Andrew Curtis

Andrew Curtis
The University of Edinburgh | UoE · School of GeoSciences

Ph. D.

About

316
Publications
46,743
Reads
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6,933
Citations
Introduction
Andrew Curtis is Professor of Mathematical Geoscience at the University of Edinburgh, in the United Kingdom. His interests are in developing new methods for tomography and imaging, seismic interferometry, Inversion and inference, acoustics, expert elicitation, and mathematical geology.
Additional affiliations
January 2005 - present
The University of Edinburgh
Position
  • Professor of Mathematical Geoscience

Publications

Publications (316)
Article
We show that interferometric theory allows recordings on a large variety of sensor types to be both spatially and temporally redatumed. Recordings of an energy source can thus be obtained at times before, during or after the period during which the sensor was physically installed. As a consequence, sensors in acoustic, elastic, electromagnetic, ele...
Article
Full-text available
The total intensity flux produced by a seismic wave-field propagating in a volcanic medium and recorded at a seismic station is more than a simple mixture of a coherent (direct) intensity and an incoherent (fluctuating) scattered intensity. Data envelopes recorded at Campi Flegrei caldera show evidence of diffusion as well as steep amplitude increa...
Article
Full-text available
We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in...
Article
Full-text available
Seismic surface wave dispersion inversion is used widely to study the subsurface structure of the Earth. The dispersion property is usually measured by using frequency-phase velocity (f-c) analysis of data recorded on a local array of receivers. The apparent phase velocity at each frequency of the surface waves travelling across the array is that a...
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Full-text available
We present a method to create an internal numerical absorbing boundary within elastic solid media whose properties are largely unknown, and use it to create the first wavefield separation method that retrieves all orders of outgoing elastic wavefield constituents for real data recorded on a closed free surface. The recorded data are injected into a...
Article
Optical fiber-based sensing technology can drastically improve Earth observations by enabling the use of existing submarine communication cables as seafloor sensors. Previous interferometric and polarization-based techniques demonstrated environmental sensing over cable lengths up to 10,500 kilometers. However, measurements were limited to the inte...
Preprint
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be quantified in order to define the family of all possible solutions. Bayesian inference provides a powerful theoretical...
Article
Full-text available
The ultimate goal of a scientific investigation is usually to find answers to specific, often low-dimensional questions: what is the size of a subsurface body? Does a hypothesised subsurface feature exist? Existing information is reviewed, an experiment is designed and performed to acquire new data, and the most likely answer is estimated. Typicall...
Preprint
Full-text available
Seismic surface wave dispersion inversion is used widely to study the subsurface structure of the Earth. The dispersion property is usually measured by using frequency-phase velocity (f-c) analysis and by picking phase velocities from the obtained f-c spectrum. However, because of potential contamination the f-c spectrum often has multimodalities a...
Article
Full-text available
Estimating the spatially varying microstructures of heterogeneous and locally anisotropic media non-destructively is necessary for the accurate detection of flaws and reliable monitoring of manufacturing processes. Conventional algorithms used for solving this inverse problem come with significant computational cost, particularly in the case of hig...
Preprint
The ultimate goal of a scientific investigation is usually to find answers to specific, often low-dimensional questions: what is the size of a subsurface body? Does a hypothesised subsurface feature exist? Which competing model is most consistent with observations? Existing information is reviewed, an experiment is designed and performed to acquire...
Article
Surface waves are a particular type of seismic wave that propagate around the surface of the Earth, but which oscillate over depth ranges beneath the surface that depend on their frequency of oscillation. This causes them to travel with a speed that depends on their frequency, a property called dispersion. Estimating surface wave dispersion is of i...
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Full-text available
Ground‐penetrating radar (GPR) is widely used on polythermal glaciers to image bed topography and detect internal scatter due to water inclusions in temperate ice. The glaciological importance of this is twofold: bed topography is a primary component for modeling the long‐term evolution of glaciers and ice sheets, and the presence of temperate ice...
Preprint
Full-text available
The Ediacaran-Cambrian transition, which incorporates the radiation of animals, lacks a robust global temporal and spatial framework, resulting in major uncertainty in the evolutionary dynamics of this critical radiation and its relationship to changes in palaeoenvironmental geochemistry. We first present a new δ13Ccarb composite reference curve fo...
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Full-text available
The Ediacaran-Cambrian transition, which incorporates the radiation of animals, lacks a robust global temporal and spatial framework, resulting in major uncertainty in the evolutionary dynamics of this critical radiation and its relationship to changes in palaeoenvironmental geochemistry. We first present a new δ¹³Ccarb composite reference curve fo...
Preprint
Full-text available
Many modelling studies of wave scattering require repeated numerical simulations through models with properties that differ only in a small sub-domain. Hence, it is of interest to recompute the wavefields that account for wave propagation through the whole domain, using simulations that are performed only in the sub-domain. Immersive boundary condi...
Preprint
Catastrophic failure in brittle, porous materials initiates when smaller-scale fractures localize along an emergent failure plane or 'fault' in a transition from stable crack growth to dynamic rupture. Due to the extremely rapid nature of this critical transition, the precise micro-mechanisms involved are poorly understood and difficult to capture....
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Full-text available
There is significant uncertainty over how ice sheets and glaciers will respond to rising global temperatures. Limited knowledge of the topography and rheology of ice-bed interface is a key cause of this uncertainty, as models show that small changes in the bed can have a large influence on predicted rates of ice loss. Most of our detailed knowledge...
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Full-text available
Rendering objects invisible to impinging acoustic waves (cloaking) and creating acoustic illusions (holography) has been attempted using active and passive approaches. While most passive methods are inflexible and applicable only to narrow frequency bands, active approaches attempt to respond dynamically, interfering with broadband incident or scat...
Article
Finite-difference time-domain (FDTD) forward modeling is often used to gain a more quantitative understanding of the interactions between electromagnetic fields and targets. To undertake full 3D simulations the computational demands are challenging, so simulations are often undertaken in 2D where assumptions in the propagation of electromagnetic fi...
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We test a fully non-linear method to solve Bayesian seismic tomographic problems using data consisting of observed travel times of first-arriving waves. Rather than using Monte Carlo methods to sample the posterior probability distribution that embodies the solution of the tomographic inverse problem, we use variational inference. Variational metho...
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Full-text available
It is a well-established principle that cross-correlating seismic observations at different receiver locations can yield estimates of band-limited inter-receiver Green’s functions. This principle, known as Green’s function retrieval or seismic interferometry, is a powerful technique that can transform noise into signals which enable remote interrog...
Article
Full-text available
Constraining geophysical models with observed data usually involves solving nonlinear and nonunique inverse problems. Neural mixture density networks (MDNs) provide an efficient way to estimate Bayesian posterior marginal probability density functions (pdf's) that represent the nonunique solution. However, it is difficult to infer correlations betw...
Article
Seismic full-waveform inversion (FWI) uses full seismic records to estimate the subsurface velocity structure. This requires a highly nonlinear and nonunique inverse problem to be solved, so Bayesian methods have been used to quantify uncertainties in the solution. Variational Bayesian inference uses optimization to provide solutions efficiently. H...
Preprint
Full-text available
Rendering objects invisible to impinging acoustic waves (cloaking) and creating acoustic illusions (holography) has been attempted using active and passive approaches. While passive methods are applicable only to narrow frequency bands, active approaches attempt to respond dynamically, interfering with broadband incident or scattered wavefields by...
Preprint
Full-text available
It is a well-established principle that cross-correlating seismic observations at different receiver locations can yield estimates of band-limited inter-receiver Green's functions. This principle, known as seismic interferometry, is a powerful technique that can transform noise into signals which allow us to remotely image and interrogate subsurfac...
Preprint
Estimating the spatially varying microstructures of heterogeneous and locally anisotropic media non-destructively is necessary for the accurate detection of flaws and reliable monitoring of manufacturing processes. Conventional algorithms used for solving this inverse problem come with significant computational cost, particularly in the case of hig...
Article
Full-text available
To reduce the probability of future large earthquakes, traffic light systems (TLSs) define appropriate reactions to observed induced seismicity depending on each event's range of local earthquake magnitude (ML). The impact of velocity uncertainties and station site effects may be greater than a whole magnitude unit of ML, which can make the differe...
Chapter
In a variety of scientific applications, we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has nonunique solutions so uncertainty must be quantified in order to define the family of all possible solutions. Bayesian inference provides a powerful theoretical...
Article
Throughout the Phanerozoic, sessile metazoans grew in close association with various microbial carbonates to form reefs. The first metazoans with calcareous hard‐parts appeared in the terminal Ediacaran, ca 550 million years ago, and these also commonly grew associated with microbial mats, thrombolites and stromatolites, to form the oldest known me...
Article
Full-text available
Travel-time tomography for the velocity structure of a medium is a highly nonlinear and nonunique inverse problem. Monte Carlo methods are becoming increasingly common choices to provide probabilistic solutions to tomographic problems but those methods are computationally expensive. Neural networks can often be used to solve highly nonlinear proble...
Article
Statistical experimental design (SED) is the field of statistics concerned with designing experiments to obtain as much information as possible about a target of interest. SED algorithms can be divided into two categories: those that assume a linear or linearized relationship between measured data and parameters, and those that account for a fully...
Article
The deep crustal structure beneath the North Sea is poorly understood since it is constrained by only a few seismic reflection and refraction profiles. However, it is widely acknowledged that the mid to lower crust plays important roles in rift initiation and evolution, particularly when large scale sutures and/or terrane boundaries are present, si...
Article
Full-text available
The ability to extract information from scattered waves is usually limited to singly scattered energy even if multiple scattering might occur in the medium. As a result, the information in arrival times of higher-order scattered events is underexplored. This information is extracted using fingerprinting theory. This theory has never previously been...
Article
We present a 1D shear-velocity model for Los Humeros geothermal field (Mexico) obtained from three-component beamforming of ambient seismic noise, imaging for the first time the bottom of the sedimentary basement ∼5 km below the volcanic caldera, as well as the brittle-ductile transition at ∼10 km depth. Rayleigh-wave dispersion curves are extracte...
Article
Anton Ziolkowski and fellow organizers look back at the British Seismology Meeting 2019, which discussed events of all scales as well as new hardware and software techniques.
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Full-text available
Determining an optimal component design is fundamental to many applications including many of those in the aerospace, automotive and civil engineering industries. Previously, the compatibility of the component with future non-destructive testing (NDT) requirements has not been considered at the design stage. As a result, NDT operators are often cha...
Article
Seismic full-waveform inversion (FWI) can produce high-resolution images of the Earth’s subsurface. Since full-waveform modelling is significantly nonlinear with respect to velocities, Monte Carlo methods have been used to assess image uncertainties. However, because of the high computational cost of Monte Carlo sampling methods, uncertainty assess...
Article
Full-text available
We immerse a two-dimensional physical wave-propagation experiment in a virtual (simulated) environment in real time. This enables broadband hybrid wave experimentation in physical media that may be governed by unknown physics, embedded seamlessly within virtual media with either modeled or measured physics. Using the theory of immersive boundary co...
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Full-text available
Radar surveys across ice sheets typically measure numerous englacial layers that can often be regarded as isochrones. Such layers are valuable for extrapolating age–depth relationships away from ice-core locations, reconstructing palaeoaccumulation variability, and investigating past ice-sheet dynamics. However, the use of englacial layers in Antar...
Article
Full-text available
Imaging defects in austenitic welds presents a significant challenge for the ultrasonic non-destructive testing community. Due to the heating process during their manufacture, a dendritic structure develops, exhibiting large grains with locally anisotropic properties which cause the ultrasonic waves to scatter and refract. When basic imaging algori...
Article
The Ediacaran-Cambrian cloudinomorphs, which include Cloudina, are the first putative skeletal metazoans. They have a benthic ecology and tubular, organic, or biomineralized stacked funnel morphologies but an unresolved phylogenetic affinity. Rare dichotomous branching has been described in Cloudina, but here we demonstrate the presence of multiple...
Article
Seismic body wave travel time tomography and surface wave dispersion tomography have been used widely to characterise earthquakes and to study the subsurface structure of the Earth. Since these types of problem are often significantly non-linear and have non-unique solutions, Markov chain Monte Carlo (McMC) methods have been used to find probabilis...
Article
Full-text available
Seismic tomography is a methodology to image the interior of solid or fluid media and is often used to map properties in the subsurface of the Earth. In order to better interpret the resulting images, it is important to assess imaging uncertainties. Since tomography is significantly nonlinear, Monte Carlo sampling methods are often used for this pu...
Article
Full-text available
Seismic attributes (derived quantities) such as P-wave and S-wave impedances and P-wave to S-wave velocity ratios may be used to classify subsurface volume of rock into geological facies (distinct lithology-fluid classes) using pattern recognition methods. Seismic attributes may also be used to estimate subsurface petrophysical rock properties such...
Article
Full-text available
In a variety of geoscientific applications we require 3‐D maps of properties of the Earth's interior and the corresponding map of uncertainties to assess their reliability. On the seabed it is common to use Scholte wave dispersion data to infer these maps using inversion‐based imaging theory. Previously we introduced a 3‐D fully nonlinear Monte Car...
Article
Marchenko methods are a suite of geophysical techniques that convert seismograms of energy created by surface sources and measured by surface receivers into seismograms that would have been recorded by a virtual receiver at an arbitrary point inside the subsurface—an operation called redatuming. In principle these redatumed seismograms contain all...
Preprint
Full-text available
A physical boundary mounted with active sources can cancel acoustic waves arriving at the boundary, and emit synthesized waves into the neighboring medium to fully control the acoustic wavefield in an experimental setup such as a water tank or air-filled cavity. Using the same principles, a physical experiment can be artificially immersed within an...
Article
No PDF available ABSTRACT A physical boundary with embedded active sources can cancel acoustic waves incident on the boundary and also synthesize waves to fully control the acoustic field in an experimental setup (e.g., a water tank) such that the physical experiment is artificially immersed into a virtual domain and waves propagate seamlessly betw...
Article
No PDF available ABSTRACT The physical implementation of immersive boundary conditions (IBCs) allows acoustic or elastic waves to propagate seamlessly between a physical domain, such as a wave propagation laboratory, and a numerical simulation virtually enclosing the physical domain. IBCs correctly account for all wavefield interactions between bot...
Preprint
The mid-lower crust beneath the North Sea is poorly understood, largely because it has only been probed by a few deep seismic reflection and refraction profiles. Yet it played a key role in determining how and where the crust extended during failed rifting, which lead to the depositional environments responsible for endowing the region with its hyd...
Article
With the advent of large and dense seismic arrays, novel cheap and fast imaging and inversion methods are needed to exploit the information captured by stations in close proximity to each other and produce results in near real-time. The main objective of this study is to propose a sequence of fast seismic acquisition for dispersion curve extraction...
Preprint
Full-text available
Surface wave tomography uses measured dispersion properties of surface waves to infer the spatial distribution of subsurface properties such as shear-wave velocities. These properties can be estimated vertically below any geographical location at which surface wave dispersion data are available. As the inversion is significantly non-linear, Monte C...
Article
Full-text available
We report the experimental realization of real-time and broadband acoustic cloaking and holography by manipulating wave fields through their boundary conditions. The method of immersive boundary conditions (IBCs) enables us to virtually replace part of a physical experiment with a virtual computational environment. By introducing a source surface e...
Preprint
Full-text available
Travel time tomography for the velocity structure of a medium is a highly non-linear and non-unique inverse problem. Monte Carlo methods are becoming increasingly common choices to provide probabilistic solutions to tomographic problems but those methods are computationally expensive. Neural networks can often be used to solve highly non-linear pro...