Supplementary Material

We use 2D (part 1) and global (part 2) models to investigate the dynamics of a sinking slab in deep mantle. The following materials provide the detailed model setup (Tables S1 and S2) and modeling results (Figures S2-S4).

Part 1. Model setup for 2D models

We compute two-dimensional mantle convection models in a Cartesian coordinate system in which the equations are solved with the Citcom2D code to solve mass, momentum and energy equations (Moresi and Solomatov, 1995). The model domain is 5,740 km × 2,870 km (horizontal × vertical) with 256128 elements and 16 markers per element. All boundaries are free-slip, and temperatures are set to be T=0.5 (non-dimensional) at the top and T=1 at the bottom boundaries. Besides the fundamental properties like the viscosity jump and Clapeyron slope at 660 km discontinuity, we also test the properties of the isolated slab and thermochemical piles in models.

The Rayleigh Number of the ambient mantle equals based on the buoyancy and viscosity parameters in the Table S1. For the Rayleigh number of the chemical pile (, where is the density contrast), we use the buoyancy number to describe the density difference between the thermochemical pile and ambient mantle (Table S2).

The viscosity in models depends on temperature, depth and composition:

where , T is the non-dimensional temperature. is pre-factor for depth. for the upper mantle, and has different values for the lower mantle in different cases (see details in Table S2). In all models, visT equals 0, and E (active energy) equals 6.90. C is composition factor varying between 0 and 1. Viscc0 is the compositional dependent parameter, controlling the viscosity contrast between thermochemical pile and ambient mantle.

To approximate the temperature profile of the subducted slab, we use a Gaussian function to describe the cross section of the rectangular slab,

where is the distance from the perpendicular bisector of the slab width. The standard deviation is always an eighth of slab width, in order to cut off the Gaussian curve to a proper length.

In a realistic slab, the thermal structure is not symmetrical, but similar to an error function in the situation of instantaneous cooling of a semi-infinite half-space, which relates to the age of oceanic crust. When calculating the equivalent amount of buoyancy between a hypothetical slab and a realistic slab, the relationship between width and age of Gaussian slab can be obtained as

60-Myr-old and 130-Myr-old hypothetical slabs correspond to the width value 0.0563 and 0.08, respectively.

For the temperature field of thermochemical piles, we connect initial temperature with its initial composition field. We apply a hyperbolic tangent function to construct the upper boundary () of the thermochemical piles

where we take as 0.015. is the width of the LLSVP, and is the height of the LLSVP. The temperature field for the LLSVP is constructed as

Part 2. Viscosity structure in global models

In the global models, the viscosity depends on the temperature, depth and composition

where is the reference viscosity listed in Table 1. is the non-dimensional viscosity prefactor depending on depths, with value equals to 1 in the lithosphere and upper mantle. The value of in lower mantle varies in models (listed in Table 2). is the viscosity pre-factor depending on composition. The value of of the thermochemical piles is listed in Table 2, and for other materials. E is non-dimensional activation energy. E =7 in the upper mantle and equals zero in the lower mantle. T is non-dimensional temperature.

Table S1 Constant parameters in 2D models

Symbol

Description

Value

Thermal expansion coefficient

Density

Gravity acceleration

Temperature contrast

Mantle depth

Thermal diffusion constant

Reference viscosity

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Table S2 List of 2D models

Case

Phase Transition at 660km

Temperature-dependent viscosity

Lower mantle viscosity

Slab

LLSVP (Thermochemical Pile) Properties

Insert position

Initial depth (km)

Length (km)

Dip angle ()

Buoyancy number

Viscosity contrast

Pile Height

(/2870 km)

Pile Width

(/2870 km)

N01

Y

Y

10

1.0

574

1000

60

0.0

1

0.35

0.66

1

N02

Y

Y

30

1.0

574

1000

60

0.0

1

0.35

0.66

1

N03

Y

Y

60

1.0

574

1000

60

0.0

1

0.35

0.66

1

N04

Y

Y

100

1.0

574

1000

60

0.0

1

0.35

0.66

1

N05

Y

Y

30

1.0

574

1000

60

0.4

1

0.35

0.66

1

N06

Y

Y

30

1.0

574

1000

60

0.5

1

0.35

0.66

1

N07

Y

-

30

1.0

574

1000

60

0.4

900

0.35

0.66

1

N08

Y

Y

30

1.0

574

1000

60

0.4

900

0.35

0.66

1

N09

Y

Y

30

1.0

574

1000

60

0.4

300

0.35

0.66

1

N10

-

Y

30

1.0

574

1000

60

0.4

900

0.35

0.66

1

N11

Y

Y

30

0.65

574

1000

60

0.4

900

0.35

0.66

1

N12

Y

Y

30

0.50

574

1000

60

0.4

900

0.35

0.66

1

N13

Y

Y

60

0.50

574

1000

60

0.4

1

0.35

0.66

1

N14

Y

Y

60

0.50

574

1500

60

0.4

1

0.35

0.66

1

N15

Y

Y

60

0.50

574

2000

60

0.4

1

0.35

0.66

1

N16

Y

Y

60

0.50

574

1000

60

0.4

900

0.35

0.66

1

N17

Y

Y

30

0.50

574

1000

60

0.4

1800

0.35

0.66

1

N18

Y

Y

60

0.50

574

1000

60

0.4

1800

0.35

0.66

1

N19

Y

Y

30

0.60

574

1000

25

0.4

1200

0.25

0.55

1

N20

Y

Y

30

0.60

574

2000

25

0.4

1200

0.25

0.55

1

S01

Y

Y

30

0.60

574

2000

25

0.4

900

0.35

0.66

1

S02

Y

Y

30

0.60

574

2500

20

0.4

900

0.35

0.66

1

S03

Y

Y

30

0.70

718

3000

20

0.4

900

0.35

0.66

1

S04

Y

Y

30

0.80

718

4000

15

0.4

900

0.35

0.66

1

S05

Y

Y

30

0.60

574

2000

25

0.4

1200

0.25

0.55

1

S06

Y

Y

30

0.60

574

2000

25

0.4

1000

0.35

0.66

2

S07

Y

Y

30

0.60

574

2000

25

0.4

10000

0.35

0.66

2

S08

Y

Y

30

0.60

574

2000

25

0.4

1200

0.35

0.66

2

S09

Y

Y

30

0.60

574

2000

25

0.2

1000

0.35

0.66

2

S10

Y

Y

30

0.60

574

2000

25

0.2

10000

0.35

0.66

2

S11

Y

Y

30

0.60

574

2000

25

0.3

1000

0.35

0.66

2

S12

Y

Y

30

0.60

574

2000

25

0.3

10000

0.35

0.66

2

S13

Y

Y

30

0.60

574

2000

25

0.3

1000

0.3

0.55

2

S14

Y

Y

30

0.60

574

2000

25

0.3

10000

0.3

0.55

2

S15

Y

Y

30

0.60

574

2000

25

0.4

1

0.25

0.55

1

S16

Y

Y

30

0.60

574

2000

25

0.4

500

0.25

0.55

1

S17

Y

Y

30

0.60

574

2000

25

0.4

5000

0.25

0.55

1

N for cases with north dipping slab, S for cases with south dipping slab.

Slab age: 60 Myr

Clapeyron slope at 660km:

Temperature Mode (TMode) is the initial temperature field which is different between cases, the temperature anomaly in Mode 2 is smaller than Model 1

In all south dipping cases, the dipping direction has reversed from southward to northward.

In Models N01-N04 and N19-N20, because there are no LLSVPs or too small LLSVPs underlying the slab to support the slab, slab dip polarity does not change.

Supplemental Figures:

Figure S1 Comparison of global tomography models at the cross section from the Kerguelen Plateau to Indonesia (shown in Fig. 1). LLNL-G3D-JPS (Simmons et al., 2015), S20RTS (Ritsema et al., 1999), S40RTS (Ritsema et al., 2011), SMEAN (Becker and Boschi, 2002), PMEAN (Becker and Boschi, 2002), GyPSuM (Simmons et al., 2009), GAP-P4 (Obayashi et al., 2013), MONTELLI-P (Montelli et al., 2006), SB4L18 (Masters et al., 2000), SAW24B16 (Megnin and Romanowicz, 2000), MIT-P08 (Li et al., 2008), Grand2002 (Grand, 2002). Green lines represent the extent of the SEIS anomaly in LLNL-G3D-JPS model.

Figure S2 2D model setup. (a) Initial thermal (left panel) and viscosity (right panel) fields of Model N20. (b) Initial thermal (left panel) and viscosity (right panel) fields of Model S05.

Figure S3 Global models that test the effects of the inserted slab, African pile, viscosity of the lower mantle, and Clapeyron slope at the 660 km transition zone. (a) Model 2: no inserted slab below the Indian Ocean in the initial model. (b) Model 3: no African thermochemical pile is included. (c) Model 4: the buoyancy of the inserted slab presents an 80- to 120-Myr-old oceanic plate. (d) Model 5: the viscosity increase at 660 km discontinuity by a factor of 30. (e) Model 6: the Clapeyron slope at 660 km discontinuity is zero.

Figure S4 Global models that test the density and viscosity effects of thermochemical piles. (a) Model 7: the viscosity of thermochemical piles is identical as lower mantle. (d) Model 8: the thermochemical piles are 125 kg/m3 denser than ambient mantle.

Figure S1

Figure S2

Figure S3

Figure S4

Reference

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