A SIMPLE TECHNIQU= PERMEAB:LITY FROM SE:SMiC REFLECT:ON DATA BASED ON BIOT'S TEOREM
_筆
?o: zea s.GrJ/ory
′
A SI MPLE TECHNI QU=
PERMEAB: LI TY FROM SE: SMi C REFLECT: ON DATA BASED ON
BI OT' S TEOREM
St 3- b・ , Ds●
κ
87 br ●
: . S日 ■」
nd “
●l ● ●● ヽFW● N“
1
po31 t ● l B Subl y●
t●
螢
膀
G●
●摯Ⅲ
‐ ●」絆智奪
=富
L,.,rD..d,EE*d,ro,*EM@.Nd..D*tunqnds;;;
留た
蛇凛急匈
.
…“
i;;;;;-tl.,;idt;;;G;;;;p;;;ifiq,.**,**".,.
*j**::?:5I:::{,lyjr:1:Y1r-.q:
ryp,,・
筋
闘爺 め
b"∼ 0"“
・r-ner._,.,b.;;,lF;^;t-fi;';;e,
,Ⅲ
謄凛協議密猫 篭眉
=協
“
F--\.4.r-.d'rtt'
|-*
r,trtrbradr&r!rr-d
EBar t,t t ot4dpr..q.
lb-,d!l|rq,dbEdl
: ' 安撼 ) “ 」 G● ●nl
“
1) ・
●
…
"め
ふコ歯 ●
(…
・
18' ,*rd b lGifiy
r lteE…
dlrdIlrd|dr-nprcf,*;'darro
1ss;
Ⅲ峰 V●
￨―
m揃
@ , d
rr.G
6rdu4
。
●た
“
¨
Fd.'di6
、. =, ■
“
‐
●
・
静
‐ aヽ
商
呻 墨驀
手I =■ ・H=「
●●●
―
( ' ‐ ) "( 1′
●
￨
。
っ
●● ● ‐
'“
6‐
“
ⅢⅢⅢ
脚 選 菫
…
1
‐
ftr r r r+.r. i
n Fiag d
" ・ 藁-,i。
鵠￢
町 ( , 4) "F● ( 11, …
b・
“ ―
"―
――
"CO・ ―
￨●
“
"
h- 4- ●
…
( 141"- 0, ま
餞
―
“
,
rh.rle*r''fnhr,tl.d@ffi,e.
{ 獣 “・
螺 嚇
,メ
“
6 c-r' oBrt re
¨
° m"
常モ
淋
ス
'
9・
︻
■ヽ
‘
●＾
ヨ ０﹁
い
・
￨￨キ ￨
幻勧
( 1' 力 ) お ゝA■ ● 丸 〆●I ● ●●
―
"0お
●一 ""“
●‐ ぃ∞■ “●
人 0● ● , "Ⅲ 、● ●′樹
` ●
“
“ “ “ "●
,―
・
←
・
け
い
・く
デ
器レ
( 14) ● ―
6, f.i4
●
り
鮨
● ●j ヽ
4‐ ●湘 ′
‐
―
―嗜 綸
暉 口
"・
Ⅲ 町 u“ い ●
口, ・"●
…
メ‐
夕 ●
∼
― ・
ぃ
押 、
… …
“
frEcIl'J,diE!'dft
“
、
ぃ
詢コ
11ぶ 乱舞豊
窯… _1
″ ￨■ Ⅲ ` 書ギ ‐ ■
…
l t●
“
―
ヽ I n●
●
` ` ● x, ● ‐ ￨● "“ t ´ , "は 澳0“ ￨ゆ “ ■ ●●● ● ●t ● ●, ぃ
ヽ
● 閾 メ●●● ( ― ‐
―“ ″ , , ● , ぃ , ｀
1, ヽ , ● 、
ルヽ
0(Ⅲ口 壼 , “― ● ●●● 1凛 つ“・・
● "■義、 ￨"0■ 輸 ‐ ` Ⅲ
,
…
“
“
“
7, 、 oぃ
T●
,ヽ
"■
・
計,
pfr.b
lDtrh.bffi
{ebb.r*r&.bi*6
ぃ ●●
"●●●●
rq*,o
″施、
彙●4● ●薇
,
,
″・′ : =
メ" ' ' 》
` “
口
ギ￨・ ギ￨・ 詰
"〕
"1- ●
“
`
Bb,*,d!5idr:ndi*alx-6
bh..eo'*leda,q
u,ir..
●●
…
“ ""壺 “
“ "鑽
1' 01- "け 0
渕
=颯
'・
AN O "
―
…
“ …
歓
""に"“
…
―
…
●油 呵
γ。
rfl dh tus,
R‐
¨
… 9- d b…
“
“ ―・
・
…
…
コhで ●●￨… ― - 5麟
“
議χ
■ 1吾 サ
￨. ′
輛 ¨
` , 1ズ
、,
‐
・‐ r ・ 為
′ 争チ
l
=・
l・
ぃ
,
". ヽ
´
一
“
Ⅲ
…`
‐
"‐
鋼
晴
野
標
…
Ⅲ
=ヽ
・
注輩
-1
…
.〕
fdl6k{n'^trBrqB66
.fu('6deM!i.esle
r4mdfur.€n,Ejffikh
erFd.,'''i.'i'r.de@
・
ヽ
―
‐
・
‐
・
‐
・
●● ¨ ヽ¨ ●
“
―
, 3義 書● お
"¨
‐ ‐
ヽ
￨…
…
●―
● ● ●● ● ―
‐
,ry!bb?bleri!r4,
bb'-6h4rb,.fr&!
+,*E*e.**a,l4?
!b*llc.ellalrElEtE)
^6drdgEfu
w. rdrl, xrltr.nr. h G.orFr h'dra dleb
crybp6'!E&,d4hF
54"rd in, P(ya crd* le
r@.',oJthr&4
d$d&r b&LEL !.d. D €3,r,.!4[ sqia
d,LlLE.dF9b.Rl'd
´
i t盟
=警
彗・
“
=■ ==摯
‐
――=
' 営・‐ ==二
―
“
‐
A SIMPLE TECHNIQUE FOR ESTIMATION OF RESERVOIR
PERMEABILITY FROM SEISMIC REFLECTION DATA BASED ON
BIOT'S TEOR.EM
SismaDto a', D. Saotoso
b,
F.Wenzel " , S. Muoadi d,
IC Sribrotopuspito .. B. Subiyatrto.
,'Ceopbsks Diyision, Physics Deport ne , Cadjoh Mada Unversi,y, yog/aha a, tndone-ria
"Ceophlsicsl Depar.ment, Bandung Insntuk ofTechnolg, Jt. Ganesha f0. Bandun& tndoneia.
'ceophys{cal Institule, Hetusttosse 16,76187 Kotlsruhe, cermany.
ILWIGA\ Jakatta,
'PT. CPI, Runbai petanBaru Indohe\io
'CorrespoDding author. Fax: +62-27+545 185;
E-mail: sismanto@ugm.ac.id
Indonesia.
'
-
Abstract
Relatiot$hips among elastic parametefi ond rock prope ies, ahd ultimate resentor
parameErs have been ettablished in continuum ,nechonics and rock physics. Therefore, il
should be possible to estimate reseryoir Tnrmeobility lron the seisni; doo We used Biot,s
solution of\aave equation in an elastic potous mediun ond the approxiDations oJ Turgul_
Yamamoto to ollow an establishment of a lineT retationship bedr,een auenualion
coeiicient or anplitude ratio at a funclion of the iwerse of the square ofJrequency. Ihe
slope ofthisf ncrion includes the Wrmeqbility. h can be shown that th* iichiique ugrees
lo the measurement of the perneability o! a poruus mediut t /rom seisnic waviforns. We
examined this techniqrc to estin ate the resenoir perheobility by usin[ sythetic
seismogram data. The resu rhov that hos an error less than S 94, it neans that tihe study
of permeability estimalion fiom sutface seismic data is possible by usihg an accurate
calibralion step.
The procedure is tested on 3D seismic data over part of Duri field in cental
Stntatra, Indonesia. The sinplicity ofthe theoretical oppr(mch requires the ihtroductioh of
an empirical calibratiott lactor that is provided by n'ell SM\A in the area_ This lactor is
then implemented to estimarc rhe petmeability with seismic dota on the
field: it gives o
permeability nap oflhe study arca. A key result of the study is that permeability estination
with surface seistuic data are possible bul requires calibration. A confimation and
validation of this procedure vill be subject lofitture tyo*-
Kervo/ds: Seismic wqye, pemeability, Biot, Ttlrgut-yamanoto.
滞鼈] 詳域Fi 錢: 樹
l.IotroductioD
Reservoir characterizalion is one of the
advanced steps in seismic exploration 10
identiry physical prope(ies of a reservoir such
] 器彙留 ] 』艦
as thickness, porosiry, pemeability, density,
compressibility, and water saturation. These
physical propffties are used to modet the fluid
flow in a Eoducing field. Recent new
geophysical methods for example, AVO and
tomoSraphy, generally attempt to directly
bu、■ 11ふ
a
one-dimensional
(lD)
model
″ O∞ 5al ' s
me■ od t O esumat c
灘
“
of
VSP, which includes mode conversion tlu.ough
slow compresional waves as an eners/ loss
t
mecharism based on Ganley (1981). Horizonlal
and vertical seismic profiling synthetic
seismograms which include the absorption
effect
of the
日
為
( 1)
dala
Sismanto,
et a/
(2003b) developed a ,
,l
難続飾縄騨徹掘鮭
t he pemcabl H″
Bi ot ' s el ast i c mOdt l l i , ″
and″
″
4■
l tl l
1990) ■ l e Bi Ot ' s el asl c mOduLs ar c
=需
+亀
ん
＾
Ｊ
／却４、
＋
，
″
・
“
π
〓
Turgut
Yarnamoto equalion, but the relationship of the
permeability estimation to the permeability
model is still multifaceted. Funhermorc,
Sismanto et a1 (2005a) published a sirhple
technique to estimate the permeability on the
real 3D seismic data based on Turgut-
‐ α
α ‐ 125( Tur gut al l d Yamamot O,
expr csscdけ ● c Fonowhg r el at i Ons
Ｃ
oo
l s t he shear modul us,
I s■ c vi mal m・・
・ exPEsscd 6″
technique to estirnate the permeability on lhe
seismogram synthetic based
:
π , c, al d ν ar e t he
︻
工
刹
［
﹃
theorctically obtained from the seismic data.
考子
ed颯 ∝me“ v認
′ i s t he secpage di spl acement vect oち θ =
di v, , , ‐ di v′ , ′ l S ul e bl l l k densi ″ ″ ‐
p:rrarnelers, Ttis
(Munadi, 1998; Saar ard Mang4 1999). Thus,
ahe reservoir palzuneters iue believed to allect
seismic wave ctEracte.s. With this point of
view, res€rvoir parameters, such as porosity ;nd
permeability should thereforc, arc able lo be
θ ―曖 ら _ρ ノ
―″
静
子
C▽
h whl ぬ ″ 、血 ぃ
of
with the field
gsh鮮
μ▽与+σ ―
がθc▽ ら=ρ t t ρ′子
v/
attenuation ofth€ fast compressional waves as a
function
ftequency. Meanwhile, most
theoretical ard experimental res€arches prove
that there is a close rclationship among waves,
and reservoil
1臨 謝
喘為棚
断温』 ふ出詩習肥讐L珊 al t t Tl
permeability, has been coostructed by Sismanto,
V
relarionship also agrees
iよ
mar l ne scdi ment s, ar e( B101195o ′
reseNoir, especially for
et.al. (2003a'). The Sisinado's techdque is to
combine the TuguCYamamoto lurd canley
mechrnism. Twgut and Yarnamoto (1988;
1990) explored the possibility of Fedictins
porosity and permeability of marine sediment
by analyzing phase velocity dispersion and
elastics,
;
Tl l e al m of al i s paper i s t O examI I l e dl e
Si smm“
estimate the reservoir physical properties ftom
the seismic data" Turgut and Ya.rnamoro (t988) y
developed
￨
′ ‐ 藤
罵
r t 7丁 瓦
「l 勇ヶ
し
f.
is the bulk modulus ofthe gain, ,!. is
the bulk modulus of the fluid in the pores, and
where
,(6 is rhe bulk modulLs of the skeletal fi.amc.
According to Turgut and Yamarnoto (1990), the
bulk modulus of skeleral SaIne
(r
and the
porosiry are related to the shear modulus as
K, ‐
, and
( ￨≒
By usi ng●
( 4)
1: : ど
鰐 ] 温鳳
α l . ( 200Sal
r el anOnsl l l P of ( σ ′
r el at l ol l shI PS ar c 8i ven by
_希
42, σ
ピ
計ち' 嗣
ヽリ
４
制
mOdi ned ul e
■ 十二 ″
2‐
讐
,0
wher e″ _瑶 ′ ぽ Accor dhg o t hc spec‐
t r al l a● o m
et hOd f or est unal i ng 2 ul
l abor at oγ , ul e dei nhi On of ●
e qual i ● f ac10r
0= 2Y,a(@)
( 10)
g i s,
一３
一
′︱︱ ︱＼
〓
ρ
κ
イ
″ _ρ
Itfl 』
α
Eq( o can bet t wH"en as
"ht O a nncar f Om
wher c t he shear modul us μ t hc POi SSCn' s r at i o
σ and ul e bul k nl odul us K ar c est i ― t ed“ m
t hc ve10ci t l es oFt he P and S waves, whcr e t hei r
on t equeney, t he
Ol e Ot hcr pannl et er s have been dct emi ned
盤
器
e r el t t a“
pcnneabut t cocFf l cl ent can be es● I nat ed, r
Si smant o,
=+=) ″
■
( 8)
lラ
3. Methods
By corDbining E{s. (9) and
(l
0), ones ottains
To estimate the permeability, we need a
seismic rxaveform velocity aDd its spctral
amlysis of ihe events. The bulk modulus of
grain X" the density p and the bulk modulus of
fluid K7 have to b€ defined previously.
According 1o Turgut-Yanamoto (1990)
(ll)
.r2r, * W2Y, _ I
o'(W -1, xtw -t) ato)
'n wht h r=d& pQrn- i1)). r.tn tetatorn
ship of a(@) and the frequency in Eq. ( ) is
approximation and Ceertsma and Smit (1961)
indication for marine sediment wilh high I Eqs.
(l) and (2) can b€ obtained in the folloiving
asrmptotic foI high frequency region (o>>).
form,
(電
01∼
′イ) 1
ct A
J+-.(YlV'\
A qt 6 o'
wherc qt =ryk?@ is the imaginary part
ar|dA =
(p
p'zr) I
=Etp
fot
of
p . Whercas,
a -+o,utd
u]=;ru,rtq-zcpryp.-
w ,-r*.
fi
歯mm t t m面ωh
nel l , I t can be Found ul e l oca● On Of t he
展
υ峨鯛F"い
in
the
high fiquency rcgion and in pEctice it is
diffcult to obtain lhe asymplotic value
b€caus. the fiequency content of the s€ismic
is
less then 200 Hz. Whilq the
relationship between ll/oJl
is
^nd U/d{a)t
linear for all fiequency. However,
the linear
dala
relarioNhip ofthe datajust takes place only in
4,
′
¨
Yo?
n-
( 6)
Unfortunately, we ai€ not interested
lhe frequency content ofthe signal.
From the slope /, we can estimate the
penneability, i.e.,
k^=
' !2!e_W
t.w-p))
_tlt.
tt2)
It is obvious thal the coeflicient of attenuation
d@) can be calculated ftom the spectral ralio
melhod by
(VSP),
d is the
distance b€tween receivers in
positions I and ,. In the refl€ction measuem€nt
d is the path difference of the recorded seismic
wave at the suface.
Substituting E4.(13) into Eq.(l l), we will
・却
+9=[
(
器
→
瀞5レ
obtain
】
The curve of Eq. (14) is asymptotic for high
fiequency (@>) arxl linier between (1/aa and
(l/ amplitude ratio in logarithmic). If the slop€
isr, we can deiermine the permeability of lhe
medium, i.e.,
L P
2Y nD
______-___:__!_
d
tlpn- p',)(w -t)
E4.(ll) are similar.
is in the dala Eq. (ll)
seismic traces to calculate $e
The forms ofEq.(14) and
The main dilference
needs morc good
attenuation cooficient but using Eq. (14) we
nerd only al leasl two tsaces of seismic dara itr
CDP gather.
d. SyDthetic s€ismogr.mt
Sismanto, et al (2003a) arsociated the
efect ofabsorption and disp€.sion acco.ding to
Ganley (1981) with dispersion and attenuaiion.
The attenuation effects are calculaled from t]rs
wave number ofBiot's equation. The theoretical
seismograms
are based on
Ganley(1981)'s
method. The dispersion effect comes ftom the
reflectivity as a fimction of frequency. For the
absorytion cslculatior\
Futterrnan(1962)'s
ab6orption-dispenior equations, are.ealized.
Therefore, the synthetic seismogmms cover
rcservoi paEuneteB, ele6tic pr[ameter alld
wave pararneteG. The perneability
depends
oflhe rnodel
on those paramete6 is given by
Ge€rtsma and Smil ( 1961 ),
︲ 一２
I
″
一
笏
\At(at )
whete A" and At are the amplitude of signal at
the ,, and posilions in the ftequency domain
respectively. In vertical s€ismic meilsrrement
〓
(B)
‘κ
,t,) =h(A.@!).d..
(r6)
The relationship of th€ permeability to rhe
velocity ard fiequency for s,andslone is
illustrated in Fig. I and Fig. 2, respectiv€ly.
Those figures show that for higher fiequency
rbe velocity dep€ndency is nor so significant
relative 1o the permeability. Otherwis€, the
permeability is strongly influenc€d by the
frequency. The rclationship of dependency
among ftequency, velocity, and permeability
has been discussed theoretically by Sismanto
et al. Qoosb\.
The basic rock prop€rtid of marine
sediment are based on Tursut and Yamamoto
(l9q)). The kinematics viscosity ofpwe fluid
7 i, t .0 x I 0r m%, lhe bulk modulus of fluid
f./ is 2.3 x loe N/mr. $e bulk modulE of
grain ,f, is 3.6- x I 0'o N/m'!, rhe density of fluid
A is L0 x I d-kg/r , and $e densiry of grain
p, is 2.65 x l0' kg/m'. While, vetociry ofrhe p
wz\e Yp is obtained ftom the seismic data,
atrd the S wave velocity I/, and the density p
are estimated by empirical equations (Mavko,
et.dl, 1998). Then, the bulk modulus of the
skeletal ftame and the porosity are estimated
by E4s.(4), Biot's elasticity pmameters are
det€.mined by Eq.(3), and the velocity of rhe
zero and the high fiequency iange
are
calculated by Eq.(?).
5.
Elamples ofNumerical Result
Syn6etic seismograms of poro-elastic
waves in two layer models of seismic
reflection are shown in Fig. 3. The model uses
a yelocity y of 3000 r/s (sandstone) over
the limestone wit\ Ve, of 4000 rrs. The
Ricker wavelet &equency is 70 Hz Fig. 4 is
the firquency spectrum of tbe
s€ismoglam events of Fig. 3. The
synthetic
spectrum
shows that there is some ftequency-shift and
amplitude attenuatiorl esp€cially in (10-70)
[Iz The frequency content is affected by the
attenuation syslem of the medium. The two-
layer model uses the thickness of first layer of
1 50 m and rcceive. interval of 20 m. Then. rhe
other physical properties can be obbined such
as the shear wave velocity y,j arld y,?, qhich
are 1594 n/s and 2157 n/s, the densiry p/ and
h xe 2.19 .rc1 kg/m3 and 2.33 .tor kg/mr, the
porosity 4 and h arc 56 yo and 17 %, and the
p€rmeability tpt and b, ue 21a mD ar 209
mD, resp€ctively. Those physical propenies a.e
enforced to constsuct the synthetic seismogram
ofthe two-layer model, which is shown in Fig.
l. The permeability value ot the s)ntheric
seismograrn, which is calculated from Eq.(16),
is implemented as a ref€rence.
Some two-layer models are constructed
with the ,/rr velocity ofsatrdstone as first layet
of3000 ,IVs and th€ thickness is 150 m over the
limestone rn which the velocity is 4000 ds.
The synthetic seismograrE use
s€veml
ftequenci€s, and several velocity variations.
w1len the velocity is put to be conslanr, the
frequency
is
va ed and vice verca.
The
permeability inveNion of the two-layer model
by the linear melhod is
it
compared
ro
the
gives equivalence
fimction for several velocities and various
frequencies. Tle scale facror of calibralion is
obtained from lhose curves. The scale factoa
reference permeability;
are not wique, but arc as a fi.mction of velocity.
In this case we divide them into 4 Sroups of
scale factor in the same range value of
permeability i.e., (33s0-3800) rn/s, (2950-3150)
ntis, Q45G2950)
r/s,
and (200G2450 rlls)
iniervals as presenred in Fig. 5a and 5b. Itrere is
a linear conelalion between the permeabiliry
of
the model and the permeability fiom estimation.
The linear function of this .elation is called thc
scale factor
the lheoretical curve
of
in
Figs.
Lrd
2,
formulated by Geertsma and Smit (1961). It
means that the synthetic seismograrn keeps the
permeability information ofthe mod€l alld rhe
inversion method is able to extsact it from rhe
(sy hetic)
seismograrns.
In rhe p€meability
estimation, the avemge erors for both linear
methods are less than 5 %. The enor come
fiom d€termination of the linear area in the
curve. However, the permeability estimation
wilh surface seismic alata is basically possible
bul requires precise calibration.
6. Field
ErrDples
We us€ 3D seismic data in a small
area of Dud field, central Sumatra, IndonesiaThe main processing steps are the True
Amplitude Recovery, the Surface Consistent
Amplitude, Velocity Analysis and NMO
Correctiorl the Field and Residual sratic, lhe
Common Offset BiDring, the Bandpass
Filtering, Muting and Killing, Alignmen!
Ensemble Stack/Combine, F-X Deconvolution, ahd Plotting.
We ta](e I I inlines and 19 xlines seismic
for (l.5 x 2.65) kn'? in subsudace. In this ar€a
we have 6 wells, and only well SM#A (in the
middle) which has core analysis.
Some
information from these wells is listed in Table
I. Each data is contoured and read ar erch
CDP for calculating with the seismic data. The
top of the target layer ofthe seismic will be I,
data.
ofthe calibEtion.
The invercion method is applied to estimate
the permeability based on the known velocity
the model on lhe sydhetic seismogram, and
the results are given in Fig. 6 for consranl
fiequency and vaDing velocfty and Fig. 7 for
constanr velocity and varjing frequenc). nre
shape of curves in Figs 6 and 7 are similar to
Tabel I. The thiclness. inierval, and nns velocity ofthe well in Duri field.
i nt ewJ ve! oci "( ws)
2J 69
212,
2000
2006
2166
2057
S04#1
SM12
SM“
Sヽ イ″
Sヽ 4″
SM″
3
4
5
A
疏
1715
1761
1775
] 782
of
calibration of thc CDP position (close to well
SM#A) is on inline 187 and xline 207. Beforc
calibrating, we calculate the permeability
estimation of lhe reservoir targel and we ger
9.429 l0' mD for alpha and I.845 lO) mD for
anplitude ralio methods. On lhe other hand, the
average of permeability core samples is 1254
l0'
mD.
lf $e
estimarion permeability is
divided by the average core p€meability, it will
give an equivalence factor. This equivalence
factor is then b€in8 applied to the formula for
calculating lhe other seismic data in the study
area- The exrmple distributions of calibration
seismic dala in slpha and arnpiitude ratio
methods are presented iD Fig.lo and Fig.ll,
resp€rtively. Equivalence faclor physically
comes ftom the simplification ofthe system lhat
malhematically
is not
formulated
in
the
equation.
The equivalence factor is to compensate
the out of system parameters that arc'not
involved in lhe equation. Consequently, this
cumulative factor forms a conection system in
the numerical rcsults,
Using the s€lected isolat€d CDP
data
perfonns lhe calculations of permeability lo all
CDP in each line. The results arc ploned as a
perm€ability map such as presented in Fig- 8 for
alpha and Fig. 9 for amplitude ratio methods on
smoothed data. The permeability maps give
difference value and distdbutio& but still in the
same treod. Which on€ is closer to reality, ne€ds
a comparison map fiom other calculation as a
reference. Unfortunately, we do not have it. If
we have the reference map, we will know the
close one afld lhe erroN, at lgast we can adjust
by
determining
the
co ection
￢
it
factor
i dmも s( m)
3475
3322
3353
3444
35, 7
310,
1789
2011
ln calibratioq we use the permeability of
the core, and log data to match the position of
the core inlo seismic dara firough the synrhetic
pan
seismogram
Duri field. The
in
vd∝ i t v( wb)
statistically. The differences of the both result
methods may b€ caused by noise in the data,
equival€nce fador, and lineariry selecrion ofl}le
data- ln this cas€, the equivalence factor is a
constant that is not a firnction of velocirv and
Bequency. Anorher effecr is rhe accura$ olrhe
slope dererminalion for each merhod, r.ihich is
subjectively delermined. Therefore, il wi eiv(
some difference errors for borh methods. We
awarc the calibration step is anorher Droblem in
this study. l! needs Dore core permeabiliry in
various velocity, fiequency. and lirholo$/.
Regardless of these problems, a simple method
to estimate the p€rmeability iom seismic data
ha3 b€€n proposed, bur ir needs an empiricat
calibration factor (Sismarlo. 2004 ).
7. Cotrclusiom
The p€rmeability ofa porous medium llas a
sigoificant eflect on the Fequency depen{ence
of the atteouation even in the low fiequency
range relevant for surface seismic. For testing in
synthetic seismograms with acceptable
approximations a linear relation-ship berween
the absorption co€{ficient and lhe inverce square
of the fiequencl
has an enor less rhan 5 qo.
However, a key result of the study suggests thal
permeability estimation with surface seismic
dala is possible tfuough
it
requires accumte
calibrarion.
The application of the melhods to
the
surface seismic reflection CDP data on Ihe 3D
seismic in small Duri field arca, central Sumatra
processing
needs
keep the relative
a
to
amplitude, attenuation effecq and remove the
noise. The lest results of both melhods give a
difference map; it is due to the noise on the
dat4 slope d€terminarior! and non-uniqueness
of the equivalence facto. in calibmtion. The
calibration step is ar imporrant sta8e, and it
needs mOr e t 洒 - 8( t eSl ngl dat a t hat va●
VdOCけ , f I Cqucncy, and nt hol 。
Acknowi eagment s
in
dan K
Sr i br ol opuspi t O,
Det emi nat i on Of Penneabi l l ●
"
Wc g at em, ackl l owl cdgc t he CcoPhysi Cal
i nst i t ut e, Kar l 諷
hc, Cennany f or pr Ovi di ng
Faci nt y dumg al e r esear cヽ t he QUE pr oJ ect Of
Ceopl l ysl cs St udy Pr o8解 叫 cadJ ah Mada
“Ui ver si t y. f Or t t anci al suppOt and t he
i nval mbl c sl l ppOr t Of PT CPI especi al l y t hc
FOl 10w■
ng col l abOmt or s FOr ul ar hel , m
ヽイahadi , VL EB Ha― h, ML Supr l adi Ant
卜を M● ■yal l t O, and ESI t eal n i n Runbal
ReFer ences
ノ
Bl ot M A, 1956 neo● oF Pr opagat l on oF
E16● c Waves h a Fl ui ι sat unt ed
PKl r Ol l s SOl i d′ И εο t t s“
И 7, 28,
168- 191
t Ft l t t enl n W I , 1962, Di sPer si ve body wa■
わ ″ ■ 6“ pケ Ra, 67: 5279‐
cs・
5291
0 canl ey, DC, 1981 A Mct hOd f or Cal c‐
l at i ng
Syn■ euc Sei smOgl ns, Ъ i ch l ne16de
ul e Ef Fect of AbsOr pt i on and dl spesi m
い
りるcs, 46, 1100- 1107
」 Cecmmal J , and Smi t DC, 1961 Some
Aspect OF El ast i c Wave Pr opagat l on l n
Fl ui d
、 Mt t ko,
C―
Sa― l ed
PoЮ us
l cs, 26, 169- 181
SOl i d
C, Muke● i , T, al l d Dvor ki ■ J , 1998
ル R∝ お■ ″ ∫む α認めた 2ガ ル/
″ 4M
〃 α
&l sz″ И , お "わ
“
Canl bndge “ Uni v Pr ess, USA pl “
ν Mul l adL S, 1998 ι ●2γ aη ´ 勿υ l r l ar ″ ″ 04g
7asぃo″
ケ 誅 Lcmt as・ J よ ar t a
l Saar ・ M
O. and Mangら
` "ρ M. 1999 Pemeabni , _
por osi ″
Rel at i onshi p i n Vesi cl l l ar
Basal t s CRι , 26, 11: - 114
ySi smant o, D Sant Om, F Wc- 1, S MunadL
an
and K S■ bl ot op■ ・pi t O, 2003a Hor l ―
and Ver t i cal Sc玉 赫 c Pr or l l bg Syn■ 9● c
Sei smognm
■ hl ch
槻 」謄ツ
Лαυ
tふ
", Sol o, I ndonesi a・
e瑞
i ncl ude
懸179
173‐
/ Si smant o, D Sant osO, F Wenzel , S Munadi ,
t he
2003b
BaSed On
Tt t ut ‐ YamamKl t O Appr OI Ki mat i On on
Synt hel c Sel sm02r anl 麟ャ∝ 銀 M8ノ υ
κ o"′ n響″ P/ 125た S π , 切
I ndonesi ●
167‐
", Sol o,
172
メ
。 Si sl ant o, F Wcnzel , S M, , い・ i ,
dan K
Sr i br ot opusPi t O, D Sant sq B
Subi yant o, 2∞ 5a A Met hod For
i t t 「 sd論 喘 e“ : 署錢l Ч
Tcst Case Sm" Pr ac″
Pヽお
ル
И sI ● 71
勁 ψ りs, ″ 溜 2ω , Decel
` 9′nber 7‐
8, 2∞ 5, Bandung, I ndOncsi a
マЫ… 11」ぶT冊 %絆亀品 静
ngan Kecepat an dan At enusi Ter ha
dap Pen, ` eabi l i 力 ヽ Dal al n 3at uan
Resewoar Ber dasakal l Pel saI I l aan Bi ot
93鳳
′ Tt l r gut f 孔首
ヽ
酬ぶ
: 静識
l鑑
Sei smOgr ams f or Ma―l ne
ic
Scd赫 、 and
Det emi nat i on OF por Osi , and
Pcmeabl ", 3∞的 ―
S4‐ R3, 10561067
0 Tur gut , Aち
and Yal l l al l l ot o, T, 1990
of Acot st c Wave
Meast r cment s
Vel Kl ci t i cs and At t cl l l at i on l n Manne
Sedi ment s ′ ′ cο 郎1 銭
И″ , 87,
2376- 2383
＾
０し ら〓鸞８貝出
Ydcity(ds)
Fi8.l. The relationship of the p€rneability
s3tr.lston€ tne. It is
shown lhal for higher hequency th€ velocity
dependency is not so significant relative to
to the velocity for
lhe permeability.
l.:r..#Fii4by drrE
Fig. 3. Synlhetic seismog.ams of poroelastic waves in two layer models ofseismic
reflectioo. The model uses yelct ity
ol
Y
^ m) over the
3000 ny's (sandstone, 150
limeston€ Fr, of 4000 n/s, using Ricker
wavelet fiequency of70 Hz
︵０ ● ︶０ 〓 ０”Ｐ Ｅ ｏＬ
EqEr09
E"s-ryGA
Fig.2. The rclationship of the permeability to
the fiequency for satrdslone type. This
relationship sho*s thal the permeability is
strongly influenced by hequency.
Fig. 4. Frequency sp€ctsum of Fig. 3.
There are some frequency-sbift and
amplitude attenuation, esp€cially in lhe
(1G.70) Hz The frequency content is
affected by lhe attenuation system of the
me..lium.
Pmabiliry orEeib!ioo
by Ampl'tud.
Mdtod
by
c*ttsieor Ar@&d,on
(o) M.rhod
―
=
︱
―
,
“
∞
(…“ D)
い ０ 和 ， 続 枷
神 ︲ ゆ 枷 知 ．
苅
O
P― ● HI t y。 1-
ofEsrrdid
¨
゛〓 δ＾ヽ ● ３じ
帥 ¨
211
と
●
＾一
一一一
わＳ Ｅ
0
・ａｎ ８ Ｒ ︶ ゞ●δ栓●＾
メし
，
，
-0
.-,-4
＾
●■３ ヽ
０８︶８一
く豊δ８ ８８ Ｒ ︶
︵
ω８Ｙ● ヨ週３こ ｏさヨ０‘首Ｆこ
´
,
P.@ebiriry
…
Per ● 動 i l i y of m●
d。
! ( mD)
Fig. 5a and b. Curve of permeability of estimation versus p€rmeabitity ofmodel. It is shown tllar
the equivalence factors are not consran! but they are as a firction of velocity. We divide the
velocity inlo 4 goups of equivalence factor h the sarne range value of permeability i.e., (33503800) n'ls, (2950-3350) m,/s, (2450-2950 )m/s, and (200G2450) rnls inrervals.
，ｏ
目 ざ，
ザＢ Ｅ，ｏ谷Ｅ︶●〓Ｂ
０２ う ＯＥ Ｏ〓 Ｓ ¨ ヽＥ く ︱ ＋ 一ｏ‘
R
↓
，
”︱
う
て し ︱ ・
︱︱
ヒ →〓
８ ■ ５ ε Ｏ■澤 ¨一Ｅ て ︱ ＋ ぜ０ ６ ２ 凛 日 、 ﹁ ︱ ● コ聖メ ー ¨ｌ ｏ
¨
→リ ョ Ｙ ８ 〓さ ﹁ ● ｏ一ｏ ゎ ヨ ｅ ざ ｇ●ｏヽ
Fig.6. The p€deability estimation cwves
(. is the alpha metho4 + is the amplitude ratio
method) ajld the model permeability (o) with
constaDt ftequency are shown as curvatue
lines. Each has about I % average ero6.
M]ry,&i!dd!m.ddildie.vp]@i,l
tl
ヽ
Fcc'sry(&)
Fig. 7. Tle permeability estimation curve
('
is alpha melhod, + is
amplitude ratio
melhod) and lhe rnodel permeability (o) wirh
constant velocity are shown as linear lines.
E3ch has about I .5 % averdge ermls.
,
●r
l・
イ
・
・
・
―
‐
・
・
多√
Fi g 8■ b The exal npl e di st Hbl l t i ons oF
cal i br at i on sei snuc dat a( at Weu s、 研→ I n
dpha memod
Fi g
9a b Thc
exampl c
cabbr at on se` mi c dat a( ■
ampl i t udc r at i O met hOd
￨
di smbut i Ons
of
Wal sM"A) h
Fig. 10. TIl. pemMbility rn p of DuIi 6eld
Fig.tl. Tlc
r€sulted ftom Alpba method on smoothed data.
rEsult€d Eom thc smplitud€ ratio (RA) method
on smoothrd data
permeability map
of Duri
field
?o: zea s.GrJ/ory
′
A SI MPLE TECHNI QU=
PERMEAB: LI TY FROM SE: SMi C REFLECT: ON DATA BASED ON
BI OT' S TEOREM
St 3- b・ , Ds●
κ
87 br ●
: . S日 ■」
nd “
●l ● ●● ヽFW● N“
1
po31 t ● l B Subl y●
t●
螢
膀
G●
●摯Ⅲ
‐ ●」絆智奪
=富
L,.,rD..d,EE*d,ro,*EM@.Nd..D*tunqnds;;;
留た
蛇凛急匈
.
…“
i;;;;;-tl.,;idt;;;G;;;;p;;;ifiq,.**,**".,.
*j**::?:5I:::{,lyjr:1:Y1r-.q:
ryp,,・
筋
闘爺 め
b"∼ 0"“
・r-ner._,.,b.;;,lF;^;t-fi;';;e,
,Ⅲ
謄凛協議密猫 篭眉
=協
“
F--\.4.r-.d'rtt'
|-*
r,trtrbradr&r!rr-d
EBar t,t t ot4dpr..q.
lb-,d!l|rq,dbEdl
: ' 安撼 ) “ 」 G● ●nl
“
1) ・
●
…
"め
ふコ歯 ●
(…
・
18' ,*rd b lGifiy
r lteE…
dlrdIlrd|dr-nprcf,*;'darro
1ss;
Ⅲ峰 V●
￨―
m揃
@ , d
rr.G
6rdu4
。
●た
“
¨
Fd.'di6
、. =, ■
“
‐
●
・
静
‐ aヽ
商
呻 墨驀
手I =■ ・H=「
●●●
―
( ' ‐ ) "( 1′
●
￨
。
っ
●● ● ‐
'“
6‐
“
ⅢⅢⅢ
脚 選 菫
…
1
‐
ftr r r r+.r. i
n Fiag d
" ・ 藁-,i。
鵠￢
町 ( , 4) "F● ( 11, …
b・
“ ―
"―
――
"CO・ ―
￨●
“
"
h- 4- ●
…
( 141"- 0, ま
餞
―
“
,
rh.rle*r''fnhr,tl.d@ffi,e.
{ 獣 “・
螺 嚇
,メ
“
6 c-r' oBrt re
¨
° m"
常モ
淋
ス
'
9・
︻
■ヽ
‘
●＾
ヨ ０﹁
い
・
￨￨キ ￨
幻勧
( 1' 力 ) お ゝA■ ● 丸 〆●I ● ●●
―
"0お
●一 ""“
●‐ ぃ∞■ “●
人 0● ● , "Ⅲ 、● ●′樹
` ●
“
“ “ “ "●
,―
・
←
・
け
い
・く
デ
器レ
( 14) ● ―
6, f.i4
●
り
鮨
● ●j ヽ
4‐ ●湘 ′
‐
―
―嗜 綸
暉 口
"・
Ⅲ 町 u“ い ●
口, ・"●
…
メ‐
夕 ●
∼
― ・
ぃ
押 、
… …
“
frEcIl'J,diE!'dft
“
、
ぃ
詢コ
11ぶ 乱舞豊
窯… _1
″ ￨■ Ⅲ ` 書ギ ‐ ■
…
l t●
“
―
ヽ I n●
●
` ` ● x, ● ‐ ￨● "“ t ´ , "は 澳0“ ￨ゆ “ ■ ●●● ● ●t ● ●, ぃ
ヽ
● 閾 メ●●● ( ― ‐
―“ ″ , , ● , ぃ , ｀
1, ヽ , ● 、
ルヽ
0(Ⅲ口 壼 , “― ● ●●● 1凛 つ“・・
● "■義、 ￨"0■ 輸 ‐ ` Ⅲ
,
…
“
“
“
7, 、 oぃ
T●
,ヽ
"■
・
計,
pfr.b
lDtrh.bffi
{ebb.r*r&.bi*6
ぃ ●●
"●●●●
rq*,o
″施、
彙●4● ●薇
,
,
″・′ : =
メ" ' ' 》
` “
口
ギ￨・ ギ￨・ 詰
"〕
"1- ●
“
`
Bb,*,d!5idr:ndi*alx-6
bh..eo'*leda,q
u,ir..
●●
…
“ ""壺 “
“ "鑽
1' 01- "け 0
渕
=颯
'・
AN O "
―
…
“ …
歓
""に"“
…
―
…
●油 呵
γ。
rfl dh tus,
R‐
¨
… 9- d b…
“
“ ―・
・
…
…
コhで ●●￨… ― - 5麟
“
議χ
■ 1吾 サ
￨. ′
輛 ¨
` , 1ズ
、,
‐
・‐ r ・ 為
′ 争チ
l
=・
l・
ぃ
,
". ヽ
´
一
“
Ⅲ
…`
‐
"‐
鋼
晴
野
標
…
Ⅲ
=ヽ
・
注輩
-1
…
.〕
fdl6k{n'^trBrqB66
.fu('6deM!i.esle
r4mdfur.€n,Ejffikh
erFd.,'''i.'i'r.de@
・
ヽ
―
‐
・
‐
・
‐
・
●● ¨ ヽ¨ ●
“
―
, 3義 書● お
"¨
‐ ‐
ヽ
￨…
…
●―
● ● ●● ● ―
‐
,ry!bb?bleri!r4,
bb'-6h4rb,.fr&!
+,*E*e.**a,l4?
!b*llc.ellalrElEtE)
^6drdgEfu
w. rdrl, xrltr.nr. h G.orFr h'dra dleb
crybp6'!E&,d4hF
54"rd in, P(ya crd* le
r@.',oJthr&4
d$d&r b&LEL !.d. D €3,r,.!4[ sqia
d,LlLE.dF9b.Rl'd
´
i t盟
=警
彗・
“
=■ ==摯
‐
――=
' 営・‐ ==二
―
“
‐
A SIMPLE TECHNIQUE FOR ESTIMATION OF RESERVOIR
PERMEABILITY FROM SEISMIC REFLECTION DATA BASED ON
BIOT'S TEOR.EM
SismaDto a', D. Saotoso
b,
F.Wenzel " , S. Muoadi d,
IC Sribrotopuspito .. B. Subiyatrto.
,'Ceopbsks Diyision, Physics Deport ne , Cadjoh Mada Unversi,y, yog/aha a, tndone-ria
"Ceophlsicsl Depar.ment, Bandung Insntuk ofTechnolg, Jt. Ganesha f0. Bandun& tndoneia.
'ceophys{cal Institule, Hetusttosse 16,76187 Kotlsruhe, cermany.
ILWIGA\ Jakatta,
'PT. CPI, Runbai petanBaru Indohe\io
'CorrespoDding author. Fax: +62-27+545 185;
E-mail: sismanto@ugm.ac.id
Indonesia.
'
-
Abstract
Relatiot$hips among elastic parametefi ond rock prope ies, ahd ultimate resentor
parameErs have been ettablished in continuum ,nechonics and rock physics. Therefore, il
should be possible to estimate reseryoir Tnrmeobility lron the seisni; doo We used Biot,s
solution of\aave equation in an elastic potous mediun ond the approxiDations oJ Turgul_
Yamamoto to ollow an establishment of a lineT retationship bedr,een auenualion
coeiicient or anplitude ratio at a funclion of the iwerse of the square ofJrequency. Ihe
slope ofthisf ncrion includes the Wrmeqbility. h can be shown that th* iichiique ugrees
lo the measurement of the perneability o! a poruus mediut t /rom seisnic waviforns. We
examined this techniqrc to estin ate the resenoir perheobility by usin[ sythetic
seismogram data. The resu rhov that hos an error less than S 94, it neans that tihe study
of permeability estimalion fiom sutface seismic data is possible by usihg an accurate
calibralion step.
The procedure is tested on 3D seismic data over part of Duri field in cental
Stntatra, Indonesia. The sinplicity ofthe theoretical oppr(mch requires the ihtroductioh of
an empirical calibratiott lactor that is provided by n'ell SM\A in the area_ This lactor is
then implemented to estimarc rhe petmeability with seismic dota on the
field: it gives o
permeability nap oflhe study arca. A key result of the study is that permeability estination
with surface seistuic data are possible bul requires calibration. A confimation and
validation of this procedure vill be subject lofitture tyo*-
Kervo/ds: Seismic wqye, pemeability, Biot, Ttlrgut-yamanoto.
滞鼈] 詳域Fi 錢: 樹
l.IotroductioD
Reservoir characterizalion is one of the
advanced steps in seismic exploration 10
identiry physical prope(ies of a reservoir such
] 器彙留 ] 』艦
as thickness, porosiry, pemeability, density,
compressibility, and water saturation. These
physical propffties are used to modet the fluid
flow in a Eoducing field. Recent new
geophysical methods for example, AVO and
tomoSraphy, generally attempt to directly
bu、■ 11ふ
a
one-dimensional
(lD)
model
″ O∞ 5al ' s
me■ od t O esumat c
灘
“
of
VSP, which includes mode conversion tlu.ough
slow compresional waves as an eners/ loss
t
mecharism based on Ganley (1981). Horizonlal
and vertical seismic profiling synthetic
seismograms which include the absorption
effect
of the
日
為
( 1)
dala
Sismanto,
et a/
(2003b) developed a ,
,l
難続飾縄騨徹掘鮭
t he pemcabl H″
Bi ot ' s el ast i c mOdt l l i , ″
and″
″
4■
l tl l
1990) ■ l e Bi Ot ' s el asl c mOduLs ar c
=需
+亀
ん
＾
Ｊ
／却４、
＋
，
″
・
“
π
〓
Turgut
Yarnamoto equalion, but the relationship of the
permeability estimation to the permeability
model is still multifaceted. Funhermorc,
Sismanto et a1 (2005a) published a sirhple
technique to estimate the permeability on the
real 3D seismic data based on Turgut-
‐ α
α ‐ 125( Tur gut al l d Yamamot O,
expr csscdけ ● c Fonowhg r el at i Ons
Ｃ
oo
l s t he shear modul us,
I s■ c vi mal m・・
・ exPEsscd 6″
technique to estirnate the permeability on lhe
seismogram synthetic based
:
π , c, al d ν ar e t he
︻
工
刹
［
﹃
theorctically obtained from the seismic data.
考子
ed颯 ∝me“ v認
′ i s t he secpage di spl acement vect oち θ =
di v, , , ‐ di v′ , ′ l S ul e bl l l k densi ″ ″ ‐
p:rrarnelers, Ttis
(Munadi, 1998; Saar ard Mang4 1999). Thus,
ahe reservoir palzuneters iue believed to allect
seismic wave ctEracte.s. With this point of
view, res€rvoir parameters, such as porosity ;nd
permeability should thereforc, arc able lo be
θ ―曖 ら _ρ ノ
―″
静
子
C▽
h whl ぬ ″ 、血 ぃ
of
with the field
gsh鮮
μ▽与+σ ―
がθc▽ ら=ρ t t ρ′子
v/
attenuation ofth€ fast compressional waves as a
function
ftequency. Meanwhile, most
theoretical ard experimental res€arches prove
that there is a close rclationship among waves,
and reservoil
1臨 謝
喘為棚
断温』 ふ出詩習肥讐L珊 al t t Tl
permeability, has been coostructed by Sismanto,
V
relarionship also agrees
iよ
mar l ne scdi ment s, ar e( B101195o ′
reseNoir, especially for
et.al. (2003a'). The Sisinado's techdque is to
combine the TuguCYamamoto lurd canley
mechrnism. Twgut and Yarnamoto (1988;
1990) explored the possibility of Fedictins
porosity and permeability of marine sediment
by analyzing phase velocity dispersion and
elastics,
;
Tl l e al m of al i s paper i s t O examI I l e dl e
Si smm“
estimate the reservoir physical properties ftom
the seismic data" Turgut and Ya.rnamoro (t988) y
developed
￨
′ ‐ 藤
罵
r t 7丁 瓦
「l 勇ヶ
し
f.
is the bulk modulus ofthe gain, ,!. is
the bulk modulus of the fluid in the pores, and
where
,(6 is rhe bulk modulLs of the skeletal fi.amc.
According to Turgut and Yamarnoto (1990), the
bulk modulus of skeleral SaIne
(r
and the
porosiry are related to the shear modulus as
K, ‐
, and
( ￨≒
By usi ng●
( 4)
1: : ど
鰐 ] 温鳳
α l . ( 200Sal
r el anOnsl l l P of ( σ ′
r el at l ol l shI PS ar c 8i ven by
_希
42, σ
ピ
計ち' 嗣
ヽリ
４
制
mOdi ned ul e
■ 十二 ″
2‐
讐
,0
wher e″ _瑶 ′ ぽ Accor dhg o t hc spec‐
t r al l a● o m
et hOd f or est unal i ng 2 ul
l abor at oγ , ul e dei nhi On of ●
e qual i ● f ac10r
0= 2Y,a(@)
( 10)
g i s,
一３
一
′︱︱ ︱＼
〓
ρ
κ
イ
″ _ρ
Itfl 』
α
Eq( o can bet t wH"en as
"ht O a nncar f Om
wher c t he shear modul us μ t hc POi SSCn' s r at i o
σ and ul e bul k nl odul us K ar c est i ― t ed“ m
t hc ve10ci t l es oFt he P and S waves, whcr e t hei r
on t equeney, t he
Ol e Ot hcr pannl et er s have been dct emi ned
盤
器
e r el t t a“
pcnneabut t cocFf l cl ent can be es● I nat ed, r
Si smant o,
=+=) ″
■
( 8)
lラ
3. Methods
By corDbining E{s. (9) and
(l
0), ones ottains
To estimate the permeability, we need a
seismic rxaveform velocity aDd its spctral
amlysis of ihe events. The bulk modulus of
grain X" the density p and the bulk modulus of
fluid K7 have to b€ defined previously.
According 1o Turgut-Yanamoto (1990)
(ll)
.r2r, * W2Y, _ I
o'(W -1, xtw -t) ato)
'n wht h r=d& pQrn- i1)). r.tn tetatorn
ship of a(@) and the frequency in Eq. ( ) is
approximation and Ceertsma and Smit (1961)
indication for marine sediment wilh high I Eqs.
(l) and (2) can b€ obtained in the folloiving
asrmptotic foI high frequency region (o>>).
form,
(電
01∼
′イ) 1
ct A
J+-.(YlV'\
A qt 6 o'
wherc qt =ryk?@ is the imaginary part
ar|dA =
(p
p'zr) I
=Etp
fot
of
p . Whercas,
a -+o,utd
u]=;ru,rtq-zcpryp.-
w ,-r*.
fi
歯mm t t m面ωh
nel l , I t can be Found ul e l oca● On Of t he
展
υ峨鯛F"い
in
the
high fiquency rcgion and in pEctice it is
diffcult to obtain lhe asymplotic value
b€caus. the fiequency content of the s€ismic
is
less then 200 Hz. Whilq the
relationship between ll/oJl
is
^nd U/d{a)t
linear for all fiequency. However,
the linear
dala
relarioNhip ofthe datajust takes place only in
4,
′
¨
Yo?
n-
( 6)
Unfortunately, we ai€ not interested
lhe frequency content ofthe signal.
From the slope /, we can estimate the
penneability, i.e.,
k^=
' !2!e_W
t.w-p))
_tlt.
tt2)
It is obvious thal the coeflicient of attenuation
d@) can be calculated ftom the spectral ralio
melhod by
(VSP),
d is the
distance b€tween receivers in
positions I and ,. In the refl€ction measuem€nt
d is the path difference of the recorded seismic
wave at the suface.
Substituting E4.(13) into Eq.(l l), we will
・却
+9=[
(
器
→
瀞5レ
obtain
】
The curve of Eq. (14) is asymptotic for high
fiequency (@>) arxl linier between (1/aa and
(l/ amplitude ratio in logarithmic). If the slop€
isr, we can deiermine the permeability of lhe
medium, i.e.,
L P
2Y nD
______-___:__!_
d
tlpn- p',)(w -t)
E4.(ll) are similar.
is in the dala Eq. (ll)
seismic traces to calculate $e
The forms ofEq.(14) and
The main dilference
needs morc good
attenuation cooficient but using Eq. (14) we
nerd only al leasl two tsaces of seismic dara itr
CDP gather.
d. SyDthetic s€ismogr.mt
Sismanto, et al (2003a) arsociated the
efect ofabsorption and disp€.sion acco.ding to
Ganley (1981) with dispersion and attenuaiion.
The attenuation effects are calculaled from t]rs
wave number ofBiot's equation. The theoretical
seismograms
are based on
Ganley(1981)'s
method. The dispersion effect comes ftom the
reflectivity as a fimction of frequency. For the
absorytion cslculatior\
Futterrnan(1962)'s
ab6orption-dispenior equations, are.ealized.
Therefore, the synthetic seismogmms cover
rcservoi paEuneteB, ele6tic pr[ameter alld
wave pararneteG. The perneability
depends
oflhe rnodel
on those paramete6 is given by
Ge€rtsma and Smil ( 1961 ),
︲ 一２
I
″
一
笏
\At(at )
whete A" and At are the amplitude of signal at
the ,, and posilions in the ftequency domain
respectively. In vertical s€ismic meilsrrement
〓
(B)
‘κ
,t,) =h(A.@!).d..
(r6)
The relationship of th€ permeability to rhe
velocity ard fiequency for s,andslone is
illustrated in Fig. I and Fig. 2, respectiv€ly.
Those figures show that for higher fiequency
rbe velocity dep€ndency is nor so significant
relative 1o the permeability. Otherwis€, the
permeability is strongly influenc€d by the
frequency. The rclationship of dependency
among ftequency, velocity, and permeability
has been discussed theoretically by Sismanto
et al. Qoosb\.
The basic rock prop€rtid of marine
sediment are based on Tursut and Yamamoto
(l9q)). The kinematics viscosity ofpwe fluid
7 i, t .0 x I 0r m%, lhe bulk modulus of fluid
f./ is 2.3 x loe N/mr. $e bulk modulE of
grain ,f, is 3.6- x I 0'o N/m'!, rhe density of fluid
A is L0 x I d-kg/r , and $e densiry of grain
p, is 2.65 x l0' kg/m'. While, vetociry ofrhe p
wz\e Yp is obtained ftom the seismic data,
atrd the S wave velocity I/, and the density p
are estimated by empirical equations (Mavko,
et.dl, 1998). Then, the bulk modulus of the
skeletal ftame and the porosity are estimated
by E4s.(4), Biot's elasticity pmameters are
det€.mined by Eq.(3), and the velocity of rhe
zero and the high fiequency iange
are
calculated by Eq.(?).
5.
Elamples ofNumerical Result
Syn6etic seismograms of poro-elastic
waves in two layer models of seismic
reflection are shown in Fig. 3. The model uses
a yelocity y of 3000 r/s (sandstone) over
the limestone wit\ Ve, of 4000 rrs. The
Ricker wavelet &equency is 70 Hz Fig. 4 is
the firquency spectrum of tbe
s€ismoglam events of Fig. 3. The
synthetic
spectrum
shows that there is some ftequency-shift and
amplitude attenuatiorl esp€cially in (10-70)
[Iz The frequency content is affected by the
attenuation syslem of the medium. The two-
layer model uses the thickness of first layer of
1 50 m and rcceive. interval of 20 m. Then. rhe
other physical properties can be obbined such
as the shear wave velocity y,j arld y,?, qhich
are 1594 n/s and 2157 n/s, the densiry p/ and
h xe 2.19 .rc1 kg/m3 and 2.33 .tor kg/mr, the
porosity 4 and h arc 56 yo and 17 %, and the
p€rmeability tpt and b, ue 21a mD ar 209
mD, resp€ctively. Those physical propenies a.e
enforced to constsuct the synthetic seismogram
ofthe two-layer model, which is shown in Fig.
l. The permeability value ot the s)ntheric
seismograrn, which is calculated from Eq.(16),
is implemented as a ref€rence.
Some two-layer models are constructed
with the ,/rr velocity ofsatrdstone as first layet
of3000 ,IVs and th€ thickness is 150 m over the
limestone rn which the velocity is 4000 ds.
The synthetic seismograrE use
s€veml
ftequenci€s, and several velocity variations.
w1len the velocity is put to be conslanr, the
frequency
is
va ed and vice verca.
The
permeability inveNion of the two-layer model
by the linear melhod is
it
compared
ro
the
gives equivalence
fimction for several velocities and various
frequencies. Tle scale facror of calibralion is
obtained from lhose curves. The scale factoa
reference permeability;
are not wique, but arc as a fi.mction of velocity.
In this case we divide them into 4 Sroups of
scale factor in the same range value of
permeability i.e., (33s0-3800) rn/s, (2950-3150)
ntis, Q45G2950)
r/s,
and (200G2450 rlls)
iniervals as presenred in Fig. 5a and 5b. Itrere is
a linear conelalion between the permeabiliry
of
the model and the permeability fiom estimation.
The linear function of this .elation is called thc
scale factor
the lheoretical curve
of
in
Figs.
Lrd
2,
formulated by Geertsma and Smit (1961). It
means that the synthetic seismograrn keeps the
permeability information ofthe mod€l alld rhe
inversion method is able to extsact it from rhe
(sy hetic)
seismograrns.
In rhe p€meability
estimation, the avemge erors for both linear
methods are less than 5 %. The enor come
fiom d€termination of the linear area in the
curve. However, the permeability estimation
wilh surface seismic alata is basically possible
bul requires precise calibration.
6. Field
ErrDples
We us€ 3D seismic data in a small
area of Dud field, central Sumatra, IndonesiaThe main processing steps are the True
Amplitude Recovery, the Surface Consistent
Amplitude, Velocity Analysis and NMO
Correctiorl the Field and Residual sratic, lhe
Common Offset BiDring, the Bandpass
Filtering, Muting and Killing, Alignmen!
Ensemble Stack/Combine, F-X Deconvolution, ahd Plotting.
We ta](e I I inlines and 19 xlines seismic
for (l.5 x 2.65) kn'? in subsudace. In this ar€a
we have 6 wells, and only well SM#A (in the
middle) which has core analysis.
Some
information from these wells is listed in Table
I. Each data is contoured and read ar erch
CDP for calculating with the seismic data. The
top of the target layer ofthe seismic will be I,
data.
ofthe calibEtion.
The invercion method is applied to estimate
the permeability based on the known velocity
the model on lhe sydhetic seismogram, and
the results are given in Fig. 6 for consranl
fiequency and vaDing velocfty and Fig. 7 for
constanr velocity and varjing frequenc). nre
shape of curves in Figs 6 and 7 are similar to
Tabel I. The thiclness. inierval, and nns velocity ofthe well in Duri field.
i nt ewJ ve! oci "( ws)
2J 69
212,
2000
2006
2166
2057
S04#1
SM12
SM“
Sヽ イ″
Sヽ 4″
SM″
3
4
5
A
疏
1715
1761
1775
] 782
of
calibration of thc CDP position (close to well
SM#A) is on inline 187 and xline 207. Beforc
calibrating, we calculate the permeability
estimation of lhe reservoir targel and we ger
9.429 l0' mD for alpha and I.845 lO) mD for
anplitude ralio methods. On lhe other hand, the
average of permeability core samples is 1254
l0'
mD.
lf $e
estimarion permeability is
divided by the average core p€meability, it will
give an equivalence factor. This equivalence
factor is then b€in8 applied to the formula for
calculating lhe other seismic data in the study
area- The exrmple distributions of calibration
seismic dala in slpha and arnpiitude ratio
methods are presented iD Fig.lo and Fig.ll,
resp€rtively. Equivalence faclor physically
comes ftom the simplification ofthe system lhat
malhematically
is not
formulated
in
the
equation.
The equivalence factor is to compensate
the out of system parameters that arc'not
involved in lhe equation. Consequently, this
cumulative factor forms a conection system in
the numerical rcsults,
Using the s€lected isolat€d CDP
data
perfonns lhe calculations of permeability lo all
CDP in each line. The results arc ploned as a
perm€ability map such as presented in Fig- 8 for
alpha and Fig. 9 for amplitude ratio methods on
smoothed data. The permeability maps give
difference value and distdbutio& but still in the
same treod. Which on€ is closer to reality, ne€ds
a comparison map fiom other calculation as a
reference. Unfortunately, we do not have it. If
we have the reference map, we will know the
close one afld lhe erroN, at lgast we can adjust
by
determining
the
co ection
￢
it
factor
i dmも s( m)
3475
3322
3353
3444
35, 7
310,
1789
2011
ln calibratioq we use the permeability of
the core, and log data to match the position of
the core inlo seismic dara firough the synrhetic
pan
seismogram
Duri field. The
in
vd∝ i t v( wb)
statistically. The differences of the both result
methods may b€ caused by noise in the data,
equival€nce fador, and lineariry selecrion ofl}le
data- ln this cas€, the equivalence factor is a
constant that is not a firnction of velocirv and
Bequency. Anorher effecr is rhe accura$ olrhe
slope dererminalion for each merhod, r.ihich is
subjectively delermined. Therefore, il wi eiv(
some difference errors for borh methods. We
awarc the calibration step is anorher Droblem in
this study. l! needs Dore core permeabiliry in
various velocity, fiequency. and lirholo$/.
Regardless of these problems, a simple method
to estimate the p€rmeability iom seismic data
ha3 b€€n proposed, bur ir needs an empiricat
calibration factor (Sismarlo. 2004 ).
7. Cotrclusiom
The p€rmeability ofa porous medium llas a
sigoificant eflect on the Fequency depen{ence
of the atteouation even in the low fiequency
range relevant for surface seismic. For testing in
synthetic seismograms with acceptable
approximations a linear relation-ship berween
the absorption co€{ficient and lhe inverce square
of the fiequencl
has an enor less rhan 5 qo.
However, a key result of the study suggests thal
permeability estimation with surface seismic
dala is possible tfuough
it
requires accumte
calibrarion.
The application of the melhods to
the
surface seismic reflection CDP data on Ihe 3D
seismic in small Duri field arca, central Sumatra
processing
needs
keep the relative
a
to
amplitude, attenuation effecq and remove the
noise. The lest results of both melhods give a
difference map; it is due to the noise on the
dat4 slope d€terminarior! and non-uniqueness
of the equivalence facto. in calibmtion. The
calibration step is ar imporrant sta8e, and it
needs mOr e t 洒 - 8( t eSl ngl dat a t hat va●
VdOCけ , f I Cqucncy, and nt hol 。
Acknowi eagment s
in
dan K
Sr i br ol opuspi t O,
Det emi nat i on Of Penneabi l l ●
"
Wc g at em, ackl l owl cdgc t he CcoPhysi Cal
i nst i t ut e, Kar l 諷
hc, Cennany f or pr Ovi di ng
Faci nt y dumg al e r esear cヽ t he QUE pr oJ ect Of
Ceopl l ysl cs St udy Pr o8解 叫 cadJ ah Mada
“Ui ver si t y. f Or t t anci al suppOt and t he
i nval mbl c sl l ppOr t Of PT CPI especi al l y t hc
FOl 10w■
ng col l abOmt or s FOr ul ar hel , m
ヽイahadi , VL EB Ha― h, ML Supr l adi Ant
卜を M● ■yal l t O, and ESI t eal n i n Runbal
ReFer ences
ノ
Bl ot M A, 1956 neo● oF Pr opagat l on oF
E16● c Waves h a Fl ui ι sat unt ed
PKl r Ol l s SOl i d′ И εο t t s“
И 7, 28,
168- 191
t Ft l t t enl n W I , 1962, Di sPer si ve body wa■
わ ″ ■ 6“ pケ Ra, 67: 5279‐
cs・
5291
0 canl ey, DC, 1981 A Mct hOd f or Cal c‐
l at i ng
Syn■ euc Sei smOgl ns, Ъ i ch l ne16de
ul e Ef Fect of AbsOr pt i on and dl spesi m
い
りるcs, 46, 1100- 1107
」 Cecmmal J , and Smi t DC, 1961 Some
Aspect OF El ast i c Wave Pr opagat l on l n
Fl ui d
、 Mt t ko,
C―
Sa― l ed
PoЮ us
l cs, 26, 169- 181
SOl i d
C, Muke● i , T, al l d Dvor ki ■ J , 1998
ル R∝ お■ ″ ∫む α認めた 2ガ ル/
″ 4M
〃 α
&l sz″ И , お "わ
“
Canl bndge “ Uni v Pr ess, USA pl “
ν Mul l adL S, 1998 ι ●2γ aη ´ 勿υ l r l ar ″ ″ 04g
7asぃo″
ケ 誅 Lcmt as・ J よ ar t a
l Saar ・ M
O. and Mangら
` "ρ M. 1999 Pemeabni , _
por osi ″
Rel at i onshi p i n Vesi cl l l ar
Basal t s CRι , 26, 11: - 114
ySi smant o, D Sant Om, F Wc- 1, S MunadL
an
and K S■ bl ot op■ ・pi t O, 2003a Hor l ―
and Ver t i cal Sc玉 赫 c Pr or l l bg Syn■ 9● c
Sei smognm
■ hl ch
槻 」謄ツ
Лαυ
tふ
", Sol o, I ndonesi a・
e瑞
i ncl ude
懸179
173‐
/ Si smant o, D Sant osO, F Wenzel , S Munadi ,
t he
2003b
BaSed On
Tt t ut ‐ YamamKl t O Appr OI Ki mat i On on
Synt hel c Sel sm02r anl 麟ャ∝ 銀 M8ノ υ
κ o"′ n響″ P/ 125た S π , 切
I ndonesi ●
167‐
", Sol o,
172
メ
。 Si sl ant o, F Wcnzel , S M, , い・ i ,
dan K
Sr i br ot opusPi t O, D Sant sq B
Subi yant o, 2∞ 5a A Met hod For
i t t 「 sd論 喘 e“ : 署錢l Ч
Tcst Case Sm" Pr ac″
Pヽお
ル
И sI ● 71
勁 ψ りs, ″ 溜 2ω , Decel
` 9′nber 7‐
8, 2∞ 5, Bandung, I ndOncsi a
マЫ… 11」ぶT冊 %絆亀品 静
ngan Kecepat an dan At enusi Ter ha
dap Pen, ` eabi l i 力 ヽ Dal al n 3at uan
Resewoar Ber dasakal l Pel saI I l aan Bi ot
93鳳
′ Tt l r gut f 孔首
ヽ
酬ぶ
: 静識
l鑑
Sei smOgr ams f or Ma―l ne
ic
Scd赫 、 and
Det emi nat i on OF por Osi , and
Pcmeabl ", 3∞的 ―
S4‐ R3, 10561067
0 Tur gut , Aち
and Yal l l al l l ot o, T, 1990
of Acot st c Wave
Meast r cment s
Vel Kl ci t i cs and At t cl l l at i on l n Manne
Sedi ment s ′ ′ cο 郎1 銭
И″ , 87,
2376- 2383
＾
０し ら〓鸞８貝出
Ydcity(ds)
Fi8.l. The relationship of the p€rneability
s3tr.lston€ tne. It is
shown lhal for higher hequency th€ velocity
dependency is not so significant relative to
to the velocity for
lhe permeability.
l.:r..#Fii4by drrE
Fig. 3. Synlhetic seismog.ams of poroelastic waves in two layer models ofseismic
reflectioo. The model uses yelct ity
ol
Y
^ m) over the
3000 ny's (sandstone, 150
limeston€ Fr, of 4000 n/s, using Ricker
wavelet fiequency of70 Hz
︵０ ● ︶０ 〓 ０”Ｐ Ｅ ｏＬ
EqEr09
E"s-ryGA
Fig.2. The rclationship of the permeability to
the fiequency for satrdslone type. This
relationship sho*s thal the permeability is
strongly influenced by hequency.
Fig. 4. Frequency sp€ctsum of Fig. 3.
There are some frequency-sbift and
amplitude attenuation, esp€cially in lhe
(1G.70) Hz The frequency content is
affected by lhe attenuation system of the
me..lium.
Pmabiliry orEeib!ioo
by Ampl'tud.
Mdtod
by
c*ttsieor Ar@&d,on
(o) M.rhod
―
=
︱
―
,
“
∞
(…“ D)
い ０ 和 ， 続 枷
神 ︲ ゆ 枷 知 ．
苅
O
P― ● HI t y。 1-
ofEsrrdid
¨
゛〓 δ＾ヽ ● ３じ
帥 ¨
211
と
●
＾一
一一一
わＳ Ｅ
0
・ａｎ ８ Ｒ ︶ ゞ●δ栓●＾
メし
，
，
-0
.-,-4
＾
●■３ ヽ
０８︶８一
く豊δ８ ８８ Ｒ ︶
︵
ω８Ｙ● ヨ週３こ ｏさヨ０‘首Ｆこ
´
,
P.@ebiriry
…
Per ● 動 i l i y of m●
d。
! ( mD)
Fig. 5a and b. Curve of permeability of estimation versus p€rmeabitity ofmodel. It is shown tllar
the equivalence factors are not consran! but they are as a firction of velocity. We divide the
velocity inlo 4 goups of equivalence factor h the sarne range value of permeability i.e., (33503800) n'ls, (2950-3350) m,/s, (2450-2950 )m/s, and (200G2450) rnls inrervals.
，ｏ
目 ざ，
ザＢ Ｅ，ｏ谷Ｅ︶●〓Ｂ
０２ う ＯＥ Ｏ〓 Ｓ ¨ ヽＥ く ︱ ＋ 一ｏ‘
R
↓
，
”︱
う
て し ︱ ・
︱︱
ヒ →〓
８ ■ ５ ε Ｏ■澤 ¨一Ｅ て ︱ ＋ ぜ０ ６ ２ 凛 日 、 ﹁ ︱ ● コ聖メ ー ¨ｌ ｏ
¨
→リ ョ Ｙ ８ 〓さ ﹁ ● ｏ一ｏ ゎ ヨ ｅ ざ ｇ●ｏヽ
Fig.6. The p€deability estimation cwves
(. is the alpha metho4 + is the amplitude ratio
method) ajld the model permeability (o) with
constaDt ftequency are shown as curvatue
lines. Each has about I % average ero6.
M]ry,&i!dd!m.ddildie.vp]@i,l
tl
ヽ
Fcc'sry(&)
Fig. 7. Tle permeability estimation curve
('
is alpha melhod, + is
amplitude ratio
melhod) and lhe rnodel permeability (o) wirh
constant velocity are shown as linear lines.
E3ch has about I .5 % averdge ermls.
,
●r
l・
イ
・
・
・
―
‐
・
・
多√
Fi g 8■ b The exal npl e di st Hbl l t i ons oF
cal i br at i on sei snuc dat a( at Weu s、 研→ I n
dpha memod
Fi g
9a b Thc
exampl c
cabbr at on se` mi c dat a( ■
ampl i t udc r at i O met hOd
￨
di smbut i Ons
of
Wal sM"A) h
Fig. 10. TIl. pemMbility rn p of DuIi 6eld
Fig.tl. Tlc
r€sulted ftom Alpba method on smoothed data.
rEsult€d Eom thc smplitud€ ratio (RA) method
on smoothrd data
permeability map
of Duri
field