an acoustic-logging transmission-network model

An acoustic-logging transmission-network modelLin Fa and John P. CastagnaSarkeys Energy Center, 100 East Boyd Street, Norman, Oklahoma 73019

Jens M. HovemThe Norwegian University of Science and Technology, N-7491 Trondheim, Norway

Daqun DongMarine Institute, Northwest Polytechnic University, Xi’an, Shaanxi 710071, People’s Republic of China

~Received 29 December 2000; accepted for publication 10 January 2002!

The acoustic logging process can be described as a signal transmission system with a correspondingtransmission network model. This model gives the relations between driving-voltage signal, theelectrical-acoustic conversion at the source, acoustic properties of the propagation media~boreholefluid and formation around borehole!, the pressure response in the borehole, the acoustic-electricalconversion at the receiver and recorded logging signal. ©2002 Acoustical Society of America.@DOI: 10.1121/1.1456925#

PACS numbers: 43.58.Vb, 43.58.Wc, 43.20.Bi, 43.20.Mv@SLE#

n-dth-pin

ree

icait

lecan

rnrth

anidthivf

tedr

r-ngs

s-

gencyandlec-ed-a-

thec-

icaluit-thes ofam-

thegnalr-

log-sig-orkfor

.l–l–

s of

tputrk

e-theten-

g-

e-

I. INTRODUCTION

Acoustic logging of boreholes is widely used to~1!evaluate rock properties and porosity of formation arouborehole,~2! identify fracture,~3! provide images of openhole wall and casing corrosion,~4! appraise the cement bonquality of cased-well,~5! measure the diameters of boborehole and cased-well, and~6! calibrate seismic data. Typically, some assumed source functions are used to comsynthetic microseismograms. Examples in the literatureclude the Ricker wavelet,1 Tsang wavelet,2 or Gaussian im-pulse wavelet.3 Different kinds of acoustic transducer aused as source and receiver in acoustic logging tools. Thinclude monopole and dipole transducers and thin cylindrtransducers polarized in radial and tangential directions wdifferent resonance frequencies. Cheng and Tokso¨z4 foundthat the amplitude and frequency variations of Stonewaves in synthetic microseismogram was more enhancompared with actual borehole acoustic logging signals,hypothesized that this may be because the frequencysponses of the logging tool sources and receivers arerower than the ones used in their calculations. The souspectrum of the acoustic signal has a strong effect onexcitation of pseudo-Rayleigh waves. In order to understthe acoustic signal spectrum, it is necessary to consdriving-voltage signal, electrical–acoustic conversion atsource, and acoustic–electrical conversion at the receBerlincourt, Curran, and Jaffe5 gave the equivalent circuit othe piezoelectric shell transducer. In order to calibratetransducer and separate the interrogating radiation fromscattered or reflected radiation in a test facility of limitsize, Piquette presented a method for the transient suppsion of both a spherical transducer6,7 and various transducetypes.8 Piquette and Forsthe9 put forward generalized methods for determining the required wave shape for the drivivoltage wave form that produces no transients in the acoufield radiated from an electroacoustic projector. Holly10 de-scribed a method for the generation of broadband acoutransmissions. Fa, Lin, and Chen11 derived the source func

2158 J. Acoust. Soc. Am. 111 (5), Pt. 1, May 2002 0001-4966/2002/

d

ute-

sel

h

yedde-ar-ceedereer.

ahe

es-

-tic

tic

tions of a cylindrical transducer for several driving-voltasignals and performed the analysis in the time and frequedomains. In this paper, we derive the electrical–acousticacoustic–electrical transmission functions of the piezoetric transducer, considering the effects of the output impance of the driving circuit, the input impedance of the mesurement circuit and the complex mechanical load ofsurrounding coupling medium around the transducer. Acording to the electrical–acoustic and acoustic–electrtransmission functions of the transducer, by choosing sable driving-voltage signal, the electrical parameters ofdriving and measurement circuits, the physical parameterthe coupling medium and the physical and geometric pareters of transducer, we can make the transducer radiatedesired acoustic signal to optimize the measurement sifor various applications. We also utilize the concept of infomation and signal transmission to analyze the acousticging process, describe the acoustic logging process as anal transmission system, and derive its transmission netwmodel. This model consists of three submodels: a modelthe source, a model for the propagation media~borehole fluidand formation around borehole! and a model for the receiverIn this model~1! the acoustic source acts like an electricaacoustic filter,~2! the receiver is equivalent to an acousticaelectric low-pass filter,~3! the electric terminals of both thesource and the receiver are the input and output terminalthe transmission network and,~4! the driving-voltage signaland the measured logging signal are the input and ousignals of the network. Since the input signal of the netwo~driving-voltage signal!, the properties of the source and rceiver, the physical parameters of the borehole fluid andborehole size can be assumed to be known, one can potially invert for the formation properties from the output sinal of the network~the recorded logging signal!.

II. FORMULATION

In the following, the case of the medium around borhole being an infinite elastic body is discussed.

111(5)/2158/8/$19.00 © 2002 Acoustical Society of America

s-
FIG. 1. Equivalent circuits of the spherical shell tranducer.~a! Source.~b! Receiver.
ith

nct

ol

-ten

nnce

ve

For a piezoelectric thin spherical shell transducer waverage radiusr b and wall thicknessl t , polarized in theradial direction with electrodes connected to the inner aouter surfaces, its electric–acoustic and acoustic–eleequivalents~source and receiver!5,6,11–13are shown in Figs.1~a! and ~b!. The description and expression of the symbin Fig. 1 are shown in Table I.

TABLE I. Description and expression of symbols in Fig. 1.rp is the densityof the transducer material;si11

E , si12E , di31 , and « i11

T are the strain, piezo-electric, and dielectric constants of the transducer material, respectiSiC

E 5(si11E 1si12

E )/2, ki315di31 /ASiCE « i33

T , and km5v1 /nm ; the subscripti51 stands for source andi 53 stands for receiver, where,s111

E 5s311E 5s11

E ,s112

E 5s312E 5s12

E , d1315d3315d31 , «111T 5«311

T 5«11T , k1315k3315k31 , S1C

E

5S3CE 5SC

E , l 1t5 l 3t5 l t , r 1b5r 3b5r b , andnm is the acoustic velocity ofthe coupling fluid around the transducer.

Symbol Description Expression

R1 Output resistance of driving circuitU1(t) Driving-voltage signalV(t) Voltage signal of electric terminals

of sourceP(t) Pressure response signal in boreholeX(t) Acoustic pressure output signal

of sourceR3 Input resistance of measurement

circuitU3(t) Electric output signal of receiverCi0 Clamped capacitance of transducer4pr ib

2 « i33(12ki312 )/ l it

Ni Mechanical–electrical conversioncoefficient of transducer

4pr ibdi31 /SiCE

mi Mass of transducer 4pr ib2 l itrp

Cim Elastic stiffness of transducer siCE /4p l it

Rir Radiation force resistanceof transducer

4pk2r ib3 rmnm /(11km

2 r ib2 )

mir Ratio of radiation impedanceto resonance frequency

4prmr ib2 /(11km

2 r ib2 )

Rim Friction force resistance

J. Acoust. Soc. Am., Vol. 111, No. 5, Pt. 1, May 2002

dric

s

According to Fig. 1~a!, the electrical–acoustic transmission function of the source in the time domain can be writas follows:

h1~ t !5K1 exp@2b1t#1K2 exp@2a1t#cos~v1t1u1!,~1a!

and its resonance frequency is

f 15v1/2p5)~x12y1!/4p, ~1b!

where M̃15m11m1r , R̃15R1m1R1r , a15(R1C10R̃1C1m

1C1mM̃1)/(R1C10C1mM̃1), b15@R10C1m1N12(R1C10

1R̃1C1m)#/(N12R1C10C1mM̃1), c151/(R1C10C1mM̃1), d1

5R1C1m /(R1C10C1mM̃1), e15d1R1rC1m , p15b12a12/3,

q15c112a13/272a1b1/3, D̃15(p1/3)31(q1/2)2, x1

5(2q1/21AD̃1)1/3, y15(2q1/22AD̃)1/3, a15a1/32(x1

1y1), b15(x11y1)/21a1/3, A15b12a1 , B15d1(b1

2A1)/@2(v121A1

2)#, C152d1(v121b1A1)/@2v1(v1

2

1A12)#, u15arctg(C1 /B1), K152N1d1a1 /(A1

21v12), L1

5(B121C1

2)1/2, andK25L1N1 .From Fig. 1~b!, the acoustic–electrical transmissio

function of the receiver in the time domain and its resonafrequency can be written as

h3~ t !5K3 exp@2a3t#12K4 exp@2b3t#cos~v3t1u3!,~2a!

f 35v3/2p5)~x32y3!/4p, ~2b!

where M̃35m31m3r , R̃35R3m1R3r , a35(C30R3C3mR̃3

1C3mM̃3)/C30R3C3mM̃3 , b35(C30R31C3mR̃31N32R3

3C3m)/(C30R3C3mM̃3), d35N3R3C3m /(C30R3C3mM̃3),e35d3R3rC3m , c351/(C30R3C3mM̃3), p35b32a3

2/3, q3

5c312a33/272a3b3/3, D̃35(p3/3)31(q3/2)2, x35(2q3/2

1AD̃3)1/3, y35(2q3/22AD̃3)1/3, a35a3/32(x31y3),

ly,

2159Fa et al.: Acoustic-logging model

-

st

he

-

m

bernt

;

ionig.

f

ll

e-a-f

ic

ionncynd-

ired

b35(x31y3)/21a3/3, A35b32a3 , B35v321A3

2, C3

5N3R3Cm3/2a3v3 , E352C3(v321b3A3), D35C3v3(b3

2A3)/B3 , K352d3b3 /(A321v3

2), K45(D321E3

2)1/2, andu35arctg(D3 /E3).

As shown in Fig. 2, the logging tool is set in a fluidfilled cylindrical borehole of radiusa, which embeds in aninfinite elastic medium.T0 is the acoustic source, which ilocated at the origin;R0 is the receiver, which is located aany point z on the borehole axis;r f , l f , and n f are thedensity, Lamb’s coefficient, and acoustic velocity of tborehole fluid;r, l, m, np , andns are the density, Lamb’scoefficients, and theP- andS-wave velocities of the formation around borehole. In the far field, whenT0 transmitsacoustic signals outwards, the effect of the propagationdia ~formation around borehole and borehole fluid! on thetransmitted acoustic signals can be described by

h2i l ~ t,z!5E2`

1`

H2~v!exp@ j vt#dv ~3a!

and

H2i l ~v,z!5Hd~v,z!1Hr~v,z!

5exp@ j vz/Vf #

z

11

~2p!2 E2`

1`

A~kz ,v!exp@ jkzz#dkz , ~3b!

FIG. 2. Geometrical configuration of acoustic logging.

FIG. 3. Acoustic logging transmission network in time domain.

2160 J. Acoust. Soc. Am., Vol. 111, No. 5, Pt. 1, May 2002

e-

where

A52F1kraH1

~1!~kra!1F2H0~1!~kra!

F1kraJ1~kra!1F2J0~kra!, ~3c!

F152mF2ks

2

a22~ks222k2!2

H0~1!~kr

~c!a!

kr~c!aH1

~1!~kr~c!a!

24k2kr~s!

H0~1!~kr

~s!a!

aH1~1!~kr

~s!a!G , ~3d!

F25lk2ks2, ~3e!

v is the angular frequency; the borehole fluid wave numk5v/n f ; kz is axial wave number and its radial compone

kr5Ak22kz2; J0(krr ) is the zeroth-order Bessel function

kr(c)5(kc

22k2)1/2; kr(s)5(ks

22k2)1/2; kp25v2/np

2; and ks2

5v2/ns2.

From Fig. 2 and the above relations, the transmissnetwork of acoustic logging can be obtained as shown in F3. WhenT0 is excited by the driving-voltage signalU1(t),the pressure response in the borehole at the position oR0

and the electric signal output byR0 ~i.e., the recorded log-ging signal! can be expressed by Eqs.~4! and ~5!,

P~ t,z!5U1~ t !* h1~ t,0!* h2~ t,z!, ~4!

U3~ t,z!5P~ t,z!* h3~ t,z!. ~5!

III. SIMULATION AND DISCUSSION

In the following calculation, let the thin spherical shetransducer consist of piezoelectric materialPZT-7A, its av-erage radiusr b58 cm and wall thicknessl t50.8 cm, respec-tively, the coupling fluid be transformer oil, the friction forcresistanceRm50.8pr b

2Zm , the output impedance of the driving circuit R1550V and the input impedance of the mesurement circuitR3550 kV. The physical parameters oPZT-7A and the specific acoustic impedanceZm of the cou-pling fluid are shown in Table II.11

A. Electrical–acoustic conversion properties of thetransducer

According to Eq.~1a!, the calculated electrical–acousttransmission property of the source is shown in Figs. 4~a!and ~b!. The source has the electrical–acoustic transmissproperty of negative original-phase, its resonance frequef 1 is 11.268 kHz and it acts like an electrical–acoustic bapass filter.

B. Relation between driving-voltage signal andacoustic signal radiated by source

In order to make the acoustic source radiate the desacoustic signal, according to Eqs.~1a! and~1b!, we use three

TABLE II. Physical parameters of piezoelectric materialPZT-7A andacoustic impedance of coupling fluid.

rp3103

~kg/m3!d31310212

~m/V!«33

T 31029

~F/m!s12

E 310212

~m2/N!s11

E 310212

~m2/N!Zm3106

@kg/~m2•s!#

7.6 260 3.7613 23.2 10.7 1.2205

Fa et al.: Acoustic-logging model

ofl–thetic

FIG. 4. Electric–acoustic transmission propertysource. NTR is the normalized amplitude of electricaacoustic transmission property of source and NFR isnormalized amplitude spectrum of electrical–acoustransmission property of source.~a! Time domain.~b!Frequency domain.

.rei

e-

alr

g

reedowilegstth

idas

T

e fre-

ingand

atedi-

ut 11heon-ivecyis

s inre-ngef-

carednceomin-

TheForcarve

fil-nalnal

tesal

n

kinds of driving-voltage signals:~1! a gated sinusoidal,~2!an impulse, and~3! a narrow boxcar function for computingThe chosen parameters are shown in Table III. The expsions of the above three kinds of driving-voltage signalsthe time domain are, respectively, as follows:

U1~ t !5@H~ t !2H~ t2t0!#U0 sin~v1t !, ~6!

U1~ t !5U0t3 exp@2dt#, ~7!

U1~ t !5@H~ t !2H~ t2t1!#U0 , ~8!

where U0 is the amplitude constant of the driving-voltagsignal;d is the damping coefficient of the impulsive drivingvoltage signal;t0 is the window width of the gated sinusoiddriving-voltage signal;t1 is the width of the narrow boxcafunction driving-voltage signal;H(t) andH(t2t i) ~i 50 or1! are Heaviside unit step functions.

When the source is excited by the three kinds of drivinvoltage signals, the calculated wave forms~RAWF! and am-plitude spectra~RAAS! for the radiated acoustic signals ashown in Figs. 5 and 6. The first half-wave of the gatsinusoidal driving-voltage signal, the impulsive and a narrboxcar function driving-voltage signals are positive, whthe first half waves of the radiated acoustic signals are netive. This phenomenon is caused by the electric-acoutransmission property of the negative original phase ofsource.

When the source is excited by the gated sinusodriving-voltage signal~i.e., the driving-voltage signal passethrough the electrical–acoustic filter!, the low and high fre-quency contents of the driving-voltage are suppressed.

TABLE III. Parameters of the three kinds of driving-voltage signals.

Gated sinusoidal function Impulsive function Boxcar functio

U0 ~V! t0 U0 ~V! d U0 ~V! t1

200 6p/v1 22.81031015 0.6v1 400 p/v1


s-n

-

a-ice

l

he

radiated acoustic energy concentrates near the resonancquency of the source and the radiated acoustic signal~theoutput signal of the electrical–acoustic filter! has bettermonochromaticity. This case is suitable for acoustic loggof nondispersive waves, such as the acoustic velocityamplitude logging ofP- andS- waves.

In logging, low frequency modes can be used to evalufractures and permeability of the formation. Due to limiteborehole and logging tool sizes, the lower limit of the minmal resonance frequency of the source only reaches abokHz. Using a general driving-voltage signal to excite ttransducer excites low frequency modes poorly. For the cventional acoustic logging tool, we can use the impulsdriving-voltage signal to excite the source. The frequenbandwidth of the acoustic signal radiated by the source9.870 kHz. The radiated acoustic energy evenly distributethe frequency range from 2.185 kHz to 12.055 kHz. Thefore, low frequency modes can be efficiently excited durilogging. For this case, the electrical–acoustic conversionficiency decreases somewhat.

When the transducer is excited by a narrow boxdriving-voltage signal, the radiated acoustic signal is formby two wavelets. The first wavelet is caused by appearaof the driving-voltage signal and the second one results frits disappearance. When the two wavelets constructivelyterfere, the radiated acoustic signal is the greatest.source creates less heat dissipation during its excitation.high temperature environments, using the narrow boxdriving-voltage signal to excite the transducer can improthe reliability and stability of acoustic logging tool.

The source acts like a band-pass electrical–acousticter. During its excitation process, the radiated acoustic sigdepends on the properties of both the driving-voltage sigand the source.

Because the thin spherical shell transducer radiaacoustic signal evenly in all directions, if the geometricsize of the transducer is considered andt2r b /nm is used to


tictice

l.

FIG. 5. Time domain wave forms of radiated acoussignals. RAWF is the amplitude of the radiated acoussignals. ~a! Case of gated sinusoidal driving-voltagsignal.~b! Case of impulsive driving-voltage signal.~c!Case of narrow boxcar function driving-voltage signa

t

asiodinsio

0in

al

-e

rsasof

nalsre-

replace t in Eqs. ~6!–~8!, it can be equivalent to a poinsource.

C. Calculation of recorded logging signal

From Eq. ~2a!, it can be known that the receiver islow-pass filter and has the acoustic–electrical transmisproperty of the positive original phase. There is a phaseference ofp radians between the electrical–acoustic tramission property and the acoustic–electrical transmissproperty for the transducer. From Eq.~2b!, the calculatedresonance frequencyf 3 of the receiver is equal to 13.10kHz which is greater than that of the acoustic source. Durlogging, when the sourceT0 is excited by the driving-voltagesignal U1(t) @i.e., whenU1(t) is input the electrical termi-nals of T0#, U1(t) is converted into the acoustic sign


nf--n

g

X(t,0) radiating outwards.X(t,0) passes through the propagation media~borehole fluid and formation around borehol!and then becomes the pressure response signalP(t,z) in theborehole. WhenP(t,z) is received by the receiverR0 @i.e.,P(t,z) is input to mechanical terminals of the receiver#, it isconverted into the electrical signalU3(t) ~the recorded log-ging signal!.

Let the radius of the boreholea50.1 m, the separationfrom source to receiverL52.44 m, and physical parameteof borehole fluid and formation around the boreholeshown in Table IV. The calculated electrical output signalsthe receiver in time~ERTW! and frequency~ERAS! domainsare shown in Figs. 7–10. When the pressure response sigin borehole are converted into electrical signals by the

ls.s-

e

l.

FIG. 6. Amplitude spectra of radiated acoustic signaRAAS is the amplitude spectrum of the radiated acoutic signals.~a! Case of gated sinusoidal driving-voltagsignal.~b! Case of impulsive driving-voltage signal.~c!Case of narrow boxcar function driving-voltage signa


rertt

tha

t, ttptr

thalthal

hee

apf

ticfrdm

is

atw

other

l,

owareass

ncyss.the

n of

thethepa-theiver.c-nd

by

heive

g-gethetheand

ver.enr, the. If

sesnd-so-

nd

ceiver, its high frequency contents of the signals are filteand the low frequency contents are suppressed to a ceextent. Compared with the pressure response signals inborehole, due to the acoustic–electrical filtering effect ofreceiver, the wave forms of the recorded logging sign~electrical signal output by the receiver! are smoother. Sincethe resonance frequency of the receiver is greater thancenter frequency of the pressure response in boreholepeaks of the amplitude spectra of the electric signals ouby the receiver become wider. Due to the acoustic–electransmission property of the positive original phase ofreceiver, the first arrivals of the recorded logging sign~head waves! are the negative and are the same as bothradiated acoustic signals and the pressure response signthe borehole.

For the gated sinusoidal driving-voltage signal, tsource radiates more monochromatic acoustic signals. Thfore the maximal value of the recorded logging signalspears in the frequency range between the resonancequency of the source and that of the receiver.

For the impulsive driving-voltage signal, the acousenergy radiated by the source evenly distributes over aquency range from 2.185 kHz to 12.055 kHz. The amplituspectrum of each recorded logging signal has two extrevalues: one appears near to 1.564 kHz and the other11.339 kHz. This fact shows that for the case ofa being 0.1m andL being 2.44 m, the propagation media~borehole fluidand formation around borehole! have two correspondingresonance frequencies. The propagation media have smattenuation for the frequency contents near to the above

TABLE IV. Physical parameters of borehole fluid and formation arouborehole.

Medium Density~kg/m3! Vp ~m/s! Vs ~m/s!

Borehole fluid 1200 1540Formation 1 2160 5943 3200Formation 2 2100 3500 1950


dainheels

heheuticese

s in

re--re-

e-eeat

llero

resonance frequencies and have stronger suppression atfrequencies.

For the narrow boxcar function driving-voltage signabecause its gate width is equal top/v1 , the two wavelets ofthe radiated acoustic signal interfere constructively. The land high frequencies of the radiated acoustic signalsmaller. Therefore, when the radiated acoustic signals pthe propagation media and the receiver, the low frequecontents of the logging signal output by the receiver is leSince the radiated acoustic energy mainly distributes nearresonance frequency of the source, the energy distributiothe logging signal mainly concentrates in this frequency.

From the above calculations, it can be concluded thatwave form shape, duration, amplitude, and travel time oflogging signal are determined by the properties of the progation media, source, receiver, driving-voltage signal,borehole size, and the separation from source to receCompared with high velocity formation, the moderate veloity formation is of greater low-frequency response agreater acoustic attenuation. When the source is excitedthe narrow boxcar function driving-voltage signal witht1

5p/v1 , the amplitude of the recorded logging signal is tgreatest and when the source is excited by the impulsdriving-voltage signal with 0.6v1 , the amplitude of the re-corded logging signal is the smallest.

In acoustic logging, the characteristics of recorded loging signal are determined by the type of driving-voltasignal, the electrical–acoustic transmission property ofsource, the physical properties of propagation media,borehole size, the separation from the source to receiver,the acoustic–electrical transmission property of the receiIf the driving-voltage signal is more monochromatic betwethe resonance frequencies of the source and the receiverecorded logging signal also has better monochromaticitythe driving-voltage signal is broad band, when it pasthrough the acoustic logging transmission network, the bawidth is reduced. Only the frequencies between the re

-g-

l.

FIG. 7. Wave form of recorded logging signal for formation 1. ERTW is the amplitude of recorded logginsignal.~a! Case of gated sinusoidal driving-voltage signal. ~b! Case of impulsive driving-voltage signal.~c!Case of narrow boxcar function driving-voltage signa


alf

l

FIG. 8. Amplitude spectrum of recorded logging signfor formation 1. ERAS is the amplitude spectrum orecorded logging signal.~a! Case of gated sinusoidadriving-voltage signal.~b! Case of impulsive driving-voltage signal.~c! Case of narrow boxcar functiondriving-voltage signal.

n

n

ogtic

te

anveou

lec-

ita-e ofgestic

pa---ared

ctediaand

ore-

nance frequency of the source and that of the receiver caconverted into measured electrical signal efficiently.

IV. CONCLUSIONS AND DISCUSSION

From the above derivation, calculation, simulation, aanalysis, some conclusions are as follows.

~1! The source, propagation media and receiver in lging are like electrical–acoustic, acoustic, and acouselectrical filters.

~2! The resonance frequency of the receiver is greathan that of the source for the same transducer.

~3! There is a phase difference ofp radians between theelectrical–acoustic transmission property of the sourcethe acoustic–electrical transmission property of the receiWhile the radiated acoustic signals propagate in borehfluid, and the formation around borehole and the press


be

d

-–

r

dr.lere

response signals in the borehole are converted into the etric signals~i.e., the recorded logging signals!, the originalphase of their head waves do not change. During the exction process of the transducer, there is a phase differencp radians between the original phase of the driving-voltasignal and that of the head wave of the radiated acousignal.

~4! There are two resonance frequencies for the progation media~borehole fluid and formation around borehole!. A moderate velocity formation is of greater low frequency response and greater acoustic attenuation compwith a high velocity formation. The acoustic filtering effeand frequency response property of the propagation mare determined by the physical properties of the mediathe borehole size.

~5! Compared to the pressure response signals in b

-e

l.

FIG. 9. Wave form of recorded logging signal for formation 2.~a! Case of gated sinusoidal driving-voltagsignal.~b! Case of impulsive driving-voltage signal.~c!Case of narrow boxcar function driving-voltage signa


-l

FIG. 10. Amplitude spectrum of recorded logging signal for formation 2. ~a! Case of gated sinusoidadriving-voltage signal.~b! Case of impulsive driving-voltage signal.~c! Case of narrow boxcar functiondriving-voltage signal.

nc

utheo

cgreinthth

eivheio

o-la

ds

sticics

m

o-

st.

’ J.

n to

Gen-

s-

rtyeo-

ofn-

alch-

hole, the wave form of the measured logging signal~theelectric signals output by the receiver! is smoother and thepeaks of its amplitude spectrum are wider.

~6! When the source is excited by a narrow boxcar fution driving-voltage signal witht15p/v1 , the amplitude ofthe measured logging signals is the greatest. When the sois excited by the impulsive driving-voltage signal wi0.6v1 , the amplitudes of the pressure response and msured logging signals are the smallest, but they contain mlow frequency contents.

~7! The recorded logging signal is the result of the effeof the electrical–acoustic conversion of source, the propation media, and the acoustic–electrical conversion ofceiver on the driving-voltage signal. The recorded loggsignal is not only determined by the media, but also bydriving-voltage signal, borehole size and the properties ofsource and receiver.

~8! On the basis of the acoustic logging network modfrom the recorded logging signals, source property, receproperty, and driving-voltage signal, one can invert for tformation properties more correctly and get more formatinformation from the recorded logging signals.

ACKNOWLEDGMENT

The authors would like to thank the Institute for Explration and Development Geosciences, University of Okhoma for financial support.


-

rce

a-re

ta--

gee

l,er

n

-

1K. Aki and P. G. Rechards,Quantitative Seismology, Theory and Metho~W. H. Freeman, San Francisco, 1980!, pp. 182–183.

2L. Tsang and D. Rader, ‘‘Numerical evaluation of the transient acouwaveform due to a point source in a fluid-filled bore hole,’’ Geophys44, 1706–1720~1979!.

3R. L. Gibson, Jr. and C. Peng, ‘‘Low- and high-frequency radiation froseismic sources in cased boreholes,’’ Geophysics59, 1780–1785~1994!.

4C. H. Cheng and M. Nafi Tokso¨z, ‘‘Elastic wave propagation in a fluid-filled borehole and synthetic acoustic logs,’’ Geophysics46, 1042–1053~1981!.

5D. A. Berlincourt, D. R. Curran, and H. Jaffe, ‘‘Piezoelectric and piezmagnetic materials and their function in transducers,’’ inPhysical Acous-tics, edited by W. P. Mason~Academic, New York, 1964!, Vol. 1A, pp.223–224.

6J. C. Piquette, ‘‘Method for transducer suppression. I: Theory,’’ J. AcouSoc. Am.92, 1203–1213~1992!.

7J. C. Piquette, ‘‘Method for transducer suppression. II: Experiment,’Acoust. Soc. Am.92, 1214–1221~1992!.

8J. C. Piquette, ‘‘Applications of the method for transducer suppressiovarious transducer types,’’ J. Acoust. Soc. Am.94, 646–651~1993!.

9J. C. Piquette and S. E. Forsythe, ‘‘Transducer transient suppression:eralized methods of analysis,’’ J. Acoust. Soc. Am.100, 1577–1583~1996!.

10A. C. Holly, ‘‘A method for the generation of broadband acoustic tranmission,’’ J. Acoust. Soc. Am.75, 973–976~1984!.

11L. Fa, F. Lin, and W. Chen, ‘‘Source function derivation and propeanalysis of ceramic ring transducer for petroleum exploration,’’ Acta Gphys. Sinica39, Suppl. 387–399~1996!.

12L. Fa, J. P. Castagna, and J. M. Hovem, ‘‘Derivation and simulationsource function for acoustic logging,’’ 1999 IEEE International Ultrasoics Symposium Proceedings, Vol. 1, pp. 707–710.

13L. Fa, L. An, and P. Li, ‘‘Theoretical relationship electric-driving signand radiated acoustic wave for thin shell transducer,’’ Well Logging Tenol. 22, 1004–1338~1998!.


an acoustic-logging transmission-network model

Documents