Tomotok: python package for tomography of tokamak plasma radiation

A python package, called Tomotok, focused on performing tomographic inversion of tokamak plasma radiation is being developed at the Institute of Plasma Physics of the Czech Academy of Sciences. It aims at providing multiple inversion algorithms with an user friendly interface. In order to enable and ease performing tomographic inversion on different devices worldwide, it is planned to publish this software as open source in the near future. In this contribution, the package structure allowing an easy implementation of various tokamak and diagnostic geometries is described and an overview of the package contents is given. Apart from inversion methods, overview of Tomotok auxiliary content is given. The package provides tools for creating simple synthetic diagnostic system. These can be used for testing and benchmarking the code. This includes tools for building geometry matrices that describe the view of detectors using single line of sight approximation and artificial data generators capable of creating simple or hollow Gaussian profiles. The implemented inversion methods cover the minimum Fisher regularisation, biorthogonal decomposition and linear algebraic methods. The implementation of each method is explained, example results obtained by inverting phantom models are presented and discussed. The computation speed of implemented algorithms is benchmarked and compared.

Improved three-dimensional image of the tomographic inversion of the Arraiolos aftershock sequence.

<p><span>This work puts in light the several steps followed to obtain a 3D velocity model in Arraiolos, a region located in central Portugal. After the earthquake of January 2018 occurred, a set of stations were deployed around the main shock area and has recorded the aftershock sequence during a period of six months. </span></p><p><span>The first stage of this study used a set of data recorded along the 1</span><span><sup>st</sup></span><span> month by 21 temporary seismological stations. 317 aftershocks were used to invert a 3D P and S<span>  </span>velocity model, using LOTOS program, and showing an agglomeration of events in one local point leading to a poor resolution. Therefore, we added more stations and data to the second stage of study by integrating 437 aftershocks recorded during a period of 6 months by a set of 34 stations. The tomographic inversion of this extended aftershock sequence has shown a significant improvement of the 3D velocity model resolution and suggesting an alignment of the seismic events cluster. However, the imaged crustal volume was still too small and possessing low resolution on the edges of the area. To fix this issue, additional data and seismological stations were integrated to the study in order to increase the area of interest and cover it entirely in terms of ray density. </span></p><p><span>The step which we are currently conducting concerns the location of new events followed by their integration to the tomographic study using IPMA and DOCTAR station network records. Since the later phases PmP and SmS has the potential to increase the ray coverage as similarly as the resolution of an area, we will hopefully obtain, after their integration, significant improvements in terms of accuracy and reliability of the crustal image. The main purpose of this new stage of study is to finally provide significant interpretations and figure out precisely the tectonic processes having generated the Arraiolos seismicity. </span></p><p><span>Thanks are due to FCT for the financial support to the ICT project (UID/GEO/04683/2013) with the reference POCI-01- 0145-FEDER-007690, to the IDL project (UIDB/50019/2020 – IDL).</span></p>

Determination of a stress-dependent rock-physics model using anisotropic time-lapse tomographic inversion

In the petroleum industry, time-lapse (4D) studies are commonly used for reservoir monitoring, but they are also useful to perform risk assessment for potential overburden deformations (e.g., well shearing, cap-rock integrity). Although complex anisotropic velocity changes are predicted in the overburden by geomechanical studies, conventional time-lapse inversion workflows only deal with vertical velocity changes. To retrieve the geomechanically induced anisotropy, we have adopted a reflection traveltime tomography method coupled with a time-shift estimation algorithm of prestack data of the baseline and monitor simultaneously. For the 2D approach, we parameterize the anisotropy using five coefficients, enough to cover any type of anisotropy. Before applying the workflow to a real data set, we first study a synthetic data set based on the real data set and include velocity variations between baseline and monitor found in the literature (vertical P-wave velocity decrease in the cap rock and isotropic P-wave velocity change in the reservoir). On the synthetics, we measure the angular ray coverage necessary to retrieve the target anisotropy and observe that the retrieved anisotropies depend on the offset range. Based on a synthetic experiment, we believe that the acquisition of the real case study is suitable for performing tomographic inversion. The anisotropic velocity changes obtained on three inlines separated by 375 m are consistent and show a strong positive anomaly in the cap rock along the 45° direction (the [Formula: see text] parameter in Thomsen notation), whereas the vertical velocity change is surprisingly almost negligible. We adopt a rock-physics explanation compatible with these observations and geologic considerations: a reactivation of water-filled subvertical cracks.

First arrival Q tomography based on an adjoint-state method

Under the assumption of invariant ray path in a weakly dissipative (high quality factor Q) subsurface medium, a tomographic inversion approach composed of two cascading applications of first arrival traveltime and Q tomography is proposed for compensating amplitude loss caused by near-surface anomalies, such as unconsolidated soils or the overburden gas cloud. To improve the computational efficiency, these two related tomography methods were adopted with an adjoint-state technique. First, arrival traveltime tomography will be performed to provide an inverted velocity model as one of the inputs for the following first arrival Q tomography. Then, the synthetic first break generated by the inverted velocity model will be used as a stable guidance of accessing the scopes of first arrival waveforms in the time domain where the potential attenuated time information is contained. The attenuated time will be estimated through a logarithmic spectral ratio linear regression corresponding to frequency-dependent propagation responses of different wave types. All these estimated attenuated times will be applied with reference signals to generate synthetic attenuated seismic data in the time domain, and their discrepancies with real data will be evaluated using similarity coefficients. The ones with larger values will be selected as optimal attenuated time inputs for the following Q tomographic inversion. Examples of both synthetic and field data reveal the feasibility and potential of this method.

Model–parameterization scaling for improving accuracy of seismic tomography in reconstructing near–surface velocity model

The problem of tomographic inversion is non–unique and requires regularization to solve it in a stable manner. It is highly non–trivial to choose between various regularization approaches or tune the regularization parameters themselves. We study the influence of one particular regularization parameter on the resolution and accuracy the tomographic inversion for the near–surface model building. We propose another regularization parameter, which allows to increase the accuracy of model building.