Moveout correction: reminder
In reflection seismology, the incidence
angle is close to vertical. This results in
a week reflectivity and small
signal-to-noise ratio.
To overcome this problem we perform
moveout corrections followed by trace
stacking. This results in a zerro-offset
stack.
◦ Common mid-point gathers (in this
case also a common depth gathers):
◦ Identification of coherent arrivals
◦ Moveout correction and stack
◦ Plot the stacked traces at the
mid-point position to get the zero offset
stack.
REFLECTION PROCESSING:
Actually, additional steps are involved
in the processing of reflection data. The
main steps are:
◦ Editing and muting
◦ Gain recovery
◦ Static correction
◦ Deconvolution of source
The order in which these steps are
applied is variable.
Editing and Muting:
◦ Remove dead traces
◦ Remove noisy traces
◦ Cut out pre-arrival noise and
ground-roll
Gain Recovery “Turn up the volume”
to account for seismic attenuation.
◦ Accounting for geometric spreading
by multiplying the amplitude with
the reciprocal of the geometric
spreading factor.
◦ Accounting for anelastic attenuation
by multiplying the trace with expαt ,
where α is the attenuation constant.
Static (or Datum) Correction:
Time-shifting of traces in order to
correct for surface topography and
weathered layer.
source
Es
Er
receiver
V
datum
Ed
Correction is:
Es + Er − 2Ed
∆t =
,
V
where:
Es is the source elevation
Er is the receiver elevation
Ed is the datum elevation
V is the velocity above the datum
Example of seismic profile before (top)
and after (bottom) static correction:
Deconvolution of the source: The
seismogram is the result of a
convolution between the input source
wavelet and the the subsurface
reflectivity series:
A few examples:
Mathematically, this is written as:
Seismogram = Wavelet ⊗ Ref lectivity,
where the operator ⊗ denotes
convolution.
In order to remove the source effect, we
apply deconvolution:
Ref lectivity = Seismogram ⊗− Wavelet,
where the operator ⊗− denotes
deconvolution.
Seismic profiles before (top) and after
(bottom) deconvolution.
Following deconvolution the wavelet
becomes spike-like.
Refraction: various cases
The case of two horizontal layers
The travel time of the refracted wave is:
X − 2h0 tan ic
2h0
+
=
t=
V0 cos ic
V1
p
2h0 V12 − V02 X
+
V0 V1
V1
So this is an equation of a straight line
with a slope of 1/V1 , and the intercept
is a function of the layer thickness and
the velocities above and below the
interface.
The critical distance is:
Xcrit = 2h0 tan ic
The crossover distance is:
p
Xco 2h0 V12 − V02
Xco
=
+
⇒
V0
V1
V1 V0
√
V1 + V0
Xco = 2h0 √
V1 − V0
An inclined layer
For the down-dip direction we get:
s
2zd
x
V02
td =
sin(ic + α)
1− 2 +
V0
V1
V0
The apparent head velocity in the
down-dip direction is thus,
V0
Vd =
sin(ic + α)
Similarly, for the up-dip direction:
s
V02
2zu
x
1− 2 +
tu =
sin(ic − α)
V0
V1
V0
The apparent head velocity in the
down-dip direction is thus,
V0
Vu =
sin(ic − α)
V1 , Vu and Vd are read directly from the
diagram. What is left to solve are V2
and α.
We can use the previous results to
write:
1
−1 V0
−1 V0
+ sin
]
ic = [sin
2
Vd
Vu
and
1
−1 V0
−1 V0
α = [sin
− sin
]
2
Vd
Vu
Low velocity layer