BFIT

Vertical times correct for the source horizontal offset. If the vertical distance between the source and the geophone is $Z$, if the horizontal offset of the source from the bore hole is $H$, and if the straight line slant distance from source to geophone is $S$, then the cosine of the angle, $\theta$, between the vertical and the slant is $cos(\theta)=\frac{Z}{S}$. The slant time is $T_s=\frac{S}{V_i}$ where $V_i$ is the interval velocity. Typically we don't measure $S$, but do measure $H$. So the angle, $\theta=\arctan(\frac{H}{Z})$. The vertical time is then:

$\displaystyle T_v = T_s \cdot cos(\theta) ~~=\frac{Z}{V_i} = \frac{S}{V_i} \cdot cos(\theta),$ (3)

where $T_s$ is the observed arrival time. Except in large horizontal offsets, the correction is modest. This program computes a straight line fit to vertical times, $T_v$. A similar program in OCTAVE is VFITW 8.2.3. The command line arguments are:
 bfit  infile   emin   emax  labl   
 
     infile  = input file name (4char minimum)
 
     emin    =minimum elevation for interval
     emax    =maximum elevation for interval
     labl    =2 character ID label for interval

Example for the X5 borehole: bfit twave.seg 820. 840. X5

Figure 24: BFIT: Straight line fit yields interval velocity by least squares. Title has the value of the velocity, 479 $\pm 10$ m/s.
\includegraphics[scale=0.4]{Figurebfit.pdf}