Monte Carlo Methods in Geophysical Inverse Problems

Sambridge, Malcolm; Mosegaard, Klaus

doi:10.1029/2000rg000089

Cited by 649 publications

(408 citation statements)

References 203 publications

(300 reference statements)

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“…In particular, the deterministic model can be very complex and does not need to be linear, which is the main reason why this approach has been used extensively in a wide manifold of applications (for example, Naff et al, 1998;Sambridge and Mosegard, 2002). The limit of the Monte Carlo approach is that it may be extremely time consuming when complex deterministic (numerical) models need to be computed many times (for example, systems that are three-dimensional, or with nonlinear transients).…”

Section: Stochastic Modelsmentioning

confidence: 99%

Stochastic versus Deterministic Approaches

Renard¹,

Alcolea

Ginsbourger³

2013

Environmental Modelling

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In broad sense, modelling refers to the process of generating a simplified representation of a real system. A suitable model must be able to explain past observations, integrate present data and predict with reasonable accuracy the response of the system to planned stresses (Carrera et al., 1987). Models have evolved together with science and nowadays modelling is an essential and inseparable part of scientific activity. In environmental sciences, models are used to guarantee suitable conditions for sustainable development and are a pillar for the design of social and industrial policies.Model types include analogue models, scale models and mathematical models. Analogue models represent the target system by another, more understandable or analysable system. These models rely on Feynman's principle (Feynman et al., 1989, sec. 12-1): 'The same equations have the same solutions.' For example, the electric/hydraulic analogy (Figure 8.1a) establishes the parallelism between voltage and water-pressure difference or between electric current and flow rate of water. Scale models are representations of a system that is larger or smaller (most often) than the actual size of the system being modelled. Scale models (Figure 8.1b) are often built to analyse physical processes in the laboratory or to test the likely performance of a particular design at an early stage of development without incurring the full expense of a full-sized prototype. Notwithstanding the use of these types of models in other branches of science and engineering, the most popular models in environmental sciences are mathematical. A mathematical model describes a system by a set of state variables and a set of equations that establish relationships between those variables and the governing parameters. Mathematical models can be analytical or numerical. Analytical models often require many simplifications to render the equations amenable to solution. Instead, numerical models are more versatile and make use of computers to solve the equations.Mathematical models (either analytical or numerical) can be deterministic or stochastic (from the Greek τóχoς for 'aim' or 'guess'). A deterministic model is one in which state variables are uniquely determined by parameters in the model and by sets of previous states of these variables. Therefore, deterministic models perform the same way for a given set of parameters and initial conditions and their solution is unique. Nevertheless, deterministic models are sometimes unstable -i.e., small perturbations (often below the detection limits) of the initial conditions or the parameters governing the problem lead to large variations of the final solution (Lorenz, 1963). Thus, despite the fact that the solution is unique, one can obtain solutions that are dramatically different by perturbing slightly a single governing parameter or the initial condition at a single point of the domain.

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Section: Stochastic Modelsmentioning

confidence: 99%

Stochastic versus Deterministic Approaches

Renard¹,

Alcolea

Ginsbourger³

2013

Environmental Modelling

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“…Sivia (1996) is another useful reference, and a paper by Griffiths (1982) provides some geomorphological context. A wide range of computational techniques have been developed to enable Bayesian calculations in various settings, for which a review by Sambridge and Mosegaard (2002) may be a good starting point.…”

Section: Bayesian Inferencementioning

confidence: 99%

An introduction to learning algorithms and potential applications in geomorphometry and Earth surface dynamics

Valentine

Kalnins

2016

Earth Surf. Dynam.

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Abstract. "Learning algorithms" are a class of computational tool designed to infer information from a data set, and then apply that information predictively. They are particularly well suited to complex pattern recognition, or to situations where a mathematical relationship needs to be modelled but where the underlying processes are not well understood, are too expensive to compute, or where signals are over-printed by other effects. If a representative set of examples of the relationship can be constructed, a learning algorithm can assimilate its behaviour, and may then serve as an efficient, approximate computational implementation thereof. A wide range of applications in geomorphometry and Earth surface dynamics may be envisaged, ranging from classification of landforms through to prediction of erosion characteristics given input forces. Here, we provide a practical overview of the various approaches that lie within this general framework, review existing uses in geomorphology and related applications, and discuss some of the factors that determine whether a learning algorithm approach is suited to any given problem.

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“…He stated that there is a need to establish a scientific methodology for identifying and quantifying the possible impacts of uncertainty. For complex General Circulation Models (GCMs) he concluded that the Monte Carlo approach is the only practical solution to obtain uncertainty estimates despite the lack of rigor in the determination of the sample size and the enormous computational effort that is required, see also Sambridge and Mosegard (2002). If one is interested in the climate mean response to a small change in forcing, an alternative approach, based on the Fluctuation-Dissipation Theorem (Leith 1975), has been developed, see also Ch.…”

Section: Introductionmentioning

confidence: 99%

Effect of parameter change upon the extra-tropical atmospheric variability

2011

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Global climate models contain numerous parameters with uncertain values. In the context of climate simulation and prediction, it is relevant to obtain an estimate of the range of climate outcomes given the parameter uncertainty. Instead of randomly perturbing parameters, we determine parameter perturbations from short-term integrations that potentially have a high impact on the climate of the model. For this purpose we consider a dry, spectral quasi-geostrophic, three-level model on the sphere and its tangent linear and adjoint equations. With an empirical forcing, the model produces a fairly realistic simulation of the extra-tropical winter circulation. We allowed perturbations in a 1,449 dimensional parameter space. As a measure of impact on the climate we compute the change in the probability density function of the dominant patterns of variability. We find that the largest climate response in a set of 1,000 simulations with potentially high impact perturbations is much larger than the largest response in a similar set of simulations with randomly picked perturbations. We conclude that parameter sensitivity calculations based on short term integrations contain valuable information about the sensitivity of the model climate to parameter perturbations. The approach is feasible for stateof-the-art climate models provided that the tangent linear and adjoint equations are implemented.

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Monte Carlo Methods in Geophysical Inverse Problems

Cited by 649 publications

References 203 publications

Stochastic versus Deterministic Approaches

Stochastic versus Deterministic Approaches

An introduction to learning algorithms and potential applications in geomorphometry and Earth surface dynamics

Effect of parameter change upon the extra-tropical atmospheric variability

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