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Journal articles on the topic 'Inversion theory'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Liang, Chen, John Castagna, and Marcelo Benabentos. "Reflectivity decomposition: Theory and application." Interpretation 9, no. 2 (April 21, 2021): B7—B23. http://dx.doi.org/10.1190/int-2020-0203.1.

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Sparse reflectivity inversion of processed reflection seismic data is intended to produce reflection coefficients that represent boundaries between geologic layers. However, the objective function for sparse inversion is usually dominated by large reflection coefficients, which may result in unstable inversion for weak events, especially those interfering with strong reflections. We have determined that any seismogram can be decomposed according to the characteristics of the inverted reflection coefficients that can be sorted and subset by magnitude, sign, and sequence, and new seismic traces can be created from only reflection coefficients that pass the sorting criteria. We call this process reflectivity decomposition. For example, original inverted reflection coefficients can be decomposed by magnitude, large ones removed, the remaining reflection coefficients reconvolved with the wavelet, and this residual reinverted, thereby stabilizing inversions for the remaining weak events. As compared with inverting an original seismic trace, subtle impedance variations occurring in the vicinity of nearby strong reflections can be better revealed and characterized when only the events caused by small reflection coefficients are passed and reinverted. When we apply reflectivity decomposition to a 3D seismic data set in the Midland Basin, seismic inversion for weak events is stabilized such that previously obscured porous intervals in the original inversion can be detected and mapped, with a good correlation to the actual well logs.

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2

McBroome, Jakob, David Liang, and Russell Corbett-Detig. "Fine-Scale Position Effects Shape the Distribution of Inversion Breakpoints in Drosophila melanogaster." Genome Biology and Evolution 12, no. 8 (May 21, 2020): 1378–91. http://dx.doi.org/10.1093/gbe/evaa103.

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Abstract Chromosomal inversions are among the primary drivers of genome structure evolution in a wide range of natural populations. Although there is an impressive array of theory and empirical analyses that have identified conditions under which inversions can be positively selected, comparatively little data are available on the fitness impacts of these genome structural rearrangements themselves. Because inversion breakpoints can disrupt functional elements and alter chromatin domains, the precise positioning of an inversion’s breakpoints can strongly affect its fitness. Here, we compared the fine-scale distribution of low-frequency inversion breakpoints with those of high-frequency inversions and inversions that have gone to fixation between Drosophila species. We identified a number of differences among frequency classes that may influence inversion fitness. In particular, breakpoints that are proximal to insulator elements, generate large tandem duplications, and minimize impacts on gene coding spans which are more prevalent in high-frequency and fixed inversions than in rare inversions. The data suggest that natural selection acts to preserve both genes and larger cis-regulatory networks in the occurrence and spread of rearrangements. These factors may act to limit the availability of high-fitness arrangements when suppressed recombination is favorable.

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3

Warner, Michael, and Lluís Guasch. "Adaptive waveform inversion: Theory." GEOPHYSICS 81, no. 6 (November 2016): R429—R445. http://dx.doi.org/10.1190/geo2015-0387.1.

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Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error.

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4

Beard, Les P., and Alan C. Tripp. "Investigating the resolution of IP arrays using inverse theory." GEOPHYSICS 60, no. 5 (September 1995): 1326–41. http://dx.doi.org/10.1190/1.1443869.

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Using a fast 2-D inverse solution, we examined the resolution of different resistivity/IP arrays using noisy synthetic data subject to minimum structure inversion. We compared estimated models from inversions of data from the dipole‐dipole, pole‐dipole, and pole‐pole arrays over (1) a dipping, polarizable conductor, (2) two proximate conductive, polarizable bodies, (3) a polarizable conductor beneath conductive overburden, and (4) a thin, resistive, polarizable dike. The estimated resistivity and polarizability models obtained from inversion of the dipole‐dipole data were usually similar to the pole‐dipole estimated models. In the cases examined, the estimated models from the pole‐pole data were more poorly resolved than the models from the other arrays. If pole‐pole resistivity data contain even a fraction of a percent of Gaussian noise, the transformation of such data through superposition to equivalent data of other array types may be considerably distorted, and significant information can be lost using the pole‐pole array. Though the gradient array is reputed to be more sensitive to dip than other arrays, it evidently contains little information on dip that does not also appear in dipole‐dipole data, for joint inversion of dipole‐dipole and gradient array data yields models virtually identical to those obtained from inversion of dipole‐dipole data alone.

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5

Norton, Stephen J., and John R. Bowler. "Theory of eddy current inversion." Journal of Applied Physics 73, no. 2 (January 15, 1993): 501–12. http://dx.doi.org/10.1063/1.353359.

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6

Hampson, Dan. "AVO inversion, theory and practice." Leading Edge 10, no. 6 (June 1991): 39–42. http://dx.doi.org/10.1190/1.1436820.

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7

Blok, Victor R., and Gennady M. Krochik. "Theory of lasers without inversion." Physical Review A 41, no. 3 (February 1, 1990): 1517–25. http://dx.doi.org/10.1103/physreva.41.1517.

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8

Schuster, Gerard T., and Aksel Quintus‐Bosz. "Wavepath eikonal traveltime inversion: Theory." GEOPHYSICS 58, no. 9 (September 1993): 1314–23. http://dx.doi.org/10.1190/1.1443514.

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We present a general formula for the back projection of traveltime residuals in traveltime tomography. For special choices of an arbitrary weighting factor this formula reduces to the asymptotic back‐projection term in ray‐tracing tomography (RT), the Woodward‐Rocca method, wavepath eikonal traveltime inversion (WET), and wave‐equation traveltime inversion (WT). This unification provides for an understanding of the differences and similarities among these traveltime tomography methods. The special case of the WET formula leads to a computationally efficient inversion scheme in the space‐time domain that is, in principle, almost as effective as WT inversion yet is an order of magnitude faster. It also leads to an analytic formula for the fast computation of wavepaths. Unlike ray‐tracing tomography, WET partially accounts for band‐limited source and shadow effects in the data. Several numerical tests of the WET method are used to illustrate its properties.

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9

Buland, A., and M. Landrø. "AVO inversion, theory and applications." Journal of Applied Geophysics 34, no. 2 (December 1995): 140. http://dx.doi.org/10.1016/0926-9851(96)80869-x.

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10

Bergeron, Clyde J., Juliette W. Ioup, Yan Wu, George E. Ioup, and Kenneth W. Holladay. "Multilayer MIM inversion of AEM data: Theory and field example." GEOPHYSICS 66, no. 1 (January 2001): 125–36. http://dx.doi.org/10.1190/1.1444887.

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This paper presents a multilayer generalization of an algebraic method of inverting frequency‐doma in airborne active electromagnetic (AEM) data in terms of 1-D layered earth models. The processing of the AEM data, which includes a recalibration procedure, is also outlined. The inversion is applied to synthetic fields generated from a multilayer model which is intended to approximate a measured conductivity profile of the water column in the Gulf of Mexico and to measured AEM data from a survey of the Barataria Bay estuary region of the Louisiana Gulf of Mexico coast. The inversion results from the synthetic data are in good agreement with the forward model. The conductivities calculated from the inversions of measured AEM data are compared to ground‐and water‐based measurements. The depth variations of the calculated electrical conductivities in the nearshore Gulf waters are in good agreement with measurements of conductivity versus depth by conductivity‐temperature‐depth (CTD) casts at several points on the over‐the‐water portion of two flight lines.

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11

MATSU'URA, Mitsuhiro. "Development of Inversion Theory in Geophysics." Zisin (Journal of the Seismological Society of Japan. 2nd ser.) 44, Supplement (1991): 53–62. http://dx.doi.org/10.4294/zisin1948.44.supplement_53.

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12

Barker, Laurence. "Local representation theory and möbius inversion." Communications in Algebra 27, no. 7 (January 1999): 3377–99. http://dx.doi.org/10.1080/00927879908826634.

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13

MacBain, J. A. "Inversion theory for the magnetotelluric problem." Inverse Problems 3, no. 3 (August 1, 1987): 453–61. http://dx.doi.org/10.1088/0266-5611/3/3/013.

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14

Cardimona, S. "Waveform inversion and digital filter theory." GEOPHYSICS 56, no. 4 (April 1991): 534–36. http://dx.doi.org/10.1190/1.1443069.

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For many years, we have used seismic data processing techniques such as digital filter theory to enhance the signal‐to‐noise (S/N) ratio of the observed data to obtain the best possible image of the subsurface. With our increased knowledge and the increasingly sophisticated computers at our disposal, modern methods of data analysis are tending to be inversions through model fitting, i.e., actually finding the best model of the subsurface which would produce the observed data.

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15

Loftus, Geoffrey R., Martin A. Oberg, and Allyss M. Dillon. "Linear theory, dimensional theory, and the face-inversion effect." Psychological Review 111, no. 4 (2004): 835–63. http://dx.doi.org/10.1037/0033-295x.111.4.835.

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16

Ha, Wansoo, and Changsoo Shin. "Laplace-domain full-waveform inversion of seismic data lacking low-frequency information." GEOPHYSICS 77, no. 5 (September 1, 2012): R199—R206. http://dx.doi.org/10.1190/geo2011-0411.1.

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The lack of the low-frequency information in field data prohibits the time- or frequency-domain waveform inversions from recovering large-scale background velocity models. On the other hand, Laplace-domain waveform inversion is less sensitive to the lack of the low frequencies than conventional inversions. In theory, frequency filtering of the seismic signal in the time domain is equivalent to a constant multiplication of the wavefield in the Laplace domain. Because the constant can be retrieved using the source estimation process, the frequency content of the seismic data does not affect the gradient direction of the Laplace-domain waveform inversion. We obtained inversion results of the frequency-filtered field data acquired in the Gulf of Mexico and two synthetic data sets obtained using a first-derivative Gaussian source wavelet and a single-frequency causal sine function. They demonstrated that Laplace-domain inversion yielded consistent results regardless of the frequency content within the seismic data.

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17

Huang, Henry He, Li Sun, and Tong (Robert Yu. "Are Socially Responsible Firms Less Likely to Expatriate? An Examination of Corporate Inversions." Journal of the American Taxation Association 39, no. 2 (September 1, 2017): 43–62. http://dx.doi.org/10.2308/atax-51790.

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ABSTRACT This study examines whether corporate social responsibility (CSR) is related to the likelihood of corporate inversions, a legal tax-planning strategy. We use a full sample to test stakeholder theory and a risk management view of CSR. We find that firms with higher CSR performance are less likely to expatriate compared to firms with lower CSR performance. Although equity investors react positively to inversion announcements, we find that the reaction is less positive for firms with higher CSR ratings. These results are consistent with stakeholder theory. We do not find evidence that inversion firms experience significant improvements in operating performance after inversion. Overall, this study improves our understanding of the role of CSR in corporate expatriation decisions and has practical implications for a firm's stakeholders. Data Availability: Data are available from sources identified in the paper.

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18

Anderson, Walter L. "Approximate inversion of high‐frequency electromagnetic soundings using complex image theory." GEOPHYSICS 56, no. 7 (July 1991): 1087–92. http://dx.doi.org/10.1190/1.1443120.

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Electromagnetic (EM) soundings in an intermediate range between quasi‐static and radar frequencies (e.g., 30 kHz – 300 MHz) were studied with an approximate inversion method for shallow‐layered earth models using complex image theory. The half‐space image theory formulas for calculating forward soundings for any dipole source are easily extended to accommodate a multilayered earth, and only involve elementary complex functions. Approximate inversion using the modified image formulas is compared with more exact numerical integration inversion for horizontal‐layered models to yield the conductivity, thickness, and dielectric permittivity of each layer. A nonlinear least‐squares algorithm was used to obtain parameter and linear parameter error estimates. The results, using known exact forward models and one field data case, indicate that approximate image inversion is more than an order‐of‐magnitude faster than numerical integration inversion. However, approximate inversion could not always resolve deeper layer parameters as well as with exact inversion. Accuracy of both methods, however, depends on the frequency range used. Nevertheless, approximate inversion can be a useful quick reconnaissance tool, and could easily be written for on‐site personal computers.

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19

Zhu, Shi-Yao, Jim Cresser, and Heidi Fearn. "Comment on ‘‘Theory of lasers without inversion’’." Physical Review A 43, no. 9 (May 1, 1991): 5170–72. http://dx.doi.org/10.1103/physreva.43.5170.

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20

Jones, R. Michael, E. C. Shang, and T. M. Georges. "Nonperturbative modal tomography inversion. Part I. Theory." Journal of the Acoustical Society of America 94, no. 4 (October 1993): 2296–302. http://dx.doi.org/10.1121/1.407470.

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21

Feldman, Joel, Manfred Salmhofer, and Eugene Trubowitz. "An inversion theorem in Fermi surface theory." Communications on Pure and Applied Mathematics 53, no. 11 (2000): 1350–84. http://dx.doi.org/10.1002/1097-0312(200011)53:11<1350::aid-cpa2>3.0.co;2-d.

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22

Neubauer, Andreas, and Hanna K. Pikkarainen. "Convergence rate for the Bayesian inversion theory." PAMM 7, no. 1 (December 2007): 1080103–4. http://dx.doi.org/10.1002/pamm.200700275.

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23

Blok, Victor R., and Gennady M. Krochik. "Lasing without inversion: Theory of transient behavior." Physical Review A 44, no. 3 (August 1, 1991): 2036–39. http://dx.doi.org/10.1103/physreva.44.2036.

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24

MacBain, John A. "Inversion Theory for a Parameterized Diffusion Problem." SIAM Journal on Applied Mathematics 47, no. 6 (December 1987): 1386–91. http://dx.doi.org/10.1137/0147091.

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25

Bobe, Christin, Daan Hanssens, Thomas Hermans, and Ellen Van De Vijver. "Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data." Algorithms 13, no. 6 (June 18, 2020): 144. http://dx.doi.org/10.3390/a13060144.

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Often, multiple geophysical measurements are sensitive to the same subsurface parameters. In this case, joint inversions are mostly preferred over two (or more) separate inversions of the geophysical data sets due to the expected reduction of the non-uniqueness in the joint inverse solution. This reduction can be quantified using Bayesian inversions. However, standard Markov chain Monte Carlo (MCMC) approaches are computationally expensive for most geophysical inverse problems. We present the Kalman ensemble generator (KEG) method as an efficient alternative to the standard MCMC inversion approaches. As proof of concept, we provide two synthetic studies of joint inversion of frequency domain electromagnetic (FDEM) and direct current (DC) resistivity data for a parameter model with vertical variation in electrical conductivity. For both studies, joint results show a considerable improvement for the joint framework over the separate inversions. This improvement consists of (1) an uncertainty reduction in the posterior probability density function and (2) an ensemble mean that is closer to the synthetic true electrical conductivities. Finally, we apply the KEG joint inversion to FDEM and DC resistivity field data. Joint field data inversions improve in the same way seen for the synthetic studies.

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26

Lörtzer, G. J. M., and A. J. Berkhout. "An integrated approach to lithologic inversion—Part I: Theory." GEOPHYSICS 57, no. 2 (February 1992): 233–44. http://dx.doi.org/10.1190/1.1443236.

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For the complex problem of lithologic inversion a new formalism is proposed, using a spatial distribution of seismic velocities ([Formula: see text]) and densities (ρ) as input. At each subsurface grid point, the inversion result consists of the most likely lithotype (gas, sand, shale, etc.) together with its related litho parameters (frame strength, porosity, etc.). The inversion method is based on the Bayesian theory of parameter estimation, allowing specification of inaccuracies in the input and the incorporation of geological knowledge. An important advantage of the proposed inversion method is that for each practical situation the necessary accuracy of [Formula: see text], [Formula: see text] and ρ can be predetermined to distinguish between specific lithotypes or to estimate a specific litho parameter with a prespecified accuracy. For instance, inversion results show that water saturation can only be estimated for an unrealistic accurate input. On the other hand, for the estimation of porosities it is generally sufficient to have compressional velocities available with a realistic accuracy.

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27

Domanska, Ewa. "Chris Lorenz's idea of conceptual inversion." Historein 14, no. 1 (May 27, 2013): 93. http://dx.doi.org/10.12681/historein.214.

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The text deals with Chris Lorenz’s idea of conceptual inversion, understood as an epistemological blockade that stands as a barrier to the development of a proper theory of humanities and social sciences. According to Lorenz, the methodological and theoretical views of scientific programmes embody negations (i.e. inversions) of the views being criticized by them. Because of this process of “turning upside down”, many of the conceptual problems connected with the criticized positions survive. The author asks two questions: first, about the relation between Lorenz’s idea of conceptual inversion and Imre Lakatos’ idea of reconfigurations of research programmes, and, second, about possible common ground on which Lorenz’s interest in empiricism emerging out of his criticism of narrativism, and Ewa Domanska’s interest in new empiricism related to posthumanism (also critical of textual constructivism), could meet.

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28

Kuo, M. K., and H. T. Lee. "Inversion of Residual Stress." Journal of Mechanics 17, no. 2 (June 2001): 103–8. http://dx.doi.org/10.1017/s1727719100003178.

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ABSTRACTA technique for inverting residual stress based on a theory of acoustoelasticity is presented. A general incremental constitutive relation is first derived for a pre-stressed material subjected to an additional infinitesimal elastic deformation. The theory is then employed on using ultrasonic means to evaluate residual stresses of residually stressed materials. The residual stresses are assumed to be homogeneous in materials as usual. The only major assumption in this formulation is that the additional deformations caused by ultrasonic evaluating process are infinitesimal and elastic. No assumption on the origin of residual stresses is needed, nor the assumption on the possible existence of “natural state” of the materials. Successful inversion of residual stresses are demonstrated through a preliminary numerical experiment.

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29

Lambaré, Gilles, Stéphane Operto, Pascal Podvin, and Philippe Thierry. "3D ray+Born migration/inversion—Part 1: Theory." GEOPHYSICS 68, no. 4 (July 2003): 1348–56. http://dx.doi.org/10.1190/1.1598128.

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Prestack ray+Born migration/inversion can be split in two steps : the computation of common image gathers (CIGs) and their weighted stack (the migration stack). The choice of the domain for the CIGs (shot, offset, angle, etc.) has a direct impact on the resolution of the migration stack. This resolution can be studied easily in the frame of ray+Born migration/inversion theory resulting into improved migration/inversion formulas according to the acquisition geometry. This paper is devoted to this analysis in the cases of a simple 2D acquisition and of a 3D swath acquisition, both corresponding to classical data sets from the SEG/EAGE 3D overthrust experiment. We show that the migration formula originally designed for 3D marine acquisition is not adaptable to the 3D swath acquisition. Finally, we propose a new formula for this specific acquisition, which improves the resolution of the final migrated image. The relevance of this new formula is illustrated in the frame of the SEG/EAGE experiment in the companion paper.

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30

McGaugh, Suzanne E., and Mohamed A. F. Noor. "Genomic impacts of chromosomal inversions in parapatric Drosophila species." Philosophical Transactions of the Royal Society B: Biological Sciences 367, no. 1587 (February 5, 2012): 422–29. http://dx.doi.org/10.1098/rstb.2011.0250.

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Chromosomal inversions impact genetic variation and facilitate speciation in part by reducing recombination in heterokaryotypes. We generated multiple whole-genome shotgun sequences of the parapatric species pair Drosophila pseudoobscura and Drosophila persimilis and their sympatric outgroup ( Drosophila miranda ) and compared the average pairwise differences for neutral sites within, just outside and far outside of the three large inversions. Divergence between D. pseudoobscura and D. persimilis is high inside the inversions and in the suppressed recombination regions extending 2.5 Mb outside of inversions, but significantly lower in collinear regions further from the inversions. We observe little evidence of decreased divergence predicted to exist in the centre of inversions, suggesting that gene flow through double crossovers or gene conversion is limited within the inversion, or selection is acting within the inversion to maintain divergence in the face of gene flow. In combination with past studies, we provide evidence that inversions in this system maintain areas of high divergence in the face of hybridization, and have done so for a substantial period of time. The left arm of the X chromosome and chromosome 2 inversions appear to have arisen in the lineage leading to D. persimilis approximately 2 Ma, near the time of the split of D. persimilis–D. pseudoobscura–D. miranda , but likely fixed within D. persimilis much more recently, as diversity within D. persimilis is substantially reduced inside and near these two inversions. We also hypothesize that the inversions in D. persimilis may provide an empirical example of the ‘mixed geographical mode’ theory of inversion origin and fixation, whereby allopatry and secondary contact both play a role.

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31

Colombo, Daniele, Diego Rovetta, Taqi Al-Yousuf, Ernesto Sandoval, Ersan Turkoglu, and Gary McNeice. "Multiple joint wavefield inversions: Theory and field data implementations." Leading Edge 39, no. 6 (June 2020): 411–21. http://dx.doi.org/10.1190/tle39060411.1.

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Accurate velocity models for the near surface and overburden are needed for seismic processing and reliable depth imaging. Seismic with multiphysics data, well logs, and geology information need to be quantitatively integrated to obtain high-resolution velocity models. We detail our development and application of the joint wavefield inversion software platform, which enables flexible algorithmic schemes for the integration of multiparameter data and constraints. Inversion is performed in cascade or simultaneously using a variety of input data to constrain the velocity field reconstruction at multiple scales. Coupling mechanisms based on structure similarity together with rock-physics relations are optimally combined to boost resolution and enhance accuracy of the inverted velocity models. Ill-posed inversion problems are then solved using extensive geologic and rock-physics regularization instead of relying on smoothness constraints alone. We detail workflows and algorithms to guide the application of multiparameter joint inversion for velocity model building whether the input data are seismic traveltimes, electromagnetics (time/frequency domains), gravity, and/or surface waves. Extensive applications of multiparameter joint inversion are presented for a variety of complex geologic scenarios in which various multiparameter coupling strategies are illustrated. Robust velocity modeling and enhanced seismic imaging in time and depth domains are obtained as a result, proving the importance of multiphysics integration for reliable earth model parameter estimation.

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32

Hakim, Gregory J. "A Probabilistic Theory for Balance Dynamics." Journal of the Atmospheric Sciences 65, no. 9 (September 1, 2008): 2949–60. http://dx.doi.org/10.1175/2007jas2499.1.

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Abstract Balance dynamics are proposed in a probabilistic framework, assuming that the state variables and the master, or control, variables are random variables described by continuous probability density functions. Balance inversion, defined as recovering the state variables from the control variables, is achieved through Bayes’ theorem. Balance dynamics are defined by the propagation of the joint probability of the state and control variables through the Liouville equation. Assuming Gaussian statistics, balance inversion reduces to linear regression of the state variables onto the control variables, and assuming linear dynamics, balance dynamics reduces to a Kalman filter subject to perfect observations given by the control variables. Example solutions are given for an elliptical vortex in shallow water having unity Rossby and Froude numbers, which produce an outward-propagating pulse of inertia–gravity wave activity. Applying balance inversion to the potential vorticity reveals that, because potential vorticity and divergence share well-defined patterns of covariability, the inertia–gravity wave field is recovered in addition to the vortical field. Solutions for a probabilistic balance dynamics model applied to the elliptical vortex reveal smaller errors (“imbalance”) for height control compared to potential vorticity control. Important attributes of the probabilistic balance theory include quantification of the concept of balance manifold “fuzziness,” and clear state-independent definitions of balance and imbalance in terms of the range of the probabilistic inversion operators. Moreover, the theory provides a generalization of the notion of balance that may prove useful for problems involving moist physics, chemistry, and tropical circulations.

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33

Xue-Jun, Chen, Wang Yan, and Li Yi-Gui. "He-Ne Interatomic Potential from Inversion Scattering Theory." Acta Physico-Chimica Sinica 10, no. 12 (1994): 1099–104. http://dx.doi.org/10.3866/pku.whxb19941209.

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34

Reed, B. Cameron. "Accurate and Efficient Perturbation Theory by Matrix Inversion." Journal of Chemical Education 76, no. 10 (October 1999): 1444. http://dx.doi.org/10.1021/ed076p1444.

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35

Seydou, F. "Profile inversion in scattering theory: the TE case." Journal of Computational and Applied Mathematics 137, no. 1 (December 2001): 49–60. http://dx.doi.org/10.1016/s0377-0427(00)00629-4.

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36

Kyrölä, E., E. Sihvola, Y. Kotivuori, M. Tikka, T. Tuomi, and H. Haario. "Inverse theory for occultation measurements: 1. Spectral inversion." Journal of Geophysical Research: Atmospheres 98, no. D4 (April 20, 1993): 7367–81. http://dx.doi.org/10.1029/92jd02678.

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37

Newman, G. A., and D. L. Alumbaugh. "Three-dimensional massively parallel electromagnetic inversion-I. Theory." Geophysical Journal International 128, no. 2 (February 1997): 345–54. http://dx.doi.org/10.1111/j.1365-246x.1997.tb01559.x.

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38

Wu, Han. "A note on spectral analysis in automorphic representation theory for GL2: I." International Journal of Number Theory 13, no. 10 (October 16, 2017): 2717–50. http://dx.doi.org/10.1142/s1793042117501500.

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We establish the Fourier inversion for the smooth vectors in [Formula: see text] over a number field [Formula: see text], using minimal knowledge from automorphic representation theory. We point out a possible way to establish Fourier inversion for larger classes of functions. We also point out the incompleteness of some commonly believed “proof” of Fourier inversion in the literature. Moreover, the explicit computation of the intertwining operator has independent interests.

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39

Monteil, Guillaume, Grégoire Broquet, Marko Scholze, Matthew Lang, Ute Karstens, Christoph Gerbig, Frank-Thomas Koch, et al. "The regional European atmospheric transport inversion comparison, EUROCOM: first results on European-wide terrestrial carbon fluxes for the period 2006–2015." Atmospheric Chemistry and Physics 20, no. 20 (October 26, 2020): 12063–91. http://dx.doi.org/10.5194/acp-20-12063-2020.

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Abstract. Atmospheric inversions have been used for the past two decades to derive large-scale constraints on the sources and sinks of CO2 into the atmosphere. The development of dense in situ surface observation networks, such as ICOS in Europe, enables in theory inversions at a resolution close to the country scale in Europe. This has led to the development of many regional inversion systems capable of assimilating these high-resolution data, in Europe and elsewhere. The EUROCOM (European atmospheric transport inversion comparison) project is a collaboration between seven European research institutes, which aims at producing a collective assessment of the net carbon flux between the terrestrial ecosystems and the atmosphere in Europe for the period 2006–2015. It aims in particular at investigating the capacity of the inversions to deliver consistent flux estimates from the country scale up to the continental scale. The project participants were provided with a common database of in situ-observed CO2 concentrations (including the observation sites that are now part of the ICOS network) and were tasked with providing their best estimate of the net terrestrial carbon flux for that period, and for a large domain covering the entire European Union. The inversion systems differ by the transport model, the inversion approach, and the choice of observation and prior constraints, enabling us to widely explore the space of uncertainties. This paper describes the intercomparison protocol and the participating systems, and it presents the first results from a reference set of inversions, at the continental scale and in four large regions. At the continental scale, the regional inversions support the assumption that European ecosystems are a relatively small sink (-0.21±0.2 Pg C yr−1). We find that the convergence of the regional inversions at this scale is not better than that obtained in state-of-the-art global inversions. However, more robust results are obtained for sub-regions within Europe, and in these areas with dense observational coverage, the objective of delivering robust country-scale flux estimates appears achievable in the near future.

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Dahm, T. "Relative moment tensor inversion based on ray theory: theory and synthetic tests." Geophysical Journal International 124, no. 1 (January 1996): 245–57. http://dx.doi.org/10.1111/j.1365-246x.1996.tb06368.x.

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Jiang, Qingfang. "Applicability of Reduced-Gravity Shallow-Water Theory to Atmospheric Flow over Topography." Journal of the Atmospheric Sciences 71, no. 4 (March 27, 2014): 1460–79. http://dx.doi.org/10.1175/jas-d-13-0101.1.

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Abstract Applicability of the reduced-gravity shallow-water (RGSW) theory to a shallow atmospheric layer capped by an inversion underneath a deep stratified atmosphere over a two-dimensional ridge has been investigated using linear analysis and nonlinear numerical simulations. Two key nondimensional parameters are identified: namely, and , where g′ is the reduced-gravity acceleration; H0 is the RGSW layer depth; and N and U are the buoyancy frequency and wind speed, respectively, in the layer above the inversion. If J and γ are around unity or larger, the response of the RGSW flow over the ridge can be significantly modified by pressure perturbations aloft. Any jumplike perturbations in the RGSW layer rapidly decay while propagating away from the ridge as the perturbation energy radiates into the upper layer. With J and γ much less than unity, RGSW theory is more adequate for describing RGSW flows. In addition, inversion splitting occurs downstream of a jump when , where Ni is the buoyancy frequency in the inversion and hm stands for the ridge height. A less stratified upper layer with slower winds in general has less influence on the RGSW flow below and favors the application of the RGSW theory. For a thick inversion (d), the equivalent RGSW flow depth is approximately given by H + d/2, where H is the depth of the neutral layer below the inversion.

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Mart�nez, M. D., and X. Lana. "Some elements of mathematical information theory and total inversion algorithm applied to travel time inversion." Pure and Applied Geophysics PAGEOPH 137, no. 1-2 (1991): 113–32. http://dx.doi.org/10.1007/bf00876892.

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Shrestha, Binod Babu, Sangita Karanjit, Shuhei Higashibayashi, and Hidehiro Sakurai. "Correlation between bowl-inversion energy and bowl depth in substituted sumanenes." Pure and Applied Chemistry 86, no. 5 (May 19, 2014): 747–53. http://dx.doi.org/10.1515/pac-2013-1212.

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AbstractThe correlation between the bowl-inversion energy and the bowl depth for sumanenes monosubstituted with an iodo, formyl, or nitro group was investigated experimentally and by theoretical calculations. The bowl-inversion energies of the substituted sumanenes were determined experimentally by two-dimensional NMR exchange spectroscopy measurements. Various density functional theory methods were examined for the calculation of the structure and the bowl-inversion energy of sumanene, and it was found that PBE0, ωB97XD, and M06-2X gave better fits of the experimental value than did B3LYP. The experimental value was well reproduced at these levels of theory. The bowl structures and bowl-inversion energies of monosubstituted sumanenes were therefore calculated at the ωB97XD/6-311+G(d,p) level of theory. In both the experiments and the calculations, the correlation followed the equation ΔE = acos4 θ, where a is a coefficient, ΔE is the bowl-inversion energy, and cos θ is the normalized bowl depth, indicating that the bowl inversion follows a double-well potential energy diagram.

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Monteil, Guillaume, and Marko Scholze. "Regional CO<sub>2</sub> inversions with LUMIA, the Lund University Modular Inversion Algorithm, v1.0." Geoscientific Model Development 14, no. 6 (June 7, 2021): 3383–406. http://dx.doi.org/10.5194/gmd-14-3383-2021.

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Abstract. Atmospheric inversions are used to derive constraints on the net sources and sinks of CO2 and other stable atmospheric tracers from their observed concentrations. The resolution and accuracy that the fluxes can be estimated with depends, among other factors, on the quality and density of the observational coverage, on the precision and accuracy of the transport model used by the inversion to relate fluxes to observations, and on the adaptation of the statistical approach to the problem studied. In recent years, there has been an increasing demand from stakeholders for inversions at higher spatial resolution (country scale), in particular in the framework of the Paris agreement. This step up in resolution is in theory enabled by the growing availability of observations from surface in situ networks (such as ICOS in Europe) and from remote sensing products (OCO-2, GOSAT-2). The increase in the resolution of inversions is also a necessary step to provide efficient feedback to the bottom-up modeling community (vegetation models, fossil fuel emission inventories, etc.). However, it calls for new developments in the inverse models: diversification of the inversion approaches, shift from global to regional inversions, and improvement in the computational efficiency. In this context, we developed LUMIA, the Lund University Modular Inversion Algorithm. LUMIA is a Python library for inverse modeling built around the central idea of modularity: it aims to be a platform that enables users to construct and experiment with new inverse modeling setups while remaining easy to use and maintain. It is in particular designed to be transport-model-agnostic, which should facilitate isolating the transport model errors from those introduced by the inversion setup itself. We have constructed a first regional inversion setup using the LUMIA framework to conduct regional CO2 inversions in Europe using in situ data from surface and tall-tower observation sites. The inversions rely on a new offline coupling between the regional high-resolution FLEXPART Lagrangian particle dispersion model and the global coarse-resolution TM5 transport model. This test setup is intended both as a demonstration and as a reference for comparison with future LUMIA developments. The aims of this paper are to present the LUMIA framework (motivations for building it, development principles and future prospects) and to describe and test this first implementation of regional CO2 inversions in LUMIA.

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Gessel, Ira M. "Lagrange inversion." Journal of Combinatorial Theory, Series A 144 (November 2016): 212–49. http://dx.doi.org/10.1016/j.jcta.2016.06.018.

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Maharramov, Musa, Biondo L. Biondi, and Mark A. Meadows. "Time-lapse inverse theory with applications." GEOPHYSICS 81, no. 6 (November 2016): R485—R501. http://dx.doi.org/10.1190/geo2016-0131.1.

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Compaction in the reservoir overburden can impact production facilities and lead to a significant risk of well-bore failures. Prevalent practices of time-lapse seismic processing of 4D data above compacting reservoirs rely on picking time displacements and converting them into estimated velocity changes and subsurface deformation. This approach relies on prior data equalization and requires a significant amount of manual interpretation and quality control. We have developed methods for automatic detection of production-induced subsurface velocity changes from seismic data. We have evaluated a time-lapse inversion technique based on a simultaneous regularized full-waveform inversion (FWI) of multiple surveys. In our approach, baseline and monitor surveys are inverted simultaneously with a model-difference regularization penalizing nonphysical differences in the inverted models that are due to survey or computational repeatability issues. The primary focus of our work was the inversion of long-wavelength “blocky” changes in the subsurface model, and this was achieved using a phase-only FWI with a total-variation model-difference regularization. However, we have developed a multiscale extension of our method for recovering long- and short-wavelength production effects. We have developed a theoretical foundation of our method and analyzed its sensitivity to a realistic 1%–2% velocity deformation. The method was applied in a study of overburden dilation above the Gulf of Mexico Genesis field and recovered blocky negative-velocity anomalies above compacting reservoirs.

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Kite, Mary E., and Kay Deaux. "Gender Belief Systems: Homosexuality and the Implicit Inversion Theory." Psychology of Women Quarterly 11, no. 1 (March 1987): 83–96. http://dx.doi.org/10.1111/j.1471-6402.1987.tb00776.x.

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Beliefs about the characteristics of male and female homosexuals and heterosexuals were assessed to determine the degree to which stereotypes of homosexuals are consistent with the inversion model proposed by Freud (1905) and others, i.e., the assumption that homosexuals are similar to the opposite-sex heterosexual. Results showed that people do subscribe to an implicit inversion theory wherein male homosexuals are believed to be similar to female heterosexuals, and female homosexuals are believed to be similar to male heterosexuals. These results offer additional support for a bipolar model of gender stereotyping, in which masculinity and femininity are assumed to be in opposition.

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Shephard, N. G. "From Characteristic Function to Distribution Function: A Simple Framework for the Theory." Econometric Theory 7, no. 4 (December 1991): 519–29. http://dx.doi.org/10.1017/s0266466600004746.

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A unified framework is established for the study of the computation of the distribution function from the characteristic function. A new approach to the proof of Gurland's and Gil-Pelaez's univariate inversion theorem is suggested. A multivariate inversion theorem is then derived using this technique.

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Yan, Binpeng, Shangxu Wang, Yongzhen Ji, Xingguo Huang, and Nuno V. da Silva. "Frequency-dependent spherical-wave reflection coefficient inversion in acoustic media: Theory to practice." GEOPHYSICS 85, no. 4 (June 15, 2020): R425—R435. http://dx.doi.org/10.1190/geo2019-0643.1.

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As an approximation of the spherical-wave reflection coefficient (SRC), the plane-wave reflection coefficient does not fully describe the reflection phenomenon of a seismic wave generated by a point source. The applications of SRC to improve analyses of seismic data have also been studied. However, most of the studies focus on the time-domain SRC and its benefit to using the long-offset information instead of the dependency of SRC on frequency. Consequently, we have investigated and accounted for the frequency-dependent spherical-wave reflection coefficient (FSRC) and analyzed the feasibility of this type of inversion. Our inversion strategy requires a single incident angle using reflection data for inverting the density and velocity ratios, which is distinctly different from conventional inversion methods using amplitude variation with offset. Hence, this investigation provides an alternative approach for estimating media properties in some contexts, especially when the range of aperture of the reflection angles is limited. We apply the FSRC theory to the inversion of noisy synthetic and field data using a heuristic algorithm. The multirealization results of the inversion strategy are consistent with the feasibility analysis and demonstrate the potential of the outlined method for practical application.

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Koltracht, I., B. A. Kon, and L. Lerer. "Inversion of structured operators." Integral Equations and Operator Theory 20, no. 4 (December 1994): 410–48. http://dx.doi.org/10.1007/bf01197570.

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