Statistical considerations on the Raman inversion algorithm: data inversion and error assessment

2004 ◽  
Author(s):  
Francesc Rocadenbosch ◽  
Michael Sicard ◽  
Albert Ansmann ◽  
Ulla Wandinger ◽  
Volker Matthias ◽  
...  
Keyword(s):  
Error Assessment ◽  
Inversion Algorithm ◽  
Data Inversion

Calibration and data reduction for X-hotwires using cross validation

2021 ◽  
pp. 095441002110403
Author(s):  
Mohan Vijaya Anoop ◽  
Budda Thiagarajan Kannan
Keyword(s):  
Cross Validation ◽  
Low Flow ◽  
Calibration Data ◽  
Inversion Algorithm ◽  
Present Scheme ◽  
Wire Probe ◽  
Data Inversion ◽  
Turbulent Jet Flow ◽  
High Reynolds ◽  
Yaw Angle

A strategy for calibration of X-wire probes and data inversion is described in this article. The approach used has elements of full velocity vs yaw-angle calibration with robust curve fitting. The responses of an X-wire probe placed in a calibration jet are recorded for a set of velocity and yaw inputs followed by fitting cross-validated splines. These spline functions trained from calibration data are evaluated for the probe responses during measurement. X-wire probes are calibrated for low to moderate velocities (0.65 m/s to 32 m/s) and yaw angles in the range −40° to 40° and comparisons with conventional interpolation schemes are made. The proposed algorithm can be extended to calibration of other multiple wire probes and for higher velocities. Some measurements in a single round turbulent jet flow at high Reynolds number using the proposed inversion algorithm are also presented. The present scheme is found to perform better particularly at low flow magnitudes and/or extreme flow angles than the schemes used previously.

A new data inversion algorithm for DMPS and TDMA measurements

1999 ◽  
Vol 30 ◽  
pp. S775-S776 ◽  
Author(s):  
A. Voutilainen ◽  
F. Stratmann ◽  
J.P. Kaipio
Keyword(s):  
Inversion Algorithm ◽  
Data Inversion

A compressed implicit Jacobian scheme for 3D electromagnetic data inversion

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. F173-F183 ◽  
Author(s):  
Maokun Li ◽  
Aria Abubakar ◽  
Jianguo Liu ◽  
Guangdong Pan ◽  
Tarek M. Habashy
Keyword(s):  
Electric Fields ◽  
Jacobian Matrix ◽  
Iterative Solvers ◽  
Computational Time ◽  
Memory Usage ◽  
Inversion Algorithm ◽  
Linear System Of Equations ◽  
Electromagnetic Data ◽  
Data Inversion ◽  
Computational Overhead

We developed a compressed implicit Jacobian scheme for the regularized Gauss-Newton inversion algorithm for reconstructing 3D conductivity distributions from electromagnetic data. In this algorithm, the Jacobian matrix, whose storage usually requires a large amount of memory, is decomposed in terms of electric fields excited by sources located and oriented identically to the physical sources and receivers. As a result, the memory usage for the Jacobian matrix reduces from O(NFNSNRNP) to O[NF(NS + NR)NP], where NF is the number of frequencies, NS is the number of sources, NR is the number of receivers, and NP is the number of conductivity cells to be inverted. When solving the Gauss-Newton linear system of equations using iterative solvers, the multiplication of the Jacobian matrix with a vector is converted to matrix-vector operations between the matrices of the electric fields and the vector. In order to mitigate the additional computational overhead of this scheme, these fields are further compressed using the adaptive cross approximation (ACA) method. The compressed implicit Jacobian scheme provides a good balance between memory usage and computational time and renders the Gauss-Newton algorithm more efficient. We demonstrated the benefits of this scheme using numerical examples including both synthetic and field data for both crosswell and controlled-source electromagnetic (CSEM) applications.

scholarly journals Airborne multiwavelength High Spectral Resolution Lidar (HSRL-2) observations during TCAP 2012: vertical profiles of optical and microphysical properties of a smoke/urban haze plume over the northeastern coast of the US

2014 ◽  
Vol 7 (2) ◽  
pp. 1059-1073 ◽  
Author(s):  
D. Müller ◽  
C. A. Hostetler ◽  
R. A. Ferrare ◽  
S. P. Burton ◽  
E. Chemyakin ◽  
...  
Keyword(s):  
Spectral Resolution ◽  
Phase 1 ◽  
Department Of Energy ◽  
High Spectral Resolution ◽  
Inversion Algorithm ◽  
Data Inversion ◽  
Microphysical Properties ◽  
The Us ◽  
Langley Research Center ◽  
High Spectral Resolution Lidar

Abstract. We present measurements acquired by the world's first airborne multiwavelength High Spectral Resolution Lidar (HSRL-2), developed by NASA Langley Research Center. The instrument was operated during Phase 1 of the Department of Energy (DOE) Two-Column Aerosol Project (TCAP)in July 2012. We observed pollution outflow from the northeast coast of the US out over the West Atlantic Ocean. Lidar ratios were 50–60 sr at 355 nm and 60–70 sr at 532 nm. Extinction-related Ångström exponents were on average 1.2–1.7 indicating comparably small particles. Our novel automated, unsupervised data inversion algorithm retrieves particle effective radii of approximately 0.2 μm, which is in agreement with the large Ångström exponents. We find good agreement with particle size parameters obtained from coincident in situ measurements carried out with the DOE Gulfstream-1 aircraft.

scholarly journals Performance Improvement of Spaceborne Carbon Dioxide Detection IPDA LIDAR Using Optimization of Optical Detector and Amplifier Linearity

2021 ◽  
Vol 13 (10) ◽  
pp. 2007
Author(s):  
Yadan Zhu ◽  
Juxin Yang ◽  
Xiaoxi Zhang ◽  
Jiqiao Liu ◽  
Xiaopeng Zhu ◽  
...  
Keyword(s):  
Circuit Board ◽  
Transfer Model ◽  
Circuit Optimization ◽  
Inversion Algorithm ◽  
Lidar System ◽  
Amplifier Circuit ◽  
Detector Module ◽  
Data Inversion ◽  
Air Mixing ◽  
Carbon Dioxide Detection

The spaceborne double-pulse integrated-path differential absorption (IPDA) light detection and ranging (LIDAR) system was found to be helpful in observing atmospheric CO2 and understanding the carbon cycle. The airborne experiments of a scale prototype of China’s planned spaceborne IPDA LIDAR was implemented in 2019. A problem with data inversion caused by the detector module nonlinearity was found. Through many experiments, the amplifier circuit board (ACB) of the detector module was proved to be the main factor causing the nonlinearity. Through amplifier circuit optimization, the original bandwidth of the ACB was changed to 1 MHz by using a fifth-order active filter. Compared with the original version, the linearity of optimized ACB is improved from 42.6% to 0.0747%. The optimized ACB was produced and its linearity was verified by experiments. In addition, the output waveform of the optimized ACB changes significantly, which will affect the random error (RE) of the optimized IPDA LIDAR system. Through the performance simulation, the RE of more than 90% of the global area is less than 0.728 ppm. Finally, the transfer model of the detector module was given, which will be helpful for the further optimization of the CO2 column-averaged dry-air mixing ratio (XCO2) inversion algorithm.

scholarly journals 3D induced-polarization data inversion for complex resistivity

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. F157-F171 ◽  
Author(s):  
Michael Commer ◽  
Gregory A. Newman ◽  
Kenneth H. Williams ◽  
Susan S. Hubbard
Keyword(s):  
Environmental Remediation ◽  
Large Scale ◽  
Forward Modeling ◽  
Induced Polarization ◽  
Inversion Method ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Data Set ◽  
Complex Resistivity ◽  
Data Inversion

The conductive and capacitive material properties of the subsurface can be quantified through the frequency-dependent complex resistivity. However, the routine three-dimensional (3D) interpretation of voluminous induced polarization (IP) data sets still poses a challenge due to large computational demands and solution nonuniqueness. We have developed a flexible methodology for 3D (spectral) IP data inversion. Our inversion algorithm is adapted from a frequency-domain electromagnetic (EM) inversion method primarily developed for large-scale hydrocarbon and geothermal energy exploration purposes. The method has proven to be efficient by implementing the nonlinear conjugate gradient method with hierarchical parallelism and by using an optimal finite-difference forward modeling mesh design scheme. The method allows for a large range of survey scales, providing a tool for both exploration and environmental applications. We experimented with an image focusing technique to improve the poor depth resolution of surface data sets with small survey spreads. The algorithm’s underlying forward modeling operator properly accounts for EM coupling effects; thus, traditionally used EM coupling correction procedures are not needed. The methodology was applied to both synthetic and field data. We tested the benefit of directly inverting EM coupling contaminated data using a synthetic large-scale exploration data set. Afterward, we further tested the monitoring capability of our method by inverting time-lapse data from an environmental remediation experiment near Rifle, Colorado. Similar trends observed in both our solution and another 2D inversion were in accordance with previous findings about the IP effects due to subsurface microbial activity.

2.5D forward and inverse modeling for interpreting low-frequency electromagnetic measurements

Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. F165-F177 ◽  
Author(s):  
A. Abubakar ◽  
T. M. Habashy ◽  
V. L. Druskin ◽  
L. Knizhnerman ◽  
D. Alumbaugh
Keyword(s):  
Cost Function ◽  
Regularization Parameter ◽  
A Priori ◽  
Low Frequency ◽  
Inversion Algorithm ◽  
Forward Algorithm ◽  
Linear System Of Equations ◽  
Controlled Source ◽  
Data Inversion ◽  
The Cost

We present 2.5D fast and rigorous forward and inversion algorithms for deep electromagnetic (EM) applications that include crosswell and controlled-source EM measurements. The forward algorithm is based on a finite-difference approach in which a multifrontal LU decomposition algorithm simulates multisource experiments at nearly the cost of simulating one single-source experiment for each frequency of operation. When the size of the linear system of equations is large, the use of this noniterative solver is impractical. Hence, we use the optimal grid technique to limit the number of unknowns in the forward problem. The inversion algorithm employs a regularized Gauss-Newton minimization approach with a multiplicative cost function. By using this multiplicative cost function, we do not need a priori data to determine the so-called regularization parameter in the optimization process, making the algorithm fully automated. The algorithm is equipped with two regularization cost functions that allow us to reconstruct either a smooth or a sharp conductivity image. To increase the robustness of the algorithm, we also constrain the minimization and use a line-search approach to guarantee the reduction of the cost function after each iteration. To demonstrate the pros and cons of the algorithm, we present synthetic and field data inversion results for crosswell and controlled-source EM measurements.

Global Rainbow Thermometry: Improvements in the Data Inversion Algorithm and Validation Technique in Liquid-Liquid Suspension

2004 ◽  
Vol 43 (18) ◽  
pp. 3600 ◽  
Author(s):  
Maria Rosaria Vetrano ◽  
Jeronimus Petrus Antonius Johannes van Beeck ◽  
Michel L�on Riethmuller
Keyword(s):  
Inversion Algorithm ◽  
Data Inversion ◽  
Liquid Suspension ◽  
Validation Technique

scholarly journals Statistically optimized inversion algorithm for enhanced retrieval of aerosol properties from spectral multi-angle polarimetric satellite observations

2011 ◽  
Vol 4 (5) ◽  
pp. 975-1018 ◽  
Author(s):  
O. Dubovik ◽  
M. Herman ◽  
A. Holdak ◽  
T. Lapyonok ◽  
D. Tanré ◽  
...  
Keyword(s):  
A Priori ◽  
Algorithm Design ◽  
Statistical Optimization ◽  
Satellite Observations ◽  
Spatial And Temporal Variability ◽  
Inversion Algorithm ◽  
Simultaneous Inversion ◽  
Data Inversion ◽  
Retrieval Scheme ◽  
Aerosol Properties

Abstract. The proposed development is an attempt to enhance aerosol retrieval by emphasizing statistical optimization in inversion of advanced satellite observations. This optimization concept improves retrieval accuracy relying on the knowledge of measurement error distribution. Efficient application of such optimization requires pronounced data redundancy (excess of the measurements number over number of unknowns) that is not common in satellite observations. The POLDER imager on board the PARASOL micro-satellite registers spectral polarimetric characteristics of the reflected atmospheric radiation at up to 16 viewing directions over each observed pixel. The completeness of such observations is notably higher than for most currently operating passive satellite aerosol sensors. This provides an opportunity for profound utilization of statistical optimization principles in satellite data inversion. The proposed retrieval scheme is designed as statistically optimized multi-variable fitting of all available angular observations obtained by the POLDER sensor in the window spectral channels where absorption by gas is minimal. The total number of such observations by PARASOL always exceeds a hundred over each pixel and the statistical optimization concept promises to be efficient even if the algorithm retrieves several tens of aerosol parameters. Based on this idea, the proposed algorithm uses a large number of unknowns and is aimed at retrieval of extended set of parameters affecting measured radiation. The algorithm is designed to retrieve complete aerosol properties globally. Over land, the algorithm retrieves the parameters of underlying surface simultaneously with aerosol. In all situations, the approach is anticipated to achieve a robust retrieval of complete aerosol properties including information about aerosol particle sizes, shape, absorption and composition (refractive index). In order to achieve reliable retrieval from PARASOL observations even over very reflective desert surfaces, the algorithm was designed as simultaneous inversion of a large group of pixels within one or several images. Such multi-pixel retrieval regime takes advantage of known limitations on spatial and temporal variability in both aerosol and surface properties. Specifically the variations of the retrieved parameters horizontally from pixel-to-pixel and/or temporary from day-to-day are enforced to be smooth by additional a priori constraints. This concept is expected to provide satellite retrieval of higher consistency, because the retrieval over each single pixel will be benefiting from coincident aerosol information from neighboring pixels, as well, from the information about surface reflectance (over land) obtained in preceding and consequent observations over the same pixel. The paper provides in depth description of the proposed inversion concept, illustrates the algorithm performance by a series of numerical tests and presents the examples of preliminary retrieval results obtained from actual PARASOL observations. It should be noted that many aspects of the described algorithm design considerably benefited from experience accumulated in the preceding effort on developments of currently operating AERONET and PARASOL retrievals, as well as several core software components were inherited from those earlier algorithms.

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