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This paper presents a new derivative-free search method for finding models of acceptable data fit in a multidimensional parameter space. It falls into the same class of method as simulated annealing and genetic algorithms, which are commonly used for global optimization problems. The objective here is to find an ensemble of models that preferentially sample… (More)

Monte Carlo direct search methods, such as genetic algorithms, simulated annealing etc., are often used to explore a finite dimensional parameter space. They require the solving of the forward problem many times, that is, making predictions of observables from an earth model. The resulting ensemble of earth models represents all ‘information’ collected in… (More)

- Kurt Lambeck, Hélène Rouby, Anthony W Purcell, Yiying Sun, Malcolm Sambridge
- Proceedings of the National Academy of Sciences…
- 2014

The major cause of sea-level change during ice ages is the exchange of water between ice and ocean and the planet's dynamic response to the changing surface load. Inversion of ∼1,000 observations for the past 35,000 y from localities far from former ice margins has provided new constraints on the fluctuation of ice volume in this interval. Key results are:… (More)

We present simulations of large-scale landscape evolution on tectonic time scales obtained from a new numerical model which allows for arbitrary spatial discretization. The new method makes use of e cient algorithms from the field of computational geometry to compute the set of natural neighbours of any irregular distribution of points in a plane. The… (More)

- Thomas Bodin, Malcolm Sambridge, Hrvoje Tkalcic, P. Arroucau, K. Gallagher, Nicholas Rawlinson
- 2012

[1] We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme… (More)

[1] Monte Carlo inversion techniques were first used by Earth scientists more than 30 years ago. Since that time they have been applied to a wide range of problems, from the inversion of free oscillation data for whole Earth seismic structure to studies at the meter-scale lengths encountered in exploration seismology. This paper traces the development and… (More)

S U M M A R Y The reversible jump algorithm is a statistical method for Bayesian inference with a variable number of unknowns. Here, we apply this method to the seismic tomography problem. The approach lets us consider the issue of model parametrization (i.e. the way of discretizing the velocity field) as part of the inversion process. The model is… (More)

S U M M A R Y In most geophysical inverse problems the properties of interest are parametrized using a fixed number of unknowns. In some cases arguments can be used to bound the maximum number of parameters that need to be considered. In others the number of unknowns is set at some arbitrary value and regularization is used to encourage simple,… (More)

Monte Carlo methods have become important in analysis of nonlinear inverse problems where no analytical expression for the forward relation between data and model parameters is available, and where linearization is unsuccessful. In such cases a direct mathematical treatment is impossible, but the forward relation materializes itself as an algorithm allowing… (More)

- M. de Kool, Nicholas Rawlinson, Malcolm Sambridge
- 2006

S U M M A R Y We present a practical grid-based method in 3-D spherical coordinates for computing multiple phases comprising any number of reflection and transmission branches in heterogeneous layered media. The new scheme is based on a multistage approach which treats each layer that the wave front enters as a separate computational domain. A… (More)