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I Gradient of travel time in layered media?

  1. Mar 7, 2016 #1
    I have a problem of the following picture. x_0, y_0, z_0, V_0, and V_1 are fixed.

    http://postimg.org/image/6r0ogcx3f/

    gradient.jpg


    The travel time is obviously [tex]t = \frac{1}{{{V_1}}}{[{({x_1} - {x_c})^2} + D_1^2]^{1/2}} + \frac{1}{{{V_0}}}{[{({x_c} - {x_0})^2} + D_0^2]^{1/2}}[/tex]

    According to a high-profile publication, the derivative of traveltime with regard to x1 is [tex]\frac{{\partial t}}{{\partial {x_1}}} = \frac{1}{{{V_1}}}\frac{{({x_1} - {x_c})}}{{\sqrt {{{({x_1} - {x_c})}^2} + D_1^2} }}[/tex]. Here, it seems to ignore dx_c/dx_1, is it correct?

    I guess it is wrong.

    Thanks a lot!
     
  2. jcsd
  3. Mar 9, 2016 #2
    Please, someone give me a hint.
     
  4. Mar 10, 2016 #3
    What is that publication? Can you give a reference to the article?
     
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