein and Geller

(1977) for the theoretical amplitude and phase of the singlets excited by an earthquake source: a double couple of arbitrary orientation resulting from slip on a fault plane. Figure 1, from Geller and Stein (1977), shows the spectra of the spheroidal

4 0 0

300 14_

200 c o7 o

_oS:

I O 0

00180

' r ' l ' ' ' 1 '

÷2

I i J i i

0 0 1 8 5 0 0 1 9 0 F r e q u e n c y , c y c l e s / r a i n

I I -2 0+2

2 0 0 ' ' ' ' ] ' ' ' ' I ' '

-5. I _o S 3

o /I A I I +a 0 +i I 0 0 - 5 + 5 ~ I l l l l

- -2 0+2

C i i i i I I i i i i i i

0 0 2 7 5 0 0 2 8 0 0 0 2 8 5 F r e q u e n c y , c y c l e s / r a m

FIG. 1. Split spheroidal mode spectra for 0S2 (top) and 0Sa (bottom) excited by the Chilean earthquake, as observed on a strainmeter at Isabella, California. The Eigenfrequency separation is taken from Dahlen (1968), but the central frequency has been chosen to yield a best fit with the observed peaks. Synthetic relative spectra for the finite fault geometry of Kanamori and Cipar (1974) are given for each mode. The amplitudes are normalized and plotted with regular spacing.

multiplets 0,92 and 0Ss excited by the Chilean earthquake, as observed on a strainmeter (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,92 multiplet 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.

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 correlación entre anomalías en atenuación (1/Q) y velocidad.

At 150 km, the old-continental points maintain a shallower-than-predicted slope, whereas the oceanic regions more closely match themagnitude and trend predicted by the mineral-physics model. Thispattern holds at 200-km depth. At 250 km, however, it is no longer truethat old-continental regions deviate significantly from the predictedcurves.

We have established that the results in Fig. 3 are robust withrespect to how strongly the attenuation model is damped. Inconstructing QRFSI12, the squared gradient of the attenuationperturbations is minimized, and we have found that, as expected,the strength of the horizontal-smoothness constraint influences boththe data variance and the magnitude of lateral attenuation variations.Stronger damping results in a smoother, weaker model that providesa worse fit to the data (Dalton et al., 2008). Concerning the patterns inFig. 3, weaker damping results in a wider spread of attenuation valuesand slightly larger values for the slope (dQ!1/dVS) of the best-fittinglines. However, the relationships between young oceans, old oceans,and old continents that are apparent in Fig. 3 are found for attenuationmodels determined with a wide range of horizontal-dampingcoefficients. Furthermore, the relationships between the seismolog-ical and mineral-physics models are also robust with respect tostrength of damping, as the slopes of the seismological best-fittinglines do not vary considerably for models constructedwith reasonablevalues of the smoothness coefficient.We note that the relationships inFig. 3 are also found when the velocity and attenuation models aretruncated at a lower spherical-harmonic degree; in other words, thepatterns are not dominated by the small-scale features in the models.

From the comparison of seismological and laboratory-predictedvalues in Fig. 3, it is clear that laterally varying temperature in drymelt-free forsterite-90 olivine can explain much of the variability inglobal seismic models for oceanic regions at depths N100 km and old-continental regions at 250 km. This simple explanation is not

sufficient for oceanic regions at 100-km depth and continentalregions at depths b250 km, as indicated by the less favorableagreement between seismological values and predictions. As dis-cussed by Dalton et al. (2009), laterally variable temperature likelydoes exert a strong influence over the seismic properties of theseregions, especially in the shallow mantle. However, we infer fromFig. 3 that other factors, such as composition and partial melt, mayalso be important. In the following sections, we investigate explana-tions for the discrepancies. In particular, we focus on the shallower-than-predicted slopes for oceanic regions at 100-km depth and forcratonic regions at depths "200 km.

3. Identification of outliers

We identify outliers as seismological points that fall outside of therange defined by the mineral-physics predictions. In Figs. 4–7, pointsthat fall to the left and right of the experimentally defined range arecolored red and blue, respectively, while points falling within theexperimental range are shaded grey. The experimental range isdefined to include the mineral-physics predictions for activationvolumes between V=12!20!10!6 m3/mol and grain-size values of1–50 mm. The experimental range is allowed to be slightly wider thanthese bounds to allow for smaller and larger grain-size and activation-volume parameters as well as experimental uncertainties. Thegeographical location of each of those points is plotted on theaccompanying maps. At 100-km depth (Fig. 4), 49.5% of all points fallwithin the experimental range; 11.5% of the points fall to the left ofthe range and are characterized by lower-than-experimental velocityand/or lower-than-experimental attenuation, and 39% fall to the right.The majority of the anomalously low-velocity/low-attenuation pointsare geographically located beneath oceanic crust of age b70 Myr. The

-0.010 -0.005 0.000 0.005 0.010 -6 -4 -2 0 2 4 6

dv/v (%)

100 km

QRFSI12 S362ANI

-0.005 0.000 0.005

dQ-1

dQ-1

-2 0 2

dv/v (%)

400 km

Fig. 1. Comparison of global shear-attenuation (left) and shear-velocity (right) models at 100-km and 400-km depth. The attenuationmodel QRFSI12 is plotted as the deviation awayfrom the globally averaged Q μ

!1 value at each depth; 1-D Q μ!1 is 0.0126 and 0.00577 at 100 and 400 km, respectively. Isotropic velocity frommodel S362ANI (Kustowski et al., 2008)

is shown here expanded in spherical harmonics up to degree 12.

162 C.A. Dalton, U.H. Faul / Lithos 120 (2010) 160–172

decrease in attenuation down to !450 km. Strong radialgradients in attenuation are penalized by the regularizationscheme adopted here, and thus it is not possible to obtain anaverage global profile like that corresponding to referencemodel 1 in Figure 4 unless strong gradients are containedwithin the reference model. The fundamental mode ampli-tude data do not discriminate between the two averageprofiles in Figure 4, and the variance reduction for bothcases is nearly identical.[37] Strong regional trends in the three-dimensional at-

tenuation model can be seen by comparing regionallyaveraged vertical profiles (Figure 5). The global tectonicregionalization [GTR1; Jordan, 1981] is used to divide thesurface of the Earth into three oceanic regions, eachdistinguished by age of the ocean floor (0–25 Myr, 25–100 Myr, >100 Myr), and three continental regions accord-ing their tectonic behavior during the Phanerozoic (Phaner-ozoic orogenic zones and magmatic belts, platformsoverlain by undisturbed Phanerozoic cover, and Archeanand Proterozoic shields and platforms). The regional aver-aging is performed by populating the globe with 1442evenly spaced points, finding the appropriate attenuationprofile at each point, and determining in which region eachpoint is located. Above 200 km, young oceanic regions arethe most highly attenuating of the six areas, and in generalattenuation decreases with seafloor age in Figure 5, partic-ularly at depths shallower than 200 km. On the continents,orogenic zones and magmatic belts are characterized bystronger attenuation than the Precambrian shields and plat-forms and the undisturbed Phanerozoic platforms. Below!200–250 km, the six tectonic regions are not character-ized by distinctively different attenuative properties. Com-parison with the pure path estimates of oceanic andcontinental Rayleigh wave attenuation by Dziewonski andSteim [1982] shows a similar level of difference between the

two regions, although the absolute Q"1 values of our studyare slightly lower than in the earlier work.[38] In the following sections, we discuss the results of

tests performed to quantify the robustness of the model. Theimportance of the correction for crustal attenuation isinvestigated in section 4.1, the influence of regularizationis explored in section 4.2, and the results of resolution testsare presented in section 4.3. Interpretation of QRFSI12 ispursued in section 5 through comparison with earlierattenuation models and with global models of shear wavevelocity.

4.1. Crustal Corrections

[39] It is well established that crustal structure contributessignificantly to the observed lateral variations in the phasevelocity of fundamental mode surface waves, particularlyfor Love waves and short-period Rayleigh waves [e.g.,Ekstrom et al., 1997; Ritsema et al., 2004]. Typically, inorder to interpret surface-wave dispersion measurements interms of upper-mantle velocity structure, crustal effectsmust be removed from the observations before inversion,and global models of crustal thickness and seismic proper-ties, such as CRUST2.0 [Bassin et al., 2000], can be usedfor this purpose. To date, there have been considerablyfewer studies of crustal attenuation, and applicability ofthese studies to intermediate- and long-period Rayleighwaves is limited by assumptions about the frequencydependence of attenuation. However, attenuation in thecrust is known to exist and has been explained by factorsincluding fluid movement [Mitchell, 1995], crack structure[Hauksson and Shearer, 2006], and temperature variations,among others. Overall, Qm in the crust is probably fairlyhigh [Qm = 300 in QL6; Durek and Ekstrom, 1996], and thesensitivity to crustal structure of the intermediate- and long-period Rayleigh waves used here is relatively small. Forthese reasons, it is not expected that crustal Qm will have an

Figure 5. Regionally averaged attenuation profiles for the six tectonic regions of the GTR1regionalization scheme. (a) Results correspond to the reference model 1 of Figure 4. (b) Resultscorrespond to reference model 2 of Figure 4.

B09303 DALTON ET AL.: GLOBAL UPPER-MANTLE ATTENUATION

9 of 24

B09303

MODELOS GLOBALES DE ATENUACIÓN anomalously high-velocity points are generally associated withoceanic crust older than 70 Myr and old-continental areas.

At 150 km (Fig. 5), almost all of the oceanic points fall within theexperimental range, with only !25% of the young-oceanic pointscharacterized by lower-than-experimental velocities and/or lower-than-experimental attenuation. In contrast, 72% of the old-continentalpoints have larger velocity and/or higher attenuation than theexperimental range. This trend persists at 200-km depth, where!50% of old-continental points fall to the right of the experimentalrange while nearly all of the oceanic points are located within theexperimental range. At 250 km, a handful of old-continental points(15%) are located to the right of the range, but the vast majority of allpoints agree with the mineral-physics model.

At 100 km, outliers located to the left of the experimental range arealmost all located along the global mid-ocean-ridge system. This isespecially true for the East Pacific Rise, the PacificAntarctic Ridge, and theSoutheast Indian Ridge. Areas of the Mid-Atlantic Ridge near the Azoreshotspot and centered on the equator also exhibit anomalously lowvelocity and/or low attenuation. Small clusters of these points can befound in the northeastern Pacific and centered on the Red Sea. Beneaththe oceans, outliers located to the right of the experimental trendcomprisemuch of the western Atlantic, offshore Africa, and the northerncentral Pacific. Some of the anomalously high-velocity/high-attenuationpoints that are adjacent to continental areas could result from smearingof the continental properties into the oceanic regions, given that theglobal models used for this analysis have a relatively coarse resolution(spherical-harmonic degree 12). However, many of the outliers are farfrom any continental region (e.g., the central Pacific) and are not likely tobe artefacts. Within the old continents, 84% of the points are located tothe rightof the experimental range. The remaining16%of old-continentalpoints that fall within or to the left of the experiments are generallylocated adjacent to tectonically younger provinces, as is the case for Egyptand Sudan, which are adjacent to the Red Sea, and for southeast China.

At 150 km, almost all outliers located to the right of theexperimental range (i.e., higher velocity and/or higher attenuationthan the mineral-physics model) are found within old-continentalregions: only 1.3% and 8.1% of young and old oceanic regions,respectively, fall to the right of the experimental trend, whereas 72%of the old-continental points do. As is the case for 100 km, the old-continental points that fall within the experimental range aregenerally adjacent to tectonically younger areas. The few oceanicpoints with values to the right of the experimental range almost alladjoin an old continent, perhaps indicating some smearing of thecontinental seismic properties into the nearby ocean basins. Outlierslocated to the left of the experimental trends are found mostly inoceanic regions b70 Myr. As with 100 km, many of these points arelocated near the East Pacific Rise, Pacific Antarctic Ridge, andequatorial Mid-Atlantic Ridge. Iceland, the eastern Pacific, and thecentral Indian Ridge also have lower velocity and/or lower attenua-tion than the mineral-physics model predicts at 150 km.

At depths of 200 and 250 km, the number of outliers shrinks, in partbecause the width of the experimental range expands. Nearly all of theyoung and old oceanic points fall within the experimental range; at200 km, exceptions include the Pacific Antarctic Ridge, northeasternPacific, equatorial mid-Atlantic Ridge, and a swath of the central IndianRidge. Approximately 50% of the old-continental points fall outside theexperimental trends at 200 km. Those outliers are almost all associated

800 900 1000 1100 1200 1300 1400 1500 16003.8

4

4.2

4.4

4.6

4.8

5

Vel

ocity

(km

/s)

800 900 1000 1100 1200 1300 1400 1500 16000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08A

ttenu

atio

n (1

/Q)

Temperature (oC)

Temperature (oC)

(a)

(b)

(c)

3.8 4 4.2 4.4 4.6 4.8 50

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Velocity (km/s)

Atte

nuat

ion

(1/Q

)

Fig. 2. Predicted shear velocity (a) and attenuation (b) as a function of temperature at100-km depth, using the model of Faul and Jackson (2005). (c) Predicted relationshipbetween velocity and attenuation at 100 km. Velocities are calculated at a period of 1 sand attenuation is calculated at 71 s. Predictions are shown for a range of grain-sizevalues and for activation volumes of 12!10"6 and 20!10"6 m3/mol. In (c), the blackcurves represent predictions of attenuation made at periods of 10 and 50 s to illustratethe effect of frequency.

163C.A. Dalton, U.H. Faul / Lithos 120 (2010) 160–172

anomalously high-velocity points are generally associated withoceanic crust older than 70 Myr and old-continental areas.

At 150 km (Fig. 5), almost all of the oceanic points fall within theexperimental range, with only !25% of the young-oceanic pointscharacterized by lower-than-experimental velocities and/or lower-than-experimental attenuation. In contrast, 72% of the old-continentalpoints have larger velocity and/or higher attenuation than theexperimental range. This trend persists at 200-km depth, where!50% of old-continental points fall to the right of the experimentalrange while nearly all of the oceanic points are located within theexperimental range. At 250 km, a handful of old-continental points(15%) are located to the right of the range, but the vast majority of allpoints agree with the mineral-physics model.

At 100 km, outliers located to the left of the experimental range arealmost all located along the global mid-ocean-ridge system. This isespecially true for the East Pacific Rise, the PacificAntarctic Ridge, and theSoutheast Indian Ridge. Areas of the Mid-Atlantic Ridge near the Azoreshotspot and centered on the equator also exhibit anomalously lowvelocity and/or low attenuation. Small clusters of these points can befound in the northeastern Pacific and centered on the Red Sea. Beneaththe oceans, outliers located to the right of the experimental trendcomprisemuch of the western Atlantic, offshore Africa, and the northerncentral Pacific. Some of the anomalously high-velocity/high-attenuationpoints that are adjacent to continental areas could result from smearingof the continental properties into the oceanic regions, given that theglobal models used for this analysis have a relatively coarse resolution(spherical-harmonic degree 12). However, many of the outliers are farfrom any continental region (e.g., the central Pacific) and are not likely tobe artefacts. Within the old continents, 84% of the points are located tothe rightof the experimental range. The remaining16%of old-continentalpoints that fall within or to the left of the experiments are generallylocated adjacent to tectonically younger provinces, as is the case for Egyptand Sudan, which are adjacent to the Red Sea, and for southeast China.

At 150 km, almost all outliers located to the right of theexperimental range (i.e., higher velocity and/or higher attenuationthan the mineral-physics model) are found within old-continentalregions: only 1.3% and 8.1% of young and old oceanic regions,respectively, fall to the right of the experimental trend, whereas 72%of the old-continental points do. As is the case for 100 km, the old-continental points that fall within the experimental range aregenerally adjacent to tectonically younger areas. The few oceanicpoints with values to the right of the experimental range almost alladjoin an old continent, perhaps indicating some smearing of thecontinental seismic properties into the nearby ocean basins. Outlierslocated to the left of the experimental trends are found mostly inoceanic regions b70 Myr. As with 100 km, many of these points arelocated near the East Pacific Rise, Pacific Antarctic Ridge, andequatorial Mid-Atlantic Ridge. Iceland, the eastern Pacific, and thecentral Indian Ridge also have lower velocity and/or lower attenua-tion than the mineral-physics model predicts at 150 km.

At depths of 200 and 250 km, the number of outliers shrinks, in partbecause the width of the experimental range expands. Nearly all of theyoung and old oceanic points fall within the experimental range; at200 km, exceptions include the Pacific Antarctic Ridge, northeasternPacific, equatorial mid-Atlantic Ridge, and a swath of the central IndianRidge. Approximately 50% of the old-continental points fall outside theexperimental trends at 200 km. Those outliers are almost all associated

800 900 1000 1100 1200 1300 1400 1500 16003.8

4

4.2

4.4

4.6

4.8

5

Vel

ocity

(km

/s)

800 900 1000 1100 1200 1300 1400 1500 16000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Atte

nuat

ion

(1/Q

)

Temperature (oC)

Temperature (oC)

(a)

(b)

(c)

3.8 4 4.2 4.4 4.6 4.8 50

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Velocity (km/s)

Atte

nuat

ion

(1/Q

)

Fig. 2. Predicted shear velocity (a) and attenuation (b) as a function of temperature at100-km depth, using the model of Faul and Jackson (2005). (c) Predicted relationshipbetween velocity and attenuation at 100 km. Velocities are calculated at a period of 1 sand attenuation is calculated at 71 s. Predictions are shown for a range of grain-sizevalues and for activation volumes of 12!10"6 and 20!10"6 m3/mol. In (c), the blackcurves represent predictions of attenuation made at periods of 10 and 50 s to illustratethe effect of frequency.


Dalton & Faul 2010

• Experimentos con olivino seco en un rango de frecuencias, temperaturas y tamaño de granos (a-c)

• (a) comparación entre los experimentos y los modelos globales.

• Hay diferencia entre océanos jóvenes, océanos viejos y continentes viejos.

with cratons with tectono-thermal ages N1100 Myr (Artemieva, 2006).At 250 km, more than 85% of old-continental points fall inside theexperimental range, with the few outlier points located in northernCanada, central Australia, South America, and western Europe.

4. Discussion

In Sections 2 and 3, we presented a comparison of the seismologicalmodels and the experimentally derived model of Faul and Jackson(2005). The following observations can be drawn from this comparison(e.g., Figs. 3–7): (1) Oceanic and old-continental regions are character-ized by different values of dQ!1/dVS at 150 and 200 km, and bothregions undergo a change toward a steeper slope that provides betteragreement with the mineral-physics model. This slope-steepeningoccurs in the depth range 100–150 km for the oceans and 200–250 kmfor the old continents. (2) At 100-km depth, almost all points that fall tothe left side of the experimental range are located along or nearbymid-ocean ridges. Points that fall to the right side of the experimental rangeare located within continental cratons, beneath old seafloor (some of

which is adjacent to continental cratons), and in the central Pacific.(3)At 150 km, points to the left of the experimental range are found alongsections ofmid-ocean ridge and in the northeastern Pacific. Points to theright of the experiments are located almost exclusively in continentalcratons and oceanic areas that adjoin these continental regions. (4) At200 and 250 km, the number of outliers continues to shrink, with mostof the low-velocity/low-attenuation outliers found near mid-oceanridges and high-velocity/high-attenuation outliers contained withincontinental cratons.

If we assume that the mineral-physics model is appropriate for theEarth's upper mantle, then explanations are required for the following:lower seismological velocities and/or lower attenuation than predictedfor parts of the mid-ocean ridge system and northeastern Pacific; andhigher velocities and/orhigher attenuation thanpredicted formanyold-continental areas, associated with portions of old oceanic seafloor, andthe central Pacific at 100-kmdepth. In the following sections,wediscussseveral possible origins for these anomalies, including artefacts of theseismological analysis as well as physical mechanisms. In particular, wefocus on the mid-ocean ridges and continental cratons and delay a

data1mm, V=121cm, V=125cm, V=121mm, V=201cm, V=205cm, V=20oceans < 70 myoceans > 70 myold continents

4.2 4.3 4.4 4.5 4.6 4.7 4.80

0.005

0.01

0.015

0.02

0.025(a) 100 km

Velocity (km/s)

Atte

nuat

ion

(1/Q

)

4.2 4.3 4.4 4.5 4.6 4.7 4.80

0.005

0.01

0.015

0.02

0.025(b) 150 km

Velocity (km/s)

Atte

nuat

ion

(1/Q

)

4.2 4.3 4.4 4.5 4.6 4.7 4.80

0.005

0.01

0.015

0.02

0.025(c) 200 km

Velocity (km/s)

Atte

nuat

ion

(1/Q

)

4.2 4.3 4.4 4.5 4.6 4.7 4.80

0.005

0.01

0.015

0.02

0.025(d) 250 km

Velocity (km/s)

Atte

nuat

ion

(1/Q

)

Fig. 3. From Dalton et al. (2009). Grey points show seismological shear velocity (Voigt average from S362ANI) and attenuation (QRFSI12) models sampled at 5762 points. Coloredcontours enclose 75% of points from oceanic regions of age b70 Myr and N70 Myr and from old-continental regions. Best-fitting lines through the three groups are also shown. Blacklines show the predicted relationship between shear velocity and attenuation using the model of Faul and Jackson (2005) for two activation volumes (V=12 and 20!10!6 m3/mol)and three grain sizes. For predicted curves calculated with constant activation volume, grain size increases from left to right.

164 C.A. Dalton, U.H. Faul / Lithos 120 (2010) 160–172

MODELOS GLOBALES DE ATENUACIÓN

• Los puntos afuera del rango de los experimentos están en las dorsales oceánicas jóvenes y en las partes más viejos de la litósfera.

• Océanos: “melt squirt”, no “grain boundary sliding”.

• Continentes: composición diferente, empobrecido hasta 200km de profundidad.

discussion of the northeastern and central Pacific and old oceanicseafloor to a subsequent publication.

We recognize that the mineral-physics model may not be appropri-ate for the upper mantle, given the conditions of the experiments fromwhich it was derived (e.g., Jackson et al., 2002). For example,experimental grain size and pressure are too small, requiring extrap-olation of both variables. Dislocation-related anelasticity may beunderestimated since the synthetic olivine samples were preparedwith minimal dislocation densities so that grain-boundary processes

could be studied. Also, the experiments were performed only onsamples of pure olivine; effects related to the coexistence of olivinewithother mineral phases (e.g., Sundberg and Cooper, 2007) and major-element compositional variations were not considered. However, theseexperiments represent the best quantitative laboratory constraintscurrently available and offer an opportunity for direct comparison withseismological models. We note that the experimental results on whichFaul and Jackson (2005) based their model have been recentlyreanalyzed and now indicate higher attenuation at low temperatures

4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.90

0.005

0.01

0.015

0.02

0.025

Velocity (km/s)

Atte

nuat

ion

(1/Q

)

(a) 100 km

4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.90

0.005

0.01

0.015

0.02

0.025

Velocity (km/s)

Atte

nuat

ion

(1/Q

)

(b) after dispersion correction

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). Greypoints 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. Trianglesindicate old-continental points, squares indicate oceanic regions b70 Myr, and circles show oceanic regions N70 Myr. For a depth of 100 km. (b) Estimated changes in velocity as aresult 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.


Dalton & Faul 2010

MODELOS REGIONALES DE ATENUACIÓN -UNA ZONA DE SUBDUCCIÓN

• Xenolitos muestran un manto con más agua, y más fusión.

• Restringido - Q-1 no negativo.

• No toman en cuenta multitrayectoria.

also reflect other factors such as the presence ofvolatiles [Karato, 2003; Aizawa et al., 2008] andmelt [Jackson et al., 2004], complicating interpre-tations to some degree but also offering importantinsight regarding the location of volatiles and/ormelt. The relationship between the high-resolution

attenuation information provided by the TUCANarray to the relatively simple, yet strong, geochem-ical variations has the potential to illuminate volatileand temperature anomalies, and aid in determiningthe factors that control melting dynamics in subduc-tion zones.

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 markSeismogenic Zone Experiment (SEIZE) array. Slab contours are shown with blue line. Black dashed line traces theQuesada Sharp Contortion (QSC) [Protti et al., 1995]. Purple arrow denotes direction of increases in geochemicalindicators 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 etal., 2008].

GeochemistryGeophysicsGeosystems G3G3 rychert et al.: attenuation beneath nicaragua and costa rica 10.1029/2008GC002040rychert et al.: attenuation beneath nicaragua and costa rica 10.1029/2008GC002040

3 of 26

Rychert et al 2008

MODELOS REGIONALES DE ATENUACIÓN -UNA ZONA DE SUBDUCCIÓN

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 forbulk and shear attenuation (shear attenuation is shown), (g–h) constrained inversion of P and S wave data for shearand bulk attenuation (shear attenuation is shown), and (i–j) unconstrained inversion of P and S wave data for shearand bulk attenuation where damping parameters permit bulk attenuation in the crust and mantle (bulk attenuation isshown). Constrained inversions enforce nonnegativity in QS

!1. Green line represents resolution = 0.4. Yellow circlesindicate seismicity. Red inverted triangles mark station locations. Green triangles mark volcanoes. The projectionwidth is 50 km on either side of the cross-section line.


11 of 26

• 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 forbulk and shear attenuation (shear attenuation is shown), (g–h) constrained inversion of P and S wave data for shearand bulk attenuation (shear attenuation is shown), and (i–j) unconstrained inversion of P and S wave data for shearand bulk attenuation where damping parameters permit bulk attenuation in the crust and mantle (bulk attenuation isshown). Constrained inversions enforce nonnegativity in QS

!1. Green line represents resolution = 0.4. Yellow circlesindicate seismicity. Red inverted triangles mark station locations. Green triangles mark volcanoes. The projectionwidth is 50 km on either side of the cross-section line.


11 of 26

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?

atenuaciÓnusuarios.geofisica.unam.mx/vala/cursos/sismologia...descripciÓn de atenuaciÓn -...

Documents