Bayesian linearized seismic inversion with locally varying spatial anisotropy

Bongajum, Emmanuel; Boisvert, Jeff B.; Sacchi, Mauricio D.

doi:10.1016/j.jappgeo.2012.10.001

Cited by 26 publications

(5 citation statements)

References 29 publications

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“…Non-stationarity can be modelled by introducing locally varying anisotropy (e.g. Boisvert & Deutsch 2011;Bongajum et al 2013;Pereira et al 2023), but these methods can be computationally challenging for large models. Thus, practical tools needed for estimating the non-stationarity are currently sparse and not easily deployed for practitioners (Madsen et al 2020).…”

Section: Discussion and Outlookmentioning

confidence: 99%

Machine learning-based estimation and clustering of statistics within stratigraphic models as exemplified in Denmark

Falk,

Bødker Madsen

2023

GEUS Bulletin

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Estimating a covariance model for kriging purposes is traditionally done using semivariogram analyses, where an empirical semivariogram is calculated, and a chosen semivariogram model, usually defined by a sill and a range, is fitted. We demonstrate that a convolutional neural network can estimate such a semivariogram model with comparable accuracy and precision by training it to recognise the relationship between realisations of Gaussian random fields and the sill and range values that define it, for a Gaussian type semivariance model. We do this by training the network with synthetic data consisting of many such realisations with the sill and range as the target variables. Because training takes time, the method is best suited for cases where many models need to be estimated since the actual estimation itself is about 70 times faster with the neural network than with the traditional approach. We demonstrate the viability of the method in three ways: (1) we test the model’s performance on the validation data, (2) we do a test where we compare the model to the traditional approach and (3) we show an example of an actual application of the method using the Danish national hydrostratigraphic model.

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Section: Discussion and Outlookmentioning

confidence: 99%

Machine learning-based estimation and clustering of statistics within stratigraphic models as exemplified in Denmark

Falk,

Bødker Madsen

2023

GEUS Bulletin

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“…To generalize anisotropic modeling, Eriksson and Siska () investigated the ellipses in an attempt to consistently model the directional varying parameters such as sill, range, nugget, and power in a universal framework. In addition to modeling anisotropicity globally in the sense of fitting the semivariogram, more and more work is aiming to model locally varying spatial anisotropy as well (Boisvert & Deutsch, ; Bongajum, Boisvert, & Sacchi, ; Te Stroet & Snepvangers, ), by which more complicated spatial patterns could be revealed such as channels and veins from geological deposits.…”

Section: Where Direction Has Been Consideredmentioning

confidence: 99%

Making direction a first‐class citizen of Tobler's first law of geography

Zhu

Janowicz

Mai

2019

Transactions in GIS

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Waldo Tobler frequently reminded us that the law named after him was nothing more than calling for exceptions. This article discusses one of these exceptions. Spatial relations between points are frequently modeled as vectors in which both distance and direction are of equal prominence. However, in Tobler's first law of geography, such a relation is described only from the perspective of distance by relating the decreasing similarity of observations in some attribute space to their increasing distance in geographic space. Although anisotropic versions of many geographic analysis techniques, such as directional semivariograms, anisotropy clustering, and anisotropic point pattern analysis, have been developed over the years, direction remains on the level of an afterthought. We argue that, compared to distance, directional information is still under‐explored and anisotropic techniques are substantially less frequently applied in everyday GIS analysis. Commonly, when classical spatial autocorrelation indicators, such as Moran's I, are used to understand a spatial pattern, the weight matrix is only built from distance, without direction being considered. Similarly, GIS operations, such as buffering, do not take direction into account either, with distance in all directions being treated equally. In reality, meanwhile, particularly in urban structures and when processes are driven by the underlying physical geography, direction plays an essential role. In this article we ask whether the development of early GIS, data (sample) sparsity, and Tobler's law lead to a theory‐induced blindness for the role of direction. If so, is it possible to envision direction becoming a first‐class citizen of equal importance to distance instead of being an afterthought only considered when the deviation from a perfect circle becomes too obvious to be ignored?

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“…The first step of seismic inversion usually employs a linear forward modelling operator (e.g., a linearization of the full Zoeppritz equations) under Gaussian assumptions for noise and model parameter distributions (e.g., the popular approach proposed by Buland & Omre, 2003). To mitigate the ill‐conditioning, geostatistical vertical constraints are usually employed to correctly preserve plausible vertical variability in the predicted elastic parameters (Bongajum et al ., 2013; Bosch et al ., 2015; Azevedo & Soares, 2017). To simplify the classification process, standard approaches estimate facies independently at each location, although it is known that the facies model must be vertically correlated to mimic depositional processes and gravity effects.…”

Section: Introductionmentioning

confidence: 99%

Elastic properties and litho‐fluid facies estimation from pre‐stack seismic data through bidirectional long short‐term memory networks

Aleardi

2022

Geophysical Prospecting

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One of the main goals of pre‐stack seismic inversion is the estimation of elastic properties (i.e. P‐, S‐ wave velocities and density) and litho‐fluid classes in the investigated area. To this end, many inversion strategies have been proposed, but the most popular is based on a two‐step inversion approach: First, elastic properties are inferred from pre‐stack data, and then a classification algorithm is used to convert the outcomes of the first stage into litho‐fluid facies. In this work, we propose an alternative approach based on recurrent neural networks. We train two bidirectional long short‐term memory networks to predict the inverse mappings from pre‐stack seismic data to elastic properties, and litho‐fluid classes. In the elastic inversion, we also use a Monte Carlo simulation approach to properly propagate onto the model space both the uncertainties related to noise contamination in the data and to the modelling error introduced by the network approximation. One crucial aspect of any machine‐learning inversion strategy is the definition of an appropriate training set. In this case, the models forming the training and validation examples are drawn according to a previously defined elastic and facies prior models derived from actual well log recordings. In particular, we assume a Gaussian‐mixture elastic prior, and we also take into account the uncertainties affecting the estimation of the transition probabilities of facies. We invert each seismic gather independently, and in this context, the generation of the training set, and the learning process can be accomplished with a very limited computational effort on a common notebook. Once trained, the networks estimate the elastic properties, the litho‐fluid facies and the related uncertainties from the pre‐stack data in near real‐time. Synthetic and field data inversions are used to validate the proposed method. The network predictions are also benchmarked against the outcomes of a more standard two‐step approach that combines a linear elastic inversion and a subsequent point‐wise Bayesian classification. Our results demonstrate that the implemented algorithm guarantees more accurate elastic property estimations and facies predictions than the standard inversion strategy. In particular, the predictions provided by the long short‐term memory network are less affected by erroneous assumptions on the noise statistics and prior model and by errors in the estimated source wavelet.

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Bayesian linearized seismic inversion with locally varying spatial anisotropy

Cited by 26 publications

References 29 publications

Machine learning-based estimation and clustering of statistics within stratigraphic models as exemplified in Denmark

Machine learning-based estimation and clustering of statistics within stratigraphic models as exemplified in Denmark

Making direction a first‐class citizen of Tobler's first law of geography

Elastic properties and litho‐fluid facies estimation from pre‐stack seismic data through bidirectional long short‐term memory networks

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