Report on Near Surface Geophysical investigation at Ty-Cerrig Farm, North Wales
BY
AYENI, Gboyega O.
March, 2006
ear all,
Myself, Nick, Rachel and Adrian have compiled a 3 layer model for the welsh
refraction report which is needed to go on to do GRM, please find it attached.
The 3 layer models for each section were calculated using rogers 3 layer
dipping model program and then compiled. The uncertainties were calculated
using the uncertainties given by LINEST (in excel) which were then re-run
through rogers program to give max and min situations.
The model I have picked has had some values altered to a new value inbetween the
max and min limits. This is to make it more continuous in time so that there
are no jumps in the data that would effect the GRM calculation (N.b. the
velocity for the 3rd layer will have to be considered also before using the
model as it varies alot). The uncertainties for all values are also within the
spreadsheet.
This method involved the computation of offset time and travel time of one offset
shot point to the other (see appendix …..). These travel time information was
used to compute the velocity analysis function tv for different XY values (XY is
geophone separation).
tv 
(t AY  t AB  t BX )
………………………………………………………… (8)
2
Where tv is the velocity analysis function,
tAY is travel time from shot point A to Geophone Y,
tBX is travel time from shot point B to Geophone X and
tAb is travel time from shot point A to shot point B.
The velocity analysis (tv) function was plotted against the midpoint of the different
geophone spacing (XY 2) and the inverse of the slopes yields the apparent
refractor velocities. The apparent refractor velocities (Vn) and different XY values
are used to compute the generalized time-depth function which is plotted against
the midpoint of the different geophone spacing.
tg 

1
XY 
 …………………………………………….. (9)
t AY  t BX   t AB 
2
v n 

Where tg is the generalized time-depth function,
XY is the geophone separation
tAY is travel time from shot point A to Geophone Y,
tBX is travel time from shot point B to Geophone X and
Vn is the apparent refractor velocity
The velocity analysis plot closest to a straight line and the generalized time depth
plot that shows the most detail of the refractor topography is indicative of the
optimum geophone separation.
Next, the average velocity was computed using the formula
Vn2 XY
……………………………………………………. (10)
V=
XY  2t gVn
Where V is the average velocity and
Vn, XY and tg have same meaning as in equation 9 above.
Afterwards, information of the generalized time-depth function, apparent refractor
velocity, and average velocity was used to compute depth to the refractor.
h
t gVn V
Vn2  V 2
……………………………………………………….. (11)
Where h is the perpendicular distance from the refractor to the midpoint between
the geophones.
The depth obtained from the step above is not the true depth vertically below the
midpoint of the geophones and as such it needed to be migrated to its true
location. This was achieved by the trigonometric equation below.
Z  h cos 90 ………………………………………………………… (12)
Where Z is the true vertical depth from the geophone midpoint and
H is the same meaning in equation 11 above.