Muography. Группа авторов

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Muography - Группа авторов


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assume there is no contamination of low momentums due to deflection in the mountain, and no cross talk between the adjacent angular bins in all detectors for simplicity. The elements can be written as:

      (2.7)bold upper C Subscript ModifyingAbove normal d With right-arrow Baseline equals diag StartSet normal sigma Subscript italic d comma 1 Superscript 2 Baseline comma normal sigma Subscript italic d comma 2 Superscript 2 Baseline comma midline-horizontal-ellipsis EndSet

      where normal sigma Subscript italic d comma i Superscript 2 is the accidental error of di.

      (2.9)upper N Superscript i Baseline almost-equals g Superscript i Baseline left-parenthesis upper X 0 Superscript i Baseline right-parenthesis plus delta upper X Superscript i Baseline StartFraction italic d g Superscript i Baseline Over italic d upper X Superscript i Baseline EndFraction left-parenthesis upper X 0 Superscript i Baseline right-parenthesis period

      Given that N i can be written as upper N Superscript i Baseline almost-equals upper N 0 Superscript i Baseline plus delta upper N Superscript iand upper N 0 Superscript i Baseline equals g Superscript i Baseline left-parenthesis upper X Subscript o Superscript i Baseline right-parenthesis, δ N i becomes:

      Introducing a small variation from the initial density value rho Superscript j Baseline equals rho 0 Superscript j Baseline plus italic delta rho Superscript j, δN i and δX i can be given as:

      (2.14)upper A Subscript upper N Superscript italic i j Baseline equals upper A Subscript upper X Superscript italic i j Baseline StartFraction italic d g Superscript i Baseline Over italic d upper X Superscript i Baseline EndFraction left-parenthesis upper X 0 Superscript i Baseline right-parenthesis period


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