Effects of water and melt on seismic velocities and their application to characterization of seismic reflectors


Watanabe, T.

Geophysical Research Letters 20(24): 2933

1993


GEOPHYSICAL
RESEARCH
LETTERS,
VOL.
20,
NO.
24,
PAGES
2933-2936,
DECEMBER
23,
1993
EFFECTS
OF
WATER
AND
MELT
ON
SEISMIC
VELOCITIES
AND
THEIR
APPLICATION
TO
CHARACTERIZATION
OF
SEISMIC
REFLECTORS
Tohru
Watanabe
Department
of
Environmental
Geology,
Geological
Survey
of
Japan
Abstract.
The
effects
of
a
silicate
melt
and
water
on
seismic
velocities
are
compared
at
relatively
small
fluid
fraction
(less
than
20
vol.%)
on
the
basis
of
a
theoretical
model
of
composite
materials,
to
show
that
the
two
fluids
are
clearly
characterized
by
the
velocity
ratio
Vp/Vs.
For
a
silicate
melt,
Vp/Vs
increases
with
increasing
fluid
fraction.
When
a
significant
reflection
is
expected,
Vp/Vs
becomes
much
larger
than
2.
For
water,
Vp/Vs
decreases
as
the
fluid
fraction
increases
to
10
vol.%
then
it
increases.
But
it
remains
similar
to
a
solid
state
value
(about
1.8),
unless
the
amount
of
water
exceeds
15
vol.%.
This
will
be
a
good
measure
to
distinguish
between
two
candidates
for
seismic
reflectors:
partially
molten
rocks
and
rocks
containing
free
water.
If
a
reflector
can
be
treated
as
a
thin
low
velocity
layer,
the
velocity
ratio
in
it
can
be
estimated
from
the
frequency
dependence
of
reflection
coefficient.
Introduction
At
many
localities
seismic
reflectors
have
been
observed
at
mid-crustal
depths.
Their
reflectivity
is
ascribed
in
various
geological
hypotheses
to
finely
laminated
structures,
to
strongly
anisotropic
petrofabrics,
or
to
trapped
fluids.
Silicate
melt
and
free
water
from
dehydration
reactions
are
candidates
for
trapped
fluids.
However,
the
very
cause
of
the
reflections
has
not
been
clarified,
except
where
the
reflection
can
be
traced
directly
to
outcrop.
How
can
we
identify
the
cause
of
reflection
?
Separate
geoelectrical
observation
will
be
useful
in
determining
whether
a
reflection
is
caused
by
trapped
fluids
or
not
[e.g.
Jones,
1987].
Even
a
small
amount
of
fluid
can
significantly
increase
the
electrical
conductivity
of
rocks,
since
it
forms
an
interconnected
path
in
general.
A
strong
reflection
which
requires
a
body
with
very
low
rigidity
can
be
ascribed
to
a
magma
body
[e.g.
Sanford
et
al.,
1973],
i.e.
molten
rock
or
partially
molten
rock
with
more
than
20-30
vol.%
of
melt.
A
rock
containing
free
water
will
not
lose
its
rigidity
as
only
a
small
amount
of
water
is
expected
at
mid-crustal
depths.
Our
consideration
is
confined
to
reflections
caused
by
a
relatively
small
amount
of
fluid
(less
than
20
vol.%).
The
problem
is
how
we
can
distinguish
between
two
trapped
fluids:
silicate
melt
and
water.
The
large
difference
between
bulk
moduli
of
the
two
fluids
is
a
clue.
Because
of
this
difference,
the
two
fluids
will
have
much
different
influence
on
the
compressional
velocity.
On
the
contrary,
they
will
have
similar
influence
on
the
shear
velocity
for
their
zero
rigidities.
It
has
been
pointed
out
that
the
compressional
wave
velocity
is
a
measure
to
infer
a
trapped
Copyright
1993
by
the
American
Geophysical
Union.
Paper
number
93GL03170
0094-8534/93/93GL-03170$03.00
fluid.
Nur
and
Simmons
(1969)
measured
both
compressional
and
shear
velocities
of
a
cracked
rock
varying
water
saturation,
and
found
that
the
compressional
velocity
greatly
increases
with
water
saturation
while
the
shear
velocity
shows
little
change.
O'Connell
and
Budiansky
(1974)
derived
formulae
to
calculate
elastic
properties
of
cracked
solids,
and
showed
that
the
compressional
velocity
is
more
sensitive
to
water
saturation
than
the
shear
velocity.
This
sensitivity
of
the
compressional
velocity
to
water
saturation
is
attributed
to
the
large
difference
between
bulk
moduli
of
air
and
water.
In
the
area
of
petroleum
exploration,
it
has
been
proposed
that
the
compressional
velocity
can
be
used
to
estimate
the
water
saturation
of
gas
reservoirs
[Domenico,
1974]
or
to
distinguish
between
oil
and
gas
reservoirs
[Meissner
and
Hegazy,
1981].
In
this
paper,
we
will
show
that
a
silicate
melt
and
water
have
much
different
influence
on
the
compressional
velocity
and
that
the
two
fluids
are
clearly
characterized
by
the
velocity
ratio Vp/Vs.
This
ratio
will
be
a
good
measure
to
distinguish
between
two
candidates
for
seismic
reflectors:
partially
molten
rocks
and
rocks
containing
free
water.
We
will
propose
an
estimation
method
of
Vp/Vs
in
a
thin
low
velocity
layer
from
seismological
observation.
Effects
of
Melt
and
Water
on
Seismic
Velocities
Granitic
rocks
are
a
main
constituent
of
the
crust.
A
partially
molten
rock
is
assumed
to
consist
of
a
solid
granite
matrix
and
an
interstitial
rhyolite
melt.
A
rock
containing
free
water
is
also
assumed
to
consist
of
a
granite.
We
will
consider
the
effects
of
a
rhyolite
melt
and
water
on
seismic
velocities
of
a
granite.
Velocities
can
be
calculated
from
physical
properties
of
solid
and
fluid
phases
and
fluid
phase
shapes.
Many
formulae
have
been
proposed
to
calculate
seismic
properties
of
rocks
containing
fluid
in
various
shapes.
Jurewicz
and
Watson
(1985)
experimentally
showed
that
in
equilibrium
state
the
melt
in
a
partially
molten
granite
takes
a
triangular
tube
shape
at
edges
and
corners
of
solid
grains.
Watson
and
Brenan
(1987)
showed
that
H2O
in
equilibrium
state
also
takes
a
similar
shape
at
edges
and
corners
around
quartz
grains,
which
are
a
major
constituent
of
granitic
rocks.
Such
a
distribution
of
fluids
is
modeled
by
randomly-oriented
triangular
tubes
in
rocks.
Mavko
(1980)
formulated
seismic
properties
of
such
materials.
Later,
Schmeling
(1985)
pointed
out
that
the
self-
consistency
is
imperfect
in
the
formula
of
Mavko
and
modified
it.
If
the
fluid
volume
fraction
is
less
than
5%,
the
discrepancy
between
the
original
and
modified
formulae
is
negligible.
However,
if
the
fluid
fraction
is
10%
or
higher,
the
original
formula
seriously
underestimate
the
effect
of
the
fluid.
We
adopted
the
modified
formula.
The
fluid
in
different
shapes
(e.g.
crack
shape)
cannot
be
completely
excluded.
However,
it
disappears
rapidly
in
geological
period
of
time,
since
it
is
not
in
equilibrium
with
solid
grains.
2933
granite(a)
45.6
30.4
rhyolite
melt(b)
14
water(c)
1.7
2.63
625
0.42
0
2.2
1000
0.0
0
0.8
600
0.5
Vp
melt
water
melt
water
2934
Watanabe:
Characterization
of
Seismic
Reflectors
Table
1
Physical
properties
of
rocks
and
fluids
Material
Ks(GPa)
G(GPa)
p(g/cm
3
)
T
(°C)
P(GPa)
(a)Fielitz
(1971),
(b)
Murase
and
McBirney
(1973),
(c)
Burhnam
et
al.
(1969)
Elastic
moduli
and
densities
used
in
our
calculation
are
summarized
in
Table
1.
The
large
difference
between
bulk
moduli
of
a
melt
and
water
should
be
noted.
The
bulk
modulus
and
the
density
of
free
water
were
estimated
from
thermodynamical
data
[Burhnam,
1969].
In
this
estimation,
we
assumed
that
a
reflector
is
sited
at
15
km
depth
and
that
P=0.5
GPa
and
T=
600°C,
which
is
petrologically
estimated
beneath
the
Japan
islands
[Kushiro,
1986].
Although
the
temperature
of
a
partially
molten
rock
is
higher
than
600°C,
the
temperature
effect
is
neglected.
The
velocity
in
it
is
mainly
controlled
by
the
melt
volume
fraction,
so
that
the
temperature
will
not
change
the
following
arguments.
The
bulk
modulus
of
a
rhyolite
melt
is
assumed
to
be
the
same
as
that
of
an
andesite
melt,
since
the
bulk
modulus
of
silicate
melts
has
weak
dependence
on
their
composition
[Murase
and
McBirney,
1973].
The
effect
of
pressure
on
properties
of
a
melt
is
also
neglected.
The
difference
between
properties
of
basalt
melts
at
atmospheric
pressure
by
Murase
and
McBirney
(1973)
and
that
at
high
pressures
by
Fujii
and
Kushiro
(1977)
is
minor
at
least
at
the
crustal
condition.
The
compressional
and
shear
wave
velocities
as
a
function
of
fluid
volume
fraction
are
shown
in
Figure
1.
The
shear
velocity
is
similarly
reduced
by
a
rhyolite
melt
and
water.
Because
of
zero
rigidity,
the
effective
rigidities
are
equally
reduced.
A
little
difference
in
velocities
is
due
to
the
difference
in
the
fluid
density.
A
rock
containing
free
water
is
less
dense
at
the
same
fluid
fraction,
so
that
it
shows
the
higher
shear
velocity.
The
vanishing
of
the
shear
velocity
can
be
interpreted
as
a
loss
of
coherence
of
the
material
that
is
caused
by
intersecting
tubes.
Although
the
increasing
fluid
fraction
will
indeed
has
such
an
effect,
it
is
uncertain
how
accurately
the
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0.00
0.05
0.10
0.15
0.20
Fluid
Fraction
Fig.1
The
compressional
and
shear
wave
velocities
in
rocks
containing
fluids
as
a
function
of
the
fluid
volume
fraction.
cm
2.2
2.0
1.8
1.6
0.00
0.05
0.10
0.15
Fluid
Fraction
Fig.2
The
velocity
ratio
Vp/Vs
as
a
function
of
the
fluid
volume
fraction.
self-consistent
approximation
takes
into
account
the
interaction
between
tubes.
To
avoid
uncertainty
near
the
fluid
fraction
of
20
vol.%,
the
fluid
fraction
is
limited
to
15
vol.%
in
the
following.
The
compressional
velocity
is
more
reduced
by
free
water
than
by
a
rhyolite
melt.
It
is
mainly
due
to
the
difference
between
bulk
moduli
of
two
fluids.
The
two
fluids
cannot
be
identified
only
from
the
shear
velocity,
since
the
both
have
similar
influence
on
the
shear
velocity.
Although
the
two
have
much
different
influence
on
the
compressional
velocity,
we
cannot
identify
the
fluids
only
from
the
compressional
velocity.
The
fluid
fraction
remains
an
undetermined
parameter.
O'Connell
and
Budiansky
(1974)
pointed
out
that
the
influence
of
a
fluid
on
velocities
is
well
characterized
by
the
velocity
ratio
Vp/Vs,
which
correlates
with
Poisson's
ratio.
Figure
2
shows
the
velocity
ratio
Vp/Vs
as
a
function
of
fluid
fraction.
The
two
fluids
can
be
clearly
discriminated
in
this
plot.
Vp/Vs
increases
with
increasing
fluid
fraction
for
a
rhyolite
melt.
When
a
significant
reflection
is
expected,
a
rhyolite
melt
is
characterized
by
Vp/Vs
much
larger
than
2.
On
the
other
hand,
for
water,
Vp/Vs
decreases
as
the
fluid
fraction
increases
to
10
vol.%,
then
it
increases.
Since
more
than
15
vol.%
of
free
water
is
hardly
expected
at
mid-crustal
depths,
the
water
is
characterized
by
Vp/Vs
similar
to
a
solid
state
value
(about
1.8).
The
point
is
the
large
difference
between
bulk
moduli
between
a
rhyolite
melt
and
water.
The
above
argument
can
be
applied
to
different
solid
matrices
and
different
composition
silicate
melts.
Therefore,
we
propose
Vp/Vs
as
a
good
measure
to
distinguish
between
partially
molten
rocks
and
rocks
containing
water.
Estimation
of
Vp/Vs
in
Reflectors
If
the
compressional
and
shear
wave
velocities
in
a
reflector
are
determined
by
seismic
tomography,
Vp/Vs
can
be
estimated
to
identify
the
nature
of
the
reflector.
However,
the
spatial
resolution
is
not
sufficient
to
determine
the
velocity
in
a
thin
low
velocity
body.
Here,
we
will
propose
an
estimation
method
of
Vp/Vs
in
such
a
thin
body
from
the
frequency
dependence
of
the
reflection
coefficient.
For
simplicity,
we
assume
that
the
seismic
reflection
is
caused
by
a
horizontal
low
velocity
layer.
The
thickness
and
the
velocity
of
this
layer
are
denoted
by
H
and
V,
respectively.
2.6
2.4
Ve
lo
c
ity
(
km
/s
)
Re
flec
t
io
n
Coe
ffic
ie
n
t
1.0
0.8
0.6
0.4
0.2
0.0
Watanabe:
Characterization
of
Seismic
Reflectors
2935
_
Vs=3.40
(km/s),
p=2.63
(g/cc)
H
=
100
m
Vs=1.80
(km/s),
p=2.57
(g/cc)
,
Vs=3A0
(km/s),
p=2.63
(g/cc)
0
10
20
30
40
Frequency
(Hz)
Fig.3
The
frequency
dependence
of
the
reflection
coefficient
for
a
normal
incidence.
The
assumed
layered
structure
is
shown
in
the
inserted
diagram.
The
thickness
of
the
low
velocity
layer
is
100
m.
The
velocity
in
upper
and
lower
layers
is
assumed
to
be
identical.
The
reflection
coefficient
for
normal
incidence
takes
a
maximum
value,
when
H=(X/4)(2n-1)
is
valid
[Fuchs,
1969].
X
is
a
wavelength.
n
is
a
natural
number.
Therefore,
the
reflection
coefficient
as
a
function
of
frequency
takes
a
maximum
value
at
intervals
of
V/2H
(Figure
3).
This
model
should
be
applied
to
an
observation
after
the
similarity
of
the
frequency
dependence
of
reflection
coefficient
is
confirmed.
Ake
and
Sanford
(1988)
applied
this
model
to
the
reflector
beneath
the
Rio
Grande
rift
to
roughly
estimate
its
thickness
assuming
the
compressional
wave
velocity
in
it.
If
the
frequency
dependence
of
the
reflection
coefficient
is
obtained
for
both
P
and
S
waves,
we
will
obtain
Vp/2H
and
Vs/2H,
from
which
Vp/Vs
can
be
estimated.
We
can
identify
the
cause
of
the
reflection
from
this
Vp/Vs
value.
For
example,
we
will
compare
the
frequency
dependence
of
the
reflection
coefficient
of
two
low
velocity
layers:
a
layer
of
a
partially
molten
granite
and
a
layer
of
a
granite
containing
free
water.
We
assume
that
the
thickness
is
100
m
and
that
the
fluid
fraction
is
15%.
For
the
partially
molten
layer,
Vp
and
Vs
are
calculated
to
be
4.52
and
1.80
km/s,
respectively.
The
frequency
intervals
of
maximum
reflection
coefficient
for
P
and
S
waves
are
22.6
and
9.0
Hz.
For
the
layer
containing
free
water,
Vp
and
Vs
are
calculated
to
be
3.40
and
1.87
km/s.
The
frequency
intervals
are
17.0
and
9.4
Hz.
If
such
a
difference
in
frequency
intervals
is
resolved,
the
cause
of
reflection
can
be
identified.
Domenico
(1974)
and
Meissner
and
Hegazy
(19
8
1)
proposed
that
the
reflection
coefficient
itself
can
be
used
to
characterize
petroleum
reservoirs
considering
semi-infinite
reservoirs.
However,
for
a
thin
body,
the
effect
of
the
finite
thickness
cannot
be
neglected.
We
believe
that
the
frequency
dependence
of
reflection
coefficient
should
be
used
for
identifying
the
cause
of
reflection.
Conclusions
We
compared
effects
of
a
silicate
melt
and
water
on
seismic
velocities
at
relatively
small
fluid
fraction
(less
than
20
vol.%)
on
the
basis
of
a
theoretical
model
of
composite
materials.
While
the
two
fluids
have
almost
the
same
influence
on
the
shear
velocity,
they
reduce
the
compressional
velocity
in
different
manners.
Water
more
steeply
reduces
the
compressional
velocity
than
a
melt
owing
to
its
lower
bulk
modulus.
The
two
fluids
are
clearly
characterized
by
the
velocity
ratio
Vp/Vs.
For
a
silicate
melt,
Vp/Vs
increases
with
increasing
fluid
fraction.
When
a
significant
reflection
is
expected,
Vp/Vs
becomes
much
larger
than
2.
For
water,
Vp/Vs
decreases
as
the
fluid
fraction
increases
to
10
vol.%
then
it
increases.
But
it
remains
similar
to
a
solid
state
value
(about
1.8),
unless
the
amount
of
free
water
exceeds
15
vol.%.
This
will
be
a
good
measure
to
distinguish
between
two
candidates
for
seismic
reflectors:
partially
molten
rocks
and
rocks
containing
water.
If
a
reflector
can
be
treated
as
a
thin
low
velocity
layer,
the
velocity
ratio
in
it
can
be
estimated
from
the
frequency
dependence
of
reflection
coefficient.
Acknowledgments.
I
would
like
to
thank
Y.
Kobayashi,
K.
Kurita,
K.
Fujimoto,
T.
Iidaka,
S.
Kaneshima,
and
T.
Ohminato
for
their
comments
and
suggestions.
I
also
acknowledge
two
anonymous
referees
for
careful
readings
and
helpful
comments.
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