FIG. 5 CORE DENSITY, VP RELATIONSHIP
2. 9
2. 8
2. 7
2. 6
2. 5
2. 4
2. 3
2. 2
2.0 2. 5 3.0 3. 5 4.0
C
or
e
d
e
ns
i
ty,
g
/c
c
Vp, km/sec
Basalt, basite
Andesite, mesite
Diorite-porphyrite, mesite
Granite-porphyry, acid rock
FIG. 4
0 20 40 60 80 100
VP/VS, Φ RELATIONSHIP
Castagna
Domenico
Gregory
Hamilton
Johnston
Tosaya
Trend line
8
6
4
2
0
V
p/
Vs r
ati
o
Φ,
had Vp ratios of 1.09. Water saturation
had a minor influence on Vs in the rock
samples. Vs ratios before and after water saturation were 1.05 (Table 1).
Velocity-fluid relationship
Vp is sensitive to gas content in igneous rock and Vp values for dry samples (gas-saturated) are lower than
those of water-saturated samples
(Fig. 3). A small amount of gas can
lead to a significant decrease in Vp
values. Vs is not sensitive to gas and
Vs values from rock samples before
and after water saturation underwent
little change. Vs increases slightly
with higher gas saturation. During
the experiment, some rock samples
displayed higher Vs when saturated
with water than in the dry sample,
an effect of the relatively low experimental pressure. 25
The transmission mechanism
through the media and gas and water’s physical properties result in
the difference between Vp and Vs.
The transversal wave transmits as a
sine wave that causes no change to
medium or pore volume. In addition, water is not resistant to shearing and, according to the theoretical
formula for elastic wave velocity, the
transversal wave is not affected by
water saturation and its velocity is
always close to its wave velocity in
dry rocks. The longitudinal wave,
which transmits as a compression
wave, changes the shape and volume
of medium pores and is affected by pore water saturation.
When pores are saturated with water, the longitudinal
wave can be transmitted in a coupling manner through
water and rock particles, shortening the transmission
path and making the wave velocity much higher than that
in dry rock samples (see Equation box).
Velocity-porosity relationship
Elastic wave transmission velocity in pore fluids is much
lower than in rock. The elastic wave velocity decreases as
porosity increases both in dry and water-saturated samples.
Water shear modulus (μ) is zero and rock-sample density
increases with higher porosity because the rock is saturated
with water. Vs decreases according to the theoretical formula
for elastic wave velocity.
The bulk modulus (K) of rock samples increases slightly
EQUATIONS
()
()
,/
V
Nomenclature
K Bulk modulus nondimensional
Shear modulus, nondimensional
density g cc
1
2
p
S
3
4
t
ln
n
t
=+
=
=
=
=
t
n
