物理探査

第50巻第2号

107{122頁

107

BUTSURI-TANSA

Vol.50 No.2 (1997)

pp. 107-122

Cross-well imaging by the CDP stacking and the

diffraction stacking with velocity analysis

Jun MATSUSHIMA*, Shuichi RoKUGAWA**

Toshiyuki YoKOTA*3 and Teruki MIYAZAKl*3

ABSTRACT

This paper describestwo types of data processing applied

to primary reflections and diffractions ob-

served in a cross-well seismic survey.These are the CDP (Common Depth Point) stacking and the diffrac-

tion stacking with velocityanalysisI The conventional processing of surface seismic reBection methodis

modified and appliedto

cross-well reaection anddiffraction data･ One of the biggest advantages of these

methods is that data processing can be performed withoutinformation from velocity tomograms･

Sol imag-

ing can be achieved even in the lower part of a well beyond the coverage of cross-well travel time

tomography.

Firstly, the data processing methodsare

presented･Numerical simulation models are used

for evalua-

tion of these data processing methods･Secondly,the effectiveness and robustness ofthese methods for noisy

or complicated data are shown･Thirdly, preliminary examples of the application ofthese methods to丘eld

dataina geothermalarea are presented･ Adequate stacked records could notbe obtained by application of

the CDP stacking and improved stacked recordswere produced by using the proposed

diffraction stacking.

The reasons for this result are discussed.

Animportant characteristic of the proposed data processing methodology isinsensitive to velocity負eld･

In this respect, it has potential applicationfor rough imaging, as a丘rst step before more precise

imaging is

undertaken, especiallyin geothermal or other inhomogeneous areas･

Key words.･ cross-well, velocity analysis,CDP

stacking,diffraction stacking

1. INTROI)UCTIONwells. Direct-arrival traveltime tomography

is the

most popular method and itgives a velocity distri-

Cross-well seismic methods have the poten- bution between wells･However, the observed

tial to achieve a higher resolution imaglng than data in a cross-well geometry have enoughinfor-

surface seismic methods for targets between nation to achieve higher resolution than that

1996年2月19日原稿受付; 1996年11月13日受理

物理探査学会第92, 93回(平成7年度)学術講演会に

て一部発表

*地質調査所(現 東京大学工学部)

〒305 茨城県つくば市東ト1-3

(〒113 東京都文京区弥生2-1116)

**東京大学大学院工学系研究科

〒113 東京都文京区本郷7-3-1

*3地質調査所

〒305 茨城県つくば市東トト3

◎1997 SEGJ

Manuscript receivedFebruary 19, 1996; Accepted

November 13, 1996.

A part of this paper was presented at the 92nd and 93rd

SEGJ Conference, 1995.*

Geological Survey of Japan (Presently Faculty ofEn-

gineering, The University of Tokyo)

ト1=3, Higashi, Tsukuba, Ibaraki 305, Japan

(2-1ト16, Yayoi, Bunkyo-ku, Tokyo 113, Japan)**

Division of Engineering, Graduate School,The Univer-

sity of Tokyo 7～311, Hongo, Bunkyo-ku,Tokyo 113,

Japall*3

Geological SuⅣey of Japan

ト1-3, Higashi, Tsukuba, Ibaraki 305, Japan

108 物 彗

produced by direcトarrival traveltime tomogra-

phy. Some authors have demonstrated cross-well

re且ector imaglng aS One technique which can

produce higher resolution subsurface imagiTlg

(HARRIS etal･, 1992, LAZARATOS eta1., 1993, SAM

etal･, 1992, VAN SHAACX eia1., 1992). They have

produced depth-migrated images by combining

wavefield separation processing and migration

processing, using the velocity information ob-tained from difect-arrivaltraveltime tomography.

In a volcanic or highly fractured area (gener-

ally in inhomogeneous media) , cross-well records

with a slgnal to noise ratio high enough for the

use of seismic re且ected or scattered wave丘eld are

rarely acquired, because of unsatisfactory obser-

vation system or the inhomogeneity･ Generally,

for the use of seismic reflected or scattered

wave丘eld in a cross-well geometry, those

wave丘eld must be extracted from observed cross-

well seismic data･ But it is not easy to detect and

extract reflections or diffractions clearlyfrom ob-

served data only byus1ng WaVe field separationtechエーiques.Problems are caused by the source/receiver geometrical arrangements,the contami-

nation of tubewaves, the illhomogeneity of the me-

diaand other factors. It is indispensable for this

method both to improve the slgnal to noise ratio

of data and to develop a robust data processlng

methodology.

Velocity analysis (the main element of sur-

face seismic data processing) can be a useful toolfor detecting a pattern of reflected or scattered

wave丘eld. It may be regarded as a kind of match-ing against characteristic patterns (e.g.the hyper-

bola pattern caused by re負ection events in a CDP

ensemble)IIn this paper,velocity analysis is

modi丘ed and applied to a cross-well seismic geo-

metry and further for detecting a pattern caused

一.Lー＼,

a

ⅩsV Ⅹ

Source

Receiver

//′////

(a)

採 第50巻 第 2 号

by diffTraction events. Stacked records can be ob-

tained based on results of velocity analysis. The

advantages of these methods are that data

processing can be performed without using the in-

formatiく)a from velocity tomograms and that im-

aglng Can be achieved even in the lower part of a

well beyond the coverage of cross-well travel

time tomography. The methods are also insensト

とive to velocity丘eld. The disadvantage of these

methods is that complicated structures cannot be

imaged precisely because of insensitivity to veloci-ty丘eld. They may be used to obtain rough imag-

ing as the丘rst step, in order to take the next step

and pert'ormmore precise imaging, especially in

geothermal or other inhomogeneous areas.

2. DATA PROCESSING

2.1 VELOCITY ÅNÅLYSIS ÅND COP

STACXING USING REFI.ECTIONS

This type of data processlng Was described

in detail in RoKtJGAWA and MATStJSHIMA, 1995.

This section glVeS Only an o山1ine of the methodoト

Ogy.

The following equation isthe travel time equ-

ation of re且ection for a cross-well geometry, asI

sumlng llOrizontal layerlng and straight raypaths;

t=1 (2T(0,-Xs+vXr)2･(i)2(T(0,=i)

(1)

where T(0) is one way normal travel time, V is

velocity and the other parameters are as shown in

Figure 1 (a).

The typical procedure of this method is as fol-

lows;

step 1 :Set a COP location and the standard

SOURCE

WELL

vT(0,1si+

L R&CLEL'VER

B

0))

1Rj

Fig･ 1 Parameters for calculus of travel time in case of (a) the CDP stacking and (b) the di放･action stacking.

cross-wellimagingby theCDP stackingand thediHractionstackingwithvelocityanalysisJunMATSUSHIMA, ShuichiRoxuGAWA, ToshiyukiYoKOTA and TerukiMIYAZAKl

109

depth (time=0) for the one way normal time

T(0).

step 2 : Assume a pair ofvalues for V and T(0) in

equation (1)

step 3 : Obtain the depth by the product of V and

T(0).

step 4 : Select pairs of source and receiver which

compose the common re且ection point gather･

step 5 : Substitute Xs and Xrinto

equation (1)

and obtain the travel time of reflection for each

pair. Here, Ⅹs andXr are the positions of each

pair of source and receiver obtained from step4･

step 6 : Add the amplitude corresponding to the

travel time obtained from step 5 and divide the ad-

ded amplitude by the stack number. This value

Elves the concentration of the reflection energy･

step 7 : Repeat steps 2 to 6.

This procedure glVeSa Velocity analysュs

panel at the CDP location. This panel is a table of

numbers as a function of velocity versus one-way

normal time. Velocity-time palrS are Selected

from this panel based on maximum coherency

peaks.A series of values along these velocity-

time palrS makes a CDP stacked trace.

2.2 VELOCITY ANALYSIS AND DIFFRACI

TION STACKING USING DIFFRACI

TIONS

Velocity analysュs uSlng di敷actions is similar

to velocity analysュs uSlng re且ections. Figure 2 il-

lustrates the comparison of stacked waves be-

tween common reflection point and common

diffTraction point. In the case of velocity analysis

using reflections, only common reflected waves

are stacked at a point (Figure 2 (a)).On the other

hand, in the case of velocity analysis uslng diffTrac-

(a)

平 準 *(b)

jv

雫 j･qFig. 2 Comparison of stacked waves between (a)

common reflection point and (b) common

diffraction point.

tions, common di飴acted waves are stacked at a

point (Figure 2(b)).

The following equation is the travel time equ-

ation of diffTraction in a crossIWell geometry,as-

sumlng Straight raypaths;

tij=( (VT(0)-Si)2+B2

(vT(0)-R])2+

(LIB)2)2)/v

(2)

where i and j denotes the numbers of the source

and of receiver, respectively. T (0) is one waynor-

mal time, V is velocity and the other parameters

are as shown in Figure 1(b).

The typical procedure of this method is asfol-

lows;

step 1 : Set a velocity analysis location and the

standard depth (time=0) for the one way normal

time T(0).

step 2 : Assume a pair ofvalues for V and T(0)in

equation (2) and calculate the travel times for all

the pairs of i and j based on equation (2)･

step 3 : Obtain the depthby the product of V and

T(0) and at this depth I)Oint add the amplitudes

corresponding to the travel time obtainedfrom

step 2. This calculation can be performed by the

followlng equation;

Ns N,

∑∑AT,(i,j,tij)i=1j=1

(3)

where AT, (i,j,tlj)means the amplitudecor-

responding to the travel timetl)Aand Ns and N, are

the total number of source points and receiver

points, respectively.

This value glVeS the concentration of di飴action

energy I

step 4 : Repeat steps 1 to 3･

This procedure glVeS a Velocity analysュs Panel at

the location. This panel is a table of numbers asa

function of velocity versus one-way normal time･

Velocity-time pairs are selected from this panel

based on maximum coherency peaks. A series of

values along these velocity-time palrS makes a

diffTraction stacked trace.

3. NUMERICAL EXPERIMENTS

This section describes numerical simulation

examples used to demonstrate how the methods

work, especially for noISy Or complicateddata･

110

HORIヱONTÅL DISTÅNCE (n)souRC丑 ●l●

WE1⊥

仇●.･･

^M2

旦i(

0･04

E:巨】EI

0.481･･

札5 ･･･

仇1 01 03 0.4 0..5RECEIVER

WEIJ一

●

●

●

1800n/s

●

●

●

REFLECTOR

1 5kHz 乱icker wavelet

samplingperiod: 1LLSeC

data leng血: 1024Ⅰ)t

Fig. 3 Numerical simulation model and the

speci丘catioIIS Of data acquisition. A CDP

ensemble with a common depth point at

the center of the interwell was producedby using the convolution method.

3.1 CDP STÅCXING WITⅢ VELOCITY

ANAI.YSIS

Figure 3 shows a numerical simulation

model and the specifications of data acquisition.

A CDP ensemble with a common depth point at

the center of the interwell was used for simplici-ty･ Reflections were generated for a crossIWell gel

ometry from the model shown in Figure 3, uslng

the convolution method. Figure 4(a) shows a

CDP ensemble. The data processing as described

in section 2.1 was performed for this data set.

Figure 5 (a) shows the result of velocity analysisfor the data set shown in Figure 4(a). The con-

centration of the stacked reflections can be iden-

tified clearly.

Next,丘ve Ricker wavelets which have the

same frequency and amplitude as those of the

reBection were added randomly to each trace of

the gather shown in Figure 4(a) (Figure 4(b)).Finally, forty Ricker wavelets were added ran-

domly to each trace of the gather shown in

Figure 4(a) (Figure 4(c)). Here, it is assumedthat the situation is as after AGC and bandpass

丘1tering･ Velocity analysis was performed for

each data set. The results are shown in Figure

5 (b) and Figure 5 (c), respectively. According to

the results of the velocity analysis, a CDP stacked

record was obtained for each data set (Figure

6(aト(c)). Figure 6 shows the e蝕ctiveness and

robustness of the methods for noisy data.

(a)

0.0

′ー0.1旦EE

O･2

岳..3∈)

0.4

(0.

第50巻 第 2 号

I

0.0

b)

.0

′ー 0.1

≡I-■l

EC 0..2

iEg

o･3

0.4

2〈泊.0 4W.0 600.0 8(札0 1(氾0.0

dme (卜SeC)

0.0

(c)

0.0

0.1′■ヽ

旦o.2※

已o..3巨】l∋

0.4

2(泊.0 4∝).0 6CK).0 8∝).0 1000.0

time (psec)

0.0 200.0 4W.0 6∝).0 8(め.0 1∝氾.0

time (usec)

Fig. 4 A COP ensemble (a) no random noise (b)負ve random noises are added to each trace

(c) forty random noises are added to eachtrace. Reflected wave fields and random

noise were generated by using the convolu-

tion method.

3.2 DIFFRÅCTION STACEING WITII

VELOCITY ÅNÅLYSIS

Figure 7 shows a numerical simulation

model and the speci丘cations of data acquisition.

In order to represent scatterers, low velocity

points of 3200 m/sare set randomly in a diagonal

portion of the background model, which has a

uniform velocity 3600 m/s. Numerical simulationdata were generated for a cross-well geometry in

the model shown in Figure 7 uslng the血itediffTerence

method･ Three data sets having vari-

cross-wedimagingby theCDP stackingandthediffractionstackingwithvelocityanalysisJun MATSUSHIMA, ShuichiRoxuGAWA, ToshiyukiYoKOTA and TerukiMIYAZAXl 1 1 1

葺>ト-

U

OJ【⇒>

(a)

1(X)0

2∝〉0

(b)A

召1柵0ヽ一′

已-

UO

E52(泊0

>･

(c)′ー

召1(泊0ヽ■′

>

E:U

ヨ20001d

;I

400 8(氾

time (psec)

0.0 50.0

400 8〈X)time (psec)

0.0 50.0

4(X) 8(X)

time (LLSeC)

_50.00.0 50.0

Fig･ 5 Results of velocity analysisfor each data

set shown in Figure4･ The concentration

of the stacked re且ectionscan be identified

clearly.

ous central frequencies (50 Hz, 100 Hz, 200Hz

Bicker wavelet)were generated. Figure 8 shows

examples of common source gathersfor each

type (after AGC and medianfi1tering)･Direct

waves were removed by application of median

altering thirty common source gathers were

generated for eachdata set･ Data processlng aS

described in section 2.2 was performed on each

data set after AGC and medianfi1tering.The posi-

tions of velocity analysis are shown inFigure 7･

According to the results of the velocity analysis,

di飴action stacked records were obtainedfor

each data set (Figure 9). These results lead to

the following discussion･

If a shorter wavelength compared to the size

ofinhomogeneity is used

for imaglng, high resolu-

Fig. 6

0.0

2(X).0

4(X).0

6∝).0

OZヒ弓

宅>

←<づl■一l

富戸】

育0ヽヽ_■′

Results of COP stacked recordsfor each

data set shownin Figure 4.

600m

lqm:/CDP

location

=t●●●il

1〔

600m

SOurCe

interval 20m30 shots 干転

3600m/s

3600m/s and 3200rn/s mixed

600m

reCelVer

interval 20m30 receptions

苧鞋Fig.7 Numerical simulation model and

the

specifications of thedata acquisition･ In

order to represent scattererS,low velocity

points of3200 m/s are set randomly

in a

diagonal portion of thebackground

model, whichhas a unifofm velocity

3600

m/s.

tion stacked records will be obtained butthey are

noisy. Conversely, if a longer wavelengthcom-

pared to the inhomogeneity sizeis used

for imag-

1ng,low resolution stacked records will

be ob-

tained but they are not noisy･The reason for this

is the existence of multi-scattering causedby in-

homogeneities･ Accordingly, in performlng data

processlng ln an inhomogeneous reglOn･ a Suita-

ble wavelength for adequate imaging shouldbe

selected.

4. APPLICATION TO FIELD DATA

The methods describedin section 2 were apt

plied tofielddata observed in a geothermal area･

112

(a)

o.o蔓

′一ヽ

旦2伽.0E]

已岩4W.0

棚

l】

0.0 3 10.0 620.0

dme (msec)

rb)

0.0

′■ヽ

旦2柵.0こ□

岳.....1∋

≡ヨ粧葦≡lレヽ′一′

ヽ■-■､-}

～

tid√

～～～

ヽ■ノ仙ヽ′J

触 ▲-∨叫---

I･-′∨小-

▼-～

0.0

(c)

0.0

管言2抑･Oi:岩4帆0

310.0 620.0

time (msec)

0.0 3 10.0 620.0dme (msec)

Fig･8 Examples of common source gather

(source deI)th is 360 m, after AGC alld me-

dianfi1tering), central frequency of Rick-

er wavelet (a) 50Hz, (b) 100Hz, (c)

200 Hz. Numericalsimulation data were

generated by using the finite di飽rence

method.

A seismic tomography experiment was car-

ried out by NEDO (New Energy and Industrial

Technology Development Organization) in

Yutsut)o, Oita Pref., Japan using two drillholes,

N21YT-1 and N3-YT-2. Table 1 shows the

specifications of the tomographic data acqulSl-

tion･ In this paper, only the vertical component of

the data was used for data processing. Figure 10

探 査 第50巻 第 2 号

shows an example of unprocessed common

receiver gathers. In Figure 10, the direct P-wave

and direct S--wave indicated by the circle were

used for sI)eCtrum analysis. Figure ll shows am-

plitude spectra for both the direct P-wave and

the direct S-⊥wave. The frequency of the direct S-

wave is lower than that of the P-wave. The PI

wave was used for imaglng, 1･e･, Velocity analysis

was performed almost within the range of PI

wave velocity obtained from the P-⊥wave traveレ

time tomography.

4.1 CI)P STACXING WITII VlnOCITY

ÅNÅLYSIS

Figure 12(a) shows the flow chart for this

type of data processlng･ In this case, three ranges

of bandpassfi1tering (180-280 Hz, 80-180 Hz,

30-130 Hz) were applied. The data processing as

described in section 2,1 was performed only for

the upgolng WaVe丘eld･ The velocity analysis was

performed from 55 m to 215 m at every 2 m inter-

val measuring the distance from the position of

N3-YT-12. The standard depth (time=0) for one

way normal time was 400 m. Figure 13 shows the

CDP stacked records for each frequency range.The calculation CPtT time for a sequence of data

processlmg for each frequency range, uslllg the

CRAY (:90 super computer, was about 3 hours.

4.2 DIFFRACTION STACXING WITII

VELOCITY ÅNÅLYSIS

Figure 12(b) shows the flow chart for this

type of (1ata processlng･ The data processlng aS

described in section 2.2 was performed after band-

pass altering and AGC. In this case, three ranges

of bandpassfi1tering (180-280 Hz, 801180 Hz,

30-130 ⅠIz)were applied. The positions of veloci-ty analysis were from 7･m to 263 m at every 2 m

interval measurlng the distance from N31YT-2.

The standard depth (time=0) for the one way

normal t'.ime was 400m. Figure 14 shows the

di飴action stacked records for each frequency

range･ The calculation CPU time for a sequence

of data processing for each frequency range, us-

ing the CRAY C90, was about 30 hours.

4.3 ESTIMATION OF THE INFI.UENCE

OF TRANSMITTED P-WAVES IN THE

CASE OF THE DIFFRACTION STACK.

ING

In this section, the inauence of transmitted

Cross-wellimagingby theCDP stackingand the diHractionstackingwith velocityanalysis Jun MATSUSHIMA, ShuichiRoKUGAWA, Toshiyuki YoKOTA and TerukiMrYAZAKl 1 13

HORIZONTAL DISTANCE (m)

1〔氾.0 3CK).0 5CK).0

(a)0.0

OZ

62･0 ;>･<<-

124.0音官&

186.0

0))

HORIZONTAL DISTANCE (m)

1(X),0

門T

0.0

62.0

1 24.0

86.0

OZ一再

i>i

づ

≡【司

′■ヽ

Sヽ■■′

(c

HORIZONTAL DISTANCE (m)

1(X〉.0 3α).0 5(氾.00.0

75.5

155.0

捕

i

Cl:Z亡弓

宅>･←<<

:tq

′ー

!ヽ-･l

Fig. 9 Results of diffraction stacked record for three types of data set, central frequency of Richer wavelet (a)

50Hz, (b) 100Hz, (c) 200Hz.

Table 1 Speci丘cations of data acquisition

S OURCE WELL

SOURCE1. PRIMER ANDAlRGUN

INTERVAL: 20m

SHOT DEPTIl: 700-1660m

RECEIVER WEI,I.

RECEⅣER: DS-2 3-COMPONENT RECEIVBR

mRVAL: 20m

RECEPTION DEPTH･. 660-1670m

REC ORI)

RECORD LENGTH: 1,5sec

SAMPLNG PERIOD: 0.25msec

WEI.L

PRIMER SOURCE WELL: N2-YTll

RECEⅣER WEIノL: N3-YT-2

AIRGUN SOURCE WEIJL: N3-YT-2

RECEⅣER WELL: N2-YT-1

DISTÅNCE BETWEEN WELI,S: 271m

PIWaVeS in the case of diffraction stacking lS esti-

mated. As described in section 4.2, transmitted

P-waves were not removed in processing the

丘eld data. So, it is necessary to estimate the

influence of transmitted P-waves.

4.3.1 M二UTE OF TRANSMIITTED P-WAVES

Firstly, as a simple method,丘fty points were

muted from the first arrival picking. Figure 15

shows diffraction stacked records using the mut-

edfield datainthe case of applying the 80180

Hz bandpass丘ltering. There is very littlediffer-

ence between Figure 14(b) (before mute) andFigure 15 (aftermute).

4.3.2 RESTRICTION OF THE RANGE FOR

STACKEI) WAVES

As a second method, the range of stacked

0.0 100.0 200.0

time (msec)Fig. 10 An example of unprocessed丘eld data.

Common receiver gather (receiver depth

is 1001.4m). The dュfect P-wave anddirect S-wave indicated by the circle

were used for spectrum analysis.

waves was restricted in the diffraction stacking.

Figure 16 shows the range of stacking. In Figure

16, considering one raypath from one source and

assuming a Straight raypath, diffractions going

through the shadow zone were not stacked.

Figure 17 shows the results of the diffraction

stacking for various values of 0. Again, the field

data processed by application of bandpass丘1ter-

ing (80-180 Hz) was used for imaging. Figure17

indicates that diffraction stacked records do not

fade away with increaslng ♂.

In the same way, this type of data processlng

was applied to numerical simulationdata. Figure

18 shows a numerical simulation model and the

specifications of data acquisition, which were

similar to those of the丘eld data acquisition. Nu-

114

4.0×105

¢

1;コ

.I:

五2･0×105≡q1

0

〈a〉

探

,g2･0×106

⊃

≡

ぎ1･0×106q1

0

0 200 400 600 800

frequency (Hz)

〈b)

第50巻 第 2 号

0 200 400 600 BOO

frequency (Hz)

Fig. ll Comparison of amplitude spectrum between (a) direct P～waveand (b) direct S-wave.

ORIGI HAL

D^TA

臥NDPASS

FI LTER

AGC

F-K

円LTER

州NG

柵VEFIELD

VELOCITY

∧NALYS AS

CXF

STACKED

帆

L和NG

WAVEFI ELD

VELOCI TY

AN∧LYSIS

CDP

STACKED

rf∞RD

ORIGINAL

DATA

BAN D PASS

円LTER

AGC

VELOCITY

ANALYSIS

DIFFRACT10N

STACKED

RECORD

(a) (b)

Fig･ 12 Flow charts of the data processing for (a)

the CDP stacking and (b) the diffraction

stacking.

merical simulation data for both transmitted

waves and re且ections was generated from the

model shown in Figure 18 uslng the convolution

method. Thirty common source gathers were

generated, and Figure 19 shows an example.

Velocity analysis with restriction of the stackedwaves was performed at the center of the inter-

well･ Figure 20 shows results of the velocity anal-

ysis Panel in the case of the diffraction stackingfor various values of 0. Figure 20 indicates that

the concentration of the transmitted wave does

not form a given wavelet (又icker wavelet).Fur-

thermore, Figure 20 indicates that the concentra-

tion of transm辻ted waves fades away with increas-

ing ♂.On the other hand, Figure 17 indicates that

diffraction stacked records do not fade away with

increaslng ♂.Therefore, it call be concluded that

diffTraction stacked records as shown in Figure 14

are not greatly influenced by transmitted PI

Waves.

5. DISCIJSSION

The results of applying the two types of data

processlng tO the field data leads to the following

discussion.

By application of the CDP stacking, ade-

quate slacked records were not obtained. In con-

trast, the application of the diffTraction stacking

produced improved stacked records. Some reflec-tors were delineated. There may not be any

markedl. discontinuity which isintense

enoughtobe imaged. Certainly, geological information (NE-

DO, 1992) does not show any large scale frac-

tures or large scale faults in this area. In addition,

a result of the P-wave traveltime tomograPhy

(YoKOl｢A βf αJ.,1995) suggests that geologicalstructure in this area consists of nearly horizontal

layerlng. There are two possible reasons for the

improved stacked records by the diffTractionstack-

ing.

One is the roughness of reflectors. Figure21

illustrates the influence of reflector roughness on

bothre且ection and diffraction. Of course, the

roughness should be compared tothe wave-

length. If a reflector is rough, reflections are

weakened and di飴actions are strengthened. In

this case, a re且ector may be delineated more ap-

propriat.ely by the diffraction stacking than the

CDP st;lCking.

The second explanation is that the di飴action

stacking has the potential also for imaglngflat

reflectors. This hypothesis was testedusing some

simple numerical experiments. Numerical simula-

Cross-wenimagingby theCOP stackingand thediFractionstackingwithvelocityanalysisJunMATSUSHIMA, ShuichiRoKUGAWA, ToshiyukiYoKOTA and TerukiMIYAZAK1 1 1 5

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CrossIWellimagingby theCI)P stackingand the diFractionstackingwithvelocityanalysisJun MATSUSHIMA, ShuichiRoKUGAWA, Toshiyuki YoKOTA and Teruki MIYAZAKi 11 7

HORIZONTAL DISTANCE (m)

7 50 100 150 200 250

0.0

50

101

151

20

0

OZ

o.orll

<>

･<

iO･0 ⊇l■∩

′-I

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ro10害ヽ■′

250.0

300.0

Fig. 15 Diffraction stacked records for the use of

the muted丘eld data in the case of ap-

plying a bandpass丘1ter (80-180 Hz).

tion model and data acquisition were the same as

shown in Figure 18. However, various central fre-

quencies of Bicker wavelet (10 Hz, 50 Hz, 100

Hz, 200 Hz, 400Hz) were used for obtainingboth CDP stacked records and diffTraction stacked

records. Numerical simulation data for reflections

was generated from the model shown in Figure

18 using the convolution method. Thirty common

source gathers were generated. Note that the

generated data does not have transmitted waves･

Both the CDP stacking and the ditfTraction stack-

1ng With velocity analysis were performedfor

each data set.Figure 22 shows both resulting

CDP stacked records and diffTraction stacked

records at the center of the interwel1.Figure 22 in-

dicates that the potential of the di飴action stack-

1ng for imaglngflat reflectors depends upon the

wavelength, while the CDP stacking lS not SO

wavelength dependent. The shorter wavelength

isused

in the diffraction stacking, the smaller am-

plitude of the diffTraction stacked recordis ob-

tained. However, the stack number of the CDP

stacking is30 at the most, while the stack number

of the di酔action stacking lS invariably 900. Thus

S/N of the diffTraction stacked recordis higher

than that of the CDP stacked record. So, the

diffraction stacking lS effective for obtaining lm-

SOURCE

RECEIVER

Fig. 16 Diagram illustrating the range of restric-

tion in diffraction stacking.0 is the range

of the shadow zone. The di飴actions

golng through the shadow zone are not

stacked.

proved stacked recordsin the case of noISy data･

In this respect, more research needs to be done in

connection with the shape of re且ectors and varト

ous types of noise.

Figure 14 indicates that either frequency

range of diffraction stacked records ishigher than

those of correspondingfi1tered data, because

diffTraction stacked records were transformed into

one way normal time on the time axis. Note that

this does not mean that diffTraction stacked

records transformed into one way normal time

have higher resolution than those into two way

normal time.This can be explained by Figure 23･

Equation (2), which represents the travel time

equation in the case of one way normal time, is

partially diffTerentiated with respect to T(0).

Graphically, the partial diffTerentiation coe缶cient

gives a curved surface, as shown in Figure 23 (a).

Here, i and j are constant, Si=Rj=200m,

L=271.0 m and B=135.5 m. Figure 23(a) indi-

cates the relationship,

∂tlj

aT(0)=2

except the part of a trough･ This relationship

shows that thefrequency of the diffTraction stack-

ed record is two times as much as the frequency

of the data before the diffraction stacking.There

is a trough whose peak corresponds to the depth

200 m, the depth of the source and receiver･ In

the part of a trough, the diffTraction recordis

第50巻 第 2 号

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Cross-weuimagingby theCDP slackingand thedigractionstackingwithvelocityanalysisJunMATSUSHIMA, ShuichiRoKUGAWA, ToshiyukiYoxoTA and TerukiMIYAZAK11 1 9

270m TRANSMITTED WAVEREFLEC TION

●●●

SOURCE

WELL

20m interval

30 shot

600m

4000m/s

RECEIVE A

WELL

●

●

●

20m interval

30 receive0.25msec

sampling120IIz

kicker wavelet

Fig. 18 Numerical simulation model and the

speci丘cations of the data acqusition.

concentration or the transmitted wave

(a)

/‾＼

∽

i......

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lll

ll

PI

l ～

lllr

ll

lll

lI I

lllll

0.0 100. 0 200. 0 300. 0 400. 0

time (msec)

Fig. 19 An example of numerical simulation data.

Common source gather (source depth is

O.Om). Reflections and transmitted

waves were generated by uslng the convo-

1ution method.

1 00.0

time (msec)

-20.00.0 20.0 40.0

100.0

time (msec)

120.00.0 20.0 40.0

concentratioll Or

the re爪ection

200. 0

200.0

100.0

time (msec)

200. 0

-20.00.0 20.0 40.0

Fig. 20 Results of velocity analysis in the case of diffraction stacking for various shadow angles 0, (a) 0=0.0

degree, (b) β=41.5 degree, (c) β=85.2 degree.

120

INC【DENT WAVE

軋AT

REFLECTOR

INCIDENT WAVE

INCIDENT WAVE

D肝USION

REFLECTOR

COMPLETE DIFFUS ION

ECrOR

Fig･ 21 Diagram illustrating the in且uence of

roughness of reflector on both phenome-na of reflection and diffraction.

stretched. Successfulimaglng Cannot be achieved

in this reglOn. So itis necessary to eliminate wide

angle di飴actions in the diffraction stacking.

On the other hand, the travel time equatioll

in the case of two way normal timeis represented

as follows.

tij= (A

+

(VT(0)/2-Si)2+B2(VT(0)/21Rj)2+ (L-B)2)/v

(4)

where i and j denotes the number of source and

receiver, respectively. T(0) is two way normal

time, V is velocity and the other parameters are

as shownin Figure 1. Equation (4) is partially

diffTerentiated with respect to T (0). Graphically

the partialdiffTerentiation coefhcient gives a

cuⅣed surface, as shown in Figure 23 (b).Here, i

and j are constant, Si=Rj=200m, L=271･Om

and B=135.5 m. Figure 23(b) indicates the toll

1owlng relationship ,

｡芸t(lj6)= 1

except the part of a trough. This indicates that

the frequency of the diffraction stacked record

corresponds to the frequency of the data before

the di飴action stacking. Again, there is the same

kind of troughwhose peak corresponds to the

depth 200m, the depth of the source and

探 査 第50巻 第 2 号

reCelVer.

It follows from the above that the rate of

change of travel time for one way normal time is

two times as much as that of two way normal

time.

6. CONCLUDING REMARKS

In this paper, two types of data processlng

are presented, together with numerical simula-

tion examples in order to evaluate these methods

for noisy or complicated data. Finally, a

preliminarily application of the methods to丘eld

data observed in a geothermal area is described.

The proposed data processlng methods, especial1

1y the di飴action stacking, has the potential for

rough illlaging as a丘rst step before more precise

imaglng lS Performed, especially in geothermal or

other inhomogeneous areas.

Certainly, cross-well seismic methods have

the potential for higher resolution imaglng than

surface seismic methods. However, especiallyin

the ink()mogeneous area, the use of the high fre-

quency waves may cause problems in delineating

detailed geological structure of discontinuities

(fractures of faults). In this respect, further

research needs to be done to determine

l. the most suitable wavelength for ade-

quate imaglng;

2. the relation between the roughness of

the re且ector and the wavelength; and

3. how to select the most suitable traces in

the case of the diffraction stacking.

ÅCⅨNOWI-E DGMENTS

The authoI･S WOuld like to thank the New

Energy and Industrial Technology Development

Organization for permission to use the data.

Reference 良

HARRIS, J. M., RECTOR, J. W., LAZARATOS, S. K., and

VAN ScHAACX, M. (1992) : Highresolution cross-

well imaglng Of a west Texas carbonate reservoir :

part I,♪resented at the 62nd Ann. hterna1. Mtg･ ofSEG, expanded abstracts, 35M39.

IsHII, Y.,. MuRAOKA, H., AsAKURA, N., ONISHI, M･

(1995) : Cross-weu seismic tomography for ge-

othermalexploration, Proceedings of the 3rd SEGJ/

SEG Ietemational Symposium on GeotomograPhy,

368-374.

LAZARAT()S, S. K., RECTOR, J. W., HA又RIS, J. M., and

VAN ScHAACK, M. (1993) : High-resolution, cross-

well, reflection imaglng

･. Potentialand technical

cross-we11血agingby the CDP stackingandthe diFractionstackingwithvelocityanalysisJunMATSUSHIMA･ ShuichiRoKUGAWA, ToshiyukiYoKOTA and TerukiMIYAZA瓜1 21

(a)

0))

(c)

1∝I.0

time (msec)

1∝).0

time (msec)

2∝I.0

200.0

1 ∝〉.0

I) 7010

1α).0

彗芸::

育:1:o:I:oo.

1仰.0

4> 70･0

召40･0

昔I':o:'･.o:

100.0

70.0

40.0

10.0

120.0

-50.0

1(氾.0

70.0

40.0

10.01

-20.0

-50.0

4)

｢⊃

a;∃

ぎ

q)

-8

･B冒

(d)

(e)

1 00.0 200.0

tine (msec)

100.0 2∝).0

time (mscc)

1a).0 2(泊.0

dme (msec)

1CK).0

1(X).0

4)70･0

ヨT.::g二≡::o.

100.0

a) 70.0

ca40･0

育_1Z'.o.-50.0

100.0

(a')

100.0 2CK).0

time (msec)

0)I)

1CK).0 2伽.0

time (msec)(c')

1(泊.0 200.0

time (msec)

(d')

4> 70.0

音_;.:.:.ー50.0

1 CK).0

a70･O

a?_:i:.-50.0

(e')

1(X).0

time (msec)

2(X).0

1(抑.0 200.0

time (msec)

Fig･ 22 Both results of CDP stacked records anddiffraction stacked records at the center of the

interwe11･ for

various centralfrequencies of Ricker wavelet, (a) 10 Hz, (b) 50 Hz, (c) 100 Hz, (d) 200

Iiz, (c) 400

Hz. The symbol'means the results of the

diffraction stacking･

(a)

&ij

aT(0)

211.5

1

5■

0

0

0.1

r(0)0.2

5500

5000

4500

V

a,j

aT(0)

2

1.5

1

5

0

0

0.1

r(0)0.2

4000

5500

5000

(b)

Fig. 23 3-D plot of the partial differentiation coe丘cientl∂tij/∂T(0)I

(b) in the case of two way normal time･

(a) in the case of one way normal time,

122J 物 理

di飽culties, Geophysics, 58, 1270-1280.

MATSUSHIMA, ∫.,RoKUGAWA, S., YoKOTA, T., MIYA-

zAXI, T. (1995a) : Application of CDP stacking to

cross-well data -Imaglng With cross-welldiffrac-

tion data-, Proc. of92th SEGJ Conf., 37-41, (In

Japanese with English abstract)･

MATSUSHIMA, ∫.,RoKtJGAWA, S., YoxoTA., T., MIYA-

zAKI, T. (1995b) : Application of CDP stacking to

cross-well dala -Applicationto the負eld data-,

Proc. of93rd SEGJ Conf.,236-240･

New Energy and IndustrialTechnology Development

Organization (1992) : Conjrmation study ofthe

eBTeciivenessof♪rosPectingtechniques for deep geo ther-

mal yleSOurCeS, Development of seismic exploration

techniques, Development exploration techniques for

fracture-typereservoir, Drilling, well logging, welltest

and integrated assessment of fracture characteristics

(Abstract) (22p), (In Japanese with English ab-

stract).RoxuGAWA, S. and

MATStTSHIMA, ∫.(1995) : Applica-

tion of CDP stacking to crossIWell reflection data

探 第50巻 第 2 号