Towards a 3D Reference Earth Model

A Comparison of Existing Models

NOTICE (March 2002): this page is a dynamic page because it changes as individual mantle models evolve.
Please provide input and comments to us (glaske@ucsd.edu) .

LAST UPDATE: April 2005.

Current Global Models
A Brief Visual Comparison
Download Maps
Quantitative Comparisons
Comparison of Predictions and Data
References
Statement

Current Global Models

At this point, 5 "high-resolution" mantle models are available. These are provided by Masters et al. (SIO), Dziewonski et al. (HRV), Romanowicz et al. (Berkeley), Grand (UT Austin), Ritsema et al. (Caltech). All models are available either through Web pages, anonymous ftp or by email to the author.

Each of the models has a different parameterization (a list to summarize this is under construction). For the qualitative and quantitative comparisons on this page, the models were all converted to the Scripps format (lateral: 4 deg equal area grid; radial: 18 constant layers of variable thickness).

A click on the name of the model will show a plot of maps of shear velocity perturbation at 12 depths throughout the mantle. The perturbations are in percent with respect to the mean for that particular depth which was taken out.

	Model Name	Plot	Hyper Link	Data/Parameterization	Reference
HRV	S362D1	x	Web Page	x	x
SIO	SB4L18	x	Web Page	x	x
Berk	SAW24B16	x	Web Page	x	x
Grand97	Grand¹	x	e-mail	x	x
Grand2000	G2000¹	x	e-mail	x	x
Calt	S20RTS	x	Web Page	x	x

¹ The model names for the Grand models are not original model names but assigned here to distinguish between the 1997 and the 2000 version.

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Download Maps

This section provides 4x4 degree maps, at various depths, for each of the models on this page. The downloadable files are ascii files with 90x45 numbers starting with the value assigned to the cell centered at 88N/2E (then 84N/2E, 80N/2E aso) and finishing with the cell centered at 88S/358E. The maps were obtained by converting all models using the Scripps parameterization. For each of the 18 depths, the values are read from the models using a 4 degree equal area grid, and then extrapolated to a 4x4 degree grid to provide an even grid. This looks a little clunky but it provides a laterally evenly distributed, nominal resolution. The spherical averages have been removed from the maps.

NB: In the conversion of the other models into the Scripps parameterization, no smoothing or interpolation was used. I simply picked the value at the center depth for each layer, implying that this is the 'average' value for that layer.
NBB: in the Scripps model, the first layer in the file is the bottom one, making the top layer be layer 18.

To transfer the maps, please click on an 'x' in the table and click on the 'save as' button of your web browser.

The 18 Scripps Layers and 4 Degree Maps
layer index	center depth	upper limit	lower limit	Scripps	Harvard	Berkeley	Caltech	Grand2000
18	66.5	22	111	x	x	x	x	x
17	155.5	111	200	x	x	x	x	x
16	250	200	300	x	x	x	x	x
15	350	300	400	x	x	x	x	x
14	465	400	530	x	x	x	x	x
13	595	530	660	x	x	x	x	x
12	735	660	810	x	x	x	x	x
11	885	810	960	x	x	x	x	x
10	1035	960	1110	x	x	x	x	x
9	1210	1110	1310	x	x	x	x	x
8	1410	1310	1510	x	x	x	x	x
7	1610	1510	1710	x	x	x	x	x
6	1810	1710	1910	x	x	x	x	x
5	2010	1910	2110	x	x	x	x	x
4	2210	2110	2310	x	x	x	x	x
3	2410	2310	2510	x	x	x	x	x
2	2610	2510	2710	x	x	x	x	x
1	2798.35	2710	2886.70	x	x	x	x	x
	download entire model (tar file)			x	x	x	x	x

You can download all maps at once using the "download tarfile" option. Click on an "x" then use the "save as" botton of your web browser to save the tar file on your computer. Then type "tar -xvf " to extract the 18 maps.

A Few 2 Degree Maps

These map have been obtained by inquiring the values from the models using a 2x2 degree grid. The effective point density is therefore larger at the poles but the even grid allows easy plotting. The spherical averages have been removed from the maps. This section provides 2x2 degree maps, at various depths, for each of the models on this page. The downloadable files are ascii files with 180x90 numbers starting with the value assigned to the cell centered at 89N/1E (then 87N/1E, 85N/1E aso) and finishing with the cell centered at 89S/359E. The maps were obtained by using a 2x2 degree grid and inquiring the values from each model, for each of the given depths. No smoothing or interpolation has been used. The spherical averages have been removed from the maps.

To transfer the maps, please click on an 'x' in the table and click on the 'save as' button of your web browser.

2 Degree Maps
Depth	Scripps	Harvard	Berkeley	Caltech	Grand2000
350	x	x	x	x	x
600	x	x	x	x	x
900	x	x	x	x	x
1200	x	x	x	x	x
1600	x	x	x	x	x
2000	x	x	x	x	x
2400	x	x	x	x	x
2800	x	x	x	x	x

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A Brief Visual Comparison

MAPS

View 3 maps at depths 140,925 and 2770km, for the HRV, SIO, BRK and Grand 1997 model.
click here for gif
click here for jpeg
Overall, the maps are quite similar. The upper layer traces the cold continental shields and the hot mid-ocean ridges.
Near the bottom of the mantle, all models show two large low-velocity regions, one beneath southern Africa, one beneath the central West Pacific Ocean. The relatively fast region around the Pacific is thought to be associated with the 'graveyard of subducted slabs'.
In the mid-mantle, and especially just below the transition zone, models vary the most. Anomalies in the mid-mantle are typically of smaller amplitude and so perhaps more difficult to image with high fidelity (see also 'quantitative comparison'). Also, going down across the transition zone, the datasets that constrain structure most dominantly in inversions typically changes from surface waves to body waves. In these cases, the choice of model parameterization, the inversion process, the regularization, the theory to interpret the data and the weighting of one dataset against another may have a great influence on the resulting model.

SLICES

Also view slices through 4 models that show the Farallon slab click here for gif/ click here for jpeg or along the East African Rift/African Superplume click here for gif/ click here for jpeg

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Quantitative Comparisons

RMS Amplitude as Function of Depth RMS amplitudes are highest in the upper mantle, near the top, and at the bottom of the mantle. Differences between models exist near the transition zone (see also above). The 1997 Grand model, that is shown in the plot, exhibits significantly lower amplitudes than the other models. The 2000/2001 versions now are more consistent with the other models.
show me!

Correlation as Function of Depth View graphs that show the RMS amplitudes and correlation of one model with each of the other models. The correlation generally degrades through the transition zone and just below it. For possible reasons see above. Correlation between the Scripps and Caltech models is relatively high while correlation of the Grand 1997 model with any of the others is relatively low throughout the mantle, but especially around the transition zone. One reason might be because the Grand 1997 model was constructed in such a way that structure was confined to the uppermost mantle as much as possible before solving for the rest of the mantle.

Berkeley model as reference

Caltech model as reference

Grand 1997 model as reference

Harvard model as reference

Scripps model as reference

Amplitude as Function of Wavelength
Structural variations are largest near the top and the bottom of the mantle. The spectrum of structural variations tends to be 'red' meaning that most power lies in longer wavelengths. In some models, harmonic degree two appears to be dominant throughout the mid-mantle. View a comparison of all five models here or each individual one below.

Correlation between models
Click on one of the "x" in the table to get a plot showing the correlation between two models as function of depth and harmonic degree (sorry, the comparsion with the Caltech model is not yet available).

HRV SIO Berk Grand Calt

HRV . x x x x

SIO x . x x x

Berk x x . x x

Grand x x x . x

Calt x x x x .

RCFs
Radial correlation functions are symmetric images that show the correlation of structure in one layer with that of another. For example, if the structure at the bottom of the mantle were an image of the one near the top, the RCF would have high values in the top right and bottm left corners. Large negative numbers mark pairs of layers that are mirrors of each other, with opposite sign. Since a structure correlates with itself, the diagonal of the image is one. 'Bottle necks' in such images mark regions of fundamental change with depth (e.g. across discontinuities). A marked bottle neck across the 660km discontinuity would suggest two-layered mantle convection. The marked difference between the Harvard and other models may come from the parameterization (separate sets of polynomials for upper and lower mantle and inversion for 660 topography).

... and for comparison what convection modelling predicts,
Paul Tackley's RCF

show all in 1 jpeg file

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Comparison of Predictions and Data

This comparison is incomplete and was only done with teh Scripps datasets. A helpful tool to assess how well a model represents Earth structure is by comparing predictions from a model with observed data. The following figure shows Rayleigh wave phase velocity maps at 6 mHz, observed by two groups and as predicted by 4 models. click here for maps. The Scripps and harvard models overall agree better with the observed maps than the predictions from the Grand model and the Berkeley model. Both tend to underpredict the data. Note that the Berkeley model is an V-SH model while Rayleigh waves are mostly sensitive to V-SV.

A plot shown here compares the fit of the models to the Scripps datasets. Not surprisingly, the Scripps model fits the Scripps data best and there appears a large discrepancy between the Scripps datasets and the Grand model. This comparison is incomplete and should not be understood as a rating of one model vs. another. It will be necessary to do a similar comparison with other datasets and discuss where discrepancies could come from. show me!

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References

HRV (S362D1): Gu, Y.J. and Dziewonski, A.M., 1999. "Mantle Discontinuities and 3-D Tomographic Models", EOS Trans. AGU, 80, F717. back to models

SIO (SB4L18): Masters G., Laske, G., Bolton, H. and Dziewonski, A., 2000. "The Relative Behavior of Shear Velocity, Bulk Sound Speed, and Compressional Velocity in the Mantle: Implications for Chemical and Thermal Structure" in: S. Karato, A.M. Forte, R.C. Liebermann, G. Masters and L. Stixrude (eds.) "Earth's Deep Interior", AGU Monograph 117, AGU, Washington D.C. back to models

Berk (SAW24B16): M�gnin, C. and Romanowicz, B., 2000. "The three-dimensional shear velocity structure of the mantle from the inversion of body, surface and higher-mode waveforms", Geophys. J. Int., 143, 709-728. back to models

Grand (Grand 97): Grand, S., 1997. "Global seismic tomography: a snapshot of convection in the Earth", GSA Today, 7, 1-7. back to models

Caltech (S20RTS): Ritsema, J., and van Heijst, H.-J., 2000. "Seismic imaging of structural heterogeneity in Earth's mantle: Evidence for large-scale mantle flow", Science Progress, 83, 243-259. back to models

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