Relevant bibliographies by topics / Inversion methods

Academic literature on the topic 'Inversion methods'

Author: Grafiati
Published: 10 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Inversion methods.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Inversion methods"

1

Thompson, M. J. "Inversion Methods." Symposium - International Astronomical Union 185 (1998): 125–34. http://dx.doi.org/10.1017/s0074180900238448.

Full text
Abstract:
I want to start by addressing the question, ‘What is inversion?’ My answer would be that inversion is the process of going from data to making inferences about the object under study. In the case of helioseismology, the data at the present time are principally the mode frequencies, and the object under study is the solar interior.
APA, Harvard, Vancouver, ISO, and other styles
2

Tang, J., and Q. Zhuang. "Technical Note: Methods for interval constrained atmospheric inversion of methane." Atmospheric Chemistry and Physics Discussions 10, no. 8 (August 24, 2010): 19981–20004. http://dx.doi.org/10.5194/acpd-10-19981-2010.

Full text
Abstract:
Abstract. Three interval constrained methods, including the interval constrained Kalman smoother, the interval constrained maximum likelihood ensemble smoother and the interval constrained ensemble Kalman smoother are developed to conduct inversions of atmospheric trace gas methane (CH4). The negative values of fluxes in an unconstrained inversion are avoided in the constrained inversion. In a multi-year inversion experiment using pseudo observations derived from a forward transport simulation with known fluxes, the interval constrained fixed-lag Kalman smoother presents the best results, followed by the interval constrained fixed-lag ensemble Kalman smoother and the interval constrained maximum likelihood ensemble Kalman smoother. Consistent uncertainties are obtained for the posterior fluxes with these three methods. This study provides alternatives of the variable transform method to deal with interval constraints in atmospheric inversions.
APA, Harvard, Vancouver, ISO, and other styles
3

Korda, David, Michal Švanda, and Junwei Zhao. "Comparison of time–distance inversion methods applied to SDO/HMI Dopplergrams." Astronomy & Astrophysics 629 (September 2019): A55. http://dx.doi.org/10.1051/0004-6361/201936268.

Full text
Abstract:
Context. The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) satellite has been observing the Sun since 2010. The uninterrupted series of Dopplergrams are ideal for studying the dynamics of the upper solar convection zone. Within the Joint Science Operations Center (JSOC) the time–distance inversions for flows and sound-speed perturbations were introduced. The automatic pipeline has produced flow and sound-speed maps every 8 h. We verify the results of JSOC inversions by comparing the data products to equivalent results from inverse modelling obtained by an independent inversion pipeline. Aims. We compared the results from the JSOC pipeline for horizontal flow components and the perturbations of the speed of sound at set of depths with equivalent results from an independently implemented pipeline using a different time–distance inversion scheme. Our inversion pipeline allows inversion for all quantities at once while allowing minimisation of the crosstalk between them. This gives us an opportunity to discuss the possible biases present in the JSOC data products. Methods. For the tests we used the subtractive optimally localised averaging (SOLA) method with a minimisation of the cross-talk. We compared three test inversions for each quantity at each target depth. At first, we used the JSOC setup to reproduce the JSOC results. Subsequently, we used the extended pipeline to improve these results by incorporating more independent travel-time measurements but keeping the JSOC-indicated localisation in the Sun. Finally, we inverted for flow components and sound-speed perturbations using a localisation kernel with properties advertised in the JSOC metadata. Results. We successfully reproduced the horizontal flow components. The sound-speed perturbations are strongly affected by the high level of the cross-talk in JSOC products. This leads to larger amplitudes in the inversions for the sound-speed perturbations. Different results were obtained when a target function localised around the target depth was used. This is a consequence of non-localised JSOC averaging kernels. We add that our methodology also allows inversion for the vertical flow.
APA, Harvard, Vancouver, ISO, and other styles
4

Ursenbach, Charles P., and Robert R. Stewart. "Two-term AVO inversion: Equivalences and new methods." GEOPHYSICS 73, no. 6 (November 2008): C31—C38. http://dx.doi.org/10.1190/1.2978388.

Full text
Abstract:
Most amplitude-variation-with-offset (AVO) studies use two-parameter inversion methods that are approximations of a more general three-parameter method based on the Aki-Richards approximation. Two-parameter methods are popular because the three-parameter inversion is often plagued by numerical instability. Reducing the dimensionality of the parameter space stabilizes the inversion. A variety of constraints can accomplish this, and these lead to the multiplicity of current two-parameter methods. It would be useful to understand relationships between various two-parameter methods. To this end, we derive formal expressions for inversion errors of each method. Using these expressions, conversion formulas are obtained that allow the flexibility to convert results of any two-parameter method to those of any other two-parameter method. The only requirement for the equivalence of methods is that the maximum angle of incidence be at least a few degrees less than the critical angle. In addition, error expressions result in a new formulation for a two-parameter AVO tool that combines strengths of two commonly used methods. The expressions also suggest a simple way to incorporate information from well-log calibration into legacy AVO inversions. These results should be helpful in resource exploration.
APA, Harvard, Vancouver, ISO, and other styles
5

Karimpour, Mohammadkarim, Evert Cornelis Slob, and Laura Valentina Socco. "Physically Constrained 2D Joint Inversion of Surface and Body Wave Tomography." Journal of Environmental and Engineering Geophysics 27, no. 2 (June 2022): 57–71. http://dx.doi.org/10.32389/jeeg21-031.

Full text
Abstract:
Joint inversion of different geophysical methods is a powerful tool to overcome the limitations of individual inversions. Body wave tomography is used to obtain P-wave velocity models by inversion of P-wave travel times. Surface wave tomography is used to obtain S-wave velocity models through inversion of the dispersion curves data. Both methods have inherent limitations. We focus on the joint body and surface waves tomography inversion to reduce the limitations of each individual inversion. In our joint inversion scheme, the Poisson ratio was used as the link between P-wave and S-wave velocities, and the same geometry was imposed on the final velocity models. The joint inversion algorithm was applied to a 2D synthetic dataset and then to two 2D field datasets. We compare the obtained velocity models from individual inversions and the joint inversion. We show that the proposed joint inversion method not only produces superior velocity models but also generates physically more meaningful and accurate Poisson ratio models.
APA, Harvard, Vancouver, ISO, and other styles
6

Rosa, Daiane R., Juliana M. C. Santos, Rafael M. Souza, Dario Grana, Denis J. Schiozer, Alessandra Davolio, and Yanghua Wang. "Comparing different approaches of time-lapse seismic inversion." Journal of Geophysics and Engineering 17, no. 6 (November 4, 2020): 929–39. http://dx.doi.org/10.1093/jge/gxaa053.

Full text
Abstract:
Abstract Time-lapse (4D) seismic inversion aims to predict changes in elastic rock properties, such as acoustic impedance, from measured seismic amplitude variations due to hydrocarbon production. Possible approaches for 4D seismic inversion include two classes of method: sequential independent 3D inversions and joint inversion of 4D seismic differences. We compare the standard deterministic methods, such as coloured and model-based inversions, and the probabilistic inversion techniques based on a Bayesian approach. The goal is to compare the sequential independent 3D seismic inversions and the joint 4D inversion using the same type of algorithm (Bayesian method) and to benchmark the results to commonly applied algorithms in time-lapse studies. The model property of interest is the ratio of the acoustic impedances, estimated for the monitor, and base surveys at each location in the model. We apply the methods to a synthetic dataset generated based on the Namorado field (offshore southeast Brazil). Using this controlled dataset, we can evaluate properly the results as the true solution is known. The results show that the Bayesian 4D joint inversion, based on the amplitude difference between seismic surveys, provides more accurate results than sequential independent 3D inversion approaches, and these results are consistent with deterministic methods. The Bayesian 4D joint inversion is relatively easy to apply and provides a confidence interval of the predictions.
APA, Harvard, Vancouver, ISO, and other styles
7

Hicks, Graham J., and R. Gerhard Pratt. "Reflection waveform inversion using local descent methods: Estimating attenuation and velocity over a gas‐sand deposit." GEOPHYSICS 66, no. 2 (March 2001): 598–612. http://dx.doi.org/10.1190/1.1444951.

Full text
Abstract:
Prestack seismic reflection data contain amplitudes, traveltimes, and moveout information; waveform inversion of such data has the potential to estimate attenuation levels, reflector depths and geometry, and background velocities. However, when inverting reflection data, strong nonlinearities can cause reflectors to be incorrectly imaged and can prevent background velocities from being updated. To successfully recover background velocities, previous authors have resorted to nonlinear, global search inversion techniques. We propose a two‐step inversion procedure using local descent methods in which we perform alternate inversions for the reflectors and the background velocities. For our reflector inversion we exploit the efficiency of the back‐propagation method when inverting for a large parameter set. For our background velocity inversion we use Newton inverse methods. During the background velocity inversions it is crucial to adaptively depth‐stretch the model to preserve the vertical traveltimes. This reduces nonlinearity by largely decoupling the effects of the background velocities and reflectors on the data. Nonlinearity is further reduced by choosing to invert for slownesses and by inverting for a sparse parameter set which is partially defined using geological reflector picks. Applying our approach to shallow seismic data from the North Sea collected over a gas‐sand deposit, we demonstrate that the proposed method is able to estimate both the geometry and internal velocity of a significant velocity structure not present in the initial model. Over successive iterations, the use of adaptive depth stretching corrects the pull‐down of the base of the gas sand. Vertical background velocity gradients are also resolved. For an insignificant extra cost the acoustic attenuation parameter Q is included in the inversion scheme. The final attenuation tomogram contains realistic values of Q for the expected lithologies and for the effect of partial fluid saturation associated with a shallow bright spot. The attenuation image may also indicate the presence of fracturing.
APA, Harvard, Vancouver, ISO, and other styles
8

Poroshina, N. I., and V. M. Ryabov. "Methods for laplace transform inversion." Vestnik St. Petersburg University: Mathematics 44, no. 3 (August 24, 2011): 214–22. http://dx.doi.org/10.3103/s1063454111030071.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Johnson, Lane. "Methods and Applications of Inversion." Eos, Transactions American Geophysical Union 81, no. 52 (2000): 645. http://dx.doi.org/10.1029/eo081i052p00645-03.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Chapman, Ross. "Assessment of geoacoustic inversion methods." Journal of the Acoustical Society of America 131, no. 4 (April 2012): 3240. http://dx.doi.org/10.1121/1.4708090.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Inversion methods"

1

Kamm, Jochen. "Inversion and Joint Inversion of Electromagnetic and Potential Field Data." Doctoral thesis, Uppsala universitet, Geofysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-215673.

Full text
Abstract:
In this thesis, four inversion problems of different scale and difficulty are solved. Two of them are electromagnetic inverse problems. Two more are joint inversion problems of potential field data and other types of data. First, a linear approximation, which is a generalization of the low-induction-number approximation standard in slingram dual-loop interpretation is developed and used for rapid two and three dimensional inversion. The approximation takes induction within a background half-space into account and can thus be applied in conductive scenarios, where otherwise a rigorous electromagnetic modeling would be required. Second, a three-dimensional inversion of airborne tensor very-low-frequency data with a rigorous forward modeling at its core is developed. For dealing with the large scale of the forward problem, a nested fast-Fourier-transform-based integral equation method is introduced, wherein electromagnetic interactions are arranged according to their range and larger ranges are treated with less accuracy and effort. The inversion improves the traditional interpretation through data derived maps by providing a conductivity model, thus constraining the upper few hundred meters of the crust down to the shallowest conductor and allowing the study of its top in three dimensions. The third inversion problem is the the joint inversion of refraction and geoelectric data. By requiring the velocity and resistivity models to share a common, laterally variable layered geometry, easily interpretable models, which are reasonable in many geological near surface situations (e.g., groundwater exploration in Quaternary sediments), are produced directly from the joint inversion. Finally, a joint inversion of large scale potential field data from a gabbro intrusion is presented. Gravity and magnetic data are required to abide to a petrophysical constraint, which is derived from extensive field sampling. The impact of the constraint is maximized under the provision that both data sets are explained equally well as they would be through individual inversions. This leads to a simple and clearly defined intrusion geometry, consistent for both the density and magnetic susceptibility distribution. In all presented inversion problems, field data sets are successfully inverted, the results are appraised through synthetic tests and, if available, through comparison with independent data.
Diese Arbeit hat die Lösung von vier geophysikalischen Umkehraufgaben, sogenannten Inversionsproblemen, zum Gegenstand. Zwei dieser Aufgaben befassen sich mit der Inversion elektromagnetischer Daten, zwei weitere sind Probleme der kombinierten Inversion von Datensätzen aus unterschiedlichen geophysikalischen Messverfahren. Im ersten Problem wird die für die Auswertung elektromagnetischer Zweispulensystemdaten typische lineare Näherung der kleinen Induktionszahlen als Bornsche Näherung verallgemeinert, ihre Anwendbarkeit durch exakte Berücksichtigung der Induktionsvorgänge in einem beliebigen homogenen Halbraum von schlechtleitenden auf gutleitende Untergründe ausgedehnt und schließlich zur zwei- und dreidimensionalen Inversion eingesetzt. Dadurch kann auch im leitfähigen Untergrund eine aufwändige exakte Modellierung vermieden werden. Im zweiten Problem wird eine dreidimensionale Inversion von flugzeuggestützten Längstwellenmessungen entwickelt und als ihre Grundlage eine exakte elektromagnetische Rechnung erdacht. Damit wird traditionelle kartengestützte Dateninterpretation durch ein dreidimensionales Leitfähigkeitsmodell ergänzt, welches die oberen hundert bis dreihundert Meter der Erdkruste bis hin zur Tiefe des obersten Leiters abbildet, so dass dessen Oberflächenform erkundet werden kann. Die enorme Problemgröße wird durch eine Fouriertransformationsmethode bewältigt, welche die elektromagnetischen Wechselwirkungen nach ihrer Reichweite einteilt, die Fernwirkungen mit entsprechend verringerter Genauigkeit behandelt und dadurch eine erhebliche Anzahl an Rechnungen einspart. Im dritten Problem werden refraktionsseismische und geoelektrische Messungen kombiniert, indem sowohl das Geschwindigkeits- als auch das Widerstandsmodell mit einer gemeinsamen, lateral veränderlichen und durch beide Datensätze bestimmten Schichtstruktur versehen werden. Ein solches, durch Schichten definiertes Inversionsergebnis, stellt in vielen oberflächennahen Anwendungen, beispielsweise im Grundwasserbereich, ein sinnvolles Abbild der Erde dar. Im vierten Problem werden Schweremessungen und Magnetfeldmessungen, die über einer Gabbrointrusion aufgenommen wurden, mittels einer empirischen petrophysikalischen Beziehung vereinigt, welche aus Labormessungen an einer großen Anzahl von Gesteinsproben abgeleitet wurde. Hierbei wird der Einfluss dieser Modellkopplung solange maximiert, wie beide Datensätze mit derjenigen Genauigkeit angepasst werden können, welche vorher in Einzelinversionen erreicht wurde. Das Ergebnis ist ein einfaches, geometrisch konsistentes Modell der Verteilungen von Dichte und magnetischer Suszeptibilität. In allen vier Aufgaben wurden erfolgreich reale Felddaten invertiert. Die Güte der Ergebnisse wurde mittels synthetischer Experimente untersucht und, so vorhanden, mit unabhängigen Informationen verglichen.
APA, Harvard, Vancouver, ISO, and other styles
2

Saunders, Jonathan Howard. "Electrical inversion and characterisation methods in geophysics." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.413721.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

MACIEL, Jonathas da Silva. "Structural constraints for image-based inversion methods." Universidade Federal do Pará, 2016. http://repositorio.ufpa.br/jspui/handle/2011/9021.

Full text
Abstract:
Submitted by Cássio da Cruz Nogueira (cassionogueirakk@gmail.com) on 2017-07-26T14:09:55Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_StructuralconstraintsImage.pdf: 21057747 bytes, checksum: c218ce93af99d33375ec25eeec4aa33e (MD5)
Approved for entry into archive by Irvana Coutinho (irvana@ufpa.br) on 2017-08-23T13:21:47Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_StructuralconstraintsImage.pdf: 21057747 bytes, checksum: c218ce93af99d33375ec25eeec4aa33e (MD5)
Made available in DSpace on 2017-08-23T13:21:47Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Tese_StructuralconstraintsImage.pdf: 21057747 bytes, checksum: c218ce93af99d33375ec25eeec4aa33e (MD5) Previous issue date: 2016-04-22
CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Esta tese apresenta duas metodologias de regularização estrutural para os métodos de análise de velocidade com migração e inversão conjunta com migração: regularização gradiente cruzado e filtragem com operadores morfológicos. Na análise de velocidade com migração, a regularização de gradiente cruzado tem como objetivo vincular os contrates de velocidade com o mapa de refletividade, através da paralelização dos vetores gradiente de velocidade com os vetores gradiente da imagem. Propõe-se uma versão com gradiente cruzado das funções objeto de minimização: Differential Semblance, Stack Power e Partial Stack Power. Combina-se a função Partial Stack Power com sua versão de gradiente cruzados, com o objetivo de aumentar gradativamente a resolução do modelo de velocidade, sem comprometer o ajuste das componentes de longo comprimento de onda do modelo de velocidade. Na inversão conjunta com migração propõe-se aplicar os operadores morfológicos de erosão e dilatação, no pré-condicionamento do modelo de velocidade em cada iteração. Os operadores usam o mapa de refletividade para delimitar as regiões com mesmo valor de propriedade física. Eles homogenizam a camada geológica e acentuam o contraste de velocidade nas bordas. Os vínculos estruturais não apenas irão reduzir a ambiguidade na estimativa do modelo de velocidade, mas tornará os métodos de inversão com migração mais estáveis, reduzindo artefatos, delineando soluções geologicamente plausíveis e acelerando a convergência da função objeto de minimização.
This thesis presents two methodologies of structural regularization for Wave-Equation Migration Velocity Analysis and Joint Migration Inversion: cross-gradient regularization and filtering with morphological operators. In Wave-Equation Migration Velocity Analysis, the cross-gradient regularization aims to constrain the velocity contrasts with the reflectivity map by parallelization of the velocity gradient vector and the image gradient vector. We propose a version with cross-gradient of the objective functions: Differential Semblance, Stack Power and Partial Stack Power. We combine the Partial Stack Power with its version of cross-gradient, in order to gradually increase the resolution of the velocity model without compromising the adjustment of the long wavelengths of the velocity model. In Joint Migration Inversion, we propose to apply morphological operators of erosion and dilation in the preconditioning of the velocity model in each iteration. Operators use the reflectivity map to mark the regions with the same value of physical property. They homogenize the geological layer and accentuate the velocity contrast at the edges. Structural constraints do not only reduce the ambiguity in estimating a velocity model, but also make the migration/inversion methods more stable, reducing artifacts, delineating geologically plausible solutions, and accelerating the convergence of the objective function.
APA, Harvard, Vancouver, ISO, and other styles
4

Walker, Matthew James. "Methods for Bayesian inversion of seismic data." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10504.

Full text
Abstract:
The purpose of Bayesian seismic inversion is to combine information derived from seismic data and prior geological knowledge to determine a posterior probability distribution over parameters describing the elastic and geological properties of the subsurface. Typically the subsurface is modelled by a cellular grid model containing thousands or millions of cells within which these parameters are to be determined. Thus such inversions are computationally expensive due to the size of the parameter space (being proportional to the number of grid cells) over which the posterior is to be determined. Therefore, in practice approximations to Bayesian seismic inversion must be considered. A particular, existing approximate workflow is described in this thesis: the so-called two-stage inversion method explicitly splits the inversion problem into elastic and geological inversion stages. These two stages sequentially estimate the elastic parameters given the seismic data, and then the geological parameters given the elastic parameter estimates, respectively. In this thesis a number of methodologies are developed which enhance the accuracy of this approximate workflow. To reduce computational cost, existing elastic inversion methods often incorporate only simplified prior information about the elastic parameters. Thus a method is introduced which transforms such results, obtained using prior information specified using only two-point geostatistics, into new estimates containing sophisticated multi-point geostatistical prior information. The method uses a so-called deep neural network, trained using only synthetic instances (or `examples') of these two estimates, to apply this transformation. The method is shown to improve the resolution and accuracy (by comparison to well measurements) of elastic parameter estimates determined for a real hydrocarbon reservoir. It has been shown previously that so-called mixture density network (MDN) inversion can be used to solve geological inversion analytically (and thus very rapidly and efficiently) but only under certain assumptions about the geological prior distribution. A so-called prior replacement operation is developed here, which can be used to relax these requirements. It permits the efficient MDN method to be incorporated into general stochastic geological inversion methods which are free from the restrictive assumptions. Such methods rely on the use of Markov-chain Monte-Carlo (MCMC) sampling, which estimate the posterior (over the geological parameters) by producing a correlated chain of samples from it. It is shown that this approach can yield biased estimates of the posterior. Thus an alternative method which obtains a set of non-correlated samples from the posterior is developed, avoiding the possibility of bias in the estimate. The new method was tested on a synthetic geological inversion problem; its results compared favourably to those of Gibbs sampling (a MCMC method) on the same problem, which exhibited very significant bias. The geological prior information used in seismic inversion can be derived from real images which bear similarity to the geology anticipated within the target region of the subsurface. Such so-called training images are not always available from which this information (in the form of geostatistics) may be extracted. In this case appropriate training images may be generated by geological experts. However, this process can be costly and difficult. Thus an elicitation method (based on a genetic algorithm) is developed here which obtains the appropriate geostatistics reliably and directly from a geological expert, without the need for training images. 12 experts were asked to use the algorithm (individually) to determine the appropriate geostatistics for a physical (target) geological image. The majority of the experts were able to obtain a set of geostatistics which were consistent with the true (measured) statistics of the target image.
APA, Harvard, Vancouver, ISO, and other styles
5

Li, Song. "Numerical methods for stable inversion of nonlinear systems." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/15028.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Wilson, Adam. "Theory and methods of frequency-dependent AVO Inversion." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4740.

Full text
Abstract:
Amplitude-versus-offset, AVO, approximations allow the estimation of various properties from pre-stack seismic gathers. Recently it has been suggested that fluid mobility is a controlling factor in pore pressure equalisation and can result in anomalous velocity dispersion in the seismic bandwidth. However, current approximations all assume an elastic subsurface and are unable to account for velocity dispersion. I have applied existing methodologies to a real dataset to qualitatively detect and interpret spectral amplitude anomalies. Three areas had AVO and spectral signature consistent with frequency-dependent AVO theory. The results suggest that it is feasible to measure such effects on real data in the presence of random noise. It would imply that the relaxation parameter, tau, is larger in the field than has been measured in water-saturated real and synthetic sandstones in the laboratory. I extended a two-term AVO approximation by accounting for velocity dispersion and showed how the resultant reflection coefficient becomes frequency-dependent. I then used this to measure P- and S-wave reflectivity dispersion using spectrally-balanced amplitudes. The inversion was able to quantify the affect of the P-wave velocity dispersion as an instantaneous effect on the reflection. NMO stretch was an issue at the far offsets and I limited myself to the near offsets and effectively measured only the P-wave reflectivity dispersion. I showed how the P-wave reflectivity dispersion signs depend on the AVO classification of the reflection whilst the magnitude depends on the crack density of my model. I showed how the effect of noise and thin-bed tuning can enter uncertainties into the interpretation of spectral anomalies. Whilst it is possible to detect frequency-dependent AVO signatures on pre-stack gathers, the interpretation remains non-unique. I have quantitatively measured a new physical property, reflectivity dispersion, from pre-stack seismic data. I have presented a method of detecting and measuring velocity dispersion in pre-stack gathers but there remain ambiguities in the interpretation of such results. The approach incorporates spectrally decomposed data in an extended AVO inversion scheme. Future work should investigate the application of the methodology to a real seismic dataset.
APA, Harvard, Vancouver, ISO, and other styles
7

Sawyer, Nicolas B. E. "Novel optical surface metrology methods." Thesis, University of Nottingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287239.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Thurin, Julien. "Uncertainties estimation in Full Waveform Inversion using Ensemble methods." Thesis, Université Grenoble Alpes, 2020. https://tel.archives-ouvertes.fr/tel-02570602.

Full text
Abstract:
L'inversion de forme d'onde complète (FWI) est une méthode d'inversion non-linéaire qui a pour but l'obtention de modèles précis des propriétés physiques du sous-sol terrestre. Ces modèles, véritables cartes de propriétés physiques, sont indispensables pour l'exploration et l'étude des structures internes de la Terre.Généralement formulée sous la forme d'un schéma d'optimisation par la méthode des moindres carrés, la FWI compare des enregistrements sismiques observés en surface, avec des données synthétiques calculées à partir d'un modèle numérique de sous-sol. Alors qu'une infinité de modèles peut potentiellement expliquer les observations, la FWI, du fait de sa formulation, ne permet d'obtenir qu'un seul modèle du sous-sol fortement conditionné par le choix de modèle de départ. À cette ambiguïté s'ajoute la difficulté d'estimer l'incertitude de la solution, à cause du coût de calcul prohibitif de la FWI. La non-unicité de la solution et le manque de moyens d'estimation d'incertitude rend l'exploitation des modèles de FWI compliquée.Dans cette thèse, nous proposons une méthode non conventionnelle et abordable, intégrant l’estimation d’incertitude au coeur de la solution de FWI. Notre méthode combine la FWI conventionnelle et l’assimilation de données par méthodes d’ensemble. De ce fait, elle tire avantage de la vitesse de convergence de la FWI conventionnelle, ainsi que des capacités d'estimation d'incertitude du Filtre de Kálmán d'Ensemble dit "Transform" (ETKF). Cette combinaison est permise par les fondements théoriques communs aux problèmes d'optimisation en FWI conventionnelle et au filtrage bayésien de l'ETKF. Nous utilisons ce schéma, l’ETKF-FWI, afin de transposer le problème de FWI dans le cadre de l'inférence Bayésienne locale. Au lieu d’une unique solution, l’ETKF-FWI retourne un ensemble de modèles qui permet à la fois de calculer la meilleure solution au sens des moindres carrés, mais aussi l'information d’incertitude et de résolution associée à chaque paramètre. Cette estimation d’incertitude est rendue possible par l’approximation de bas-rang de la matrice de covariance a posteriori, calculée à partir de l’ensemble. Les valeurs de variance permettent d’évaluer le degré de variabilité de la solution au sein de l’ensemble. La résolution est quant à elle, donnée par les termes hors diagonaux de la matrice de corrélation, qui est préférée à la matrice de covariance pour sa nature adimensionnelle.L'application de l'ETKF-FWI à deux cas d'études (un test synthétique et une application sur données de terrain) nous permet d'évaluer la faisabilité, ainsi que les limites de notre technique. Malgré le coût de calcul important lié à la représentation d’ensemble, cette stratégie permet une implémentation complètement parallèle, la rendant avantageuse au regard des solutions existant dans la littérature.Ces tests nous permettent d’évaluer l’influence de la taille de l’ensemble sur l’estimation de la variance, en caractérisant le biais de sous-échantillonnage associé aux petits ensembles. Bien que ce biais soit classiquement corrigé grâce aux méthodes d’inflation d’ensemble, celles-ci ne semblent pas adaptées à l’ETKF-FWI, limitant l’estimation d’incertitude à des évaluations qualitatives. De plus, la complexité de l’application sur données de terrain impacte la création de l’ensemble initial, ce qui influence directement les capacités de l’ETKF-FWI à produire une estimation quantitative de l’incertitude.Nous terminons par l’application de l'ETKF-FWI à une inversion de plusieurs paramètres physique (vitesse des ondes P et densité), considéré comme un défi majeur en FWI conventionnelle. Ce test nous permet d’évaluer qualitativement les liens de corrélation et d'ambiguïté entre vitesse et densité, ainsi que leurs incertitude et résolution respectives. De plus, le modèle moyen issu de l’ETKF-FWI semble être de qualité supérieure, ce qui laisse supposer d’un possible effet de préconditionnement fourni par la covariance
Full Waveform Inversion (FWI) is an ill-posed non-linear inverse problem, aiming at recovering detailed pictures of subsurface physical properties, which are crucial to explore and understand Earth structures.Classically formulated as a least-squares optimization scheme, FWI yields a single subsurface model amongst an infinite possibility of solutions. With the general lack of systematic and scalable uncertainty estimation, this formulation makes interpretation of FWI's outcomes complex.In this thesis, we propose an unconventional, scalable way of tackling the lack of uncertainty estimation in FWI, thanks to data assimilation ensemble methods. We develop a scheme combining both classical FWI and the Ensemble Transform Kalman Filter, that we call ETKF-FWI, and which is successfully applied on two 2-D test cases. This scheme takes advantage of the theoretical common-ground between least-squares optimization problems and Bayesian filtering. We use it to recast FWI in a local Bayesian inference framework, thanks to the ensemble representation. The ETKF-FWI provides high-resolution subsurface tomographic models and yields a low-rank approximation of the posterior covariance, holding the uncertainty and resolution information of the proposed solution. We show how the ETKF-FWI can be applied to qualitatively evaluate uncertainty and resolution of the solution. Instead of providing a single solution, the filter yields an ensemble of models, from which statistical information can be inferred.Uncertainty is evaluated from the ensemble's variance, which relates to the diversity of solution amongst the ensemble members for each parameter. We show that lines of the correlation matrix are ideal to evaluate qualitatively parameters resolution, thanks to their adimentionality. While the methodology is computationally intensive, it has the benefit of being fully scalable. Its applicability is demonstrated on a synthetic benchmark. This preliminary test allows us to assess the sensitivity of the ensemble representation to the common undersampling bias encountered in ensemble data assimilation. While undersampling does not affect the image reconstruction in any way, it results in variance underestimation, which makes the whole exercise of quantitative uncertainty assessment complicated. Ensemble inflation has been used to mitigate this bias, but does not seems to be a practical solution.A field data experiment is also discussed in this thesis. It makes it possible to test the sensitivity of the ETKF-FWI to complex noise structure and realistic physics. As it stands, the complexity of the problem reduces flexibility in the ensemble generation, and hence on the uncertainty estimate. Despite these limitations, results are consistent with the synthetic benchmark, and we are able to provide a qualitative uncertainty assessment. The field data case also allows us to evaluate the possibilities to use the ETKF-FWI on multiparameter inversion, which is still regarded as a challenging topic in FWI. The ETKF-FWI multiparameter inversion yields improved models compared with conventional ones. More importantly, it makes it possible to assess the uncertainty associated with parameters cross-talks
APA, Harvard, Vancouver, ISO, and other styles
9

Kim, Junkyoung. "Complex seismic sources and time-dependent moment tensor inversion." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184841.

Full text
Abstract:
There are many examples of earthquakes whose surface expressions are much more complicated than the seismologically derived faulting models. Seismologists also have found seismic source complexity and improved seismicity data have shown that rupture may occur on irregular or multiple shear surfaces. To simultaneously map both geometrical and temporal variation of the seismic sources for a complex rupture history from observed seismograms, it is possible to use a time dependent moment tensor (TDMT) inversion. The TDMT inversion algorithm has been tested with three synthetic data examples with varying degrees of complexity. The first example demonstrates that a multiple source with no focal depth change can be recovered, and the source parameters of each of the subevents can be accurately determined. In the second case we allowed the depth to vary for subevents (9-km and 13-km source depth, respectively). The two subevents can be identified on the basis of simultaneous shape-change of the moment tensor elements along with non-causality and the size of the CLVD component. The third example introduced source complexity by having two subevents which overlapped in time. The overlapped period could be seen in the moment tensor elements as unusually abrupt changes in the time function shape. The TDMT inversion was also performed on long-period body waves for three earthquakes: the 1982 Yemen earthquake, the 1971 San Fernando earthquake, and the 1952 Kern County earthquake. The Yemen earthquake was mapped as two simple, normal-slip subevents (with onset timing of the second subevent 5 seconds after the first) without a significant component of left- or right-lateral displacement or source depth change. The San Fernando earthquake is interpreted as two shear dislocation sources with changing source depths, possibly indicating upward rupture propagation (from 13-km to 7-km). The interpretation of the TDMT inversion for the Kern County earthquake was also a double point source which propagates upward from 20-km to 5-km. The resultant moment tensor functions from inversion of the synthetic waveforms, a combination of isotropic and tectonic release, demonstrated that the tectonic release associated with underground nuclear explosion can be separated and identified if the source depth between the explosions and tectonic release are different.
APA, Harvard, Vancouver, ISO, and other styles
10

Michelen, Strofer Carlos Alejandro. "Machine Learning and Field Inversion approaches to Data-Driven Turbulence Modeling." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/103155.

Full text
Abstract:
There still is a practical need for improved closure models for the Reynolds-averaged Navier-Stokes (RANS) equations. This dissertation explores two different approaches for using experimental data to provide improved closure for the Reynolds stress tensor field. The first approach uses machine learning to learn a general closure model from data. A novel framework is developed to train deep neural networks using experimental velocity and pressure measurements. The sensitivity of the RANS equations to the Reynolds stress, required for gradient-based training, is obtained by means of both variational and ensemble methods. The second approach is to infer the Reynolds stress field for a flow of interest from limited velocity or pressure measurements of the same flow. Here, this field inversion is done using a Monte Carlo Bayesian procedure and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. The two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions.
Doctor of Philosophy
The Reynolds-averaged Navier-Stokes (RANS) equations are widely used to simulate fluid flows in engineering applications despite their known inaccuracy in many flows of practical interest. The uncertainty in the RANS equations is known to stem from the Reynolds stress tensor for which no universally applicable turbulence model exists. The computational cost of more accurate methods for fluid flow simulation, however, means RANS simulations will likely continue to be a major tool in engineering applications and there is still a need for improved RANS turbulence modeling. This dissertation explores two different approaches to use available experimental data to improve RANS predictions by improving the uncertain Reynolds stress tensor field. The first approach is using machine learning to learn a data-driven turbulence model from a set of training data. This model can then be applied to predict new flows in place of traditional turbulence models. To this end, this dissertation presents a novel framework for training deep neural networks using experimental measurements of velocity and pressure. When using velocity and pressure data, gradient-based training of the neural network requires the sensitivity of the RANS equations to the learned Reynolds stress. Two different methods, the continuous adjoint and ensemble approximation, are used to obtain the required sensitivity. The second approach explored in this dissertation is field inversion, whereby available data for a flow of interest is used to infer a Reynolds stress field that leads to improved RANS solutions for that same flow. Here, the field inversion is done via the ensemble Kalman inversion (EKI), a Monte Carlo Bayesian procedure, and the focus is on improving the inference by enforcing known physical constraints on the inferred Reynolds stress field. To this end, a method for enforcing boundary conditions on the inferred field is presented. While further development is needed, the two data-driven approaches explored and improved upon here demonstrate the potential for improved practical RANS predictions.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Inversion methods"

1

Hansen, Per Christian, Bo Holm Jacobsen, and Klaus Mosegaard, eds. Methods and Applications of Inversion. Berlin/Heidelberg: Springer-Verlag, 2000. http://dx.doi.org/10.1007/bfb0010278.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Cohen, A. M. Numerical methods for Laplace transform inversion. New York: Springer, 2011.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

1948-, Stoffa Paul L., ed. Global optimization methods in geophysical inversion. Amsterdam: Elsevier, 1995.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Vogel, Andreas, Charles O. Ofoegbu, Rudolf Gorenflo, and Bjorn Ursin, eds. Geophysical Data Inversion Methods and Applications. Wiesbaden: Vieweg+Teubner Verlag, 1990. http://dx.doi.org/10.1007/978-3-322-89416-8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Maurya, S. P., N. P. Singh, and K. H. Singh. Seismic Inversion Methods: A Practical Approach. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45662-7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Earth soundings analysis: Processing versus inversion. Boston: Blackwell Scientific Publications, 1992.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
7

Diachok, O., A. Caiti, P. Gerstoft, and H. Schmidt, eds. Full Field Inversion Methods in Ocean and Seismo-Acoustics. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8476-0.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Diachok, O. Full Field Inversion Methods in Ocean and Seismo-Acoustics. Dordrecht: Springer Netherlands, 1995.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
9

Waveform inversion of seismic reflection data through local optimisation methods. Uppsala: [University of Uppsala], 1992.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
10

O, Diachok, ed. Full field inversion methods in ocean and seismo-acoustics: Edited by O. Diachok ... [et al.]. Dordrecht: Kluwer Academic Publishers, 1995.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Book chapters on the topic "Inversion methods"

1

Thompson, M. J. "Inversion Methods." In New Eyes to See Inside the Sun and Stars, 125–34. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-4982-2_28.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Bertero, Mario, Patrizia Boccacci, and Christine De MoI. "Inversion methods revisited." In Introduction to Inverse Problems in Imaging, 183–212. 2nd ed. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003032755-8.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Berdichevsky, Mark, and Vladimir I. Dmitriev. "Inversion Strategy." In Models and Methods of Magnetotellurics, 453–544. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-77814-1_12.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Maurya, S. P., N. P. Singh, and K. H. Singh. "Geostatistical Inversion." In Seismic Inversion Methods: A Practical Approach, 177–216. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45662-7_7.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Maurya, S. P., N. P. Singh, and K. H. Singh. "Pre-stack Inversion." In Seismic Inversion Methods: A Practical Approach, 81–105. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45662-7_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Fichtner, Andreas. "Finite-Difference Methods." In Full Seismic Waveform Modelling and Inversion, 23–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15807-0_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Fichtner, Andreas. "Spectral-Element Methods." In Full Seismic Waveform Modelling and Inversion, 59–81. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15807-0_4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Shen, Qiuyang, Jiefu Chen, Xuqing Wu, Yueqin Huang, and Zhu Han. "Bayesian Inversion and Sampling Methods." In SpringerBriefs in Petroleum Geoscience & Engineering, 17–29. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-57097-2_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Pike, E. R., G. Hester, B. McNally, and G. D. de Villiers. "Mathematical Methods for Data Inversion." In Light Scattering from Microstructures, 41–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-46614-2_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Kythe, Prem K., and Pratap Puri. "Inversion of Laplace Transforms." In Computational Methods for Linear Integral Equations, 375–415. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0101-4_12.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Inversion methods"

1

Jackiewicz, Jason, Joyce Ann Guzik, and Paul A. Bradley. "Seismic Inversion Methods." In STELLAR PULSATION: CHALLENGES FOR THEORY AND OBSERVATION: Proceedings of the International Conference. AIP, 2009. http://dx.doi.org/10.1063/1.3246565.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Thore, P., H. Klemm, and L. Azevedo. "The Impact of Seismic Inversion Methods on Facies Prediction." In First EAGE Conference on Seismic Inversion. European Association of Geoscientists & Engineers, 2020. http://dx.doi.org/10.3997/2214-4609.202037021.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Royle, Gillian. "Viscoelastic orthorhombic full wavefield inversion: Development of multiparameter inversion methods." In SEG Technical Program Expanded Abstracts 2011. Society of Exploration Geophysicists, 2011. http://dx.doi.org/10.1190/1.3628112.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Jensås, I., J. Eidsvik, and U. Theune. "Methods for Blocky Seismic AVA Inversion." In 70th EAGE Conference and Exhibition - Workshops and Fieldtrips. European Association of Geoscientists & Engineers, 2008. http://dx.doi.org/10.3997/2214-4609.20148055.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Yiding, Wang, Wang Yunhong, and Zhao shi. "Errors Analysis of Spectrum Inversion Methods." In 2007 IEEE International Conference on Signal Processing and Communications. IEEE, 2007. http://dx.doi.org/10.1109/icspc.2007.4728304.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Katz, Simon, and Alex Beylin. "Hybrid methods of seismic data inversion." In SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, edited by Sergio E. Zarantonello. SPIE, 1993. http://dx.doi.org/10.1117/12.164844.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Russell, Brian, and Dan Hampson. "Comparison of poststack seismic inversion methods." In SEG Technical Program Expanded Abstracts 1991. Society of Exploration Geophysicists, 1991. http://dx.doi.org/10.1190/1.1888870.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Cho, Jeongik, and Adam Krzyzak. "Dynamic Latent Scale for GAN Inversion." In 11th International Conference on Pattern Recognition Applications and Methods. SCITEPRESS - Science and Technology Publications, 2022. http://dx.doi.org/10.5220/0010816800003122.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Stoffa, P. L., and M. K. Sen. "Seismic Waveform Inversion Using Global Optimization Methods." In 2nd International Congress of the Brazilian Geophysical Society. European Association of Geoscientists & Engineers, 1991. http://dx.doi.org/10.3997/2214-4609-pdb.316.156.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Bockmann, C., and S. Samaras. "Regularization Methods for Microphysical Aerosol Parameter Inversion." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics. Global Science and Technology Forum (GSTF), 2015. http://dx.doi.org/10.5176/2251-1911_cmcgs15.09.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Inversion methods"

1

McGehee, Duncan E., Mark C. Benfield, D. Van Holliday, and Charles F. Greenlaw. Advanced Multifrequency Inversion Methods for Classifying Acoustic Scatterers. Fort Belvoir, VA: Defense Technical Information Center, August 2001. http://dx.doi.org/10.21236/ada633271.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Benfield, Mark C. Advanced Multi-frequency Inversion Methods for Classifying Acoustic Scatterers. Fort Belvoir, VA: Defense Technical Information Center, September 2001. http://dx.doi.org/10.21236/ada612285.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

McGehee, Duncan E., Mark C. Benfield, Charles F. Greenlaw, and D. V. Holliday. Advanced Multi-Frequency Inversion Methods for Classifying Acoustic Scatterers. Fort Belvoir, VA: Defense Technical Information Center, September 2002. http://dx.doi.org/10.21236/ada621142.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Turgut, Altan. Rapid Geoacoustics Inversion Methods Used in LWAD98-2 Sea Test,. Fort Belvoir, VA: Defense Technical Information Center, April 1999. http://dx.doi.org/10.21236/ada361913.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Michalopoulou, Zoi-Heleni. Efficient Inversion in Underwater Acoustics with Iterative and Sequential Bayesian Methods. Fort Belvoir, VA: Defense Technical Information Center, September 2012. http://dx.doi.org/10.21236/ada574976.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Michalopoulou, Zoi-Heleni. Efficient Inversion in Underwater Acoustics with Analytic, Iterative, and Sequential Bayesian Methods. Fort Belvoir, VA: Defense Technical Information Center, September 2014. http://dx.doi.org/10.21236/ada617529.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Reimus, Paul W. Binary Tracers and Multiple Geophysical Data Set Inversion Methods to Improve EGS Reservoir Characterization and Imaging. Office of Scientific and Technical Information (OSTI), April 2014. http://dx.doi.org/10.2172/1130518.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Goodwin, J. A., W. Jiang, A. J. Meixner, S. R. B. McAlpine, S. Buckerfield, M. G. Nicoll, and M. Crowe. Estimating cover thickness in the Southern Thomson Orogen: results from the pre-drilling application of refraction seismic, audio-magnetotelluric and targeted magnetic inversion modelling methods on proposed borehole sites. Geoscience Australia, 2017. http://dx.doi.org/10.11636/record.2017.021.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Tolstoy, A. Low Frequency Geoacoustic Inversion Method. Fort Belvoir, VA: Defense Technical Information Center, September 2011. http://dx.doi.org/10.21236/ada571774.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Tolstoy, A. Low Frequency Geoacoustic Inversion Method. Fort Belvoir, VA: Defense Technical Information Center, September 2012. http://dx.doi.org/10.21236/ada575210.

Full text
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Inversion methods' for particular source types:
Journal articles Dissertations / Theses Books
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography