h
TSG = TSA + TAB + TBG = 2TSA + TAB
(
x − 2h tan ic )
h
=2
+
v1 cosic
v2
x 2h cosic
= +
v2
v1
= delay time
Delay time ti
t
1
----v1
1
----v2
2
2
2h v2 – v1
x +-------------------t = --v2
v1 v 2
ti
x
xcross
x
t = ----- + ti
v2
x
h=
h
v1
v2
v1v2
2 v22 − v12
ti
t AG = x / V2 + δt g + δt a
t BG = ( L − x) / V2 + δt g + δtb
t AB = L / V2 + δt a + δtb
Hagendoorn’s T- term
T − = t AG − t BG
= (2 x − L) / V2 + δt a − δtb
Hagendoorn’s T+ term
T + = t AG + t BG − t AB =
2δt g = 2 z g cos(Θ c ) / V1
z g = T +V1 / 2 cos(Θ c ) =
T +V1V2 / 2 V22 − V12
(a) Composite travel time-distance
(b) Hagedoorns T- graph and (c) calculated
Depths to a refractor