Is a pyrolitic adiabatic mantle compatible with seismic data?

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Earth and Planetary Science Le

Is a pyrolitic adiabatic mantle compatible with seismic data?

Fabio Cammaranoa,b,T, Saskia Goesa,1, Arwen Deussc,2, Domenico Giardinia,3

aInstitute of Geophysics, ETH Honggerberg (HPP), CH-8093 Zurich, SwitzerlandbBerkeley Seismological Laboratory, UC Berkeley, CA, USA

cInstitute of Theoretical Geophysics, Department of Earth Sciences, Madingley Road, Cambridge CB3 0EZ, UK

Received 17 August 2004; received in revised form 22 October 2004; accepted 28 January 2005

Available online 16 March 2005

Editor: B. Wood

Abstract

In this paper, the simplest average physical model of a mantle convecting as a whole (i.e., following an adiabatic temperature

gradient) with a single composition (pyrolite with phase transitions) is tested directly against global seismic data, instead of

against spherically symmetric seismic models. Constraints from seismic data on average velocities and lower mantle velocity

gradients are hard to reconcile with an adiabatic pyrolitic mantle, given the current state of knowledge of elastic and anelastic

mineral parameters at high pressure and temperature. This physical model generally gives (a) a stronger baseline offset between

upper and lower mantle average travel-time residuals than allowed by the data and (b) an insufficient decrease in velocity with

depth in the lower mantle (above 2500 km). We tested 105 upper and 105 lower mantle models that were selected randomly

within the mineral parameter uncertainties. Only 2 lower mantle models and 24 upper mantle models yield whole mantle

seismic structures that are compatible with global ISC P and S travel times and central frequencies of toroidal and spheroidal

fundamental modes with angular order higher than 18. To improve the fit to the seismic data, the physical model would require

(a) a lower velocity transition zone composition than dry pyrolite (at least around continents and subduction zones) as well as

(b) a gradual change in physical state of the lower mantle that decreases the velocity-depth gradient, e.g., a superadiabatic

temperature gradient.

D 2005 Elsevier B.V. All rights reserved.

Keywords: mantle; seismic models; mineral physics; temperature

0012-821X/$ - see front matter D 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.epsl.2005.01.031

T Corresponding author. Seismo Lab, UC Berkeley, 215 McCone

Hall, Berkeley, CA 94720, USA. Tel.: +1 510 6428374; fax: +1 510

6435811.

E-mail addresses: [email protected] (F. Cammarano)8

[email protected] (S. Goes)8 [email protected] (A. Deuss)8

[email protected] (D. Giardini).1 Tel.: +41 1 6332907.2 Tel.: +44 1223 337185.3 Tel.: +41 1 6332610.

1. Introduction

Composition and thermal structure of the Earth’s

mantle are the key physical parameters for under-

standing the Earth’s dynamics and the origin and

evolution of our planet. Detailed knowledge of the

Earth’s deep interior is mainly derived from records

of seismic waves, which, while traveling through the

tters 232 (2005) 227–243

F. Cammarano et al. / Earth and Planetary Science Letters 232 (2005) 227–243228

Earth, store information about its elastic and ane-

lastic structure. Spherically symmetric Earth struc-

ture (e.g., PREM [1] and AK135 [2]) can explain a

large part of the available global seismic data.

Departures from it, accounted for in 3-D models,

amount to only a few percent. Although strides have

been made in global seismology to image the Earth’s

velocity structure, the interpretation of seismic

models in terms of physical parameters is still

difficult.

The simplest hypothesis for the mantle’s average

physical state is a dry pyrolitic composition with

phase transitions and an adiabatic thermal structure.

Several authors [3–5] inferred that this suffices to

explain 1-D reference seismic models (PREM or

AK135), if uncertainties in the seismic models and

mineral physics data are taken into account. How-

ever, seismic models are a non-unique interpretation

of the data that depends on the parametrization and

data used (e.g., [6]). Seismic-model uncertainties

PREMAK135PEM-OPEM-C

28 PREF models

average pyrolite

2500

2000

1500

1000

500

0

dept

h (k

m)

8 10 12 14 4 5VP (km/s) VS

Fig. 1. Commonly used seismic reference models (in red and blue) are com

dashed gray, potential temperature of 1300 8C, average mineral properties

temperature corrections to extrapolate at high P–T conditions). Although d

the difference between the seismic and the physical models, some features

of temperature and composition [21]. Furthermore, similarly looking mode

our analysis will show. Only 28 pyrolite models (dPREFT in black) out of 1

an acceptable fit to seismic travel time and mode frequency data.

may be characterized by determining a set of

similarly acceptable models (e.g., [2]). The envelope

around these models gives some idea of the possible

velocity uncertainties at each depth. But velocities at

different depths are correlated and therefore not all

the models that fall within the envelope necessarily

satisfy the original seismic data. Consequently, the

similarities between a pyrolitic model and commonly

used 1-D seismic models (Fig. 1) are no guarantee

for a satisfactory seismic data fit (as we will show).

Also, since the shape of best-fit seismic models

depends on the chosen parametrization, and

employed data and inversion regularization, they

may not be suitable for a direct physical interpre-

tation [7]. Thus alternative strategies are necessary

for assessing the constraints that seismic data

provide on physical structure, starting with spherical

background structure.

Pyrolite is the most widely accepted compositional

model for the upper mantle and satisfies a large range

6 7 3 4 5 6(km/s) ρ (g/cm3)

pared with velocity and density for an adiabatic pyrolitic mantle (in

, but low KpvV and GpvV=3.8 and 1.5, 3rd order finite strain plus linear

ifferences in the upper mantle between seismic models are as large as

of the (non-unique) seismic models are difficult to interpret in terms

ls also in lower mantle may yield very different seismic data fits, as

010 investigated mineral parameter combinations pass our criteria for

F. Cammarano et al. / Earth and Planetary Science Letters 232 (2005) 227–243 229

of data [8]. If the mantle convects as a whole, the

lower mantle should have the same composition. The

average thermal structure of a vigorously convecting

fluid closely follows that of an adiabat, except in the

upper and lower boundary layers. The petrology of

mid-ocean ridge basalts constrains the potential

temperature of the mantle adiabat to be around 1300

8C [9]. Whole mantle convection is consistent with

seismological observations of slabs penetrating the

660 km discontinuity and extending until the core–

mantle boundary [10,11]. However, a deeper change

in mantle composition, not precluded by seismology,

is sometimes invoked, e.g. [12,13], mainly on the

basis of geochemical observations that require the

existence of several, long-lived, reservoirs in the

mantle.

In this paper, adiabatic-pyrolite velocity profiles

are tested against seismic data instead of comparing

with seismic models. In the conversion from physical

to seismic structure we take into account uncertainties

in elastic and anelastic mineral parameters. The

seismic data used (teleseismic travel times and normal

mode frequencies) are similar to those on which

global 1-D seismic models have been based. We find

that adiabatic pyrolitic structure is unlikely to be an

acceptable average for the whole mantle.

2. Method

2.1. Physical model

Our physical model has the thermal structure of an

adiabat with a potential temperature of 1300 8Coverlain by the geotherm for 60 m.y. old oceanic

lithosphere. An average oceanic structure was used

because the physical structure of continental litho-

sphere is more poorly understood. The seismic data

used have little sensitivity to details of the structure

above 300 km, and we chose to map uncertainties in

shallow structure into the crust (Section 3.5). We do

not include the bottom thermal boundary layer, i.e. we

do not consider any physical reference for DU layer.

The seismic signature in the bottom part of the lower

mantle (DU) is known to be complex (e.g. strong

anisotropy, deviation from 1-D structure), consistent

with its role as a thermal (and possibly also chemical)

boundary layer. Its interpretation in terms of a

physical reference should include at least a non-

adiabatic thermal gradient with appropriate mineral

physics properties that are both difficult to assess. A

recent discovery of a new post-perovskite phase close

to the core–mantle boundary [14,15] can make the

pattern even more complex. Consequently, we do not

test against seismic data that are sensitive to the

bottom 400 km of the mantle. From here on, we will

refer to lower mantle and whole mantle, implying the

mantle until 2500 km depth.

The pyrolite composition is taken from [16]. Other

proposed versions of pyrolite are seismically indis-

tinguishable. Phase transitions in the upper mantle are

computed according to the experimental phase-dia-

gram compiled by Ita and Stixrude [4], including iron

and aluminum partitioning between the various

phases. In the lower mantle, neither phase changes

nor a variation in iron partitioning with depth between

the minerals are taken into account. The one-dimen-

sional crustal structure is that of PREM.

Our physical model is isotropic. Although aniso-

tropy may be considerable in the shallow upper

mantle (and in DU), there is no obvious physical

reference model to account for seismic anisotropy.

However, anisotropy is usually localized in boundary

layers, e.g. [17], and is probably negligible for the

bulk part of the lower mantle [18], consistent with a

dominant diffusion creep mechanism [19].

2.2. Testing procedure

An inversion is formulated, where we search for a

set of mineral physics parameters that yields pyrolite

models compatible with the seismic data. The search

space is defined by the uncertainties in the mineral

physics parameters. We perform the inversion by a

Monte Carlo search. This fully explorative approach is

justified by the large number of parameters involved

and by the extremely non-linear dependence of the

seismic data fit on those parameters. Optimally, only

thermodynamically consistent sets of mineral param-

eters (consistent with the original data) should be

explored, but this is not straightforward to implement.

The number of acceptable models is limited in steps

(Fig. 2) consisting of: (a) A separate analysis of upper

mantle (UM) and lower mantle (LM) structure, with

the boundary where the post-spinel transition takes

place according to the adopted phase diagram [4], i.e.

Calculate 100000

Combined best-fit models

28 PREF models

STEP 2

Calculate 100000

Apply selection criteria on <VP,S> (0-664km) and ∆VP,S at 410 km 15952 models selected

Apply selection criteria on <VP,S> (664-2500km)

6477 models selected

Combined UM+LM models

4693 X 21 = 98553 WM models

Traveltime selection



21 models selected

Apply selection criteria on ∆VP,S at 660 km



826 models selected

Mode selection

923 models selected

convert to seismic structure using mineral parameters randomly selected

within uncertainties

adiabatic pyrolitephysical structure

STEP 3

STEP 4

STEP 5

10.76% of the parameter combinations are not

consistent with 4E 89243 models

STEP 1

pyrolite UM modelspyrolite LM models

Fig. 2. Flowchart of the procedure to test adiabatic pyrolite physical

model against seismic data. UM—upper mantle, LM—lower

mantle, WM—whole mantle.


at 664 km. Note that the mineral physics parameters

governing UM and LM behavior are largely

decoupled. In this part of the analysis, promising

models are selected if they satisfy a set of seismic

selection criteria on depth-averaged velocity and

seismic jump amplitude (step 1), and a first-order fit

to the travel time data (step 2). Travel time calcu-

lations are quite fast and can be performed for a large

number of models. No test against normal mode data

is done at this point. (b) A re-combination of UM and

LM parameters to find whole mantle (WM) physical

models. After a first selection based on the size of the

jump at the 660 km discontinuity (step 3), the

remaining WM models are tested separately against

travel time and normal mode data (step 4). The final

set of solutions has an acceptable fit to both data

types. A similar procedure was used by Cammarano et

al. [7], who analyzed the upper mantle and transition

zone (TZ) down to 800 km depth, whereas this paper

also includes the bulk of the lower mantle. It is not our

intention to find better fitting reference models than

PREM and AK135, which are seismically optimized.

Also, the updated data sets we use here do not provide

significantly better constraints than the original ones.

But if the average physical mantle structure is that of

adiabatic pyrolite, we should find a set of solutions

that provides a similarly acceptable fit to the seismic

data as the seismic reference models.

2.3. Seismic data

We have used P-(compressional) and S-(shear)

wave travel times from the re-processed ISC catalog

until 2000 ([20], Engdahl, personal communication),

and normal mode mean frequency data from the REM

(Reference Earth Model) webpage (http://mahi.ucsd.

edu/Gabi/rem.html). Body waves are sensitive only to

velocity structure, while normal modes are also

affected by attenuation and density. Only data with

sensitivity above 2500 km have been selected.

P travel time data have smaller uncertainties and

they are 10 times more numerous than S-phase data.

Epicentral distances between 18.5–908 and 19.5–808have been used for P- and S-phases, respectively.

Arrivals at far-regional distances (b258) sample the

upper mantle, and are complicated by triplications. In

addition, spatial coverage at these distances is sparse

and strongly biased towards continents and subduc-

tion zones. However, the data for both P- and S-

phases show a Gaussian distribution and similar

scatter as the arrivals at larger epicentral distances.

Hence, they have been included in our analysis. Note

that details on velocity structure of the transition zone

http://www.mahi.ucsd.edu/Gabi/rem.html


(i.e. upper mantle below circa 300 km) can only be

extracted from P- and S-phases at far-regional

distances. Teleseismic data (recorded at distances

N258), which also sample the lower mantle, have a

more even geographic coverage. AK135 was based on

analysis of teleseismic travel times of direct P and S

as well as several other phases [2]. Multiply surface-

reflected phases like PP and SS could improve global

sampling of the upper mantle. However the re-

processed ISC catalog contains only a limited number

of such data and their quality is significantly less than

that of the direct phases. Core-reflected and trans-

mitted phases also sample the mantle, but are addi-

tionally affected by core structure.

The normal-mode mean frequency measurements

correspond to the degree-zero part of phase velocity

maps, and are only sensitive to spherically averaged

Earth structure. The sensitivity kernels of fundamental

mode branches with angular order larger than 18, are

confined above 2500 km. Both spheroidal and

toroidal modes have been used. The fundamental

mode-frequency data add better constraints on S-

structure of the whole mantle. Most of the used modes

are sensitive to both upper and lower mantle structure.

Surface waves (lN608) have their main sensitivity in

the shallow part of the UM. The inversion for PREM

[1] used a subset of these fundamental modes, as well

as modes with lower angular orders, body-wave travel

times, surface wave dispersion curves and constraints

on mass and moment of inertia.

2.4. Mineral physics data

Seismic velocities depend on the elastic and

anelastic properties of all minerals that make up the

mantle composition at given pressure and temperature

conditions. For the inversion, we only vary the

parameters that have a significant effect on seismic

structure [7], i.e. the elastic parameters of the Mg-end

members of the principal upper mantle minerals

(olivine, cpx, opx, garnet, wadsleyite and ringwoodite)

and of three LM minerals (perovskite, magnesiowus-

tite and calcium-perovskite). Extrapolation to high

pressure and temperature for the upper mantle minerals

is performed by linear high-temperature corrections

and a third-order Birch-Murnagham equation of state

(3E) [21]. The parameters varied are bulk and shear

modulus (K, G), their first order pressure and temper-

ature derivatives (KV, GV, BKS/BT, BG/BT), and

thermal expansion (a). The uncertainty bounds have

been taken from Cammarano et al. [21] and they span a

large range of values for each parameter.

For the lower mantle minerals, a non-linear

temperature extrapolation for both elastic moduli,

and third- to fourth-order (4E) Birch-Murnagham

equation of state was used. In addition to the

parameters listed above, the second-order pressure

derivatives (KU, GU) were also varied, by up to 220%

(perovskite GU even until 250%) from the value

assumed in a 3E approximation. There are virtually no

constraints on the values of these derivatives. The

thresholds were chosen after tests showed that large

negative values, resulting in more non-linear behavior

with depth, were preferred by the seismic data.

Additionally, expanded ranges for several of the

perovskite parameters were used to test the robustness

of our conclusions for the lower mantle:

KSV=4.0F10%, GV=1.8F25%, BKS/BT and BG /

BT=�0.017 and �0.029 GPa, respectively, F60%.

These ranges include most published values for these

parameters, e.g. [22,23]. Note that these elastic

parameters are not strictly data, as they have been

derived from an EOS fit to experimental or numerical

data. An improved procedure might try to take this

into account, thereby also ensuring thermodynamic

consistency of a parameter set.

Shear anelasticity (QS) was also varied, by using 8

different models based on seismological attenuation 1-

D models and mineral physics studies [21]. The

models were taken to be representative for the full

pyrolite assemblage. We neglected the (debated, e.g.

[24–26]) effect of frequency-dependence of QS, as

was done in construction of most seismic reference

models. Including it would not significantly affect our

results as it only influences the step-4 mode-based

selection. Bulk anelasticity has no significant effect

and it is kept constant at a large value (1000 in the

upper and 10000 in the lower mantle). Anelasticity

affects seismic velocity systematically. Its effect is

large in the UM, where it introduces a non-linear

dependence of seismic velocities on temperature [21].

But it is small in the LM, where temperatures are far

from the solidus (in which proximity anelasticity

effects are enhanced) and where creep mechanisms

governing anelastic deformation probably do not

change. A sharp change in anelastic properties may


occur at the post-spinel transition between upper and

lower mantle, and is incorporated in most one-

dimensional seismic attenuation models [27]. We also

allow such jumps and separately vary upper and lower

mantle QS.

3. Results

3.1. Step 1: average velocity and velocity jump

constraints on UM and LM models

100,000 UM models and 100,000 LM models have

been computed by randomly varying all 70 mineral

physics parameters. In 10.75% of the cases, the LM

mineral parameter combinations were not consistent

with the 4E EOS used, especially due to problems

with magnesiowustite. The remaining LM models

(89243) are used for the first selection step.

Average UM velocities and the amplitudes of the

jump at the 410 km discontinuity have been used as a-

priori constraints to reduce the number of UM models.

Global seismic data constrain UM average velocities

(Table 1), but not detailed UM structure [7]. Still we

found that models fit poorly when their jump at the

olivine-wadsleyite transition (around 410 km) much

exceeds the range of amplitudes spanned by a

Table 1

Step 1: first selection upper and lower mantle

Model range Constraints

min max

Upper Mantle (0:664 km)

DVP 410a (%) 6–10.5 2 8.5

DVS 410 (%) 6–12.5 2.5 8.5

Dq 410b (%) 2.7–4.5 2 12

hVPi (km/s) 8.72–8.97 8.78 8.8

hVSi (km/s) 4.70–4.92 4.77 4.8

hqib (g/cm3) 3.57–3.61 3.54 3.6

Total

Lower Mantle (664:2500 km)

hVPi (km/s) 11.60–12.80 12.19 12.2

hVSi (km/s) 6.10–7.30 6.65 6.7

hqib (g/cm3) 4.83–5.15 4.84 4.9

Total

PREM wt is with water layer.a Discontinuity lies at 400 km in PREM, 410 km in AK135, and pyrolb Note that AK135 density structure is derived from PEM-C and not coc AK135-F value is 11.42 g/cm3.

compilation of regional seismic studies (using refracted

and converted phases) [28]. This second criterion also

discards a significant number of models (Table 1).

Seismic data constrain average velocities of the

bulk part of the lower mantle (664–2500 km depth)

even better than UM average velocities. In contrast,

models based on mineral physics data have a large

scatter in average velocity values (Table 1, Fig. 3).

After several tests, we decided to apply quite tight

boundaries on average LM velocities. Models with

average values outside the applied bounds can not fit

travel time residuals at teleseismic distances (25–908)satisfactorily (Fig. 3). This constraint is very effective

in reducing the number of models. The first selection

reduces the UMmodels from 100000 to 15952, and the

LMmodels from 89243 to 6477 (see Table 1 where the

selectivity of each single criterion is given). The

remaining models span a much smaller range of ave-

rage LM velocity gradients than the starting set (Fig. 3).

3.2. Step 2: travel time selection of UM and LM

models

The second selection is based on the relative UM

and LM structure of the travel time residuals. The

cut-off epicentral distance between upper and lower

mantle structure is fixed at 258. At closer (farther)

PREM

(PREM wt)

AK135 % of original models

selected

Original 105 models

2.54 3.59 72.3

3.35 4.22 23.4

4.97 5.72c 100

8 8.85 (8.83) 8.82 80.0

7 4.82 (4.81) 4.84 88.1

2 3.58 (3.57) 3.58 100

15.95 (15,952 models)

Original 89,243 models

9 12.25 12.24 22.4

5 6.70 6.69 20.4

4 4.89 4.88 96.2

7.26 (6477 models)

ite models have a finite discontinuity between 400 and 415km.

nstrained by data.

6 6.5 7 7.511.5 12 12.5 130

20

40

60

80

1 1.2 1.4 1.6 1.8 20

10

20

30

40

50

0 0.5 1

PREMAK135

<dVp/dz> (s-1) x 10-3<dVs/dz> (s-1) x 10-3

% o

f mod

els

% o

f mod

els

771-2500 Km

664-2500 Km

initialafter step 1after step 2

<Vp> (m s-1) <Vs> (m s-1)

Fig. 3. Distributions of depth-averaged lower mantle velocities and

their depth-gradients after various steps of the procedure: initial

distributions in dashed lines, after step 1 (only shown for gradients)

in dots, after step 2 in solid lines. In the gradient calculation the

steep gradients just below 660 were excluded. Although there are

trade-offs between velocities at different depths, the average LM

velocity and gradient are tightly constrained by the seismic data.

The tight average velocity selections (gray shaded regions in top

panels) are justified by the subsequently even tighter distribution of

solutions. The difference between the pyrolite gradients and those of

AK135 and PREM hampers a good seismic data fit.

(tob

s-tm

od)

(s)

Epicentral distance (degrees)

(tob

s-tm

od)

(s)

EHB data - AK135 EHB data - AK135-FEHB data - PREM

30 40 50 60 70 80 90-5

-4

-3

-2

-1

0

1

2

3

4

5

6

30 40 50 60 70 80-15

-10

-5

0

5

10

standard deviation EHB data

P

S

FAST

SLOW

Fig. 4. Travel time residuals at teleseismic distances for P- and S

phases that sample the lower mantle down to 2500 km depth. The

observed travel times are from the Engdahl’s [20] catalog (EHB)

Shown are 1000 representative models. The dominantly concave

shapes of the residuals indicate that the velocity gradient is no

steepening sufficiently with depth to satisfy the data. Most of the

models are slower than required in the descending part of the curves

and they are faster than required after the turning point. In 3E finite

strain models, the concave shape is generally more pronounced than

with a 4E approximation. In spite of large scatter in the travel time

data, most pyrolite models have to be rejected because thei

residuals show too much structure.


distances, seismic rays turn in the UM (LM) and the

residual shape is strictly related to UM (LM)

structure. The standard deviations within the distance

range 18.58(19.58 for S)–258 and 258–908(808 for S)of each model’s residual from its mean (r(P), r(S))are used as a proxy for upper and lower mantle

structure, respectively. Mantle structure shallower

than about 300 (660) km affects the average offset

of far-regional (teleseismic) travel time residuals but

barely influences r.P and S travel-time residuals for a representative

set of 1000 of the 6477 LM models are shown in Fig.

4. The UM model residuals have the same character-

istics as in our previous analysis [7]. Residuals for the

global models AK135 [2], AK135-F ([29], a mod-

ification of AK135 with added constraints from

normal modes to obtain density and anelasticity

structure), and PREM [1], are shown for comparison

(Fig. 4). Many models poorly fit the travel time data at

epicentral distances around 508, where coverage and

quality of the data are highest. The concave shape for

both P- and S-phase of the model residuals indicates

that most of the models have a larger velocity gradient

than required by the data. The 3E models generally

have higher average gradients than the 4E models

resulting in more concave travel time distributions.

Seismic travel times at teleseismic distances do not

only constrain average velocities well, but also

gradients (Fig. 3).

-

.

t

r


For the upper mantle, we select the models having

less travel time residual structure (r) than PREM

(Table 2) as was done in Cammarano et al. [7]. All the

UM models have a similar P-residual structure, which

is governed by the velocity jump between olivine and

wadsleyite. We do not reject any UM model on the

basis of this criterion for P, but several models have

too much S structure (Table 2). A total of 4693 UM

models are selected.

Only 21 models have a lower mantle travel time

residual structure less than PREM (Table 2). None of

the models have both r(P) and r(S) as low as the

AK135 models. This illustrates the difficulty of our

physical models to produce acceptable gradients for

both VP and VS, within the used boundaries for the

mineral physics parameters.

3.3. Characteristics of step 2 solution: mineral

physics parameters

The solution characteristics of the UM models

reproduce our previous results [7]: dry pyrolite

models require olivine and wadsleyite parameters

that minimize the jump near 410 km, while

ringwoodite parameters balance upper mantle veloc-

ities towards the well-constrained seismic average

velocity.

Despite the high selectivity, the lower mantle

minerals parameters of the 6477 (7.26%) models that

pass the first selection, based on average velocities, do

not show any systematics (i.e., no preference for any

particular value) (Fig. 5). And the total range of

variation allowed for each parameter is covered by the

solutions.

Table 2

Second selection, travel-time based for upper and lower mantle


Upper Mantle

r( P)a (18.5–258) 0.28–0.55 bPREM

r(S)a (19.5–258) 0.20–2.15 bPREM

Total

Lower Mantle

r( P)a (258–908) 0.10–2.70 bPREM

r(S)a (258–808) 0.20–6.90 bPREM

Total

a r( P,S) are the standard deviations of a model’s travel time residuals

In the 21 LM models selected after step 2 there is a

systematic preference for perovskite BG/BT towards

less negative values than average, and perovskite GWassumes only very negative values (Fig. 5). Also the

Mg-wustite parameters prefer a 4E equation of state,

with strongly negative GU or KU (with the used non-

linear temperature correction for elastic moduli and

their pressure derivatives). These parameters reduce

the lower mantle gradients. There is some anti-

correlation between bulk parameters and shear param-

eters, indicative of the problem to fit both P and S

data simultaneously. E.g., if KU is close to the 3E

value, GU is very negative. Parameter combinations

other than those of the acceptable models found

cannot be excluded, as our exploration of the solution

space is inevitably incomplete. Among 3E models

there is a systematic preference for perovskite KV, GV,BKS/BT and BG/BT on the lower end of the expanded

(Section 2.4) range. These values are similar to those

found by Jackson [23]. Even lower values for the P-

and T-derivatives may result in a preference for 3E

models. However, the expanded bounds reduce the

percentage of acceptable models. Thus even with

different parameters or a different EOS it remains very

difficult to find mineral parameter combinations that

produce lower mantle average P and S velocities and

gradients that are seismically acceptable.

A light preference for models with low anelasticity

(compared to 1-D profiles derived from seismological

observations, [21,27]) is observed for both upper and

lower mantle models after the second selection.

Although travel times have no direct sensitivity to

anelasticity, its systematic effect on VS and VP helps to

jointly fit P- and S-phase data.

PREM AK135 % of step-1 models selected

Original 15,952 models

0.5574 0.2861 100

0.9179 0.5543 29.42

29.42 (4693 models)

Original 6477 models

0.2977 0.0975 9.65

0.5694 0.1711 2.09

0.32 (21 models)

from its mean.

261 2650

30

172 178 3.8 4 4.2 1.6 1.8 2 -2 -1.5 -3.4 -2.4 -0.04 -0.02 -0.03 -0.015

161 1630

30

128 130 132 3.8 4.2 2 2.5 -2.5 -2 -3 -2 -0.07 -0.03 -0.04 -0.02

Pv

Mw

K(GPa)

G(GPa)

K' G' K"(GPa-1)

∂K/∂T ∂G/∂T(Gpa/K X 100)

G"(GPa-1)

%%

Fig. 5. Distribution of the main mineral parameters for perovskite and magnesiowustite after step 1 (solid lines) and step 2 (dashed) for lower

mantle models. For a similar diagram of the upper mantle minerals we refer to Cammarano et al. [7]. In spite of the very small number of

accepted models, the selected parameters span almost the whole uncertainty range (box boundaries) and there is little preference for specific

values except for 4E second-order derivatives and BG/BT. Some correlations of high values for bulk parameters with low values for shear

parameters or vice versa are found.


3.4. Step 3: seismic jump and mass constraint for WM

models

Combining the 4693 UM and 21 LM models gives

98553 WM models, already a drastic reduction of the

starting number of 1010 (105 UM�105 LM). We apply

a further constraint on the 660 km amplitude jump,

again based on the compilation by Shearer [28]. This

mainly rejects some models with a DVPb2% ([7],

Table 3).

A constraint on Mass (M) has also been applied,

where core structure was taken from PREM, but it is

not selective (Table 3). We use the mean mass value

(M=5.9733�1024 kg) and its uncertainties defined by

[30]. Satellite laser-ranging data provide a precise

measurement of GM. But uncertainties in mass are as

high as F0.0090�1024 kg, due to large uncertainties

in G (the gravitational constant). Although several

laboratories performed measurements of this funda-

Table 3

Third selection: whole mantle


DVP 660 (%)a 0–5.0 2–8

DVS 660 (%) 1.3–8.0 2–8

Massb (�1024 kg) 5.965–5.997 5.9733�1024F0.090�1024 kg

I coeff.b,c (�10�6) 0.3306–0.3311 –

Total

a PREM’s discontinuity is at 670, AK135’s at 660, physical model discb (Chambat and Valette, 2001-[30]).c Inertia coefficient is 0.330713F8�10�6.

mental constant in the last decades (http://www.

phys.lsu.edu/mog/mog21/node12.html), the uncer-

tainties remain very large.

The inertia coefficient (I) is independent of

uncertainties in G as it is only sensitive to the

distribution of mass inside the Earth. Therefore its

value (0.330713F8�10�6) is much better con-

strained than mass [30]. Our models span a large

range of values for the inertial coefficient (again

assuming PREM core structure)(Table 3). However,

we decide to not apply any selection based on this

parameter, because we do not invert for core density

structure, where large uncertainties exist. In addition,

our models are hydrostatic and we assume a 1D

crustal structure. Large variations in crustal structure

can remarkably change the rotational inertia value,

as it varies with r4. Note that also PREM and

AK135-F values fall outside the formal uncertainties

in I.

PREM AK135-F % of combined step-2 models selected

Original 98553 models

4.62 5.62 76.47

6.51 6.05 99.55

5.9758 5.9735 100

0.3308 0.3310 –

76.37 (75265 models)

ontinuity at c664 km.

http://www.phys.lsu.edu/mog/mog21/node12.html

(tob

s-tm

od)

(s)

Epicentral distance (degrees)

(tob

s-tm

od)

(s)

EHB data - AK135 EHB data - AK135-FEHB data - PREM

20 30 40 50 60 70 80 90-5

-4

-3

-2

-1

0

1

2

3

4

5

6

20 30 40 50 60 70 80-15

-10

-5

0

5

10

standard deviations EHB data

P

S

Fig. 6. P and S residuals of whole mantle models that pass the step-

4 travel-time selection (in black). High pyrolitic velocities below

400 km result in UM residuals with significantly more structure than

those of the lower mantle, but still within data scatter. In orange, the

same models are shown after crustal corrections to remove base line

shifts. Because of uncertainties in structure above 300 km, all

models with not too extreme crustal corrections are potentially

acceptable. But the difference between optimal upper mantle and

lower mantle base line shifts indicates that modifications in

transition zone structure are necessary.


A total of 75,265 whole mantle models pass to the

following step where independent travel-time and

normal-mode frequency calculations are performed.

3.5. Step 4: travel-time selection of WM models

The residuals of a subset of 1000 representative

WM models show that several models have large

negative S-residuals throughout the teleseismic dis-

tance range, while the P-residuals overall have

values more balanced around zero (Fig. 6, black

lines). In contrast, at far-regional distances, P

structure is usually characterized by positive resi-

duals and S structure more balanced around zero.

The baseline shift at far-regional and teleseismic

distances is related to the structure in the first 300

km and 660 km, respectively. When UM and LM

models are combined, the different baseline shift

between far-regional and teleseismic distances pro-

duces whole mantle models that introduce significant

structure in the travel time residuals. Only the WM

models with less structure than PREM are selected

(Table 4).

Our models have PREM’s average crustal struc-

ture, (for travel-time calculations without the water

layer). Consistent with the continental bias of the

source and receiver distribution, a more continental

crustal structure helps to improve the UM travel time

fit by reducing the baseline shift [7]. However, the

LM models left after step 3 require a different crust to

optimize the fit (Fig. 6), even though the distribution

of sources and receivers is similar. At this stage, we

reject all models that require a baseline shift that

would correspond to an extreme average crustal

structure. To do this, we invert for a 1-D average

crustal structure (with a fixed thickness of 24 km but

variable average hVPic and hVSic) that optimizes the

travel-time fit along the whole distance range (18.5–

908 for P and 19.5–808 for S). Residuals of the WM

models after baseline shift removal are plotted in

orange in Fig. 6. Many of the lower mantle models

require a baseline shift that translates in a hVSic that isout of the bounds based on the crustal model CRUST

2.0 ([31], Table 4). The bounds of hVP,Sic were chosenliberally as crustal velocities also absorb uncertainties

in lithospheric structure.

A total of 826 whole mantle models have less

structure (lower r(P,S)) than PREM and a plausible

crustal structure. Only three lower mantle models

have been found suitable when combined with various

UM models (550 models), of which one only works

with a single UM structure. The average VS structure

above 410 km of the selected UM models is shifted

towards the fast side of the total range allowed by the

original models after step 2, because this helps to

reduce the baseline shift between UM and LM parts of

the WM models. Note that the travel-time data used

do not put any constraint on the velocity structure in

Table 4

Fourth selection: travel-time and mode-frequency selection

Model range Constraints PREM AK135-F % of step-3 models selected

Travel-time selection Original 75,265 models

r( P) (18.5–908) 0.18–1.18 bPREM 0.3440 0.1815 9.04

r(S) (19.5–808) 0.3–2.3 bPREM 0.8175 0.2416 45.51

hVPi (0:24 km) 4.6–7.4 N4.0 b6.0 6.1750 – 73.83

hVSi (0:24 km) 2.8–5.5 N2.4 b3.7 3.4625 – 18.07

Total 1.097 (826 models)

Mode-frequency selection Original 75,265 models

Spheroidal 0.38–22.55 VPREM-iso 1.04 0.80 1.37

Toroidal+Spheroidal 2.67–37.73 VPREM-iso 5.46 2.15 18.21

Total 1.226 (923 models)

Constraints for modes are misfit values of isotropic PREM. Anisotropic PREM misfit values are 0.52 for spheroidal and 0.76 and

spheroidal+toroidal. PREM travel-time misfit values are r( P)=0.1268, r(S)=0.2192.


the first 300 km apart from the average velocity. The

residual shape of the 826 WM models is never as low

as for AK135(-F) (Table 4). Furthermore, there are

very few models with r(S) less than 0.4 and none of

those have a r(P) less than 0.18, again illustrating the

intrinsic difficulty to reconcile our physical models

with the travel time data.

Because of the different baseline shift at far-

regional and teleseismic distances, optimizing the fit

globally, means worsening the fit at far-regional

distances (Fig. 6). Non-homogenous spatial sampling

of the crust, i.e. 3-D crustal corrections, can not

account for this offset as it was found to have little

differential effect on UM and LM travel time data

[7,32]. A geographical bias may however still play a

role as the far-regional rays mainly traverse mantle

under continents and around subduction zones,

whereas the teleseismic rays have a more homoge-

neous coverage. In addition, average P- and S-

residual structure differs by circa 2s (Fig. 6). Different

VP,S crustal structure and anelasticity can reconcile the

two types of data, but again limit the number of

possible solutions. Additional differences between

bulk and shear properties of either transition zone

minerals and/or LM minerals may be required.

Possible biases in the S data due to phase misidenti-

fications should also be considered.

3.6. Step 4: mode-frequency selection of WM models

Almost all synthetic pyrolite models have an

overall fit to modes with lN188 worse than anisotropic

PREM (Table 4). Without anisotropy it is difficult to

reconcile spheroidal and toroidal modes. However,

there are models that have an overall fit similar to or

better than isotropic PREM. As a compromise, we

have selected the models that have a spheroidal misfit

less than anisotropic PREM and combined misfit

better than isotropic PREM, leaving 923 models out

of 75,265. The degree of selectivity (Table 4) is high,

also for the mode selection. In this case, more LM

models are selected. Twenty (out of 21) LM models

can be coupled with 130 (out of 4693) UM models to

provide a satisfactory fit to mode data. These UM

models have different characteristics than the UM

models selected based on travel times: they can have

larger jumps near 410 km and they do not show an

average VS on the fast-side of the range inferred from

the original UM models. And, last but not the least,

strong VS velocity gradients in the upper mantle are

precluded by the modes. Such strong velocity

gradients can easily be generated in the shallow upper

mantle (below lithosphere) by strongly T-dependent

attenuation. We found that the UM models with the

lowest QS (high attenuation) structures (i.e. Q1, Q4

and Q7) never satisfy fundamental-mode data, when

combined with the 21 LM models. A light preference

for a more positive QS jump at 660 is also observed.

This result is consistent with the seismological

observations constraining 1-D attenuation structure

[27]. In fact, the most recurrent combination is Q5

(UM)–Q6 (LM).

The fundamental-mode frequency residuals for the

remaining 923 WM models vary with angular order

50 100 150 200

Fundamental branch Love waves

-1.0

0.0

1.0

2.0

Diff

eren

ce fo

bs -

fsyn

(%

)

angular order l

AK135-FPREM aniPREM iso

0.0

1.0

50 100 150 200

Fundamental branch Rayleigh waves

-2.0

-1.0

100angular order l

Fig. 7. Fundamental mode frequency residuals for WM models left

after step 4 largely fall between residuals for PREM and those for

AK135. The trend with frequency is more similar to that of AK135.


(Fig. 7), but they are globally comparable with the

residuals for seismic models. Most of the models give

residuals of the mode frequencies that fall between

anisotropic PREM and AK135-F. At increasing

angular order, the residuals show a pattern similar to

the misfit trend of AK135-F.

Despite some normal-mode sensitivity to density

structure, we do not observe any preference of the

mode-selected models for specific value of inertia

coefficient. Interesting enough, even if the 1-D

density profiles of the models look quite similar, the

variations on the inertia coefficient between these

profiles are large. Thus, when coupled to a crust and

core structure of choice, this parameter could be used

to reject most of the remaining models.

3.7. Step 5: best-fit WM models

From the WM models selected by travel times and

modes, we finally identify 28 acceptable mantle

models (excluding the lower 400 km). All these

models have a DQSb0 at the 660 km discontinuity.

The reason is purely accidental. In fact, the 2 LM

models satisfying travel times have the lowest QS

structure and the mode selection rejects UM models

with a low anelasticity structure. This leaves only

models with DQSb0 at 660 km. But it is likely that

models with a positive jump in QS are also possible

for a slightly different combination of parameters.

There are more acceptable UM than LM models,

but still only 24 models have been found. These UM

models, when combined with the 2 LM models give

WM models with a satisfactory fit to both travel time

and fundamental mode data. Specifically, they have

less deviation from travel time data residuals than

PREM and a plausible crustal structure; in addition

they fit spheroidal+toroidal fundamental modes

(lN188) better than isotropic PREM.

The shape of these models (Fig. 1) is very similar

to the seismic reference models in the lower mantle,

indicating that the seismic data tightly constrain LM

structure. In the UM, the shape of the models is

governed by the higher amplitude jump of the olivine-

wadsleyite transition, which implies seismic velocities

lower than PREM or AK135 above 410 km and

higher in the transition zone.

4. Discussion

The main constraints that the used seismic data

provide are on average velocities (for UM, LM and

WM) and on lower mantle gradients. Lower-mantle

models deviating even slightly from PREM and

AK135 (which are almost coincident there) signifi-

cantly worsen the fit to global seismic data (especially

the travel times). These uncertainties are much less

than often assumed. For example, in their physical

interpretation tests, Deschamps and Trampert [33]

evaluated all models within 1% of PREM, which is a

very liberal bound for the lower mantle. Other work

interpreted bulk sound velocity profiles [3,4,23],

which are seismically only indirectly constrained,

and for which uncertainties are more difficult to

assess.

Due to the many mineral physics parameters

involved (70), our search of the solution space in

inevitably incomplete and our solutions are not the

only ones possible. However, because of the random-

ness of the search, the results are probably a

representative subset. A more comprehensive search

may yield a slightly different percentage of successful

models and some other possible combinations of the

mineral physics parameters, but the solution space

appears to be extremely small. Other procedures (e.g.,

the neighborhood algorithm [34]) may be able to

better characterize viable parts of the solution space,

but are unlikely to find significantly larger numbers of

solutions. Thus, our procedure indicates that pyrolitic,

adiabatic models are probably not compatible with


these seismic constraints, within the uncertainty

bounds of the mineral physics data as they emerge

from compiling the literature.

The two main features required by the seismic data

that are difficult for the pyrolitic models to produce are

(1) a compatible average travel-time residual baseline

for upper and lower mantle, and (2) the decreasing

radial velocity with depth in the lower mantle. The first

point requires a change in the pyrolitic velocities in

either the upper mantle or at the transition to the lower

mantle, at least below continents and subduction

zones. The second point requires a gradual change in

the lower mantle. Such deviations from the adiabatic

pyrolite models we tested could be accomplished if

either (a) the extrapolation of the mineral data to

mantle temperatures and pressures, i.e. the EOS and

temperature extrapolation we used is not appropriate or

some key mineral parameters are found to actually

have very different values from those we tested, and/or

(b) the physical model is incorrect. Note that an

alternative physical structure does not need to be one-

dimensional. Significant three-dimensional heteroge-

neity could also shift average physical structure away

from adiabatic pyrolite.

4.1. Extrapolation to high pressure and temperature

The pressure and temperature extrapolation used

here is consistent with available data at upper mantle

pressures and temperatures [21]. Furthermore, we

allow for large uncertainties in all mineral parameters

that encompass significant uncertainties in the EOS.

The UM extrapolation is not so large that a somewhat

different formulation would significantly change the

results.

This is different in the lower mantle. It is still

questioned what the right equation of state for

minerals undergoing pressure and temperatures typi-

cal of the lower mantle is. Both 3E and 4E, with

specific combinations of values, can be used to fit

seismic models satisfactorily [23]. Unfortunately, in

spite of advances in experimental techniques, high

pressure and temperature data do not yet allow

discrimination between different EOS. Experiments

are routinely interpreted with 3E. Some authors, e.g.

[35,36], argue on theoretical grounds for other

equations of state, more physically based than the

Birch-Murnagham formulation and more non-linear

than 3E. Note that for the lower mantle, the mineral

parameter bounds that we use are also quite liberal,

allowing a range of behavior covering various

possible EOS. Within our parameter range there is a

preference for 4E, but with lower values of the P and

T derivatives of perovskite 3E models may be equally

acceptable. A different temperature extrapolation of

the elastic moduli and their pressure derivatives can

also have an effect, e.g., a linear temperature

extrapolation of K and G slightly increases average

velocities and reduces velocity gradients compared to

the non-linear temperature extrapolation used. Hence,

such linear extrapolation will tend to favor 3E over

4E, but it will not change the result that only few

models can be found. Note that our parameter ranges

plus a 4E equation of state produce model sets with

distributions of average velocities and gradients that

peak near the seismic values (Fig. 3). Yet, most of the

parameter combinations do not produce acceptable

values of all the (narrow) seismic constraints (hVPi,hVSi, hBVP/Bzi and hBVS/Bzi) at the same time.

Linear temperature extrapolation and 3E will thus not

solve this problem.

P- and S-velocity sensitive seismic data put

different constraints on the mineral parameters of a

pyrolitic average mantle. A more non-linear behavior

for shear than bulk modulus as a function of

increasing P (and T) is apparently required in the

lower mantle. Conversely to what happens in the UM,

anelasticity structure cannot help to reconcile K and G

behavior in the LM. Note, however, that most EOS

are derived for the bulk modulus, and their applic-

ability to G is uncertain. Adding an (ad-hoc) effect of

cross-derivatives between temperature and pressure

may allow for a somewhat differential behavior of G

and K [33]. However, within the uncertainty range

investigated here (which is larger for shear than bulk

modulus), the S constraints do reject a large number

of solutions.

4.2. Uncertainties in adiabatic pyrolite model

Uncertainties in the physical reference model are

not large enough to change our main conclusion that

the number of possible solutions is extremely small.

Changing the potential temperature within the F508uncertainties affects seismic velocities much less than

variations resulting from the uncertainty range used


for the elastic properties of mantle minerals. A

different version of pyrolite has a negligible effect

on seismic velocities. LM phase transitions have

sometimes been proposed, e.g. [37], and could

introduce velocity gradients if smeared out over a

large enough depth range to avoid seismic reflections.

However, recent studies have not confirmed their

existence, e.g. [38,39]. Gradual changes in iron

partitioning between perovskite (impoverishment)

and magnesiowustite (enrichment) may occur below

about 2000 km depth [40] and were not taken into

account. However, the effect on seismic velocities is

probably not very strong. Experiments and calcula-

tions indicate that Mg-perovskite velocities barely

deviate from those of a more iron-rich perovskite, e.g.

[41]. A large increase in the Fe-content of magnesio-

wustite (to (Mg0.6, Fe0.4)O) also does not significantly

affect its bulk properties and thermal expansion [42].

It is possible that a change in iron partitioning has a

stronger effect on shear than on bulk properties [43].

Also incorporation of aluminum into perovskite may

affect elastic properties, by reducing bulk modulus by

about 2% at shallow lower mantle conditions and 1%

at the bottom [44] (effects on shear modulus are still

unknown). Variations of this magnitude are however

comprised by the uncertainty range used for the elastic

parameters of perovskite. Moreover, the reduced

effect of dweakeningT with depth exacerbates the

problem of fitting the LM velocity-depth gradient.

4.3. Alternative physical model

It is not likely that a different extrapolation of

mineral parameters can solve the discrepancy between

UM and LM travel time residual baselines. This

seems to require a different physical model for at least

part of the mantle, in particular under continents and

around subduction zones. Although the UM seismic

data allow quite some structure to the travel time

residuals, the strong structure resulting from the

pyrolite models (Fig. 6) is certainly not required.

Lower seismic velocities in the transition zone would

help to reduce this structure as well as reduce the

baseline shift between far-regional and teleseismic

distances. Such slower velocities would imply that

velocities above 410 km should be higher than the

models we now selected, to preserve average upper

mantle velocities. Higher shallow mantle velocities

fall within the pyrolitic solution space, sufficiently

lower transition zone (TZ) velocities do not. It has

been speculated that water may concentrate in TZ

minerals [45]. The elastic velocities of hydrous

wadsleyite and ringwoodite could be sufficiently

reduced, e.g. [46,47], from their dry equivalents

(depending on the amount of hydration) to reconcile

UM and LM baselines, as well as have a differential

effect on VP and VS. Instead of lowering TZ

velocities, the composition could change at 660 km.

However, compositional layering would probably also

result in dynamical layering [48], which is not

compatible with three-dimensional seismic structure

[10]. Solutions, like hydration of the TZ, that do not

cause dynamic layering seem preferable.

In the lower mantle, the extrapolation to high

pressure is more uncertain. Alternatively, a gradual

compositional change with depth from pyrolite could

help to explain the seismic data. Abrupt changes are

difficult to reconcile with seismic observations, as no

evidence for a global discontinuity between 660 km

and DW has been found. Compositional gradients

should satisfy constraints on bulk silicate Earth

composition, and have a dynamically feasible evolu-

tion mechanism, e.g. formation during mantle differ-

entiation, as a result of lithospheric recycling or due to

reaction with the core. It may be problematic to

maintain a gradual compositional gradient without

developing full layering. Various changes have been

proposed, e.g., an increase in Si content or in Fe

content (not only partitioning between minerals).

Increasing the Si content with depth, corresponding

to more perovskite and less magnesiowustite, would

increase seismic velocities, and thereby increase rather

than flatten the seismic gradients. Increasing the Fe

content with depth would have the opposite effect, but

very large variations may be required to produce a

seismically significant effect.

Other authors [33,49], using a 3rd order EOS, have

interpreted difficulties in fitting seismic models (not

data) as evidence for changes in chemistry and/or

superadiabatic temperature gradients in the LM. Such

temperature gradients would indeed help to lower the

seismic velocity with depth. However, composition-

ally homogeneous mantle with internal heat sources

tends towards subadiabaticity [50]. To dynamically

maintain significantly superadiabatic thermal gra-

dients may require accompanying physical changes


(in composition?) with depth. The overall effect has to

be one that lowers seismic gradients with depth, i.e.,

either the compositional variations also flatten BV/Bz

or the change in temperature is strong enough to offset

opposite compositional effects. Note again that the

change need not be one-dimensional. For example,

seismically imaged deep-mantle dpilesT with anti-

correlated bulk and shear velocities [11,33] might

bias average physical structure if their signature is

strong enough.

5. Conclusions

A physical reference model for the Earth’s mantle

that satisfies seismic global data similarly to classical

seismic reference models would facilitate seismic

interpretation. We tested whether the simplest average

physical model, representing a mantle that convects as

a whole can serve this purpose. It has a pyrolitic

composition (including phase transitions) and the

thermal structure of a lithospheric geotherm for 60

m.y. oceans, underlain by a mantle adiabat with a

potential temperature of 1300 8C, and extends down

to 2500 km depth.

We perform a Monte Carlo search to find adiabatic

pyrolite models that are (a) compatible with elastic

and anelastic mineral data within their uncertainties

and (b) satisfy global travel time (P and S) and

fundamental mode central frequency data (spheroidal

and toroidal), which are the type of data that entered

the most commonly used seismic reference models

(AK135 and PREM). Testing directly against seismic

data is necessary, as seismic models are non-unique

and there is significant trade-off between seismic

structures at different depths. To extrapolate mineral

parameters to mantle conditions, we used a linear

temperature extrapolation and 3rd order finite strain in

the upper mantle and a non-linear temperature

extrapolation and 3rd to 4th order finite strain in the

lower mantle, employing a wide range of parameters.

Only 28 whole mantle models (comprising 24 differ-

ent upper mantle and only 2 lower mantle structures)

out of 1010 satisfy the seismic constraints. This

essentially rejects this physical structure as a plausible

mantle average, unless there is a major problem with

the employed (extrapolations of) mineral physics

parameters.

Although different spherically symmetric seismic

models vary in their velocity structure by up to 0.5%

at a given depth, the seismic data actually constrain

several aspects very tightly. The average upper mantle

velocity as well as the maximum contrast between

shallow mantle and transition zone are well con-

strained by the global data, although detailed jumps

and gradients are not. For the lower mantle, both

average velocity and the velocity gradient as a

function of depth can deviate only in a minor way

from those of PREM and AK135.

The pyrolitic models have problems to (1) fit the

average upper and lower mantle travel time residuals

simultaneously, and (2) produce the low velocity-

depth gradient that the seismic data require along the

bulk part of the lower mantle. Furthermore, P and S

data prefer bulk and shear parameters that change

differently with increasing pressure, especially under

lower mantle conditions. A transition zone that is

slower than adiabatic dry pyrolite and a lower mantle

where velocities increase with depth less fast than our

physical reference model would alleviate these prob-

lems. If the equations of state do not affect the results,

this would require (1) a change in transition zone

composition that does not introduce dynamical layer-

ing (e.,g., hydration as proposed by [45] ) and (2) a

gradual change in physical state of the lower mantle,

e.g., a superadiabatic temperature gradient. Note that

sufficient three-dimensional compositional heteroge-

neity may also bias average structure away from a

background pyrolitic model.

Our analysis can certainly be improved by

including seismic data with better transition zone

sensitivity (PP, SS traveltimes and overtone frequen-

cies), by evaluating only thermodynamically consis-

tent combinations of mineral parameters and

improved constraints on these parameters, and by a

more comprehensive search algorithm. However, this

first study has shown the discriminative potential of

the approach and calls the most commonly accepted

physical reference structure of the mantle into

question.

Acknowledgments

We thank Brian Kennett, Jeroen Ritsema and Ian

Jackson for their positive reviews that helped us


clarify the paper. Lapo Boschi, Chris Hieronymus,

Jeannot Trampert and Artem Oganov are thanked for

discussions. This work was supported by the ETH

Zurich, Swiss National Fonds (Assistant Professorship

SG) and the EUFP5-TMR Network MAGE: Mars

Geophysical European Network. Contribution number

1381 of the Institute of Geophysics, ETH Zurich.

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