Skip to main content
main-content

Über dieses Buch

This book describes the methods and numerical approaches for data assimilation in geodynamical models and presents several applications of the described methodology in relevant case studies. The book starts with a brief overview of the basic principles in data-driven geodynamic modelling, inverse problems, and data assimilation methods, which is then followed by methodological chapters on backward advection, variational (or adjoint), and quasi-reversibility methods. The chapters are accompanied by case studies presenting the applicability of the methods for solving geodynamic problems; namely, mantle plume evolution; lithosphere dynamics in and beneath two distinct geological domains – the south-eastern Carpathian Mountains and the Japanese Islands; salt diapirism in sedimentary basins; and volcanic lava flow.
Applications of data-driven modelling are of interest to the industry and to experts dealing with geohazards and risk mitigation. Explanation of the sedimentary basin evolution complicated by deformations due to salt tectonics can help in oil and gas exploration; better understanding of the stress-strain evolution in the past and stress localization in the present can provide an insight into large earthquake preparation processes; volcanic lava flow assessments can advise on risk mitigation in the populated areas. The book is an essential tool for advanced courses on data assimilation and numerical modelling in geodynamics.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
In this chapter, we introduce direct and inverse problems as well as well- and ill-posed problems, which are characterised by the existence, uniqueness, and stability of the problem solution. We present some examples of unstable problems and discuss the basic elements in forward and backward numerical modelling and the errors associated with the modelling. Finally we briefly review the methods for data assimilation used in geodynamic modelling.
Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev

Chapter 2. Backward Advection Method and Its Application to Modelling of Salt Tectonics

Abstract
This chapter deals with the simplest method in data assimilation allowing for solving a geodynamic problem backward in time by suppressing thermal diffusion. The method is suitable in the advection-dominated regimes of thermal convective flows. We present an application of the method to three-dimensional numerical modelling of salt diapirism in sedimentary basins.
Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev

Chapter 3. Variational Method and Its Application to Modelling of Mantle Plume Evolution

Abstract
In this chapter, we present a variational (VAR) method for assimilation of data related to models of thermal convective flow. This approach is based on a search for model parameters (e.g., mantle temperature and flow velocity in the past) by minimizing the differences between present-day observations of the relevant physical parameters (e.g., temperature derived from seismic tomography, geodetic measurements) and those predicted by forward models for an initial guess temperature. To demonstrate the applicability of this method, we present a numerical model of the evolution of mantle plumes and show that the initial shape of the plumes can be accurately reconstructed. Finally we discuss some challenges in the VAR data assimilation including a smoothness of data.
Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev

Chapter 4. Application of the Variational Method to Lava Flow Modelling

Abstract
In this chapter, we present an application of the variational data assimilation method to the problem for determination of thermal and dynamic characteristics of lava flow from thermal measurements at lava’s upper surface. Assuming that the temperature and the heat flow are known at the lava’s upper surface, the missing condition at the lower surface of the lava is determined at first, and then the flow characteristics (temperature and flow velocity) are resolved in the entire model domain.
Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev

Chapter 5. Quasi-Reversibility Method and Its Applications

Abstract
In this chapter, we introduce a quasi-reversibility (QRV) approach to data assimilation, which allows for incorporating observations (at present) and unknown initial conditions (in the past) for physical parameters (e.g., temperature and flow velocity) into a three-dimensional dynamic model in order to determine the initial conditions. The dynamic model is described by the backward heat, motion, and continuity equations. The use of the QRV method implies the introduction into the backward heat equation of the additional term involving the product of a small regularization parameter and a higher order temperature derivative. The data assimilation in this case is based on a search of the best fit between the forecast model state and the observations by minimizing the regularization parameter. We present the application of the QRV method to two case studies: evolution of (i) mantle plumes and (ii) a relic lithospheric slab.
Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev

Chapter 6. Application of the QRV Method to Modelling of Plate Subduction

Abstract
This chapter presents the application of the QRV method to dynamic restoration of the thermal state of the mantle beneath the Japanese islands and their surroundings. The geodynamic restoration for the last 40 million years is based on the assimilation of the present temperature inferred from seismic tomography, and the present plate movement derived from geodetic observations, paleogeographic and paleomagnetic plate reconstructions.
Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev

Chapter 7. Comparison of Data Assimilation Methods

Abstract
Following Ismail-Zadeh et al. (Geophys J Int 170:1381–1398, 2007), we compare in this chapters the backward advection (BAD), variational (VAR), and quasi-reversibility (QRV) methods in terms of solution stability, convergence, and accuracy, time interval for data assimilation, analytical and algorithmic works, and computer performance.
Alik Ismail-Zadeh, Alexander Korotkii, Igor Tsepelev
Weitere Informationen