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All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniqueness and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability distribution functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSim) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.

58 GEOSCIENCES↗
DOE OSTI2013

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

In this study, we evaluate the possibility of monitoring soil moisture variation using tomographic ground penetrating radar travel time data through Bayesian inversion, which is integrated with entropy memory function and pilot point concepts, as well as efficient sampling approaches. It is critical to accurately estimate soil moisture content and variations in vadose zone studies. Many studies have illustrated the promise and value of GPR tomographic data for estimating soil moisture and associated changes, however, challenges still exist in the inversion of GPR tomographic data in a manner that quantifies input and predictive uncertainty, incorporates multiple data types, handles non-uniqueness and nonlinearity, and honors time-lapse tomograms collected in a series. To address these challenges, we develop a minimum relative entropy (MRE)-Bayesian based inverse modeling framework that non-subjectively defines prior probabilities, incorporates information from multiple sources, and quantifies uncertainty. The framework enables us to estimate dielectric permittivity at pilot point locations distributed within the tomogram, as well as the spatial correlation range. In the inversion framework, MRE is first used to derive prior probability density functions (pdfs) of dielectric permittivity based on prior information obtained from a straight-ray GPR inversion. The probability distributions are then sampled using a Quasi-Monte Carlo (QMC) approach, and the sample sets provide inputs to a sequential Gaussian simulation (SGSIM) algorithm that constructs a highly resolved permittivity/velocity field for evaluation with a curved-ray GPR forward model. The likelihood functions are computed as a function of misfits, and posterior pdfs are constructed using a Gaussian kernel. Inversion of subsequent time-lapse datasets combines the Bayesian estimates from the previous inversion (as a memory function) with new data. The memory function and pilot point design takes advantage of the spatial-temporal correlation of the state variables. We first apply the inversion framework to a static synthetic example and then to a time-lapse GPR tomographic dataset collected during a dynamic experiment conducted at the Hanford Site in Richland, WA. We demonstrate that the MRE-Bayesian inversion enables us to merge various data types, quantify uncertainty, evaluate nonlinear models, and produce more detailed and better resolved estimates than straight-ray based inversion; therefore, it has the potential to improve estimates of inter-wellbore dielectric permittivity and soil moisture content and to monitor their temporal dynamics more accurately.

Bayesian Inversion↗
DOE OSTI2015

Fabrication of Au- and Ag–SiO{sub 2} inverse opals having both localized surface plasmon resonance and Bragg diffraction

The inverse opal films of SiO{sub 2} containing metal nanoparticles can have both the localized surface plasmon resonance (LSPR) of metal nanoparticles and the Bragg diffraction of inverse opal crystals of SiO{sub 2}, which are very useful properties for applications, such as tunable photonic structures, catalysts and sensors. However, effective processes for fabrication of these films from colloidal particles have rarely been reported. In our study, two methods for preparation of inverse opal films of SiO{sub 2} with three different crystal sizes and containing gold or silver nanoparticles (NPs) via self-assembly using electrostatic interactions and capillary forces are reported. The Bragg diffraction of inverse opal films of SiO{sub 2} in the presence and absence of the template was measured and predicted on the basis of with UV–vis spectroscopy and scanning electron microscopy. The preparation methods used provided good-quality inverse opal SiO{sub 2} films containing highly dispersed, plasmonic AuNPs or AgNPs and having both Bragg diffractions and LSPRs. - Graphical abstract: For syntheses of SiO{sub 2} inverse opals containing Au/Ag nanoparticles two approaches and three template sizes were employed. Self-assembly of template molecules and metal nanoparticles occurred using electrostatic interactions and capillary forces. Both the Bragg diffraction of the photonic crystal and the localized surface plasmon resonance of Au/Ag nanoparticles were detected. - Highlights: • Fabrication methods of silica inverse opals containing metal nanoparticles studied. • Three template sizes used to produce SiO{sub 2} inverse opals with Au/Ag nanoparticles. • PS templates with Au nanoparticles adsorbed used in formation of inverse opals. • Ag particles infiltrated in inverse opals with capillary and electrostatic forces. • Bragg diffractions of IOs and surface plasmon resonances of nanoparticles observed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Sparsity-based acoustic inversion in cross-sectional multiscale optoacoustic imaging

Purpose: With recent advancement in hardware of optoacoustic imaging systems, highly detailed cross-sectional images may be acquired at a single laser shot, thus eliminating motion artifacts. Nonetheless, other sources of artifacts remain due to signal distortion or out-of-plane signals. The purpose of image reconstruction algorithms is to obtain the most accurate images from noisy, distorted projection data. Methods: In this paper, the authors use the model-based approach for acoustic inversion, combined with a sparsity-based inversion procedure. Specifically, a cost function is used that includes the L1 norm of the image in sparse representation and a total variation (TV) term. The optimization problem is solved by a numerically efficient implementation of a nonlinear gradient descent algorithm. TV–L1 model-based inversion is tested in the cross section geometry for numerically generated data as well as for in vivo experimental data from an adult mouse. Results: In all cases, model-based TV–L1 inversion showed a better performance over the conventional Tikhonov regularization, TV inversion, and L1 inversion. In the numerical examples, the images reconstructed with TV–L1 inversion were quantitatively more similar to the originating images. In the experimental examples, TV–L1 inversion yielded sharper images and weaker streak artifact. Conclusions: The results herein show that TV–L1 inversion is capable of improving the quality of highly detailed, multiscale optoacoustic images obtained in vivo using cross-sectional imaging systems. As a result of its high fidelity, model-based TV–L1 inversion may be considered as the new standard for image reconstruction in cross-sectional imaging.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1985

Adaptive Inverse Control for Rotorcraft Vibration Reduction

This thesis extends the Least Mean Square (LMS) algorithm to solve the mult!ple-input, multiple-output problem of alleviating N/Rev (revolutions per minute by number of blades) helicopter fuselage vibration by means of adaptive inverse control. A frequency domain locally linear model is used to represent the transfer matrix relating the higher harmonic pitch control inputs to the harmonic vibration outputs to be controlled. By using the inverse matrix as the controller gain matrix, an adaptive inverse regulator is formed to alleviate the N/Rev vibration. The stability and rate of convergence properties of the extended LMS algorithm are discussed. It is shown that the stability ranges for the elements of the stability gain matrix are directly related to the eigenvalues of the vibration signal information matrix for the learning phase, but not for the control phase. The overall conclusion is that the LMS adaptive inverse control method can form a robust vibration control system, but will require some tuning of the input sensor gains, the stability gain matrix, and the amount of control relaxation to be used. The learning curve of the controller during the learning phase is shown to be quantitatively close to that predicted by averaging the learning curves of the normal modes. For higher order transfer matrices, a rough estimate of the inverse is needed to start the algorithm efficiently. The simulation results indicate that the factor which most influences LMS adaptive inverse control is the product of the control relaxation and the the stability gain matrix. A small stability gain matrix makes the controller less sensitive to relaxation selection, and permits faster and more stable vibration reduction, than by choosing the stability gain matrix large and the control relaxation term small. It is shown that the best selections of the stability gain matrix elements and the amount of control relaxation is basically a compromise between slow, stable convergence and fast convergence with increased possibility of unstable identification. In the simulation studies, the LMS adaptive inverse control algorithm is shown to be capable of adapting the inverse (controller) matrix to track changes in the flight conditions. The algorithm converges quickly for moderate disturbances, while taking longer for larger disturbances. Perfect knowledge of the inverse matrix is not required for good control of the N/Rev vibration. However it is shown that measurement noise will prevent the LMS adaptive inverse control technique from controlling the vibration, unless the signal averaging method presented is incorporated into the algorithm.

Jacklin, Stephen A.↗
DOE OSTI2022

DNA Sequence Analysis of an Inversion Hot Spot in Lobeliaceae Plastomes

The evolution of plastid genomes (plastomes) in land plants is typically conservative, with extensive structural rearrangements present in only a few groups. Early Southern blot analysis identified two Lobelia species that minimally required deletion of the plastid gene accD and five inversions to account for their plastome arrangement relative to the ancestral organization. Sixty alternative 5-step inversion scenarios could account for the observed arrangement, but only one scenario was consistent with the criterion of ‘common cause’ attributable to a putative rearrangement hot spot at the accD deletion-site. Plastome sequencing demonstrated that this previously hypothesized inversion order is historically accurate. Detailed reconstructions of the ancestral plastome organization before and after each inversion are presented herein. Stem-loop and disruption-rescue models were evaluated for each inversion. One inversion has an obvious stem-loop basis, but the other four inversions were primarily caused by serial insertion of foreign (extra-plastid) DNA bearing large open-reading frames that disrupted plastome organization at the accD deletion-site, and complete plastomes were rescued by seemingly arbitrary ligation or fortuitous recombination at the other inversion endpoint. Transposed copies of DNA segments from elsewhere in the plastome are frequently inserted at inversion junctions, and four junctions are consistent with the stem-loop ligation model.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Evaluation of assumptions made by Hygroscopic Tandem Differential Mobility Analyzer inversion routines

The Hygroscopic Tandem Differential Mobility Analyzer (H-TDMA) measures the hygroscopicity of atmospheric particles, and many atmospheric processes that change this hygroscopicity also change the atmospheric size distribution. Two assumptions made during H-TDMA inversion create spurious hygroscopic trends as a function of the changing inlet size distribution. These two assumptions—that the particles exiting the first Differential Mobility Analyzer (DMA1) are singly charged and that the inlet size distribution has a slope of zero (flat)— generate Multi-Charge Dispersion (MCD) bias and Slope bias, respectively. First, we use a model, named TAO, to show that the inlet size distribution could theoretically change the measured ammonium sulfate hygroscopicity by 10%–20% as a function of diameter or experimental time with no change in relative humidity. Secondly, we show experimentally that aerosol emitted from the flaming combustion of grass creates MCD bias. Here, in this experiment, we measure the CPC response of the first three charges and invert these responses using a new routine named Junior. Junior's inversion of each charge shows that one growth factor distribution describes all measured diameters (no growth dependence on diameter). As in the modeling study above, previous publications of this aerosol system, using traditional inversion assumptions, report a decrease in hygroscopicity as DMA1 diameter increases. Unlike traditional inversions, Junior's inversion does not assume the particles are singly charged nor does it make the flat inlet size distribution assumption. Instead, both the inlet size distribution and each charge's CPC response are measured quantities. Thus, the discrepancy between our inversion results and previous publications is likely due to the traditional inversion routine assumptions. This underscores the importance for accounting for Slope and MCD bias during inversions. Experimental results should be carefully analyzed when reporting hygroscopic trends with respect to diameter or experimental time when using the traditional inversion assumptions.

42 ENGINEERING↗
DOE OSTI2017

3-D decoupled inversion of complex conductivity data in the real number domain

Complex conductivity inversion, aslo called spectral induced polarization inversion, involves estimating the frequency dependent complex electrical conductivity distribution of the subsurface. The superior diagnostic capabilities provided by complex conductivity spectra have driven advancements in mechanistic understanding of complex conductivity as well as modelling and inversion appraoches over the past several decades. In this work, we demonstrate the theory and application for an approach to three-dimensional modeling and inversion of complex conductivity data in the real number domain. Beginning from first principles, we demonstrate how the equations for the real and imaginary components of the complex potential may be decoupled. This leads to a description of the real and imaginary source current terms, and a corresponding assessment of error arising from an assumption necessary complete the decoupled modeling. We show that for most earth materials, which exhibit relatively small phases (e.g. less than 0.2 radians) in complex conductivity, these errors become insignificant. For higher phase materials, the errors may be quantified and corrected through an iterative procedure. We demonstrate the accuracy of numerical forward solutions by direct comparison to corresponding analytic solutions. We demonstrate the inversion using both synthetic and field examples with data collected over a waste infiltration trench, at frequencies ranging from 0.5 to 7.5 Hz. In addition to insight provided by the decoupled equations, we see three primary advantages of the decoupled inversion in comparison to fully coupled inversion in complex number domain. First, memory requirements are reduced by a factor of two because it is unnecessary to simultaneously store both the real and complex components and associated Jacobian matrices. Second, data noise is specified separately for the real and imaginary components of potential (or magnitude and phase), which removes the ambiguity in data misfit residuals that exists in the complex number domain, thereby enabling the inversion to appropriately fit the data. Final, except for the source current terms, the modeling and inversion algorithms are equivalent to the direct current electrical resistivity tomography counterpart. In conclusion, this enables direct application of advancements and approaches developed originally for electrical resistivity tomography.

58 GEOSCIENCES↗
DOE OSTI2014

Anthropogenic emissions of NOx over China: Reconciling the difference of inverse modeling results using GOME-2 and OMI measurements

Inverse modeling using satellite observations of nitrogen dioxide (NO2) columns has been extensively used to estimate nitrogen oxides (NOx) emissions in China. Recently, the Global Ozone Monitoring Experiment-2 (GOME-2) and Ozone Monitoring Instrument (OMI) provide independent global NO2 column measurements on a nearly daily basis at around 9:30 and 13:30 local time across the equator, respectively. Anthropogenic NOx emission estimates by applying previously developed monthly inversion (MI) or daily inversion (DI) methods to these two sets of measurements show substantial differences. We improve the DI method by conducting model simulation, satellite retrieval, and inverse modeling sequentially on a daily basis. After each inversion, we update anthropogenic NOx emissions in the model simulation with the newly obtained a posteriori results. Consequently, the inversion-optimized emissions are used to compute the a priori NO2 profiles for satellite retrievals. As such, the a priori profiles used in satellite retrievals are now coupled to inverse modeling results. The improved procedure was applied to GOME-2 and OMI NO2 measurements in 2011. The new daily retrieval-inversion (DRI) method estimates an average NOx emission of 6.9 Tg N/yr over China, and the difference between using GOME-2 and OMI measurements is 0.4 Tg N/yr, which is significantly smaller than the difference of 1.3 Tg N/yr using the previous DI method. Using the more consistent DRI inversion results, we find that anthropogenic NOx emissions tend to be higher in winter and summer than spring (and possibly fall) and the weekday-to-weekend emission ratio tends to increase with NOx emission in China.

Gu, Dasa↗
DOE OSTI2024

Selecting Appropriate Model Complexity: An Example of Tracer Inversion for Thermal Prediction in Enhanced Geothermal Systems

Abstract A major challenge in the inversion of subsurface parameters is the ill‐posedness issue caused by the inherent subsurface complexities and the generally spatially sparse data. Appropriate simplifications of inversion models are thus necessary to make the inversion process tractable and meanwhile preserve the predictive ability of the inversion results. In this study, we investigate the effect of model complexity on fracture aperture inversion and thermal performance prediction in a field‐scale EGS model. Principal component analysis was used to map the aperture field to a low‐dimensional latent space. The complexity of the inversion model was quantitatively represented by the percentage of total variance in the original aperture fields preserved by the latent space. Tracer, pressure and flow rate data were used to invert for fracture aperture through an ensemble‐based inversion method, and the inferred aperture field was used to predict thermal performance. With an over‐simplified aperture model, ensemble collapse occurred. The inverted aperture models failed to resolve necessary flow and transport features, leading to a biased thermal performance prediction. A complex aperture model involved excessive features and was prone to overinterpreting the inversion data. Both the tracer/pressure/flow rate data reproduction and thermal prediction showed significant uncertainties, making it difficult to properly estimate long‐term thermal performance. Fortunately, our results indicate that there exists an appropriate model complexity which can simultaneously match inversion data and predict thermal performance with an acceptable uncertainty. The quality of the fit of tracer data appears to be a useful indicator of such an appropriate model complexity.

15 GEOTHERMAL ENERGY↗
DOE OSTI2017

Young inversion with multiple linked QTLs under selection in a hybrid zone

Fixed chromosomal inversions can reduce gene flow and promote speciation in two ways: by suppressing recombination and by carrying locally favoured alleles at multiple loci. However, it is unknown whether favoured mutations slowly accumulate on older inversions or if young inversions spread because they capture pre-existing adaptive quantitative trait loci (QTLs). By genetic mapping, chromosome painting and genome sequencing, we have identified a major inversion controlling ecologically important traits in Boechera stricta. The inversion arose since the last glaciation and subsequently reached local high frequency in a hybrid speciation zone. Furthermore, the inversion shows signs of positive directional selection. To test whether the inversion could have captured existing, linked QTLs, we crossed standard, collinear haplotypes from the hybrid zone and found multiple linked phenology QTLs within the inversion region. These findings provide the first direct evidence that linked, locally adapted QTLs may be captured by young inversions during incipient speciation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Arctic Summer Airmass Transformation, Surface Inversions, and the Surface Energy Budget

During the Arctic Clouds in Summer Experiment (ACSE) in summer 2014 a weeklong period of warm-air advection over melting sea ice, with the formation of a strong surface temperature inversion and dense fog, was observed. Based on an analysis of the surface energy budget, we formulated the hypothesis that, because of the airmass transformation, additional surface heating occurs during warm-air intrusions in a zone near the ice edge. To test this hypothesis, we explore all cases with surface inversions occurring during ACSE and then characterize the inversions in detail. We find that they always occur with advection from the south and are associated with subsidence. Analyzing only inversion cases over sea ice, we find two categories: one with increasing moisture in the inversion and one with constant or decreasing moisture with height. During surface inversions with increasing moisture with height, an extra 10–25 W m −2 of surface heating was observed, compared to cases without surface inversions; the surface turbulent heat flux was the largest single term. Cases with less moisture in the inversion were often cloud free and the extra solar radiation plus the turbulent surface heat flux caused by the inversion was roughly balanced by the loss of net longwave radiation.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1996

Wavelet Sparse Approximate Inverse Preconditioners

There is an increasing interest in using sparse approximate inverses as preconditioners for Krylov subspace iterative methods. Recent studies of Grote and Huckle and Chow and Saad also show that sparse approximate inverse preconditioner can be effective for a variety of matrices, e.g. Harwell-Boeing collections. Nonetheless a drawback is that it requires rapid decay of the inverse entries so that sparse approximate inverse is possible. However, for the class of matrices that, come from elliptic PDE problems, this assumption may not necessarily hold. Our main idea is to look for a basis, other than the standard one, such that a sparse representation of the inverse is feasible. A crucial observation is that the kind of matrices we are interested in typically have a piecewise smooth inverse. We exploit this fact, by applying wavelet techniques to construct a better sparse approximate inverse in the wavelet basis. We shall justify theoretically and numerically that our approach is effective for matrices with smooth inverse. We emphasize that in this paper we have only presented the idea of wavelet approximate inverses and demonstrated its potential but have not yet developed a highly refined and efficient algorithm.

Chan, Tony F.↗
NASA NTRS2008

Updated Results for the Wake Vortex Inverse Model

NorthWest Research Associates (NWRA) has developed an Inverse Model for inverting aircraft wake vortex data. The objective of the inverse modeling is to obtain estimates of the vortex circulation decay and crosswind vertical profiles, using time history measurements of the lateral and vertical position of aircraft vortices. The Inverse Model performs iterative forward model runs using estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Iterations are performed until a user-defined criterion is satisfied. Outputs from an Inverse Model run are the best estimates of the time history of the vortex circulation derived from the observed data, the vertical crosswind profile, and several vortex parameters. The forward model, named SHRAPA, used in this inverse modeling is a modified version of the Shear-APA model, and it is described in Section 2 of this document. Details of the Inverse Model are presented in Section 3. The Inverse Model was applied to lidar-observed vortex data at three airports: FAA acquired data from San Francisco International Airport (SFO) and Denver International Airport (DEN), and NASA acquired data from Memphis International Airport (MEM). The results are compared with observed data. This Inverse Model validation is documented in Section 4. A summary is given in Section 5. A user's guide for the inverse wake vortex model is presented in a separate NorthWest Research Associates technical report (Lai and Delisi, 2007a).

Robins, Robert E.↗
DOE OSTI2020

Detecting an underground tunnel by applying joint traveltime and waveform inversion

Underground tunnel and void detection is a challenging geophysical problem, and many methods have been proposed. Seismic techniques are promising because of the large seismic velocity contrasts between the air-filled void and the surrounding sediment and concrete. We apply a joint seismic traveltime and waveform inversion method to image a buried tunnel with concrete walls and a void space inside. The joint inversion images the top of the concrete tunnel as a high-velocity anomaly and the void space as a low-velocity anomaly. The location of the velocity anomalies predicted by the method agrees with the known location of the tunnel. As a comparison, the stand-alone full waveform inversion is also applied to the data. The first-arrival traveltime tomography shows weak nonlinearity but fails to image the hidden low-velocity layer. Full waveform inversion is able to image complex near-surface structures, but fitting waveforms may not honor the traveltime fit, especially when the data contain noise. Synthetic and real data tests show that the joint inversion method retains the advantages of both traveltime inversion and full waveform inversion and overcomes their respective drawbacks at the same time. The field example shows the joint inversion provides a better reconstruction of the high-velocity feature representing the top of the concrete wall in terms of its magnitude and location.

58 GEOSCIENCES↗
DOE OSTI2019

Acoustic- and elastic-waveform inversion with total generalized p-variation regularization

Geophysical models usually contain both sharp interfaces and smooth variations, and it is difficult to accurately account for both of these two types of medium parameter variations using conventional full-waveform inversion methods. We develop a novel full-waveform inversion method for acoustic and elastic waves using a total generalized p-variation regularization scheme to address these challenging problems. We decompose the full-waveform inversion into two subproblems and solve these two minimization subproblems using an alternating-direction minimization strategy. One significant advantage of the total generalized p-variation regularization scheme is that it can simultaneously reconstruct sharp interfaces and smooth background variations of geophysical parameters. Such capability can also effectively suppress the noises in source-encoded inversion and sparse-data inversion, or inversion of noisy data. We demonstrate the advantages of our full-waveform inversion method using a checkerboard model, a modified elastic SEG/EAGE overthrust model, and a land field seismic data set. Our conclusions of synthetic and field seismic data demonstrate that our method reconstructs both smooth background variations and sharp interfaces of subsurface geophysical properties accurately, and provides a useful tool for accurate and reliable inversion of field seismic data.

58 GEOSCIENCES↗
DOE OSTI2016

Quantifying the influences of spectral resolution on uncertainty in leaf trait estimates through a Bayesian approach to RTM inversion

The remote monitoring of plant canopies is critically needed for understanding of terrestrial ecosystem mechanics and biodiversity as well as capturing the short- to long-term responses of vegetation to disturbance and climate change. A variety of orbital, sub-orbital, and field instruments have been used to retrieve optical spectral signals and to study different vegetation properties such as plant biochemistry, nutrient cycling, physiology, water status, and stress. Radiative transfer models (RTMs) provide a mechanistic link between vegetation properties and observed spectral features, and RTM spectral inversion is a useful framework for estimating these properties from spectral data. However, existing approaches to RTM spectral inversion are typically limited by the inability to characterize uncertainty in parameter estimates. Here, we introduce a Bayesian algorithm for the spectral inversion of the PROSPECT 5 leaf RTM that is distinct from past approaches in two important ways: First, the algorithm only uses reflectance and does not require transmittance observations, which have been plagued by a variety of measurement and equipment challenges. Second, the output is not a point estimate for each parameter but rather the joint probability distribution that includes estimates of parameter uncertainties and covariance structure. We validated our inversion approach using a database of leaf spectra together with measurements of equivalent water thickness (EWT) and leaf dry mass per unit area (LMA). The parameters estimated by our inversion were able to accurately reproduce the observed reflectance (RMSE VIS = 0.0063, RMSE NIR-SWIR = 0.0098) and transmittance (RMSE VIS = 0.0404, RMSE NIR-SWIR = 0.0551) for both broadleaved and conifer species. Inversion estimates of EWT and LMA for broadleaved species agreed well with direct measurements (CV EWT = 18.8%, CV LMA = 24.5%), while estimates for conifer species were less accurate (CV EWT = 53.2%, CV LMA = 63.3%). To examine the influence of spectral resolution on parameter uncertainty, we simulated leaf reflectance as observed by ten common remote sensing platforms with varying spectral configurations and performed a Bayesian inversion on the resulting spectra. We found that full-range hyperspectral platforms were able to retrieve all parameters accurately and precisely, while the parameter estimates of multispectral platforms were much less precise and prone to bias at high and low values. We also observed that variations in the width and location of spectral bands influenced the shape of the covariance structure of parameter estimates. Lastly, our Bayesian spectral inversion provides a powerful and versatile framework for future RTM development and single- and multi-instrumental remote sensing of vegetation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Pre-conditioned BFGS-based uncertainty quantification in elastic full-waveform inversion

SUMMARY Full-waveform inversion has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss–Newton method, we formulate different initial, diagonal Hessian matrices as pre-conditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of pre-conditioned BFGS for large-scale FWI and uncertainty quantification.

58 GEOSCIENCES↗