# Klaus MosegaardUniversity of Copenhagen · Niels Bohr Institute

Klaus Mosegaard

Dr Scient

## About

160

Publications

26,408

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6,281

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Citations since 2017

Introduction

Additional affiliations

February 2010 - March 2014

February 2010 - March 2014

January 1993 - January 2010

## Publications

Publications (160)

Numerous studies have demonstrated the capability of supervised deep learning techniques for predicting geologic features of interest from seismic sections, including features that are difficult to identify using traditional interpretation methods. However, the successful application of these techniques in practice has been limited by the difficult...

Seismic facies classification aims to predict a facies model, or a set of facies models, from measured seismic data. We focus on stochastic classification methods to estimate the probability distribution of facies conditioned on seismic data. Bayesian classification methods based on analytical solutions are generally applied to seismically inverted...

Purpose
We present a probabilistic approach to medical image analysis that requires, and makes use of, explicit prior information provided by a medical expert. Depending on the choice of prior model the method can be used for image enhancement, analysis, and segmentation.
Methods
The methodology is based on a probabilistic approach to medical imag...

The mapping of faults provides essential information on many aspects of seismic exploration, characterisation of reservoirs for compartmentalisation and cap-rock integrity. However, manual interpretation of faults from seismic data is time-consuming and challenging due to limited resolution and seismic noise. In this study, we apply a convolutional...

Shear wave velocity information is valuable in many aspects of seismic exploration and characterization of reservoirs. However, shear wave logs are not always available in the interval of interest due to cost and time‐saving purposes. In this study, we present a tailored supervised learning approach to estimate shear wave velocity from well log mea...

Inversion of seismic data using information from horizontal wells is often hampered by cumulative well‐location errors. These errors can have a significant influence on the final subsurface model derived from the data. To achieve a proper data integration and arrive at correct uncertainty estimates, we formulate the problem in a fully probabilistic...

Numerous studies have demonstrated the capability of supervised deep learning techniques for predicting geological features of interest from seismic sections, including features that are difficult to identify using traditional interpretation methods. However, successful application of these techniques in practice has been limited by the difficulty...

When hydrocarbon reservoirs are used as a CO2 storage facility, an accurate uncertainty analysis and risk assessment is essential. An integration of information from geological knowledge, geological modelling, well log data, and geophysical data provides the basis for this analysis. Modelling the time development of stress/strain changes in the ove...

Mapping landforms on the Moon is of great interest and importance for future human settlements and resources exploration. One of the first steps is to map the topography in great detail and resolution. However, data from the Lunar Orbiter Laser Altimeter (LOLA) provide low-resolution elevation maps in comparison to the size of detailed geological f...

Markov Chain Monte Carlo (MCMC) sampling of solutions to large-scale inverse problems is, by many, regarded as being unfeasible due to the large number of model parameters. This statement, however, is only true if arbitrary, local proposal distributions are used. If we instead use a global proposal, informed by the physics of the problem, we may dr...

Geological facies modeling is a key component in exploration and characterization of subsurface reservoirs. While traditional geostatistical approaches are still commonly used nowadays, deep learning is gaining a lot of attention within geoscientific community for generating subsurface models, as a result of recent advance of computing powers and i...

Analysis of processed seismic data still plays a major role in exploration geophysics for understanding the structure and properties of the subsurface. In this work we address the problem of inverting, in a probabilistic fashion, angle-versus-amplitude (AVA) seismic data directly for porosity, using the Hamiltonian Monte Carlo method (HMC). To infe...

Stochastic petrophysical inversion is a method to predict reservoir properties from seismic data. Recent advances in stochastic optimization allow generating multiple realizations of rock and fluid properties conditioned on seismic data. To match the measured data and represent the uncertainty of the model variables, a large number of realizations...

Stochastic methods for seismic inversion problems for the estimation of rock and fluid properties are commonly adopted in reservoir characterization studies. Among the numerous algorithms, Markov chain Monte Carlo (McMC) methods represent a family of algorithms for the estimation of the posterior distribution of the variables of interest. In seismi...

When hydrocarbon reservoirs are used as a CO2 storage facility, an accurate uncertainty analysis and risk assessment is essential. An integration of information from geological knowledge, geological modelling, well log data, and geophysical data provides the basis for this analysis. Modelling the time development of stress/strain changes in the ove...

Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a consequence of the No-Free-Lunch Theorem, the only way we can ensure a significantly better performance of search...

Plain Language Summary
Forward magnetic calculation plays a major role in geophysics to model magnetization, location, and shape of magnetic sources. One of the most popular approaches to calculate magnetic anomalies due to two‐dimensional bodies is based on the formulas of Talwani and Heirtzler (1962, 1964), that have been widely used both for sci...

Heat storage in the Danish subsurface is gaining increasing interest for optimizing the use of energy resources, but no deep heat storage facilities have yet been established. As an analogue we study the Gassum Formation in the Stenlille structure that is presently used for gas storage. This allows us to discuss geological and technical characteris...

We present a framework to solve geophysical inverse problems using the Hamiltonian Monte Carlo (HMC) method, with a focus on Bayesian tomography. Recent work in the geophysical community has shown the potential for gradient-based Monte Carlo sampling for a wide range of inverse problems across several fields.
Many high-dimensional (non-linear) pro...

Geostatistical simulation methods have been used to quantify spatial variability of reservoir models since the 80s. In the last two decades, state of the art simulation methods have changed from being based on covariance-based 2-point statistics to multiple-point statistics (MPS), that allow simulation of more realistic Earth-structures. In additio...

Sought-after reservoir properties of interest are linked only indirectly to the observable geophysical data which are recorded at the earth’s surface. In this framework, seismic data represent one of the most reliable tool to study the structure and properties of the subsurface for natural resources. Nonetheless, seismic analysis is not an end in i...

Large amounts of reflection seismic data are routinely collected to investigate the subsurface. This demands for fast and reliable algorithms to invert the seismic data for desired properties, such as acoustic impedance or other physical properties. The algorithm for inversion, in case of linear forward model and Gaussian uncertainties, based on th...

In this study, we analyze 26,000 posterior realizations obtained through Monte Carlo sampling from the posterior distribution of a reflection seismic inverse problem and show that the posterior realizations cluster around multimodal peaks. This problem is based on a seismic trace recorded in the southern part of Jutland, Denmark. Prior information...

In this study, we analyze 26000 posterior realizations obtained through Monte Carlo sampling from the posterior distribution of a reflection seismic inverse problem and show that the posterior realizations cluster around multimodal peaks. This problem is based on a seismic trace recorded in the southern part of Jutland, Denmark. Prior information i...

Multiple-point-based geostatistical methods are used to model complex geological structures. However, a training image containing the characteristic patterns of the Earth model has to be provided. If no training image is available, two-point (i.e., covariance-based) geostatistical methods are typically applied instead because these methods provide...

Heat Storage in Hot Aquifers
Petrophysical, Geological, Geostatistical, Flow and Temperature models of Stenlille Structure
Lisa Pasquinelli a, Ida Lykke Fabricius a, Klaus Mosegaard b
a Department of Civil Engineering, DTU-BYG, 2800 Kgs Lyngby.
b Niels Bohr Institute, Copenhagen University, Department of Climate and Geophysics, 2100 Copenhagen Ø....

The problem of inferring information about the Earth can be described as a data integration problem, where the solutions a probability distribution that combines all available information. This chapter presents the methods for probabilistic characterization of different kinds of geo-information. Then a number of methods that allow inferring informa...

Noise-contaminated data and prior information on model parameters are the basic elements of any inverse problem. Probability can be seen from two viewpoints: a purely mathematical perspective and a heuristic perspective. This chapter deals with Kolmogorov's mathematical definition of probability. In probabilistic, nonlinear inversion with complex p...

This chapter describes a quantitative approach that integrates data and results from mineral physics, petrological analyses, and geophysical inverse calculations to map geophysical data directly for mantle composition and thermal state. Seismic tomography has proved an important tool to image the inaccessible parts of the Earth. Computation of phys...

Mathematical physics is based on the fundamental assumption that physical predictions must be the same, independently of the parameterization of the system. This principle even constitutes the very foundation of certain physical theories, of which the theory of relativity is perhaps the most notable. The importance of the principle is that it seeks...

It is commonly accepted that layers thinner than about 1/8 of the dominant wavelength cannot be resolved from reflection seismic normal incidence data. We demonstrate that there is in theory no limit the resolution of normal incidence reflection seismic data. The resolution of reflection seismic data is linked to the noise level, parameterization a...

Determination of a petroleum reservoir structure and rock bulk properties relies extensively on inference from reflection seismology. However, classic deterministic methods to invert seismic data for reservoir properties suffer from some limitations, among which are the difficulty of handling complex, possibly nonlinear forward models, and the lack...

Almost all methods used in geophysical data inversion and history matching are based on the least-squares
method. This method is essentially an application of Gaussian statistics, and when it is used in
classical voxel-based models to defeat underdetermination (through a quadratic penalty function) it
adds unphysical information to our inverse prob...

Methods that rely on Gaussian statistics require a choice of a mean and
covariance to describe a Gaussian probability distribution. This is the case using for
example kriging, sequential Gaussian simulation, least-squares collocation, and least squares-based inversion, to name a few examples. Here, an approach is presented that
provides a general d...

There is some truth in a comment by Ernest Rutherford, the British chemist who laid the groundwork for the development of nuclear physics: "If your experiment needs statistics, you ought to have done a better experiment"! However, there is no doubt that in geophysics our data are often so sparse, so insufficient, so inaccurate, and so inconsistent...

Sound source localization with sensor arrays involves the estimation of the direction-of-arrival (DOA) from a limited number of observations. Compressive sensing (CS) solves such underdetermined problems achieving sparsity, thus improved resolution, and can be solved efficiently with convex optimization. The DOA estimation problem is formulated in...

Sound source localization with sensor arrays involves the estimation of the direction-of-arrival (DOA) from a limited number of observations. Compressive sensing (CS) is a method for solving such undetermined problems which achieves simultaneously sparsity, thus super-resolution, and computational speed. We formulate the DOA estimation as a sparse...

We propose a smooth formulation of multiple-point statistics that enables
us to solve inverse problems using gradient-based optimization techniques. We introduce
a differentiable function that quantifies the mismatch between multiple-point
statistics of a training image and of a given model. We show that, by minimizing this
function, any continuous...

Some multiple-point-based sampling algorithms, such as the snesim algo-rithm, rely on sequential simulation. The conditional probability distributions that are used for the simulation are based on statistics of multiple-point data events obtained from a training image. During the simulation, data events with zero probability in the training image s...

Inversion of geophysical data relies on knowledge about how to solve the forward problem, that is, computing data from a given set of model parameters. In many applications of inverse problems, the solution to the forward problem is assumed to be known perfectly, without any error. In reality, solving the forward model (forward-modeling process) wi...

We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear, multi-step forward model (rock physics and seismolog...

Extraterrestrial seismology saw its advent with the deployment of seismometers during the Apollo missions that were undertaken from July 1969 to December 1972. The Apollo lunar seismic data constitute a unique resource being the only seismic data set which can be used to infer the interior structure of a planetary body besides the Earth. On-going a...

We present a study on the analysis of petroleum reservoir models consistent with seismic data and geostatistical constraints performed on a synthetic reservoir model. Our aim is to invert directly for structure and rock bulk properties of the target reservoir zone. To infer the rock facies, porosity and oil saturation seismology alone is not suffic...

The challenge of a deep-water oil leak is that a significant quantity of oil remains in the water column and possibly changes properties. There is a need to quantify the oil settled within the water column and determine its physical properties to assist in the oil recovery. There are currently no methods to map acoustically submerged oil in the sea...

In an acoustic backscattering model of a stationary field of volume inhomogeneities, a stochastic description of the field is more useful than a deterministic description due to the complex nature of the field. A method based on linear inversion is developed to infer information about the statistical properties of the scattering field from the obta...

We present a new method for solving the history matching problem by gradient-based optimization within a probabilistic framework. The focus is on minimizing the number of forward simulations and conserving geological realism of the solutions. Geological a priori information is taken into account by means of multipoint statistics borrowed from train...

The study of weak scattering from inhomogeneous media or interface roughness has long been of interest in sonar applications. In an acoustic backscattering model of a stationary field of volume inhomogeneities, a stochastic description of the field is more useful than a deterministic description due to the complex nature of the field. A method base...

The frequency matching method defines a closed form expression for a complex prior that quantifies the higher order statistics of a proposed solution model to an inverse problem. While existing solution methods to inverse problems are capable of sampling the solution space while taking into account arbitrarily complex a priori information defined b...

In order to move beyond simplified covariance based a priori models, which are typically used for inverse problems, more complex multiple-point-based a priori models have to be considered. By means of marginal probability distributions ‘learned’ from a training image, sequential simulation has proven to be an efficient way of obtaining multiple rea...

In a probabilistic formulation, the solution to an inverse problem can be expressed an a posteriori probability density function (pdf) that combines the independent states of information provided by data and a priori information. Here, we define an a posteriori probability density function that defines the solution to a tomographic full waveform in...

From a probabilistic point-of-view solving inverse problems can be seen as a way of combining states of information in form of probability density functions. Typically, the states of information are provided by a set of observed data and some a priori information obtained independently of the data. The solution to the inverse problem is then the co...

Inversion of prestack seismic data is a highly non-unique inverse problem. Many elastic models exists that
fit seismic data observations equally well within the data uncertainty. In a probabilistic formulation of the
inverse problem, a full description of such variability is described by the a posteriori probability
distribution. Local inversion al...

Very often history-matched models happen to be inconsistent with the prescribed complex geological model. Therefore, in recent years the need for use of multiple-point statistics as prior information in reservoir characterization problems became evident. In traditional approach one often looks only for a maximum likelihood solution in the space of...

Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis algorithm can be used to sample solutions to non-linear inverse problems. In principle, these methods allow incorporation of prior information of arbitrary complexity. If an analytical closed form description of the prior is available, which is the case when the prior can...

It is often said that Monte Carlo methods are less efficient than
deterministic methods when applied to the solution of inverse problems.
This statement is rather imprecise, but its vagueness hides at least two
interesting properties of inverse problems. Firstly, the shortest
possible computation time needed to solve an inverse problem depends on
t...

We present a general Monte Carlo full-waveform inversion
strategy that integrates a priori information described by geostatistical
algorithms with Bayesian inverse problem theory. The
extended Metropolis algorithm can be used to sample the a posteriori
probability density of highly nonlinear inverse problems,
such as full-waveform inversion. Sequen...

This paper presents a Frequency Matching Method (FMM) for generation of a priori sample models based on training images and illustrates its use by an example. In geostatistics, training images are used to represent a priori knowledge or expectations of models, and the FMM can be used to generate new images that share the same multi-point statistics...

On 6 December 2009, the distinguished Spanish-French physicist and geoscientist, Albert Tarantola, passed away at the age of 60. Born in Barcelona in 1949, he went to Paris where he lived most of his life, and worked as a professor at Institut de Physique du Globe de Paris. His extensive scientific production and remarkable achievements in inverse...