ytht100
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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/
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!
http://postimg.org/image/6r0ogcx3f/
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!