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Simultaneous inversion of mantle properties and initial conditions using an adjoint of mantle convection

Liu, Lijun and Gurnis, Michael (2008) Simultaneous inversion of mantle properties and initial conditions using an adjoint of mantle convection. Journal of Geophysical Research B, 113 (B8). Art. No. B08405. ISSN 0148-0227.

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Through the assimilation of present-day mantle seismic structure, adjoint methods can be used to constrain the structure of the mantle at earlier times, i.e., mantle initial conditions. However, the application to geophysical problems is restricted through both the high computational expense from repeated iteration between forward and adjoint models and the need to know mantle properties (such as viscosity and the absolute magnitude of temperature or density) a priori. We propose that an optimal first guess to the initial condition can be obtained through a simple backward integration (SBI) of the governing equations, thus lessening the computational expense. Given a model with known mantle properties, we show that a solution based on an SBI-generated first guess has smaller residuals than arbitrary guesses. Mantle viscosity and the effective Rayleigh number are crucial for mantle convection models, neither of which is exactly known. We place additional constraints on these basic mantle properties when the convection-induced dynamic topography on Earth's surface is considered within an adjoint inverse method. Besides assimilating present-day seismic structure as a constraint, we use dynamic topography and its rate of change in an inverse method that allows simultaneous inversion of the absolute upper and lower mantle viscosities, scaling between seismic velocity and thermal anomalies, and initial condition. The theory is derived from the governing equations of mantle convection and validated by synthetic experiments for both one-layer viscosity and two-layer viscosity regionally bounded spherical shells. For the one-layer model, at any instant of time, the magnitude of dynamic topography is controlled by the temperature scaling while the rate of change of topography is controlled by the absolute value of viscosity. For the two-layer case, the rate of change of topography constrains upper mantle viscosity while the magnitude of dynamic topography determines the temperature scaling (lower mantle viscosity) when upper-mantle (lower-mantle) density anomaly dominates the flow field; this two-stage scheme minimizes the tradeoff between temperature and lower mantle viscosity. For both cases, we show that the theory can constrain mantle properties with errors arising through the adjoint recovery of the initial condition; for the two-layer model, this error is manifest as a tradeoff between the temperature scaling and lower mantle viscosity.

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Additional Information:© 2008 American Geophysical Union. Received 16 January 2008; revised 7 April 2008; accepted 21 April 2008; published 8 August 2008. We thank Malcolm Sambridge for numerous discussions on inverse methods. The original CitcomS software was obtained from CIG, Computational Infrastructure for Geodynamics ( This is contribution 8998 of the Division of Geological and Planetary Sciences and 78 of the Tectonics Observatory, Caltech. All calculations carried out on the Caltech Geosciences Supercomputer Facility partially-supported by NSF EAR-0521699. Additional support provided through the Caltech Tectonics Observatory by the Gordon and Betty Moore Foundation.
Group:Caltech Tectonics Observatory, Seismological Laboratory
Funding AgencyGrant Number
NSF EAR-0521699
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:inverse algorithm; mantle viscosity; dynamic topography
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Other Numbering System NameOther Numbering System ID
Caltech Division of Geological and Planetary Sciences8998
Caltech Tectonics Observatory78
Record Number:CaltechAUTHORS:20101112-135453272
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Official Citation:Citation: Liu, L., and M. Gurnis (2008), Simultaneous inversion of mantle properties and initial conditions using an adjoint of mantle convection, J. Geophys. Res., 113, B08405, doi:10.1029/2008JB005594.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20778
Deposited By: Tony Diaz
Deposited On:17 Nov 2010 22:13
Last Modified:11 Jun 2015 12:58

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