Effects of mantle convection upon the Earth's surface:
a comparison between dynamic topography and ocean depth anomalies

Motoyuki Kido

Earthquake Research Institute
University of Tokyo

Master Thesis of Science presented to
Geophysics, Division of Science, Graduate School
University of Tokyo

March, 1993

Abstract. The seismic velocity anomalies from standard Earth models in the whole mantle were resolved by many authors using the tomography technique in the last decade. The lateral seismic velocity anomalies should reflect large scale flows within the mantle which may produce effects on the surface of the Earth. So, surface observables, such as topography, geoid, and plate motions, should be explained by the mantle convection. Once density perturbations and viscosity structure of the mantle are assumed, the instantaneous convection induced by the density perturbations can be calculated. We can predict the surface topography, geoid and the surface flow as well as flow patterns in the mantle from this convection calculation.

In this study, three-dimensional instantaneous mantle convection of a spherical geometry were calculated and three surface effects mentioned above were predicted. One-dimensional viscosity structure was assumed so that the observed geoid is consistent with that predicted. Density perturbations were obtained from three seismic tomography models, assuming that the density perturbation is proportional to the velocity perturbation. While the geoid and the plate motions have been well observed or estimated, the dynamic topography, which is defined as deformation departing from isostatically compensated heights, has not been yet. So I estimated the observed topography in ocean basins by evaluating the depth anomalies from predicted depth as a function of the plate age.

Good correlation coefficients ranging from 0.75 to 0.80 were obtained between the predicted and observed geoids for each of the three tomography models. The predicted surface flows were similar to the observed plate motions. The predicted dynamic topography have correlation coefficients of about 0.5 with the observed depth anomalies for each models. Then it was found that the large scale ocean depth anomalies were explained by mantle convection.

As an application of this result, we redetermined the age-depth curves, taking into account the dynamic topography. If we do not take into account the dynamic topography, the seafloor subsidence versus age was expressed by the square root of age younger than 70 Ma, and the bathymetry is flattened for older ages. This is consistent with previous studies. But after removing dynamic topography effects, the square root of age relation holds until 110 Ma. It means that ocean depths in the older regions are systematically biased toward high by mantle convection. This result would produce important implication to the plate cooling models, such as the plate model. The asymptotic thickness of the plate in the plate model should be much larger than those previously estimated.

0. Abstract -----------------------------  0
1. Introduction -------------------------  1

2. Surface observables 
     2-1. Depth anomalies ---------------  2
     2-2. Other observations ------------  4

3. Calculation of mantle convection
     3-1. Outline -----------------------  4
     3-2. Density perturbations ---------  5
     3-3. Viscosity structure -----------  7
     3-4. Propagator matrix method ------  7
     3-5. Response functions ------------ 10

4. Results and comparisons
     4-1. Geoid ------------------------- 11
     4-2. Flow patterns ----------------- 12
     4-3. Dynamic topography ------------ 12

5. Applications to age-depth curves ----- 14

6. Discussion --------------------------- 15

7. Conclusions -------------------------- 20

8. Acknowledgements --------------------- 21

9. References --------------------------- 21

   Tables ------------------------------- 26

   Figure captions ---------------------- 29

   Figures ------------------------------ 31

   Appendix ----------------------------- 50 - 51

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