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Journal articles on the topic 'Inversion methods'

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Published: 10 March 2023

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1

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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Liu, Hongxing, Jingye Li, Xiaohong Chen, Bo Hou, and Li Chen. "Amplitude variation with offset inversion using the reflectivity method." GEOPHYSICS 81, no. 4 (July 2016): R185—R195. http://dx.doi.org/10.1190/geo2015-0332.1.

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Most existing amplitude variation with offset (AVO) inversion methods are based on the Zoeppritz’s equation or its approximations. These methods assume that the amplitude of seismic data depends only on the reflection coefficients, which means that the wave-propagation effects, such as geometric spreading, attenuation, transmission loss, and multiples, have been fully corrected or attenuated before inversion. However, these requirements are very strict and can hardly be satisfied. Under a 1D assumption, reflectivity-method-based inversions are able to handle transmission losses and internal multiples. Applications of these inversions, however, are still time-consuming and complex in computation of differential seismograms. We have evaluated an inversion methodology based on the vectorized reflectivity method, in which the differential seismograms can be calculated from analytical expressions. It is computationally efficient. A modification is implemented to transform the inversion from the intercept time and ray-parameter domain to the angle-gather domain. AVO inversion is always an ill-posed problem. Following a Bayesian approach, the inversion is stabilized by including the correlation of the P-wave velocity, S-wave velocity, and density. Comparing reflectivity-method-based inversion with Zoeppritz-based inversion on a synthetic data and a real data set, we have concluded that reflectivity-method-based inversion is more accurate when the propagation effects of transmission losses and internal multiples are not corrected. Model testing has revealed that the method is robust at high noise levels.

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12

Rigola, Maria A., Neus Baena, Vicenç Català, Iris Lozano, Elisabet Gabau, Miriam Guitart, and Carmen Fuster. "A 11.7-Mb Paracentric Inversion in Chromosome 1q Detected in Prenatal Diagnosis Associated with Familial Intellectual Disability." Cytogenetic and Genome Research 146, no. 2 (2015): 109–14. http://dx.doi.org/10.1159/000437127.

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Most apparent balanced chromosomal inversions are usually clinically asymptomatic; however, infertility, miscarriages, and mental retardation have been reported in inversion carriers. We present a small family with a paracentric inversion 1q42.13q43 detected in routine prenatal diagnosis. Molecular cytogenetic methods defined the size of the inversion as 11.7 Mb and excluded other unbalanced chromosomal alterations in the patients. Our findings suggest that intellectual disability is caused by dysfunction, disruption, or position effects of genes located at or near the breakpoints involved in this inversion.

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13

Um, Evan Schankee, Michael Commer, and Gregory A. Newman. "A strategy for coupled 3D imaging of large-scale seismic and electromagnetic data sets: Application to subsalt imaging." GEOPHYSICS 79, no. 3 (May 1, 2014): ID1—ID13. http://dx.doi.org/10.1190/geo2013-0053.1.

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Offshore seismic and electromagnetic (EM) imaging for hydrocarbons can require up to tens of millions of parameters to describe the 3D distribution of complex seabed geology and relevant geophysical attributes. The imaging and data volumes for such problems are enormous. Descent-based methods are the only viable imaging approach, where it is often challenging to manage the convergence of stand-alone seismic and EM inversion experiments. When a joint seismic-EM inversion is implemented, convergence problems with descent-based methods are further aggravated. Moreover, resolution mismatches between seismic and EM pose another challenge for joint inversion. To overcome these problems, we evaluated a coupled seismic-EM inversion workflow and applied it to a set of full-wave-seismic, magnetotelluric (MT) and controlled-source electromagnetic (CSEM) data for subsalt imaging. In our workflow, we address disparate resolution properties between seismic and EM data by implementing the seismic inversion in the Laplace domain, where the wave equation is transformed into a diffusion equation. The resolution of seismic data thus becomes comparable to that of EM data. To mitigate the convergence problems, the full joint seismic-EM inverse problem is split into manageable components: separate seismic and EM inversions and an intermediate step that enforces structural coupling through a cross-gradient-only inversion and resistivity-velocity crossplots. In this workflow, stand-alone seismic and MT inversion are performed first. The cross-gradient-only inversion and the crossplots are used to precondition the resistivity and velocity models for subsequent stand-alone inversions. By repeating the sequence of the stand-alone seismic, MT, and cross-gradient-only inversions along with the crossplots, we introduce the seismic structural information into the resistivity model, and vice versa, significantly improving the salt geometry in both resistivity and velocity images. We conclude that the improved salt geometry can then be used to precondition a starting model for CSEM inversions, yielding significant improvement in the resistivity images of hydrocarbon reservoirs adjacent to the salt.

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14

Scalzo, Richard, David Kohn, Hugo Olierook, Gregory Houseman, Rohitash Chandra, Mark Girolami, and Sally Cripps. "Efficiency and robustness in Monte Carlo sampling for 3-D geophysical inversions with Obsidian v0.1.2: setting up for success." Geoscientific Model Development 12, no. 7 (July 15, 2019): 2941–60. http://dx.doi.org/10.5194/gmd-12-2941-2019.

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Abstract. The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multi-modal; properties of any single mode become inadequate uncertainty measures, and sampling methods become inefficient for irregular posteriors or high-dimensional parameter spaces. We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study. The inversion is performed using an updated version of the Obsidian distributed inversion software. We find that the posterior for this inversion has a complex local covariance structure, hindering the efficiency of adaptive sampling methods that adjust the proposal based on the chain history. Within the context of a parallel-tempered Markov chain Monte Carlo scheme for exploring high-dimensional multi-modal posteriors, a preconditioned Crank–Nicolson proposal outperforms more conventional forms of random walk. Aspects of the problem setup, such as priors on petrophysics and on 3-D geological structure, affect the shape and separation of posterior modes, influencing sampling performance as well as the inversion results. The use of uninformative priors on sensor noise enables optimal weighting among multiple sensors even if noise levels are uncertain.

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15

Zhang Yu, Yang Xi, Gou Ming-Jiang, and Shi Qing-Fan. "Two inversion methods for electromagnetic scattering." Acta Physica Sinica 59, no. 6 (2010): 3905. http://dx.doi.org/10.7498/aps.59.3905.

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16

Kimes, D. S., Y. Knyazikhin, J. L. Privette, A. A. Abuelgasim, and F. Gao. "Inversion methods for physically‐based models." Remote Sensing Reviews 18, no. 2-4 (September 2000): 381–439. http://dx.doi.org/10.1080/02757250009532396.

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17

Ritter, Gerson Luis da Silva. "Water velocity estimation using inversion methods." GEOPHYSICS 75, no. 1 (January 2010): U1—U8. http://dx.doi.org/10.1190/1.3280232.

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It is known that the propagation velocity of sound waves in water can vary over time. For a 3D seismic survey, if data are acquired in adjacent lines but at different dates, this implies the same reflection point will be recorded at different times. To take this effect into account in seismic processing, it is necessary to measure the sound velocity in water. I have developed a 3D tomographic method that directly estimates it. It assumes a constant sound velocity for a group of shots belonging to a single sail line. Using a picked water-bottom reflection and an initial depth and velocity model, results good for use in subsequent processing can be obtained by estimating only two parameters: the variation of the propagation velocity and a constant vertical shift of the reflector depth in relation to the initial model. The method was tested with both synthetic and real data. The real data results were validated using two methods. First, I analyzed the histogram of the residuals of the final updated model. Second, I used a specially modified Kirchhoff migration algorithm to migrate the sea bottom. The main advantages of this method are that it takes into account the sea-bottom dips to estimate the velocities and it can be applied to each sail line separately. Also, the inversion is not ill-conditioned provided that data with large enough offsets are used. As a result, the method is simple to apply.

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Kyrion, Tobias, and Graham Alldredge. "Robust inversion methods for aerosol spectroscopy." Inverse Problems in Science and Engineering 25, no. 5 (June 3, 2016): 710–48. http://dx.doi.org/10.1080/17415977.2016.1191075.

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19

Dosso, Stan E. "Bayesian inversion methods in ocean geoacoustics." Journal of the Acoustical Society of America 121, no. 5 (May 2007): 3170–71. http://dx.doi.org/10.1121/1.4782292.

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20

CROZ, JEREMY J. DU, and NICHOLAS J. HIGHAM. "Stability of Methods for Matrix Inversion." IMA Journal of Numerical Analysis 12, no. 1 (1992): 1–19. http://dx.doi.org/10.1093/imanum/12.1.1.

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21

Pires, Carlos, and Pedro M. A. Miranda. "Tsunami waveform inversion by adjoint methods." Journal of Geophysical Research: Oceans 106, no. C9 (September 15, 2001): 19773–96. http://dx.doi.org/10.1029/2000jc000334.

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22

Pelekanos, George, Aria Abubakar, and Peter M. van den Berg. "Contrast source inversion methods in elastodynamics." Journal of the Acoustical Society of America 114, no. 5 (2003): 2825. http://dx.doi.org/10.1121/1.1618751.

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23

Chunduru, Raghu K., Mrinal K. Sen, and Paul L. Stoffa. "Hybrid optimization methods for geophysical inversion." GEOPHYSICS 62, no. 4 (July 1997): 1196–207. http://dx.doi.org/10.1190/1.1444220.

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Local and global optimization algorithms are used commonly in geophysical data inversion. Each type of algorithm has unique advantages and disadvantages. Here we propose several methods of combining the two algorithms such that we can overcome their drawbacks and make use of the salient features of the two methods. In particular, we combined a local conjugate gradient (CG) method with a global very fast simulated annealing (VFSA) approach to solve problems of geophysical interests. We conducted a systematic study to find an efficient strategy to combine CG and VFSA optimization schemes and recommend a couple of ways for future implementations. Seven different hybrid algorithms were first tested on a set of field 1-D Schlumberger resistivity sounding data and their performances were compared with stand‐alone genetic algorithm (GA), simulated annealing, and local search algorithms. Almost all of the proposed hybrid algorithms were found to be computationally more efficient than the conventional global optimization approaches. Having found the most efficient of the hybrid approaches we apply them to the problem of seismic velocity analysis using seismograms recorded in the offset‐time domain. Finally, we applied the hybrid algorithm to a 2-D field resistivity profiling data collected over a disseminated sulfide zone at Safford Arizona and compared our hybrid inversion results with the previously published results.

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24

Bossy, L. "Accuracy comparison of ionogram inversion methods." Advances in Space Research 14, no. 12 (December 1994): 39–42. http://dx.doi.org/10.1016/0273-1177(94)90235-6.

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Bai, Jianyong, David Yingst, Robert Bloor, and Jacques Leveille. "Viscoacoustic waveform inversion of velocity structures in the time domain." GEOPHYSICS 79, no. 3 (May 1, 2014): R103—R119. http://dx.doi.org/10.1190/geo2013-0030.1.

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Because of the conversion of elastic energy into heat, seismic waves are attenuated and dispersed as they propagate. The attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results. Using a viscoacoustic model consisting of a single standard linear solid, we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation. We derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion. The wave equations were numerically solved by high-order finite-difference methods on centered grids to extrapolate seismic wavefields. The finite-difference methods were implemented satisfying stability conditions, which are also presented. Numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude attenuation and phase dispersion. We tested acoustic and viscoacoustic waveform inversions with a modified Marmousi model and a 3D field data set from the deep-water Gulf of Mexico for comparison. The tests with the modified Marmousi model illustrated that the seismic attenuation can have large effects on waveform inversion and that choosing the most suitable inversion method was important to obtain the best inversion results for a specific seismic data volume. The tests with the field data set indicated that the inverted velocity models determined from the acoustic and viscoacoustic inversions were helpful to improve images and offset gathers obtained from migration. Compared to the acoustic inversion, viscoacoustic inversion is a realistic approach for real earth materials because the attenuation effects are compensated.

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Feng, Xuan, Enhedelihai Nilot, Cai Liu, Minghe Zhang, Hailong Yu, Jianyu Zhao, and Chengcheng Sun. "Joint Inversion of Seismic and Audio Magnetotelluric Data with Structural Constraint for Metallic Deposit." Journal of Environmental and Engineering Geophysics 23, no. 2 (June 2018): 159–69. http://dx.doi.org/10.2113/jeeg23.2.159.

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Audio magnetotelluric (AMT) and seismic methods are widely used to detect metallic deposits. However, each geophysical method only provides partial information of the underground target. Besides, individual methods have inherent limitations and ambiguity which leads to non-uniqueness when solving the inverse problem. To obtain a more robust and consistent ore deposit model, it is best to integrate different geophysical methods and data types. Towards this effort, we propose a joint inversion algorithm using cross-gradient constraint to build a connection between seismic and AMT data, and simultaneously invert for a resistivity and P-wave velocity model. Compared with separate AMT Gauss–Newton inversion and seismic Full waveform inversion (FWI) method, we can get more detailed and robust inversion results. In addition, frequency domain FWI with the Limited-Memory-Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm provides an effective way to reduce computer memory usage and improve convergence speed. This joint inversion algorithm has been tested using simple synthetic models with two cross targets. The results obtained with separate inversions were compared with those obtained with joint inversion. Then, we applied the algorithm to geophysical models of the Jinchuan sulfide deposit. The AMT results obtained with joint inversion of seismic data were better than those obtained with separate AMT inversion. The joint inversion approach appears more robust than the traditional separate FWI inversion and it is recommended that the proposed algorithm be considered in future projects of real field data.

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Luan, Xiaodong, Qingyun Di, Guoqing Xue, and Bin Chen. "Ground-wire Source TEM 3D Full Time Multinary Inversion Using Adaptive Regulation." Journal of Environmental and Engineering Geophysics 25, no. 3 (September 2020): 403–13. http://dx.doi.org/10.32389/jeeg19-037.

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Ground-wire source transient electromagnetic method (GTEM) provides better investigation ability than loop source TEM at a given noise level and decay time. However, at the present time, the method still stays in the one-dimensional inversion interpretation stage. Since actual geological structures are three-dimensionally distributed, the three-dimensional electromagnetic forward and inversion are crucial for understanding the electromagnetic responses of complex geological structures. Moreover, the traditional 3D smooth inversions of geophysical data have been found to inaccurately reflect small-scale and isolated anomalies. In this study, a multinary inversion method was introduced and applied to GTEM inversions. It was found that the proposed method had the ability to enable GTEM to more accurately delineate anomalous bodies when applied to detect high-resistivity target. Then, for the purpose of avoiding the need for multiple inversion tests to determine the regularization factors, a self-adaptive scheme was proposed based on the differences between the data fitting functional and the model functional during each iteration step. It was observed that by introducing the multinary inversion with adaptive regulation, more stable and accurate inversion results were obtained. In the current study, the numerical simulation results had successfully verified that the proposed multinary inversion method had provided better resolution than the traditional inversion methods.

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28

Luo, Yi, Yue Ma, Yan Wu, Hongwei Liu, and Lei Cao. "Full-traveltime inversion." GEOPHYSICS 81, no. 5 (September 2016): R261—R274. http://dx.doi.org/10.1190/geo2015-0353.1.

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Many previously published wave-equation-based methods, which attempt to automatically invert traveltime or kinematic information in seismic data or migrated gathers for smooth velocities, suffer a common and severe problem — the inversions are involuntarily and unconsciously hijacked by amplitude information. To overcome this problem, we have developed a new wave-equation-based traveltime inversion methodology, referred to as full-traveltime (i.e., fully dependent on traveltime) inversion (FTI), to automatically estimate a kinematically accurate velocity model from seismic data. The key idea of FTI is to make the inversion fully dependent on traveltime information, and thus prevent amplitude interference during inversion. Under the assumption that velocity perturbations cause only traveltime changes, we have derived the FTI method in the data and image domains, which are applicable to transmitted arrivals and reflected waves, respectively. FTI does not require an accurate initial velocity model or low-frequency seismic data. Synthetic and field data tests demonstrate that FTI produces satisfactory inversion results, even when using constant velocity models as initials.

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Dumont, Quentin, Valérie Cayol, and Jean-Luc Froger. "Mitigating bias in inversion of InSAR data resulting from radar viewing geometries." Geophysical Journal International 227, no. 1 (June 16, 2021): 483–95. http://dx.doi.org/10.1093/gji/ggab229.

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SUMMARY InSAR data acquired from ascending and descending orbits are often characterized by different magnitudes of the observed line-of-sight displacements, which may potentially bias inverse models. Using synthetic numerical models of dyke intrusions, we show that biased solutions are obtained when carrying out ‘conventional’ inversions where only observation and modelling errors are taken into consideration. To mitigate the impact of the relative magnitudes of the data, we propose two methods: a covariance weighting inversion and a wrapped data inversion. These methods are compared to a conventional inversion using synthetic data generated by models of dykes of known geometry. We find that the covariance weighting method allows to retrieve an initial source geometry better than the other methods. These methods are then applied to the July 2017 eruption of Piton de la Fournaise. Using a covariance weighting inversion, the difference in fit between data sets decreases from 50% to 20 % and the newly estimated source is in better agreement with the geological context.

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Zheglova, Polina, Peter G. Lelièvre, and Colin G. Farquharson. "Multiple level-set joint inversion of traveltime and gravity data with application to ore delineation: A synthetic study." GEOPHYSICS 83, no. 1 (January 1, 2018): R13—R30. http://dx.doi.org/10.1190/geo2016-0675.1.

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We have developed a multiple level-set method for simultaneous inversion of gravity and seismic traveltime data. The method recovers the boundaries between regions with distinct physical properties assumed constant and known, creating structurally consistent models of two subsurface properties: P-wave velocity and density. In single level-set methods, only two rock units can be considered: background and inclusion. Such methods have been applied to examples representing various geophysical scenarios, including in the context of joint inversion. In multiple level-set methods, several units can be considered, which make them far more applicable to real earth scenarios. Recently, a multiple level-set method has been proposed for inversion of magnetic data. We extend the multiple level-set formulation to joint inversion of gravity and traveltime data, improving upon previous work, and we investigate applicability of such an inversion method in ore delineation. In mineral exploration environments, traditional seismic imaging and inversion methods are challenging because of the small target size and the specific physical property contrasts involved. First-arrival seismic traveltime and gravity data complement each other, and we found that joint multiple level-set inversion is more beneficial than separate inversions, especially with limited data and slow targets. Our method is more robust than the joint inversion method based on clustering of physical properties in recovery of piecewise homogeneous models not well-constrained by the data. To justify the known property assumption, we found the degree of robustness of the multiple level-set joint inversion to uncertainties arising from incomplete knowledge of small-scale subsurface physical property variations and target composition.

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31

Xu, Yikang, Zhaohua Sun, Wei Gu, Wangping Qian, Qiangru Shen, and Jian Gong. "Three-dimensional inversion analysis of transient electromagnetic response signals of water-bearing abnormal bodies in tunnels based on numerical characteristic parameters." Mathematical Biosciences and Engineering 20, no. 1 (2022): 1106–21. http://dx.doi.org/10.3934/mbe.2023051.

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<abstract> <p>The transient electromagnetic inversion of detection signals mainly depends on fast inversion in the half-space state. However, the interpretation results have a certain degree of uncertainty and blindness, so the accuracy and applicability of the three-dimensional full-space inversion need to be investigated. Two different three-dimensional full-space inversions were carried out. First, the numerical characteristic parameters of the response signals were extracted. Then, the correlations between the numerical characteristic parameters and physical parameters of the water-bearing abnormal bodies were judged, and the judgment criterion of the iterative direction was proposed. Finally, the inversion methods of the iterative algorithm and the BP neural network were utilized based on the virtual example samples. The results illustrate that the proposed numerical characteristic parameters can accurately reflect the response curve of the full-space surrounding rock. The difference in the numerical characteristic parameters was used to determine the update direction and correction value. Both inversion methods have their advantages and disadvantages. A single inversion method cannot realize the three-dimensional inversion of the physical parameters of water-bearing abnormal bodies quickly, effectively and intelligently. Therefore, the benefits of different inversion methods need to be considered to comprehensively select a reasonable inversion method. The results can provide essential ideas for the subsequent interpretation of the three-dimensional spatial response signals of water-bearing abnormal bodies.</p> </abstract>

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32

HARDING, A. J. "INVERSION METHODS FOR tau-p MAPS OF NEAR OFFSET DATA-LINEAR INVERSION*." Geophysical Prospecting 33, no. 5 (August 1985): 674–95. http://dx.doi.org/10.1111/j.1365-2478.1985.tb00772.x.

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Shin, Changsoo, and Wansoo Ha. "A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains." GEOPHYSICS 73, no. 5 (September 2008): VE119—VE133. http://dx.doi.org/10.1190/1.2953978.

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In the frequency domain, gradient-based local-optimization methods of waveform inversions have been unsuccessful at inverting subsurface parameters without an accurate starting model. Such methods could not correct automatically for poor starting models because multiple local minima made it difficult to approach the true global minimum. In this study, we compared the behavior of objective functions in the frequency and Laplace domains. Wavefields in the Laplace domain correspond to the zero-frequency component of a damped wavefield; thus, the Laplace-domain waveform inversion can image smooth velocity models. Objective functions in the Laplace-domain inversion have a smoother surface and fewer local minima than in the frequency-domain inversion. We applied the waveform inversion to a 2D slice of the acoustic SEG/EAGE salt model in the Laplace domain and recovered smooth velocity models from inaccurate initial velocity conditions. We also successfully imaged velocities of the salt, SEG overthrust, and Institut Francais du Petrole Marmousi models with the frequency-domain inversion method by using the inverted velocity model of the Laplace-domain inversion as the initial model.

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Contreras, Arturo, Andre Gerhardt, Paul Spaans, and Matthew Docherty. "Characterization of fluvio-deltaic gas reservoirs through AVA deterministic, stochastic, and wave-equation-based seismic inversion: A case study from the Carnarvon Basin, Western Australia." Leading Edge 39, no. 2 (February 2020): 92–101. http://dx.doi.org/10.1190/tle39020092.1.

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Multiple state-of-the-art inversion methods have been implemented to integrate 3D seismic amplitude data, well logs, geologic information, and spatial variability to produce models of the subsurface. Amplitude variation with angle (AVA) deterministic, stochastic, and wave-equation-based amplitude variation with offset (WEB-AVO) inversion algorithms are used to describe Intra-Triassic Mungaroo gas reservoirs located in the Carnarvon Basin, Western Australia. The interpretation of inverted elastic properties in terms of lithology- and fluid-sensitive attributes from AVA deterministic inversion provides quantitative information about the geomorphology of fluvio-deltaic sediments as well as the delineation of gas reservoirs. AVA stochastic inversion delivers higher resolution realizations than those obtained from standard deterministic methods and allows for uncertainty analysis. Additionally, the cosimulation of petrophysical parameters from elastic properties provides precise 3D models of reservoir properties, such as volume of shale and water saturation, which can be used as part of the static model building process. Internal multiple scattering, transmission effects, and mode conversion (considered as noise in conventional linear inversion) become useful signals in WEB-AVO inversion. WEB-AVO compressibility shows increased sensitivity to residual/live gas discrimination compared to fluid-sensitive attributes obtained with conventional inversions.

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Zidikheri, Meelis Juma, and Jorgen S. Frederiksen. "Computationally efficient methods for climate model inversion." ANZIAM Journal 54 (May 28, 2013): 217. http://dx.doi.org/10.21914/anziamj.v54i0.6266.

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Yoshida, Shingo. "Waveform Inversion Methods for the Earthquake Source." Journal of Physics of the Earth 43, no. 3 (1995): 183–209. http://dx.doi.org/10.4294/jpe1952.43.183.

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Berryman, James G. "Inversion methods for ultrasonic travel‐time tomography." Journal of the Acoustical Society of America 108, no. 5 (November 2000): 2560. http://dx.doi.org/10.1121/1.4743507.

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Cline, D., A. Razdan, and P. Wonka. "A Comparison of Tabular PDF Inversion Methods." Computer Graphics Forum 28, no. 1 (March 2009): 154–60. http://dx.doi.org/10.1111/j.1467-8659.2008.01197.x.

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Schou, J., J. Christensen-Dalsgaard, and M. J. Thompson. "On comparing helioseismic two-dimensional inversion methods." Astrophysical Journal 433 (September 1994): 389. http://dx.doi.org/10.1086/174653.

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Vicente, R. O. "Inversion Methods for a Standard Earth Model." Geophysical Journal of the Royal Astronomical Society 35, no. 1-3 (September 15, 2009): 353–55. http://dx.doi.org/10.1111/j.1365-246x.1973.tb02436.x.

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Kosovichev, A. G. "Inversion methods in helioseismology and solar tomography." Journal of Computational and Applied Mathematics 109, no. 1-2 (September 1999): 1–39. http://dx.doi.org/10.1016/s0377-0427(99)00152-1.

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Jang, Ugeun, Dong-Joo Min, and Changsoo Shin. "Comparison of scaling methods for waveform inversion." Geophysical Prospecting 57, no. 1 (January 2009): 49–59. http://dx.doi.org/10.1111/j.1365-2478.2008.00739.x.

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Chapman, N. Ross. "An experimental benchmark for geoacoustic inversion methods." Journal of the Acoustical Society of America 142, no. 4 (October 2017): 2621. http://dx.doi.org/10.1121/1.5014600.

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Vargas, William E. "Inversion methods from Kubelka$ndash$Munk analysis." Journal of Optics A: Pure and Applied Optics 4, no. 4 (June 6, 2002): 452–56. http://dx.doi.org/10.1088/1464-4258/4/4/314.

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Twomey, S. "Iterafive Nonlinear Inversion Methods for Tomographic Problems." Journal of the Atmospheric Sciences 44, no. 23 (December 1987): 3544–51. http://dx.doi.org/10.1175/1520-0469(1987)044<3544:inimft>2.0.co;2.

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Sengpiel, Klaus‐Peter, and Bernhard Siemon. "Advanced inversion methods for airborne electromagnetic exploration." GEOPHYSICS 65, no. 6 (November 2000): 1983–92. http://dx.doi.org/10.1190/1.1444882.

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Airborne electromagnetic (AEM) surveys can contribute substantially to geologic mapping and target identification if good‐quality multifrequency data are produced, properly evaluated, and displayed. A set of multifrequency EM data is transformed into a set of apparent resistivity ([Formula: see text]) and centroid depth ([Formula: see text]) values, which then are plotted as a sounding curve. These [Formula: see text] curves commonly provide a smoothed picture of the vertical resistivity distribution at the sounding site. We have developed and checked methods to enhance the sensitivity of sounding curves to vertical resistivity changes by using new definitions for apparent resistivity and centroid depth. One of these new sounding curves with enhanced sensitivity to vertical resistivity contrasts is plotted from [Formula: see text] [Formula: see text] values derived from differentiation of the [Formula: see text] curve with respect to the frequency f. This approach is similar to the Niblett‐Bostick transform used in magnetotellurics. It not only enhances vertical changes in resistivity but also increases the depth of investigation. Sounding curves can be calculated directly from EM survey data and can be used to generate a resistivity‐depth parasection. Based on such a section, it can be decided whether a Marquardt‐type inversion of the AEM data into a 1-D layered half‐space model is adequate. Each sounding curve can be transformed into an initial step model of resistivity as required for the Marquardt inversion. We have inverted data from sedimentary sequences with good results. For data from a dipping conducting layer and a dipping plate, we have found that the results depend on the right choice of the starting model, in which the number of layers should be large rather than too small. Complex resistivity structures, however, often are represented better by using the sounding‐curve results than with the parameters of a layered half‐space.

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HU, Xiong, Zhen ZENG, Xun-Xie ZHANG, Dong-Ya ZHANG, and Cun-Ying XIAO. "Atmospheric Inversion Methods of GPS Radio Occultation." Chinese Journal of Geophysics 48, no. 4 (July 2005): 845–53. http://dx.doi.org/10.1002/cjg2.722.

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Wang, Yanfei, Yan Cui, and Changchun Yang. "Hybrid regularization methods for seismic reflectivity inversion." GEM - International Journal on Geomathematics 2, no. 1 (March 18, 2011): 87–112. http://dx.doi.org/10.1007/s13137-011-0014-1.

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Ren, Hao, Da Lei, Zhongxing Wang, and Changmin Fu. "A Mesh Mapping-Based Cooperative Inversion Strategy for Airborne Transient Electromagnetic and Magnetic Methods." Remote Sensing 15, no. 1 (December 26, 2022): 125. http://dx.doi.org/10.3390/rs15010125.

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Cooperative inversion is a powerful underground imaging technique that can overcome the limitations of a single detection method. However, due to the different grid divisions used by various geophysical methodologies, imposing structural constraints between grids of different scales is challenging. This paper proposes a new cooperative inversion strategy and applies it to the inversion of the quasi-two-dimensional aerial transient electromagnetic method (ATEM) with the induced polarization (IP) effect and the two-dimensional magnetic method to solve the problem of applying cross-gradient constraints under grids of different scales. The mesh mapping method is incorporated into the iterative process of cooperative inversion in this inversion strategy. The inversion of synthetic data shows that this technique can effectively employ data complementarity to increase the accuracy of the results for describing the medium boundary. The mesh mapping methodology may be applied to the cooperative inversion of geophysical methods under any grid division and successfully solves the problem of grid division mismatch in cooperative inversion.

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Li, Han, Xu Chang, Jinlai Hao, and Yibo Wang. "The general dislocation source model and its application to microseismic focal mechanism inversion." GEOPHYSICS 86, no. 4 (June 23, 2021): KS79—KS93. http://dx.doi.org/10.1190/geo2020-0844.1.

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Research on the non-double-couple (NDC) components in an earthquake is important for characterizing true source processes. The moment-tensor (MT) source model is commonly used to study NDC earthquakes. However, MT inversions are still challenging when earthquakes have small magnitudes, especially microearthquakes. The general-dislocation (GD) model specifies the focal mechanism as a shear-tensile slip on a fault plane; thus, GD inversion is better constrained than MT inversion. We focus on GD model-based waveform forward modeling and its application to microseismic source inversions. We expand the generalized reflection-transmission matrix method to synthesize waveforms based on the GD model and fully describe a GD source with five parameters: the scalar seismic moment (which defines the magnitude) and the strike, dip, rake, and slope angles (which define the fault geometry). We compare the GD, MT, and double-couple models and introduce the differences in their characterization and wave synthesis theories. We have developed a GD model-based microseismic focal mechanism inversion method that requires calculating only four angles under hybrid constraints. Two sets of solutions correspond to the same seismograms in a GD model-based inversion. These two solutions have the same scalar seismic moment and slope angle but different strike, dip, and rake angles, and we have derived formulas for mapping from one solution to the other. Synthetic and field surface microseismic data sets are used to test our GD model-based modeling and inversion methods. According to our study, the GD model is effective in microseismic focal mechanism inversion. By developing specific wave synthesis and inversion methods for the GD model, we offer a novel perspective to study this model and the NDC mechanisms for hydraulic fracturing-induced microearthquakes.

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