Page 139 - Introduction to Petroleum Engineering

126 RESERVOIR GEOPHYSICS

Answer
A. P‐wave acoustic impedance for upper layer

kg km kg km
Z = (ρ V ) = 2800 m 3 ×30 s = 8400 m 3 s
.
P
U
U
and P‐wave acoustic impedance for lower layer
kg km kg km
Z = (ρ V ) = 2600 ×28 = 7280
.
L
P L
m 3 s m 3 s
b. Reflection coefficient
Z − Z 7280 −8400
RC = L U = = 0 0714− .
Z L + Z U 7280 +8400

7.3 SEISMIC RESOLuTION

Seismic wave reflecting surfaces are due to changes in acoustic impedance between
two adjacent media. Seismic resolution is the ability to distinguish between two
reflecting surfaces that are close together. The quality of seismic resolution depends
on the orientation of the reflecting surfaces and interference effects, as we discuss in
this section.

7.3.1 Vertical Resolution

Vertical resolution tells us how close two horizontal reflecting surfaces can be and still
be separable. The two reflecting surfaces are the top and bottom of a thin layer. Maximum
vertical resolution is expressed in terms of the dominant wavelength of a seismic wavelet
λ , which is the ratio of wavelet velocity v to the dominant frequency f :
d i d
v
λ = i = vT (7.12)
d
id
f d
The dominant period T is the inverse of dominant frequency f . As an illustration,
d
d
suppose the wavelet velocity is 10 000 ft/s and the dominant period is 40 ms or 0.040 s,
then the dominant frequency f is 25 Hz and the dominant wavelength is 400 ft.
d
Maximum vertical resolution δz is one fourth of the dominant wavelength λ :
V d
λ v
δ z = d = i (7.13)
V
4 f 4 d
The maximum vertical resolution in the illustration earlier is approximately 100 ft.
If the separation between two reflecting surfaces is less than the maximum vertical
resolution, it is difficult or impossible to distinguish each of the reflecting surfaces.