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Journal articles on the topic 'Inversion modelling'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Zwaan, Frank, Guido Schreurs, Susanne J. H. Buiter, Oriol Ferrer, Riccardo Reitano, Michael Rudolf, and Ernst Willingshofer. "Analogue modelling of basin inversion: a review and future perspectives." Solid Earth 13, no. 12 (December 16, 2022): 1859–905. http://dx.doi.org/10.5194/se-13-1859-2022.

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Abstract. Basin inversion involves the reversal of subsidence in a basin due to compressional tectonic forces, leading to uplift of the basin's sedimentary infill. Detailed knowledge of basin inversion is of great importance for scientific, societal, and economic reasons, spurring continued research efforts to better understand the processes involved. Analogue tectonic modelling forms a key part of these efforts, and analogue modellers have conducted numerous studies of basin inversion. In this review paper we recap the advances in our knowledge of basin inversion processes acquired through analogue modelling studies, providing an up-to-date summary of the state of analogue modelling of basin inversion. We describe the different definitions of basin inversion that are being applied by researchers, why basin inversion has been historically an important research topic and what the general mechanics involved in basin inversion are. We subsequently treat the wide range of different experimental approaches used for basin inversion modelling, with attention to the various materials, set-ups, and techniques used for model monitoring and analysing the model results. Our new systematic overviews of generalized model results reveal the diversity of these results, which depend greatly on the chosen set-up, model layering and (oblique) kinematics of inversion, and 3D along-strike structural and kinematic variations in the system. We show how analogue modelling results are in good agreement with numerical models, and how these results help researchers to better understand natural examples of basin inversion. In addition to reviewing the past efforts in the field of analogue modelling, we also shed light on future modelling challenges and identify a number of opportunities for follow-up research. These include the testing of force boundary conditions, adding geological processes such as sedimentation, transport, and erosion; applying state-of-the-art modelling and quantification techniques; and establishing best modelling practices. We also suggest expanding the scope of basin inversion modelling beyond the traditional upper crustal “North Sea style” of inversion, which may contribute to the ongoing search for clean energy resources. It follows that basin inversion modelling can bring valuable new insights, providing a great incentive to continue our efforts in this field. We therefore hope that this review paper will form an inspiration for future analogue modelling studies of basin inversion.

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2

Chevallier, F. "On the parallelization of atmospheric inversions of CO<sub>2</sub> surface fluxes within a variational framework." Geoscientific Model Development 6, no. 3 (June 7, 2013): 783–90. http://dx.doi.org/10.5194/gmd-6-783-2013.

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Abstract. The variational formulation of Bayes' theorem allows inferring CO2 sources and sinks from atmospheric concentrations at much higher time–space resolution than the ensemble or analytical approaches. However, it usually exhibits limited scalable parallelism. This limitation hinders global atmospheric inversions operated on decadal time scales and regional ones with kilometric spatial scales because of the computational cost of the underlying transport model that has to be run at each iteration of the variational minimization. Here, we introduce a physical parallelization (PP) of variational atmospheric inversions. In the PP, the inversion still manages a single physically and statistically consistent window, but the transport model is run in parallel overlapping sub-segments in order to massively reduce the computation wall-clock time of the inversion. For global inversions, a simplification of transport modelling is described to connect the output of all segments. We demonstrate the performance of the approach on a global inversion for CO2 with a 32 yr inversion window (1979–2010) with atmospheric measurements from 81 sites of the NOAA global cooperative air sampling network. In this case, we show that the duration of the inversion is reduced by a seven-fold factor (from months to days), while still processing the three decades consistently and with improved numerical stability.

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3

Chevallier, F. "On the parallelization of atmospheric inversions of CO<sub>2</sub> surface fluxes within a variational framework." Geoscientific Model Development Discussions 6, no. 1 (January 8, 2013): 37–57. http://dx.doi.org/10.5194/gmdd-6-37-2013.

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Abstract. The variational formulation of Bayes' theorem allows inferring CO2 sources and sinks from atmospheric concentrations at much higher space-time resolution than the ensemble approach or the analytical one. However, it usually exhibits limited scalable parallelism. This limitation hinders global atmospheric inversions operated on decadal time scales and regional ones with kilometric spatial scales, because of the computational cost of the underlying transport model that has to be run at each iteration of the variational minimization. Here, we introduce a Physical Parallelisation (PP) of variational atmospheric inversions. In the PP, the inversion still manages a single physically and statistically consistent window, but the transport model is run in parallel overlapping sub-segments in order to massively reduce the computation wall clock time of the inversion. For global inversions, a simplification of transport modelling is described to connect the output of all segments. We demonstrate the performance of the approach on a global inversion for CO2 with a 32-yr inversion window (1979–2010) with atmospheric measurements from 81 sites of the NOAA global cooperative air sampling network. In this case, we show that the duration of the inversion is reduced by a seven-fold factor (from months to days) while still processing the three decades consistently and with improved numerical stability.

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4

Ellis, Robert G. "Airborne Electromagnetic 3D Modelling and Inversion." Exploration Geophysics 26, no. 2-3 (June 1, 1995): 138–43. http://dx.doi.org/10.1071/eg995138.

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5

Turunen, I., T. Nyberg, J. Järveläinen, Y. Y. Linko, P. Linko, and M. Dohnal. "Fuzzy modelling in biotechnology: Sucrose inversion." Chemical Engineering Journal 30, no. 3 (June 1985): B51—B60. http://dx.doi.org/10.1016/0300-9467(85)80028-9.

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6

Madden, T. M., and R. L. Mackie. "Three-dimensional magnetotelluric modelling and inversion." Proceedings of the IEEE 77, no. 2 (1989): 318–33. http://dx.doi.org/10.1109/5.18628.

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7

Xiaojuan, Li, Huang Mutao, and Li Jianbao. "Remote sensing inversion of lake water quality parameters based on ensemble modelling." E3S Web of Conferences 143 (2020): 02007. http://dx.doi.org/10.1051/e3sconf/202014302007.

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In this paper, combined with water quality sampling data and Landsat8 satellite remote sensing image data, the inversion model of Chl-a and TN water quality parameter concentration was constructed based on machine learning algorithm. After the verification and evaluation of the inversion results of the test samples, Chl-a TN inversion model with high correlation between model test results and measured data was selected to participate in remote sensing inversion ensemble modelling of water quality parameters. Then, the ensemble remote sensing inversion model of water quality parameters was established based on entropy weight method and error analysis. By applying the idea of ensemble modelling to remote sensing inversion of water quality parameters, the advantages of different models can be integrated and the precision of water quality parameters inversion can be improved. Through the evaluation and comparative analysis of the model results, the entropy weight method can improve the inversion accuracy to some extent, but the improvement space is limited. In the verification of the two methods of ensemble modelling based on error analysis, compared with the optimal results of a single model, the determination coefficient (R2) of Chlorophyll a and TN concentration inversion results was increased from 0.9288 to 0.9313 and from 0.8339 to 0.8838, and the root mean square error was decreased from 14.2615 μ/L to 10.4194 μ/L and from1.1002mg/L to 0.8621mg/L. At the same time, with the increase of the number of models involved in the set modelling, the inversion accuracy is higher.

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8

Giraud, Jeremie, Mark Lindsay, Vitaliy Ogarko, Mark Jessell, Roland Martin, and Evren Pakyuz-Charrier. "Integration of geoscientific uncertainty into geophysical inversion by means of local gradient regularization." Solid Earth 10, no. 1 (January 25, 2019): 193–210. http://dx.doi.org/10.5194/se-10-193-2019.

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Abstract. We introduce a workflow integrating geological modelling uncertainty information to constrain gravity inversions. We test and apply this approach to the Yerrida Basin (Western Australia), where we focus on prospective greenstone belts beneath sedimentary cover. Geological uncertainty information is extracted from the results of a probabilistic geological modelling process using geological field data and their inferred accuracy as inputs. The uncertainty information is utilized to locally adjust the weights of a minimum-structure gradient-based regularization function constraining geophysical inversion. Our results demonstrate that this technique allows geophysical inversion to update the model preferentially in geologically less certain areas. It also indicates that inverted models are consistent with both the probabilistic geological model and geophysical data of the area, reducing interpretation uncertainty. The interpretation of inverted models reveals that the recovered greenstone belts may be shallower and thinner than previously thought.

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9

RAMÍREZ, JOSÉ L., GUSTAVO N. RUBIANO, and BORUT JURČIČ ZLOBEC. "GENERATING FRACTAL PATTERNS BY USING p-CIRCLE INVERSION." Fractals 23, no. 04 (December 2015): 1550047. http://dx.doi.org/10.1142/s0218348x15500474.

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In this paper, we introduce the [Formula: see text]-circle inversion which generalizes the classical inversion with respect to a circle ([Formula: see text]) and the taxicab inversion [Formula: see text]. We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the [Formula: see text]-circle inversion.

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10

Wilson, Glenn, Art Raiche, and Fred Sugeng. "Practical 3D AEM inversion using 2.5D modelling." ASEG Extended Abstracts 2006, no. 1 (December 2006): 1–4. http://dx.doi.org/10.1071/aseg2006ab196.

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11

Conway, Dennis, and Graham Heinson. "Magnetotelluric modelling: towards a 4-D inversion." ASEG Extended Abstracts 2016, no. 1 (December 2016): 1–2. http://dx.doi.org/10.1071/aseg2016ab244.

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12

Deng, Hongling, Hemin A. Koyi, and Jinjiang Zhang. "Modelling oblique inversion of pre-existing grabens." Geological Society, London, Special Publications 487, no. 1 (January 22, 2019): 263–90. http://dx.doi.org/10.1144/sp487.5.

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AbstractA series of analogue models were run to investigate oblique inversion of pre-existing grabens when overprinted by later shortening and the effect of these grabens on development of contractional structures. Obliquity angle (α) defining the initial trend of pre-existing grabens relative to the shortening direction, was systematically changed from 0°, 10°, 20°, 30°, 40°, 50°, 65° and 90°. Different structural styles are shown in different models and also in sections cutting across different parts of the models. Model results show that existence of multi-grabens enhances lateral discontinuity of overprinted thrusts in map view. With increasing the obliquity angle, more and longer lateral ramps developed sub-parallel to the graben trends. The pre-existing grabens were apparently rotated from their initial trends during shortening. Some of the normal faults bounding the grabens were partially inverted and resulted in bulging of the syn- and post-rift graben fill sediments. Most normal faults were displaced and rotated by thrusting, and provided relatively weak zones for propagation of thrusts. By comparing with observations from Qingxi graben in western China and from the SW Taiwan fold-and-thrust belt, where oblique inversion occurred, model results can be used to interpret unclear relationships between thrusts and pre-existing extensional structures during superimposed deformation.

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13

Quesnel, Y., B. Langlais, C. Sotin, and A. Galdéano. "Modelling and inversion of local magnetic anomalies." Journal of Geophysics and Engineering 5, no. 4 (September 24, 2008): 387–400. http://dx.doi.org/10.1088/1742-2132/5/4/003.

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14

Palupi, I. R., W. Raharjo, and O. D. Alfiani. "Subduction modelling by Tomography inversion around Lombok." Journal of Physics: Conference Series 1568 (June 2020): 012031. http://dx.doi.org/10.1088/1742-6596/1568/1/012031.

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15

Raiche, Art. "Modelling and inversion -progress, problems, and challenges." Surveys in Geophysics 15, no. 2 (March 1994): 159–207. http://dx.doi.org/10.1007/bf00689859.

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16

Bally, Albert W. "Analogue modelling of fault structures: 2. Inversion." Marine and Petroleum Geology 9, no. 2 (April 1992): 222–23. http://dx.doi.org/10.1016/0264-8172(92)90094-u.

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17

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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18

Su, Benyu, Zhixiong Li, Rongyao Li, Rongfu Rao, and Jingcun Yu. "Exploration Disaster Source of Mine Water by Electromagnetic Radiation." Elektronika ir Elektrotechnika 26, no. 5 (October 27, 2020): 16–21. http://dx.doi.org/10.5755/j01.eie.26.5.25960.

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geological hazard in deep underground mining. Before the rock mass explosion, electromagnetic energy will radiate outward during the deformation and rupture of the coal rocks. Hence, it is possible to use the electromagnetic radiation to predict geological disasters in coal mines. A challenging task using the active source electromagnetic survey technique is to detect geological anomalies, such as disaster water sources and geological structures. To this end, this paper proposes a new electromagnetic radiation solution based on the forward and inversion theory to detect geological anomalies in the coal seam. Based on typical coal mine geological models, the forward modelling and inversion modelling have been performed, respectively. The forward modelling explained the geological anomalies inside the coal seam, which were very sensitive to the response of the radiated electromagnetic field; especially, for the water-bearing geological anomalies. The inversion modelling discovered that the inversion geo-electric parameter distribution agreed well with the actual model. As a result, the proposed method is feasible for geological anomalies detection.

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19

Anikeyev, S. H., S. M. Bahriy, and B. B. Hablovskiy. "SIMULATION MODELLING IN THE STRUCTURAL GRAVITY PROSPECTING." Prospecting and Development of Oil and Gas Fields, no. 2(71) (June 25, 2019): 38–48. http://dx.doi.org/10.31471/1993-9973-2019-2(71)-38-48.

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In accordance with the purpose of geophysical exploration, the gravity data interpretation is aimed at prospecting mineral resources which is based on the study of the geological cross-section structure. The task of quantitative interpretation, which uses methods of gravity modeling and gravity inversion, is the modelling of a gravity field (gravity modeling) and of a density structure of geological environments (gravity inversion). The article presents the definition and steps of the gravity data modelling technique. This technique is based on the construction of an informal sequence of equivalent solutions. The technological and geological features of methods for modelling the density structure of complex geological environments are given; among them geological content, consistency with a priori data and the subordination of modelling to geological hypotheses are important. The topicality and methods of simulation modelling are outlined. The purpose of simulation modelling is to study the properties of gravity inversion in the general formulation, as well as to evaluate the degree of detail and reliability of the methods and technologies of gravity modelling, which claim to be an effective solution to geological problems. The example of structural simulation testing of the methods of informal sequence of equivalent solutions and its computer technologies shows that a complex interpretation of seismic and gravity measurements data enables the creation of detailed density models of structural cross-sections. The ways of increasing the veracity of gravity data modelling of structural cross-sections have been studied. It is revealed that the best approximation of the regional background is an inclined plane which approximates the observed field of gravity according to characteristic pickets over the research areas that are better studied. The increase in the veracity of modeling can also be achieved by rebuilding the near side zones in the structural type models in an interactive process of solving structural gravity inversion problems. Substantive modeling depends primarily on the experience of the interpreter since computer technologies for gravity modeling and gravity inversion are merely an interpretation tool.

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20

Jordi, C., J. Doetsch, T. Günther, C. Schmelzbach, H. Maurer, and J. O. A. Robertsson. "Structural joint inversion on irregular meshes." Geophysical Journal International 220, no. 3 (December 5, 2019): 1995–2008. http://dx.doi.org/10.1093/gji/ggz550.

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SUMMARY Structural joint inversion of several data sets on an irregular mesh requires appropriate coupling operators. To date, joint inversion algorithms are primarily designed for the use on regular rectilinear grids and impose structural similarity in the direct neighbourhood of a cell only. We introduce a novel scheme for calculating cross-gradient operators based on a correlation model that allows to define the operator size by imposing physical length scales. We demonstrate that the proposed cross-gradient operators are largely decoupled from the discretization of the modelling domain, which is particularly important for irregular meshes where cell sizes vary. Our structural joint inversion algorithm is applied to a synthetic electrical resistivity tomography and ground penetrating radar 3-D cross-well experiment aiming at imaging two anomalous bodies and extracting the parameter distribution of the geostatistical background models. For both tasks, joint inversion produced superior results compared with individual inversions of the two data sets. Finally, we applied structural joint inversion to two field data sets recorded over a karstified limestone area. By including geological a priori information via the correlation-based operators into the joint inversion, we find P-wave velocity and electrical resistivity tomograms that are in accordance with the expected subsurface geology.

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21

Engebretsen, Kim Wann, Bo Zhang, Gianluca Fiandaca, Line Meldgaard Madsen, Esben Auken, and Anders Vest Christiansen. "Accelerated 2.5-D inversion of airborne transient electromagnetic data using reduced 3-D meshing." Geophysical Journal International 230, no. 1 (February 25, 2022): 643–53. http://dx.doi.org/10.1093/gji/ggac077.

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SUMMARY Airborne systems collecting transient electromagnetic data are able to gather large amounts of data over large areas in a very short time. These data are most often interpreted through 1-D inversions, due to the availability of robust, fast and efficient codes. However, in areas where the subsurface contains complex structures or large conductivity contrasts, 1-D inversions may introduce artefacts into the models, which may prevent correct interpretation of the results. In these cases, 2-D or 3-D inversion should be used. Here, we present a 2.5-D inversion code using 3-D forward modelling combined with a 2-D model grid. A 2.5-D inversion is useful where the flight lines are spaced far apart, in which case a 3-D inversion would not add value in relation to the added computational cost and complexity. By exploiting the symmetry of the transmitter and receiver system we are able to perform forward calculations on a reduced 3-D mesh using only half the domain transecting the centre of the transmitter and receiver system. The forward responses and sensitivities from the reduced 3-D mesh are projected onto a structured 2-D model grid following the flight direction. The difference in forward calculations is within 1.4 per cent using the reduced mesh compared to a full 3-D solution. The inversion code is tested on a synthetic example constructed with complex geology and high conductivity contrasts and the results are compared to a 1-D inversion. We find that the 2.5-D inversion recovers both the conductivity values and shape of the true model with a significantly higher accuracy than the 1-D inversion. Finally, the results are supported by a field case using airborne TEM data from the island of Mayotte. The inverted flight line consisted of 418 soundings, and the inversion spent an average of 6750 s per iteration, converging in 16 iterations with a peak memory usage of 97 GB, using 18 logical processors. In general, the total time of the 2-D inversions compared to a full 3-D inversion is reduced by a factor of 2.5 while the memory consumption was reduced by a factor of 2, reflecting the half-mesh approach.

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22

Günther, Thomas, Carsten Rücker, and Klaus Spitzer. "Three-dimensional modelling and inversion of dc resistivity data incorporating topography - II. Inversion." Geophysical Journal International 166, no. 2 (August 2006): 506–17. http://dx.doi.org/10.1111/j.1365-246x.2006.03011.x.

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23

Riepl, Judith, Andreas Rietbrock, and Frank Scherbaum. "Site response modelling by non-linear waveform inversion." Geophysical Research Letters 22, no. 3 (February 1, 1995): 199–202. http://dx.doi.org/10.1029/94gl02970.

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24

Sasaki, Yutaka. "3-D electromagnetic modelling and inversion incorporating topography." ASEG Extended Abstracts 2003, no. 1 (April 2003): 1–7. http://dx.doi.org/10.1071/aseg2003_3demab013.

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25

Sutton, G. R., and B. J. Moore. "Velocity modelling using a generalized linear inversion technique." Exploration Geophysics 16, no. 2-3 (June 1985): 287–88. http://dx.doi.org/10.1071/eg985287.

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26

Hoop, Adrianus T. de. "Areas for exploration in electromagnetic modelling and inversion." Inverse Problems 16, no. 5 (October 1, 2000): 1083–96. http://dx.doi.org/10.1088/0266-5611/16/5/301.

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27

Lelièvre, Peter G., and Douglas W. Oldenburg. "Magnetic forward modelling and inversion for high susceptibility." Geophysical Journal International 166, no. 1 (July 2006): 76–90. http://dx.doi.org/10.1111/j.1365-246x.2006.02964.x.

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28

Knudsen, Mads Faurschou, Bo Holm Jacobsen, and Niels Abrahamsen. "Palaeomagnetic distortion modelling and possible recovery by inversion." Physics of the Earth and Planetary Interiors 135, no. 1 (January 2003): 55–73. http://dx.doi.org/10.1016/s0031-9201(02)00203-0.

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29

Nielsen, Søren B., and Ulf Bayer. "Dynamics of sedimentary basin inversion: observations and modelling." Tectonophysics 373, no. 1-4 (September 2003): 1–3. http://dx.doi.org/10.1016/s0040-1951(03)00278-6.

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30

Kumar, Shashi, Himanshu Govil, Prashant K. Srivastava, Praveen K. Thakur, and Satya P. S. Kushwaha. "Spaceborne Multifrequency PolInSAR-Based Inversion Modelling for Forest Height Retrieval." Remote Sensing 12, no. 24 (December 10, 2020): 4042. http://dx.doi.org/10.3390/rs12244042.

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Spaceborne and airborne polarimetric synthetic-aperture radar interferometry (PolInSAR) data have been extensively used for forest parameter retrieval. The PolInSAR models have proven their potential in the accurate measurement of forest vegetation height. Spaceborne monostatic multifrequency data of different SAR missions and the Global Ecosystem Dynamics Investigation (GEDI)-derived forest canopy height map were used in this study for vegetation height retrieval. This study tested the performance of PolInSAR complex coherence-based inversion models for estimating the vegetation height of the forest ranges of Doon Valley, Uttarakhand, India. The inversion-based forest height obtained from the three-stage inversion (TSI) model had higher accuracy than the coherence amplitude inversion (CAI) model-based estimates. The vegetation height values of GEDI-derived canopy height map did not show good relation with field-measured forest height values. It was found that, at several locations, GEDI-derived forest height values underestimated the vegetation height. The statistical analysis of the GEDI-derived estimates with field-measured height showed a high root mean square error (RMSE; 5.82 m) and standard error (SE; 5.33 m) with a very low coefficient of determination (R2; 0.0022). An analysis of the spaceborne-mission-based forest height values suggested that the L-band SAR has great potential in forest height retrieval. TSI-model-based forest height values showed lower p-values, which indicates the significant relation between modelled and field-measured forest height values. A comparison of the results obtained from different SAR systems is discussed, and it is observed that the L-band-based PolInSAR inversion gives the most reliable result with low RMSE (2.87 m) and relatively higher R2 (0.53) for the linear regression analysis between the modelled tree height and the field data. These results indicate that higher wavelength PolInSAR datasets are more suitable for tree canopy height estimation using the PolInSAR inversion technique.

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31

Giraud, Jérémie, Vitaliy Ogarko, Roland Martin, Mark Jessell, and Mark Lindsay. "Structural, petrophysical, and geological constraints in potential field inversion using the Tomofast-x v1.0 open-source code." Geoscientific Model Development 14, no. 11 (November 2, 2021): 6681–709. http://dx.doi.org/10.5194/gmd-14-6681-2021.

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Abstract. The quantitative integration of geophysical measurements with data and information from other disciplines is becoming increasingly important in answering the challenges of undercover imaging and of the modelling of complex areas. We propose a review of the different techniques for the utilisation of structural, petrophysical, and geological information in single physics and joint inversion as implemented in the Tomofast-x open-source inversion platform. We detail the range of constraints that can be applied to the inversion of potential field data. The inversion examples we show illustrate a selection of scenarios using a realistic synthetic data set inspired by real-world geological measurements and petrophysical data from the Hamersley region (Western Australia). Using Tomofast-x's flexibility, we investigate inversions combining the utilisation of petrophysical, structural, and/or geological constraints while illustrating the utilisation of the L-curve principle to determine regularisation weights. Our results suggest that the utilisation of geological information to derive disjoint interval bound constraints is the most effective method to recover the true model. It is followed by model smoothness and smallness conditioned by geological uncertainty and cross-gradient minimisation.

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32

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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33

Bawahab, Nabil, Udi Harmoko, Tony Yulianto, and Irvan Ramadhan. "Identification of low resistivity layers in the “N” geothermal field using 2D magnetotelluric inversion modelling." Journal of Physics and Its Applications 2, no. 2 (May 11, 2020): 85–89. http://dx.doi.org/10.14710/jpa.v2i2.7532.

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Magnetotelluric research in the “N” geothermal field has been carried out to see the subsurface detail in the “N” geothermal field. 2D inversion model is generated by secondary data from magnetotelluric data collection in the form of time series data to become 2D models. Magnetotellurics method is used to identify geothermal system components, especially identifying layers with low resistivity values (2 Ω.m - 10 Ω.m) or also called as the cap rock which is seen with a very contrasting color difference compared to the surrounding layers. There are manifestations on the “N” geothermal field which reinforce the assumption that there is a geothermal system in this area. This research begins by processing time series data to become apparent resistivity and phase data. Time series data processing in this study uses several processing methods to produce better apparent resistivity and phase data. The final result of this study is a 2D model that illustrates the contour of the resistivity value of rocks laterally or vertically. 2D model interpretation in this study identified the cap rock layer with low resistivity distribution (2 Ω.m - 10 Ω.m), the medium resistivity zone identified as the reservoir layer (11 Ω.m - 70 Ω.m), and the resistive zone which has high resistivity value (more than 70 Ω.m).

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Binz, F., and D. Moormann. "Actuator modelling for attitude control using incremental nonlinear dynamic inversion." International Journal of Micro Air Vehicles 12 (January 2020): 175682932096192. http://dx.doi.org/10.1177/1756829320961925.

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Recently, the concept of incremental nonlinear dynamic inversion has seen an increasing adoption as an attitude control method for a variety of aircraft configurations. The reasons for this are good stability and robustness properties, moderate computation requirements and low requirements on modelling fidelity. While previous work investigated the robust stability properties of incremental nonlinear dynamic inversion, the actual closed-loop performance may degrade severely in the face of model uncertainty. We address this issue by first analysing the effects of modelling errors on the closed-loop performance by observing the movement of the system poles. Based on this, we analyse the neccessary modelling fidelity and propose simple modelling methods for the usual actuators found on small-scale electric aircraft. Finally, we analyse the actuator models using (flight) test data where possible.

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Rücker, Carsten, Thomas Günther, and Klaus Spitzer. "Three-dimensional modelling and inversion of dc resistivity data incorporating topography - I. Modelling." Geophysical Journal International 166, no. 2 (August 2006): 495–505. http://dx.doi.org/10.1111/j.1365-246x.2006.03010.x.

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Locatelli, R., P. Bousquet, F. Chevallier, A. Fortems-Cheney, S. Szopa, M. Saunois, A. Agusti-Panareda, et al. "Impact of transport model errors on the global and regional methane emissions estimated by inverse modelling." Atmospheric Chemistry and Physics 13, no. 19 (October 8, 2013): 9917–37. http://dx.doi.org/10.5194/acp-13-9917-2013.

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Abstract. A modelling experiment has been conceived to assess the impact of transport model errors on methane emissions estimated in an atmospheric inversion system. Synthetic methane observations, obtained from 10 different model outputs from the international TransCom-CH4 model inter-comparison exercise, are combined with a prior scenario of methane emissions and sinks, and integrated into the three-component PYVAR-LMDZ-SACS (PYthon VARiational-Laboratoire de Météorologie Dynamique model with Zooming capability-Simplified Atmospheric Chemistry System) inversion system to produce 10 different methane emission estimates at the global scale for the year 2005. The same methane sinks, emissions and initial conditions have been applied to produce the 10 synthetic observation datasets. The same inversion set-up (statistical errors, prior emissions, inverse procedure) is then applied to derive flux estimates by inverse modelling. Consequently, only differences in the modelling of atmospheric transport may cause differences in the estimated fluxes. In our framework, we show that transport model errors lead to a discrepancy of 27 Tg yr−1 at the global scale, representing 5% of total methane emissions. At continental and annual scales, transport model errors are proportionally larger than at the global scale, with errors ranging from 36 Tg yr−1 in North America to 7 Tg yr−1 in Boreal Eurasia (from 23 to 48%, respectively). At the model grid-scale, the spread of inverse estimates can reach 150% of the prior flux. Therefore, transport model errors contribute significantly to overall uncertainties in emission estimates by inverse modelling, especially when small spatial scales are examined. Sensitivity tests have been carried out to estimate the impact of the measurement network and the advantage of higher horizontal resolution in transport models. The large differences found between methane flux estimates inferred in these different configurations highly question the consistency of transport model errors in current inverse systems. Future inversions should include more accurately prescribed observation covariances matrices in order to limit the impact of transport model errors on estimated methane fluxes.

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Bai, Peng, Giulio Vignoli, and Thomas Mejer Hansen. "1D Stochastic Inversion of Airborne Time-Domain Electromagnetic Data with Realistic Prior and Accounting for the Forward Modeling Error." Remote Sensing 13, no. 19 (September 28, 2021): 3881. http://dx.doi.org/10.3390/rs13193881.

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Airborne electromagnetic surveys may consist of hundreds of thousands of soundings. In most cases, this makes 3D inversions unfeasible even when the subsurface is characterized by a high level of heterogeneity. Instead, approaches based on 1D forwards are routinely used because of their computational efficiency. However, it is relatively easy to fit 3D responses with 1D forward modelling and retrieve apparently well-resolved conductivity models. However, those detailed features may simply be caused by fitting the modelling error connected to the approximate forward. In addition, it is, in practice, difficult to identify this kind of artifacts as the modeling error is correlated. The present study demonstrates how to assess the modelling error introduced by the 1D approximation and how to include this additional piece of information into a probabilistic inversion. Not surprisingly, it turns out that this simple modification provides not only much better reconstructions of the targets but, maybe, more importantly, guarantees a correct estimation of the corresponding reliability.

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Y, Yatini, Djoko Santoso, Agus Laesanpura, and Budi Sulistijo. "Studi Pemodelan Respon Polarisasi Terinduksi dalam Kawasan Waktu (TDIP) terhadap Kandungan Mineral Logam, Sebuah Hasil Awal." INDONESIAN JOURNAL OF APPLIED PHYSICS 4, no. 02 (February 10, 2017): 162. http://dx.doi.org/10.13057/ijap.v4i02.4984.

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<p>Modelling studies of Time Domain Induced Polarization (TDIP) performed to obtain the relationship between parameters responses to metallic mineral content. This study includes mathematical, forward, physical and inversion modelling. Mathematical modelling is done by solving the Laplace equation to obtain the IP responses. Forward modelling is done by developing a numerical workflow to generate theoretical curves. Physical modelling obtained the data from various parameters of target measurement. TDIP responses that compared with the theoretical curves are the results of mathematical modelling. The best response of IP can be obtained by inversion modelling. TDIP responses measurement by varying target’s metallic mineral content is done for understanding the relationship between them. The amplitude of IP responses in forward modelling is determined by target’s radius and depth ratio, and ratio of background resistivity and target’s resistivity. The higher target’s radius and depth ratio, the higher the amplitude. There is a good correlation between TDIP responses to the presence of the target and the possibility of metallic mineral content in target.</p>

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Krysta, M., M. Bocquet, and J. Brandt. "Probing ETEX-II data set with inverse modelling." Atmospheric Chemistry and Physics Discussions 8, no. 1 (February 12, 2008): 2795–819. http://dx.doi.org/10.5194/acpd-8-2795-2008.

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Abstract. We give here an account on the results of source inversion of the ETEX-II experiment. Inversion has been performed with the maximum entropy method on the basis of non-zero measurements and in conjunction with a transport model Polair3D. The discrepancy scaling factor between the true and the reconstructed mass has been estimated to be equal to 7. The results contrast with the method's performance on the ETEX-I source. In the latter case its mass has been reconstructed with an accuracy exceeding 80%. The large value of the discrepancy factor for ETEX-II could be ascribed to modelling difficulties, possibly linked not to the transport model itself but rather to the quality of the measurements.

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Krysta, M., M. Bocquet, and J. Brandt. "Probing ETEX-II data set with inverse modelling." Atmospheric Chemistry and Physics 8, no. 14 (July 24, 2008): 3963–71. http://dx.doi.org/10.5194/acp-8-3963-2008.

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Abstract. We give here an account on the results of source inversion of the ETEX-II experiment. Inversion has been performed with the maximum entropy method on the basis of non-zero measurements and in conjunction with a transport model POLAIR3D. The discrepancy scaling factor between the reconstructed and the true mass has been estimated to be equal to 7. The results contrast with the method's performance on the ETEX-I source. In the latter case its mass has been reconstructed with an accuracy exceeding 80%. The large value of the discrepancy factor for ETEX-II could be ascribed to modelling difficulties, possibly linked not to the transport model itself but rather to the quality of the measurements.

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Stell, Angharad C., Michael Bertolacci, Andrew Zammit-Mangion, Matthew Rigby, Paul J. Fraser, Christina M. Harth, Paul B. Krummel, et al. "Modelling the growth of atmospheric nitrous oxide using a global hierarchical inversion." Atmospheric Chemistry and Physics 22, no. 19 (October 10, 2022): 12945–60. http://dx.doi.org/10.5194/acp-22-12945-2022.

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Abstract. Nitrous oxide is a potent greenhouse gas (GHG) and ozone-depleting substance, whose atmospheric abundance has risen throughout the contemporary record. In this work, we carry out the first global hierarchical Bayesian inversion to solve for nitrous oxide emissions, which includes prior emissions with truncated Gaussian distributions and Gaussian model errors, in order to examine the drivers of the atmospheric surface growth rate. We show that both emissions and climatic variability are key drivers of variations in the surface nitrous oxide growth rate between 2011 and 2020. We derive increasing global nitrous oxide emissions, which are mainly driven by emissions between 0 and 30∘ N, with the highest emissions recorded in 2020. Our mean global total emissions for 2011–2020 of 17.2 (16.7–17.7 at the 95 % credible intervals) Tg N yr−1, comprising of 12.0 (11.2–12.8) Tg N yr−1 from land and 5.2 (4.5–5.9) Tg N yr−1 from ocean, agrees well with previous studies, but we find that emissions are poorly constrained for some regions of the world, particularly for the oceans. The prior emissions used in this and other previous work exhibit a seasonal cycle in the extra-tropical Northern Hemisphere that is out of phase with the posterior solution, and there is a substantial zonal redistribution of emissions from the prior to the posterior. Correctly characterizing the uncertainties in the system, for example in the prior emission fields, is crucial for deriving posterior fluxes that are consistent with observations. In this hierarchical inversion, the model-measurement discrepancy and the prior flux uncertainty are informed by the data, rather than solely through “expert judgement”. We show cases where this framework provides different plausible adjustments to the prior fluxes compared to inversions using widely adopted, fixed uncertainty constraints.

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Varon, Daniel J., Daniel J. Jacob, Melissa Sulprizio, Lucas A. Estrada, William B. Downs, Lu Shen, Sarah E. Hancock, et al. "Integrated Methane Inversion (IMI 1.0): a user-friendly, cloud-based facility for inferring high-resolution methane emissions from TROPOMI satellite observations." Geoscientific Model Development 15, no. 14 (July 27, 2022): 5787–805. http://dx.doi.org/10.5194/gmd-15-5787-2022.

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Abstract. We present a user-friendly, cloud-based facility for quantifying methane emissions with 0.25∘ × 0.3125∘ (≈ 25 km × 25 km) resolution by inverse analysis of satellite observations from the TROPOspheric Monitoring Instrument (TROPOMI). The facility is built on an Integrated Methane Inversion optimal estimation workflow (IMI 1.0) and supported for use on the Amazon Web Services (AWS) cloud. It exploits the GEOS-Chem chemical transport model and TROPOMI data already resident on AWS, thus avoiding cumbersome big-data download. Users select a region and period of interest, and the IMI returns an analytical solution for the Bayesian optimal estimate of period-average emissions on the 0.25∘ × 0.3125∘ grid including error statistics, information content, and visualization code for inspection of results. The inversion uses an advanced research-grade algorithm fully documented in the literature. An out-of-the-box inversion with rectilinear grid and default prior emission estimates can be conducted with no significant learning curve. Users can also configure their inversions to infer emissions for irregular regions of interest, swap in their own prior emission inventories, and modify inversion parameters. Inversion ensembles can be generated at minimal additional cost once the Jacobian matrix for the analytical inversion has been constructed. A preview feature allows users to determine the TROPOMI information content for their region and time period of interest before actually performing the inversion. The IMI is heavily documented and is intended to be accessible by researchers and stakeholders with no expertise in inverse modelling or high-performance computing. We demonstrate the IMI's capabilities by applying it to estimate methane emissions from the US oil-producing Permian Basin in May 2018.

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Bergamaschi, Peter, Arjo Segers, Dominik Brunner, Jean-Matthieu Haussaire, Stephan Henne, Michel Ramonet, Tim Arnold, et al. "High-resolution inverse modelling of European CH₄ emissions using the novel FLEXPART-COSMO TM5 4DVAR inverse modelling system." Atmospheric Chemistry and Physics 22, no. 20 (October 17, 2022): 13243–68. http://dx.doi.org/10.5194/acp-22-13243-2022.

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Abstract. We present a novel high-resolution inverse modelling system (“FLEXVAR”) based on FLEXPART-COSMO back trajectories driven by COSMO meteorological fields at 7 km×7 km resolution over the European COSMO-7 domain and the four-dimensional variational (4DVAR) data assimilation technique. FLEXVAR is coupled offline with the global inverse modelling system TM5-4DVAR to provide background mole fractions (“baselines”) consistent with the global observations assimilated in TM5-4DVAR. We have applied the FLEXVAR system for the inverse modelling of European CH4 emissions in 2018 using 24 stations with in situ measurements, complemented with data from five stations with discrete air sampling (and additional stations outside the European COSMO-7 domain used for the global TM5-4DVAR inversions). The sensitivity of the FLEXVAR inversions to different approaches to calculate the baselines, different parameterizations of the model representation error, different settings of the prior error covariance parameters, different prior inventories, and different observation data sets are investigated in detail. Furthermore, the FLEXVAR inversions are compared to inversions with the FLEXPART extended Kalman filter (“FLExKF”) system and with TM5-4DVAR inversions at 1∘×1∘ resolution over Europe. The three inverse modelling systems show overall good consistency of the major spatial patterns of the derived inversion increments and in general only relatively small differences in the derived annual total emissions of larger country regions. At the same time, the FLEXVAR inversions at 7 km×7 km resolution allow the observations to be better reproduced than the TM5-4DVAR simulations at 1∘×1∘. The three inverse models derive higher annual total CH4 emissions in 2018 for Germany, France, and BENELUX compared to the sum of anthropogenic emissions reported to UNFCCC and natural emissions estimated from the Global Carbon Project CH4 inventory, but the uncertainty ranges of top-down and bottom-up total emission estimates overlap for all three country regions. In contrast, the top-down estimates for the sum of emissions from the UK and Ireland agree relatively well with the total of anthropogenic and natural bottom-up inventories.

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Madsen, Line Meldgaard, Gianluca Fiandaca, and Esben Auken. "3-D time-domain spectral inversion of resistivity and full-decay induced polarization data—full solution of Poisson's equation and modelling of the current waveform." Geophysical Journal International 223, no. 3 (September 23, 2020): 2101–16. http://dx.doi.org/10.1093/gji/ggaa443.

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SUMMARY We present a new algorithm for 3-D forward modelling and spectral inversion of resistivity and time-domain full-decay induced polarization (IP) data. To our knowledge, all algorithms available for handling 3-D spectral inversion of full-decay IP data use a time-domain approximation to Poisson's equation in the forward response. To avoid this approximation, we compute the response in the frequency domain solving the full version of Poisson's equation for a range of frequencies (10–8–104 Hz) and then transform the response into the time domain, where we account for the transmitted current waveform. Solving Poisson's equation in 3-D is computationally expensive and in order to balance accuracy, time, and memory usage we introduce the following: (1) We use two separate meshes for the forward response and the model update, respectively. The forward mesh is an unstructured tetrahedral mesh allowing for local refinements whereas the model (inversion) mesh is a node-based structured mesh, where roughness constraints are easily implemented. By decoupling the two meshes, they can be tuned for optimizing the forward accuracy and the inversion resolution, independently. (2) A singularity removal method known from resistivity modelling has been adapted to the complex IP case and is applied to minimize the numerical errors caused by the fast changing potential close to the source electrodes. The method includes splitting the potential field into a primary part (response of a homogenous background) and a secondary part (from the anomalies). Two different forward meshes are then used to compute the forward response: a dense mesh for the primary potential field (only computed once for each frequency) and a coarser mesh for the secondary potential field (computed in each iteration step of the inversion). With this method, the singularity is minimized and the memory usages is decreased significantly at the same time. (3) Finally, we are sparsing (downsampling) the Jacobian matrix based on a threshold value of the normalized sensitivity. The Jacobian computation is performed by time-transforming the frequency-domain Jacobian obtained through the adjoint method. The Jacobian downsampling is carried out before the time-transform in the frequency domain, thus avoiding the time-transformation of the Jacobian elements with negligible sensitivity. We invert resistivity data and all IP time-gates simultaneously and use the Gauss–Newton model update to minimize the L2 misfit function. We invert the resistivity data and all IP time-gates simultaneously and use the Gauss–Newton model update to minimize the L2 misfit function. We demonstrate the performance of our inversion approach with a synthetic data example with 3-D anomalies and a field example, where lithology logs verify the results. The data sets contain 1256 quadrupole measurements with 33 IP time-gates each. The inversions results show good data fits and model retrieval. The inversion takes approximately one hour per iteration using four CPUs. With this speed and accuracy, we believe this modelling and inversion approach will be a strong tool for 3-D spectral inversion of resistivity and full-decay IP field data for both surface and borehole applications.

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ZHAO, Guoze, and Guodong LIU. "A new inversion scheme for two-dimensional magnetotelluric modelling." Journal of geomagnetism and geoelectricity 42, no. 10 (1990): 1209–20. http://dx.doi.org/10.5636/jgg.42.1209.

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Chen, C. S., F. Hsieh, D. Zuo, J. Li, Lin Lin, and G. Xie. "Magnetotelluric Modelling and Inversion For Earthquake Studies in Taiwan." ASEG Extended Abstracts 2003, no. 1 (April 2003): 1–5. http://dx.doi.org/10.1071/aseg2003_3demab003.

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Vallée, Marc A. "New developments in AEM discrete conductor modelling and inversion." Exploration Geophysics 46, no. 1 (March 2015): 97–111. http://dx.doi.org/10.1071/eg14025.

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Van Der Meer, F. "Geophysical inversion of imaging spectrometer data for geologic modelling." International Journal of Remote Sensing 21, no. 2 (January 2000): 387–93. http://dx.doi.org/10.1080/014311600210902.

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LEEF, JEONG-WOO, and JUN-HO OHT. "Inversion of multilayer neural network with modelling error compensation." International Journal of Systems Science 28, no. 8 (July 1997): 817–30. http://dx.doi.org/10.1080/00207729708929442.

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Lee, J. W., and J. H. Oh. "Inversion control of nonlinear systems with neural network modelling." IEE Proceedings - Control Theory and Applications 144, no. 5 (September 1, 1997): 481–87. http://dx.doi.org/10.1049/ip-cta:19971360.

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