Muography. Группа авторов
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Название: Muography

Автор: Группа авторов

Издательство: John Wiley & Sons Limited

Жанр: Физика

Серия:

isbn: 9781119723066

isbn:

СКАЧАТЬ upper A Superscript upper T Baseline bold-italic upper C Subscript bold-italic d Superscript negative 1 Baseline left-parenthesis bold-italic d Subscript bold-italic o b s Baseline minus bold-italic upper A rho 0 right-parenthesis EndLayout"/>

      and

      (3.12)StartLayout 1st Row bold-italic upper C Subscript bold-italic rho Sub Superscript prime Subscript Baseline equals left-parenthesis bold-italic upper A Superscript upper T Baseline bold-italic upper C Subscript bold-italic d Superscript negative 1 Baseline bold-italic upper A plus bold-italic upper C Subscript bold-italic rho Superscript negative 1 Baseline right-parenthesis Superscript negative 1 Baseline EndLayout period

      This solution is not robust enough yet. It varies greatly depending on how the target volume is gridded. One strategy is to introduce a smoothing constraint on the prior covariance matrix C ρ , such as

Schematic illustration of three-dimensional representation of density distribution inside Showa-Shinzan lava dome.

      Redrawing Figure 6 of Nishiyama et al. (2017).

      where σ ρ is the allowance of deviation from the initial guess density, d(i,j) is the distance between the i‐th and j‐th prisms, and λ is the correlation length, which controls the correlation of neighboring prisms. When λ is large, the smoothing effect propagates to a longer distance and the inversion tends to be over‐determined, whereas it becomes ill‐posed when λ is small.

      (3.14)StartLayout 1st Row upper C Subscript rho Baseline left-parenthesis i comma j right-parenthesis equals sigma Subscript rho Superscript 2 Baseline exp left-parenthesis minus StartFraction StartRoot x Subscript italic i j Superscript 2 Baseline plus y Subscript italic i j Superscript 2 Baseline EndRoot Over lamda Subscript italic x y Baseline EndFraction minus StartFraction z Subscript italic i j Baseline Over lamda Subscript z Baseline EndFraction right-parenthesis EndLayout comma

      where x ij , y ij , and z ij are horizontal distances and vertical distance of i‐th and j‐th prisms, respectively. By assigning smaller values for vertical correlation length (λ z < λ xy ), stronger constraints are imposed on prisms at the same elevation, and then a layered structure is preferably reconstructed.

      Lelièvre et al. (2019) employed tetrahedral meshes instead of rectangular meshes, to reproduce significant topography without requiring large numbers of mesh cells. They demonstrate that such meshes could be produced by the free software TetGen (Si, 2015).

      Contrary to the success of 3D imaging, Rosas‐Carbajal et al. (2017) point out a non‐negligible offset between the density estimated from muography and that from gravity. In the case of La Soufrière de Guadeloupe lava dome, such offset amounts to 0.47 g/cm3. Specifically, muography tends to yield lower density compared to the apparent density estimated from gravity СКАЧАТЬ