Note: Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- 1 Introduction -- 1.1 The forward problem -- 1.2 The inverse problem -- 2 Examples of inverse problems -- 2.1 Density of the Earth -- 2.2 Acoustic tomography -- 2.3 Steady-state 1D flow in porous media -- 2.4 History matching in reservoir simulation -- 2.5 Summary -- 3 Estimation for linear inverse problems -- 3.1 Characterization of discrete linear inverse problems -- 3.1.1 The null space and range -- 3.1.2 Underdetermined problems -- 3.1.3 Overdetermined and mixed determined problems -- 3.2 Solutions of discrete linear inverse problems -- 3.2.1 Gradient operators -- 3.2.2 Solution of purely underdetermined problems -- 3.2.3 Solution of purely overdetermined problems -- 3.2.4 Regularized least-squares solution -- 3.2.5 General regularization -- 3.3 Singular value decomposition -- 3.4 Backus and Gilbert method -- 3.4.1 Least-squares estimation for accurate data -- 3.4.2 Example: estimation of permeability from well test data -- 4 Probability and estimation -- 4.1 Random variables -- 4.1.1 Example: permeability and porosity -- 4.2 Expected values -- 4.2.1 Variance, covariance, and correlation -- 4.2.2 Random vectors -- 4.3 Bayes' rule -- 4.3.1 Example: total depth of a well -- 4.3.2 Example: location of a barrier from well test -- 5 Descriptive geostatistics -- 5.1 Geologic constraints -- 5.2 Univariate distribution -- 5.2.1 Histogram -- 5.2.2 Cumulative distribution plot -- 5.2.3 Box plot -- 5.2.4 Representative values -- 5.3 Multi-variate distribution -- 5.3.1 Stationarity -- 5.3.2 Transformation of variables -- 5.3.3 Experimental covariance -- 5.4 Gaussian random variables -- 5.4.1 Covariance models -- 5.4.2 Covariance matrix -- 5.4.3 Covariance model selection -- 5.4.4 Anisotropic covariance -- 5.5 Random processes in function spaces -- 6 Data. , 6.1 Production data -- 6.1.1 Drawdown tests -- 6.1.2 Interference tests -- 6.1.3 Tracer tests -- 6.1.4 Water-oil ratio -- 6.1.5 Gas-oil ratio -- 6.1.6 Sources of errors in production data -- 6.2 Logs and core data -- 6.2.1 Errors in log and core data -- 6.3 Seismic data -- 6.3.1 Seismic data acquisition -- 6.3.2 Seismic data processing -- 6.3.3 Sources of errors in seismic data -- 6.3.4 Seismic data inversion -- 7 The maximum a posteriori estimate -- 7.1 Conditional probability for linear problems -- 7.1.1 Posteriori mean -- 7.1.2 Maximum of the posterior PDF -- 7.1.3 The posteriori covariance and variance -- 7.2 Model resolution -- 7.2.1 Spread of the resolution -- 7.2.2 1D example - well-logs -- 7.2.3 Well-testing example -- 7.2.4 The resolution of permeability -- 7.3 Doubly stochastic Gaussian random field -- 7.3.1 Doubly stochastic model - example -- 7.4 Matrix inversion identities -- 8 Optimization for nonlinear problems using sensitivities -- 8.1 Shape of the objective function -- 8.1.1 Evaluation of quality of estimate -- 8.2 Minimization problems -- 8.2.1 Maximum likelihood estimate -- 8.2.2 MAP estimate -- 8.2.3 Objective function for sampling with RML -- 8.3 Newton-like methods -- 8.3.1 Newton's method for minimization -- 8.3.2 Gauss-Newton method -- 8.3.3 Gauss-Newton for generating the MAP estimate -- 8.3.4 Restricted-step method for calculation of step size -- 8.4 Levenberg-Marquardt algorithm -- 8.4.1 Spectral analysis of Levenberg-Marquardt algorithm -- 8.4.2 Effects of ill-conditioning -- 8.5 Convergence criteria -- 8.5.1 Convergence tolerance for history-matching problems -- 8.5.2 Convergence of algorithms -- 8.6 Scaling -- 8.7 Line search methods -- 8.7.1 Strong Wolfe conditions -- 8.7.2 Quadratic and cubic line search algorithms -- 8.7.3 Alternate line search method -- 8.8 BFGS and LBFGS -- 8.8.1 Theoretical overview of BFGS. , 8.8.2 Convergence rate of BFGS -- 8.8.3 Scaling of BFGS -- 8.8.4 Efficient implementation of BFGS -- 8.8.5 Limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm -- 8.9 Computational examples -- 8.9.1 2D three-phase example -- 8.9.2 3D three-phase example -- 9 Sensitivity coefficients -- 9.1 The Fréchet´ derivative -- 9.1.1 Sensitivity of steady pressure to permeability -- 9.1.2 Frechet´ derivative approach -- 9.1.3 Adjoint approach to calculate Frechét derivative -- 9.2 Discrete parameters -- 9.2.1 Generic finite-dimensional problem -- 9.2.2 Sensitivity by the direct method -- 9.2.3 Sensitivity by the adjoint method -- 9.2.4 Sensitivity by finite-difference method -- 9.3 One-dimensional steady-state flow -- 9.3.1 Direct method -- 9.3.2 The adjoint method -- 9.3.3 Finite-difference method -- 9.4 Adjoint methods applied to transient single-phase flow -- 9.4.1 Discrete and semidiscrete flow equations -- 9.5 Adjoint equations -- 9.5.1 Solution of the adjoint equations -- 9.5.2 Sensitivity to subobjective functions -- 9.6 Sensitivity calculation example -- 9.6.1 Sensitivities from analytical solution -- 9.6.2 Sensitivities from the direct method -- 9.6.3 Sensitivities from the adjoint method -- 9.7 Adjoint method for multi-phase flow -- 9.7.1 The reservoir simulator -- 9.7.2 Adjoint equations and sensitivities -- 9.7.3 Compact derivation of sensitivities -- 9.7.4 G times a vector -- 9.7.5 G T times a vector -- 9.7.6 Comments on sensitivities -- 9.8 Reparameterization -- 9.8.1 Pilot- and master-point methods -- 9.8.2 The master-point method -- 9.9 Examples -- 9.9.1 Sensitivity examples -- 9.9.2 History-matching example -- 9.10 Evaluation of uncertainty with a posteriori covariance matrix -- 9.10.1 Approximate a posteriori covariance matrix -- 9.10.2 Normalized variance -- 9.10.3 Dimensionless sensitivity matrix -- 9.10.4 Example. , 10 Quantifying uncertainty -- 10.1 Introduction to Monte Carlo methods -- 10.1.1 Calculating expectations -- 10.2 Sampling based on experimental design -- 10.2.1 Screening designs -- 10.2.2 Response surface modeling -- 10.3 Gaussian simulation -- 10.3.1 Generating (pseudo) random numbers -- 10.3.2 Cholesky or square-root method -- 10.3.3 Moving average -- 10.3.4 Truncated Gaussian simulation -- 10.4 General sampling algorithms -- 10.4.1 Rejection method -- 10.4.2 Markov chain Monte Carlo -- 10.4.3 Markov random fields -- 10.5 Simulation methods based on minimization -- 10.5.1 Geostatistical approach -- 10.5.2 RML for linear inverse problems -- 10.5.3 RML for nonlinear inverse problems -- 10.5.4 RML as Markov chain Monte Carlo -- 10.6 Conceptual model uncertainty -- 10.7 Other approximate methods -- 10.7.1 Pilot point -- 10.7.2 Gradual deformation -- 10.8 Comparison of uncertainty quantification methods -- 10.8.1 Test problem -- 10.8.2 Results analysis -- 10.8.3 Discussion -- 11 Recursive methods -- 11.1 Basic concepts of data assimilation -- 11.2 Theoretical framework -- 11.3 Kalman filter and extended Kalman filter -- 11.4 The ensemble Kalman filter -- 11.5 Application of EnKF to strongly nonlinear problems -- 11.5.1 Nonlinear dynamic system -- 11.5.2 Implementation of the EnRML -- 11.6 1D example with nonlinear dynamics and observation operator -- 11.7 Example - geologic facies -- 11.7.1 Matching facies observations at wells -- 11.7.2 Matching production data -- References -- Index.

Note: Front Cover -- Advances in Spectroscopic Monitoring of the Atmosphere -- Advances in Spectroscopic Monitoring of the Atmosphere -- Copyright -- Contents -- Preface -- 1 - Current trends and future outlook in spectroscopic monitoring of the atmosphere -- 1.1 Introduction -- 1.2 Monitoring atmospheric composition -- 1.3 Spectroscopy and the composition of the atmosphere -- 1.4 Current topics of interest -- 1.4.1 Particulate matter -- 1.4.2 Flux measurements -- 1.4.3 Vertical profiles -- 1.4.4 Species of interest -- 1.5 Advances in technology -- 1.5.1 Supercontinuum sources -- 1.5.2 Mid-IR sources: quantum cascade lasers and interband cascade lasers -- 1.5.3 Mid-IR sources: frequency combs -- 1.5.4 Optical cavity techniques -- 1.5.5 Unmanned aerial systems -- 1.5.6 Other spectroscopic techniques -- 1.6 Outlook -- References -- 2 - Remote sensing using open-path dual-comb spectroscopy -- 2.1 Introduction -- 2.1.1 Long open-path atmospheric measurements -- 2.1.2 Current techniques -- 2.1.3 Advantages of open-path DCS -- 2.2 Open-path DCS technology -- 2.2.1 DCS history -- 2.2.2 DCS principle -- 2.2.3 Dual-comb sources and spectral coverage -- 2.2.4 Open-path sensing configuration -- 2.2.4.1 Telescope design -- 2.2.4.2 Telescope efficiency -- 2.2.5 SNR considerations -- 2.2.6 Data acquisition and coherent averaging -- 2.2.7 Extraction of species concentrations -- 2.2.7.1 Line parameters -- 2.2.7.2 Spectral fitting of ro-vibrationally resolved species -- 2.2.7.3 More complex fitting cases -- 2.2.8 Comparability -- 2.2.9 Long-term operation and field deployment challenges -- 2.3 Applications -- 2.3.1 Emission rate determination -- 2.3.2 Urban GHG emissions -- 2.3.3 Industrial oil and gas methane emissions -- 2.3.4 DCS with an airborne retroreflector -- 2.3.5 Agricultural emissions -- 2.3.6 VOC measurements -- 2.4 What is next in DCS-based sensing?. , 2.4.1 Extending the spectral region beyond 1.5 and 3 µm -- 2.4.2 Instrument performance -- 2.4.3 Data analysis -- 2.5 Summary -- List of Acronyms -- References -- 3 - Broadband optical cavity methods -- 3.1 Introduction -- 3.2 Optical cavities -- 3.2.1 Resonator theory -- 3.2.2 Comparison of multipass cells and optical cavities -- 3.3 Measurement strategies -- 3.3.1 Ringdown spectroscopy -- 3.3.2 Cavity-enhanced absorption -- 3.3.3 Phase shift measurements -- 3.4 Instrument design -- 3.4.1 Broadband light sources -- 3.4.2 Detectors -- 3.4.3 Cavity configuration -- 3.4.4 Mechanical design -- 3.4.5 Sample stream handling -- 3.5 Data analysis and performance characterization -- 3.5.1 Data analysis -- 3.5.2 Mirror reflectivity calibration -- 3.5.2.1 Ringdown measurements -- 3.5.2.2 Phase shift measurements -- 3.5.2.3 Samples of known extinction -- 3.5.2.4 Low-loss optical elements -- 3.5.3 Other instrument parameters -- 3.5.4 Analytical performance -- 3.5.4.1 Measurement uncertainty -- 3.5.4.2 Instrument stability and measurement precision -- 3.5.4.3 Limit of detection -- 3.5.4.4 Evaluation of instrument performance -- 3.6 Applications -- 3.6.1 Cross-section measurements -- 3.6.2 Optical properties of particles -- 3.6.3 Concentration measurements -- 3.6.3.1 Nitrogen dioxide, NO2 -- 3.6.3.2 NO3 and N2O5 -- 3.6.3.3 HONO -- 3.6.3.4 Glyoxal and methylglyoxal -- 3.6.3.5 Halogenated species -- 3.6.3.6 Other species -- 3.7 Conclusion and outlook -- References -- 4 - Atmospheric trace gas measurements using laser heterodyne spectroscopy -- 4.1 Introduction -- 4.1.1 Presentation -- 4.1.2 Elements of history -- 4.2 Underlying theoretical principles -- 4.2.1 Laser heterodyne spectrometer models -- 4.2.1.1 Heterodyne signal models -- 4.2.1.2 Noise model -- 4.2.1.3 Signal to noise ratio and noise equivalent power -- 4.2.1.4 Heterodyne efficiency -- 4.2.1.5 Summary. , 4.2.2 Atmospheric information retrieval -- 4.2.2.1 Forward model -- 4.2.2.2 Retrieval -- 4.2.2.3 Summary -- 4.3 Quantum cascade laser heterodyne spectro-radiometers -- 4.3.1 Ground-based measurements of ozone -- 4.3.1.1 Rationale -- 4.3.1.2 Observing system simulations for prior analysis -- 4.3.1.3 Experimental system development -- 4.3.1.4 Results and analysis -- 4.3.2 Ground-based measurement of greenhouse gases -- 4.3.2.1 Rationale -- 4.3.2.2 Prior analysis -- 4.3.2.3 Laboratory demonstration systems -- 4.3.2.4 Deployable LHR for greenhouse gas measurements -- 4.3.2.5 Atmospheric emission -- 4.3.3 Multispecies measurements using widely tunable local oscillators -- 4.4 Prospects for space-borne measurements -- 4.4.1 Small satellite mission concepts -- 4.4.1.1 Greenhouse gas vertical profiling -- 4.4.1.2 Prospects for meteorology applications -- 4.4.1.3 Demonstrator of the hollow waveguide integrated LHR -- 4.4.2 Constellation mission concept -- 4.4.3 Ground-based Mars atmosphere analyzer -- 4.5 Conclusion, wider context, and forward look -- List of acronyms -- Acknowledgments -- References -- 5 - Photoacoustic spectroscopy for gas sensing -- 5.1 - Basics, theory, experimental systems, and applications -- Outline placeholder -- 5.1.1 Introduction and historical perspectives -- 5.1.2 Fundamentals of gas-phase photoacoustics -- 5.1.3 Photoacoustic signal analysis -- 5.1.4 Experimental issues -- 5.1.4.1 Sources and radiation modulation -- 5.1.4.2 Photoacoustic cells -- 5.1.4.2.1 Resonant PA cell combined with multipass arrangement and multimicrophone array -- 5.1.4.2.2 Dual-mode photoacoustic cell -- 5.1.4.2.3 Heatable PA cell -- 5.1.4.2.4 Multifunctional, compact, and miniaturized PA cells -- 5.1.4.3 Quartz-enhanced photoacoustic spectroscopy -- 5.1.4.4 Cantilever-enhanced photoacoustic spectroscopy. , 5.1.5 Examples of photoacoustic spectroscopy applications in trace gas detection -- 5.1.5.1 Traffic pollutant monitoring with conventional PAS -- 5.1.5.2 Aircraft measurements with conventional PAS -- 5.1.5.3 OPO-PA system for simultaneous measurements of CH4, NO2, and NH3 -- 5.1.5.4 Intracavity PA spectroscopy for trace gas sensing -- 5.1.5.5 Alternative configurations of conventional PA method -- 5.1.5.6 QEPAS study on short-lived species -- 5.1.5.7 Most recent QEPAS developments -- 5.1.5.8 Applications of CEPAS sensors -- 5.1.5.9 Further recent CEPAS developments -- 5.1.6 Conclusions and outlook -- Acknowledgments -- References -- 5.2 - Airborne application of a photoacoustic instrument -- Outline placeholder -- 5.2.1 Introduction -- 5.2.2 A brief history of the WaSul-Hygro instrument -- 5.2.3 General advantages of the PA detection method -- 5.2.4 Near-infrared diode lasers in PA measurements -- 5.2.5 System optimization for airborne operation -- 5.2.6 Summary -- References -- 5.3 - Aerosol photoacoustic spectroscopy -- Outline placeholder -- 5.3.1 Introduction -- 5.3.2 PAS and its alternatives for the measurement of light absorption by aerosol -- 5.3.3 The principles and some practical considerations of aerosol PAS -- 5.3.4 Instrument development and its applicability -- 5.3.4.1 Single-wavelength PA instrument for light absorption and mass concentration measurement of BC aerosol -- 5.3.4.2 Multi-wavelength PA instruments for qualitative investigation and source apportionment of LAC -- 5.3.5 Application of aerosol PAS for source apportionment of ambient aerosol -- 5.3.6 Perspectives and outlook -- Acknowledgments -- References -- 6 - Unmanned aerial systems for trace gases -- 6.1 Introduction -- 6.2 Environmental considerations -- 6.2.1 Local emission sampling -- 6.2.2 Long-duration drone sampling. , 6.3 Spectroscopic approaches for sampling on sUAS -- 6.3.1 In situ -- 6.3.2 Path-integrated -- 6.3.3 Other approaches -- 6.4 Flight sampling examples -- 6.4.1 Mass balance -- 6.4.2 Inverse Gaussian dispersion methods -- 6.4.3 Spatial mapping -- 6.4.4 Vertical profiles -- 6.5 Future considerations -- References -- 7 - Measurements of aerosol optical properties using spectroscopic techniques -- 7.1 Introduction -- 7.2 Light scattering and absorption by particles -- 7.2.1 Light scattering and absorption by a single particle -- 7.2.2 Light scattering and absorption by an ensemble of particles -- 7.2.3 Aerosol optical models -- 7.2.4 Effects of optical properties on radiative balance -- 7.3 Measurement techniques of aerosol optical property -- 7.3.1 Remote sensing techniques -- 7.3.2 Filter-based photometers -- 7.3.3 Photoacoustic spectroscopy and photothermal interferometry -- 7.3.4 Integrating nephelometers -- 7.3.5 Cavity ring-down and cavity-enhanced spectroscopy -- 7.3.6 Polar nephelometry -- 7.3.7 Other techniques -- 7.4 Aerosol albedometer -- 7.4.1 Integrated photoacoustic nephelometer -- 7.4.2 Cavity ring-down/enhanced albedometer -- 7.4.2.1 Tube cell configuration -- 7.4.3 Integrating sphere configuration -- 7.5 Intercomparison in the aerosol optical property measurements -- 7.6 Application to optical property measurements of aerosol particles -- 7.6.1 Light absorption of black carbon -- 7.6.1.1 TD method -- 7.6.1.2 MAC method -- 7.6.1.3 Aerosol filter filtration-dissolution method -- 7.6.2 Optical properties of organic carbon -- 7.6.3 Optical properties of mineral dust and iron oxide particles -- 7.6.4 RH dependence of aerosol optical properties -- 7.7 Conclusion -- References -- 8 - Trace gas measurements using cavity ring-down spectroscopy -- 8.1 Introduction -- 8.2 Experimental methods of CRDS -- 8.2.1 Principles of CRDS. , 8.2.2 Optical resonant cavity.