Klaus Mosegaard

Bio: Klaus Mosegaard is an academic researcher from University of Copenhagen. The author has contributed to research in topics: Inverse problem & Monte Carlo method. The author has an hindex of 31, co-authored 116 publications receiving 5509 citations. Previous affiliations of Klaus Mosegaard include Technical University of Denmark & Denver Federal Center.

Monte Carlo sampling of solutions to inverse problems

Abstract: Probabilistic formulation of inverse problems leads to the definition of a probability distribution in the model space. This probability distribution combines a priori information with new information obtained by measuring some observable parameters (data). As, in the general case, the theory linking data with model parameters is nonlinear, the a posteriori probability in the model space may not be easy to describe (it may be multimodal, some moments may not be defined, etc.). When analyzing an inverse problem, obtaining a maximum likelihood model is usually not sucient, as we normally also wish to have infor

Past Temperatures Directly from the Greenland Ice Sheet

Abstract: A Monte Carlo inverse method has been used on the temperature profiles measured down through the Greenland Ice Core Project (GRIP) borehole, at the summit of the Greenland Ice Sheet, and the Dye 3 borehole 865 kilometers farther south. The result is a 50, 000-year-long temperature history at GRIP and a 7000-year history at Dye 3. The Last Glacial Maximum, the Climatic Optimum, the Medieval Warmth, the Little Ice Age, and a warm period at 1930 A.D. are resolved from the GRIP reconstruction with the amplitudes -23 kelvin, +2.5 kelvin, +1 kelvin, -1 kelvin, and +0.5 kelvin, respectively. The Dye 3 temperature is similar to the GRIP history but has an amplitude 1.5 times larger, indicating higher climatic variability there. The calculated terrestrial heat flow density from the GRIP inversion is 51.3 milliwatts per square meter.

Monte carlo methods in geophysical inverse problems

Abstract: [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 application of Monte Carlo methods for inverse problems in the Earth sciences and in particular geophysics. The major developments in theory and application are traced from the earliest work of the Russian school and the pioneering studies in the west by Press [1968] to modern importance sampling and ensemble inference methods. The paper is divided into two parts. The first is a literature review, and the second is a summary of Monte Carlo techniques that are currently popular in geophysics. These include simulated annealing, genetic algorithms, and other importance sampling approaches. The objective is to act as both an introduction for newcomers to the field and a comprehensive reference source for researchers already familiar with Monte Carlo inversion. It is our hope that the paper will serve as a timely summary of an expanding and versatile methodology and also encourage applications to new areas of the Earth sciences.

Monte Carlo analysis of inverse problems

Abstract: 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 data to be calculated for any given model. Monte Carlo methods can be divided into two categories: the sampling methods and the optimization methods. Monte Carlo sampling is useful when the space of feasible solutions is to be explored, and measures of resolution and uncertainty of solution are needed. The Metropolis algorithm and the Gibbs sampler are the most widely used Monte Carlo samplers for this purpose, but these methods can be refined and supplemented in various ways of which the neighbourhood algorithm is a notable example. Monte Carlo optimization methods are powerful tools when searching for globally optimal solutions amongst numerous local optima. Simulated annealing and genetic algorithms have shown their strength in this respect, but they suffer from the same fundamental problem as the Monte Carlo sampling methods: no provably optimal strategy for tuning these methods to a given problem has been found, only a number of approximate methods.

Heat flux anomalies in Antarctica revealed by satellite magnetic data.

Abstract: The geothermal heat flux is an important factor in the dynamics of ice sheets; it affects the occurrence of subglacial lakes, the onset of ice streams, and mass losses from the ice sheet base. Because direct heat flux measurements in ice-covered regions are difficult to obtain, we developed a method that uses satellite magnetic data to estimate the heat flux underneath the Antarctic ice sheet. We found that the heat flux underneath the ice sheet varies from 40 to 185 megawatts per square meter and that areas of high heat flux coincide with known current volcanism and some areas known to have ice streams.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica

Abstract: The recent completion of drilling at Vostok station in East Antarctica has allowed the extension of the ice record of atmospheric composition and climate to the past four glacial–interglacial cycles. The succession of changes through each climate cycle and termination was similar, and atmospheric and climate properties oscillated between stable bounds. Interglacial periods differed in temporal evolution and duration. Atmospheric concentrations of carbon dioxide and methane correlate well with Antarctic air-temperature throughout the record. Present-day atmospheric burdens of these two important greenhouse gases seem to have been unprecedented during the past 420,000 years.

Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica

Abstract: The recent completion of drilling at Vostok station in East Antarctica has allowed the extension of the ice record of atmospheric composition and climate to the past four glacial–interglacial cycles. The succession of changes through each climate cycle and termination was similar, and atmospheric and climate properties oscillated between stable bounds. Interglacial periods differed in temporal evolution and duration. Atmospheric concentrations of carbon dioxide and methane correlate well with Antarctic air-temperature throughout the record. Present-day atmospheric burdens of these two important greenhouse gases seem to have been unprecedented during the past 420,000 years.

An overview of full-waveform inversion in exploration geophysics

Abstract: Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

Persistent Solar Influence on North Atlantic Climate During the Holocene

Abstract: Surface winds and surface ocean hydrography in the subpolar North Atlantic appear to have been influenced by variations in solar output through the entire Holocene. The evidence comes from a close correlation between inferred changes in production rates of the cosmogenic nuclides carbon-14 and beryllium-10 and centennial to millennial time scale changes in proxies of drift ice measured in deep-sea sediment cores. A solar forcing mechanism therefore may underlie at least the Holocene segment of the North Atlantic's "1500-year" cycle. The surface hydrographic changes may have affected production of North Atlantic Deep Water, potentially providing an additional mechanism for amplifying the solar signals and transmitting them globally.