A Velocity Function including Lithology Variation.pdf

7/27/2019 A Velocity Function including Lithology Variation.pdf

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VOLUME XVIII NUMBER 2

A Journal of General and Applied Geophysics

A VELOCITY FUKCTION ISCLUDINGLITHOLOGIC VARIATION*

L. Y. FAUST?

ABSTRACTAssuming velocity (V) a function of depth (Z), geologic time (T), and lithology (L) the resistivil)log is an approach to the determination of L. Since general knowledge of water resistivity values

(X,,) is lacking, the values of true resistivity (R,) against lcu(ZT)6 were compared for 670,000feet of section widely distributed gcogral)hically. Variations in R, were presumably averaged outthereby, and the results indicate that statistically I,= [R,]/T and Ii= 1948 (ZTL)G. This formulawas applied to an additional 270,ooo feet of section more localized geographically to ohserve itsaccuracy in predicting vertical travel time If a correction map for R,. variations is applied the resultsare encouraging hut less accurate than good velocity surveys.Examination of an inconclusively small amount of data with more careful measurements of Rtsuggests that accuracy comparable to direct measurement may be attainal)le. The cooperation ofother investigators and of the electric-logging specialists is desired.

INTRODUCTIONThis paper describes an investigation of longitudinal seismic velocity in sedi-

mentary rocks as a function of depth, geologic time and lithology. i\ tentativelithologic p arameter is designed utilizing data available from conventionalresistivity logs. The variables are analyzed in nearly one million feet of sectionrepresented by one hundred and fifty velocity surveys. The goal of the investi-gation is the prediction of velocity from well logs with accuracy equal to directmeasurem ent. JYhile this accuracy has not been obtained, the results are encour-aging. The latter portion of the paper e xamines the nature of the errors of predic-tion of the derived velocity function and suggests that the desired end may beattainable. A cooperative effort is proposed for the extension of the investigation.

iz I,ITI-IOI,OGIC PARAMETERA previous paper assumed that velocity zcould be expressed as:

v = f(G T, ~9 (1 )* Presented before the Geophysical Society of Tulsa December II, 1952 and before the Annual

hleeting at Houston I\larch 24, 1953. Manuscript received by the Editor January 8, 1953.t Amerada Petroleum Corporation, Tulsa.

27=

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272 L. I FAUST

with Z the depth, T elapsed time since deposition, and L a lithologic variable.It was argued that by averaging many velocity measurem ents in essentially non-calcareous sections, the variable L was held constant and

V = cr(ZT), L = L1 (2)with L1 representing an avera ge shale and sand section. The value of LYwasdetermined as 125.3 when Z was measured in feet, T in years, and V in feet persecond.

In the previous paper evidence was presented that suggestsa velocity formulaincluding lithologic variation L would contain equation (2) as a memb er o f amore generalized equation and that the variable L would appea r either additivelyor as a coefficient of (Y. Since no generally accepted quantitative measure of lith-ologic variation L is available, a necessary first step is the formulation as a lith-ologic parame ter of a quantity related to those lithologic variables which influ-ence velocity. This quantity is found to be related to electric resistivity measure-ments. The following discussion will define first the factor in a velocity equationattributable to lithology. Next will be a description o f the quantities influencingboth this lithologic facto r and resistivity. Then the steps necessary for the dis-covery o f the desired lithologic parameter will be described in sequence.The Lithologic liaclor in a Ielocity Equation

4 Litholog ic Facto r K can be defined as:K = ~,c(z2.)li6

where AZ/at is the actual m easured velocity in the interval AZ and the denomi-nator is the appropriate value for velocity from equation (2). Then K= I fo rthe lithologic conditions spec ified in equation (2) and in general K is that factorin velocity attributable to lithologic variation. It is there fore a quantity againstwh ich any tentative lithologic para meter can be tested . Previous to the definitionof equation (3) an attempt was made to describe the effect of lithology on velocityas a term to be added to the right hand memb er o f equation (2). The measure-ments to be described later were tested against that assumption with no correla-tive results.The Resisticily Formation. Factor

Archie has shown empirically that for permeable sections the relation bc-tween true formation resistivity Rt and the resistivity R,, of the water impregnat-ing the formation is given by

RJR, = F = p- (4 )wh ere 1; is the resistivity formation facto r, p is proportional to porosity, and7%s terme d a cementation factor. The number F derived from resistivity meas-



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VELOCITY FCYCTIOA INCLUDING LITHOLOGIC VAKIATION 273

urements is unaffected by the mineralogical constituents of the formation matrixwhose wate r-free resistivity approac hes infinity but is a function of the poros ityand cementation of the formation.

That the same quantities affect the factor K in velocity is well known. Som eevidence on these facts can be found in the writers previously cited pap er andVogel3 mentions the inverse relationship of porosity and velocity when othervariables are held constant.

There is reason therefore to anticipate that the desired lithologic parame tershou ld be related to F, the resistivity formation facto r of equation (4). Unfor-tunately while the values of & can be determined with some accuracy from Resis-tivity Departure Curves, the corresponding values of R, are generally unknown.Wyllie4 h as indicated a solution for R, for permeable formations, but this methoddoes not apply to all sections.

In the absence of specific knowledge of R,, if a sufficiently large number ofmeasurements of Rt is averaged over a wide area1 distribution, the correspondingaveraged value of R, should either remain constant under differing values ofother variables or should vary in functional relationship to such variables. As afirst step in this investigation it will be assumed that under such averaging thevalue of R, remains constant. For e ase of measurement it will be assumed that thisconstant va lue of R, is unity. A quantity can then be defined

(5 )where N is the number of measuremen ts and [Rt], the magnitude of the averagevalue of R,, is dimensionless. Actually [Rt] will be in a relationship to the averagecorresponding F value determined inversely by the relationship of I/N~~R,to the variables to be studied, namely velocity, depth, geologic time and li-thology. Thus [R ] as defined in equation (5) is assume d to mea sure F or a quan-tity analogous to F.Measuremenls

Measurements of R, are derived from the value of R,, the apparent resistivity,using bit size for the hole diameter correction and the appropriate value of mudresistivity, R,, corrected for temperature. As a practical expedient some simpli-fications seem desirable. The values of R, are taken, usually measured by thelateral device, over intervals (AZ) of approximately one thousand feet. The aver-age value of R, is taken from a smoo th curve so drawn that the areas of positivedifference between this curve and the m easured trace are equal to the areas ofnegative difference. The extent of the segment of the curve is limited essentiallyby a maximum range of five to one in R, variations. When larger variations o ccurthe values of R, and corresponding RL are read over intervals less than one thou-and feet and an average value of R, determined for the desired interval. The



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departure curves5 used are those for beds of infinite thickness and no mud fil-trate invasion.

While the inaccuracies introduced by these simplifications could not betolerated by the petroleum engineer in the evaluation of thin oil bearing forma-tions, simplified techniques still require a considerable amount of time andappea r justifiable as a first approach to the problem.Measurem ents of 670,000 feet of section corresponding to 96 velocity surveyshave been taken from all available regions exclusive of Alberta and California.As wide lithologic variations as possible are included. The sections measu red are,with minor exceptions, different from tho se reported previously. These data arethen tabulated for value of geologic age T, dep th interval a;! (usually one thou-sand feet), mean dep th of burial 2 , measured velocity AZ/&, and the true forma -tion resistivity R1. Other quantities such as the appropriate velocity values fromequation (2) and the value of K are derived and tabulated.The Determination of a Lithologic Parameter

The obvious approa ch to the formulation of a tentative lithologic param eterinvolving [Rt] is the study of the variation of [R(] when K= I. All data can beselected from the tabulated measuremen ts where K = I .oo i_ 0.10. This specifica-tion is well within the limits of the data from which equation (2) w as derived.The data corresponding to this restriction of K are then grouped by geologic timeT. [R,] is determined from the data of each group. These results are plotted onlogarithmic coord inates in Figure I and indicate that [R,] is nearly proportionalto T. An attemp t to split these data to investigate [RI] against 2 for each valueof T show ed even poorer relationships but probably indicates that [R,] does notvary appreciably with depth. Although the relationship between [R,], Z, and Twas not clearly determ ined, the assum ption will be made and later verified that[R!]/T is independent. oftZ~and T:~

The quantity R,/T, tabulated for all measurements, can be classified by valueof T and subclassified for each T by the value of K in ranges of 0.10 from K 1.60. The average K, the corresponding average [Rt]jT, and N, the num-ber of measurements involved is summ arized for each subclassification in TableI. Values involving less than ten measurem ents a re considered unreliable and arenot included. Th e da ta of Table I are plotted on logarithmic coord inates inFigure 2 and indicate a close approa ch to a linear relationship between the loga-rithms of K and of [R,]/T. The values of [R,/]T show no tendency to deviateas a function of T. Figure z indicates that the required lithologic parameter Lis defined by

L = [R&T. (6)A VELOCITY FUNCTION INCLUDING LITHOLOGY

The lithologic parameter L being determined, a velocity function includingEthology can be formulated by comparison of L with K the lithologic fac tor. In



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IOT

26

43

192

=I-1 .

_.

_.

_

TABLE I. TABULATION OF DATA OF FIGURE 2(Values of K, [&I/T (reciprocal years) and number of measurements of thousand foby values of keologic time T (years) and Lithologic Factor K.

K~o~[Rtl/TN

= h


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276 I.. Y F.1UST

70605040

s IOL11 g-8 7

65

I

I I Q POST EOCENE TERTIARYA EOCENE0 CRETACEOUSq JURASSIC TRIASSIC+ PERMIANx PENNSYLVANIAN+ MISSISSIPPIAN0 ORDOVICIAN

IO 100 IC IOT x 10-6

FIG. I. [R~] as a function of geologic time T for an average shale and sand section (K= 1.00fo.10). The numbers above the plotted points show the number of thousand foot sections used inthe determination. [R~]/T is nearly constant.

the following sub-sections will be show n first, the velocity formula and second ,the predictability of this formula in individual wells. Due to the lack of know ledgeof the individual values of R, some error is to be expected. In the third part,an attempt will be made by analysis of additional data to show that the predictionerrors are ascribable to variations of R, and to suggest one method of correction.The Velocity Formula

As a result of equation (6) all individual measurem ents of K can be groupedaccording to range of L regardless of age T. As a consequence one hundred andtwenty measuremen ts excluded from Table I could be included in these classifi-cations. The average of L in each of five ranges together w ith the correspondingaverages of K are plotted on logarithmic coordinates in Figure 3. These values



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VELOCITY FUhTCTION INCLUDING LITHOLOGZC VARIATION 277

of LX1os and K are respectively: (0.048, o.gz), (0.075, 1.03), (0.183, I.I~),(0.487, 1.35), (1.03, 1.61). Th e number of measurements in each range is shownabove each plotted point. A relationship of the form

K = CLll= (7 )describes these points when IZ= 6. From equations (3) and (7) replacing AZ/Alby V

I = r(ZTL) (8)where

7 = 1948.The type of averaging and classifying necessary to arrive at the results of

Figure 3 shou ld eliminate variations of R, whethe r functional or random. Thisassum ption is partly verified by the fact that Figure 2 confirms equation (7) al-though the method of grouping individual measurements w as different. Fromequation (6) evidently

V = y(Z[Rt])6. (9 )

9.a.7.6.5

2.40 POST EOCENE TERTIARY.3 A EOCENE0 CRETAC EOUS+2 PERMIANX PENNSYLVANIAN+ MISSISSIPPIAN

[Rt]/T x IO6FIG. 2. The data of Table I plotted on logarithmic scale suggests that the lithologic factor

K is proportional to ( [Rt]/T) and that [&l/T is independent of T.



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278 L. Y. FAUST

1. 0.9.8.7.6.5

f .4.3

I I I fill I I I I IIll]1 I II/I2

.I .Ol _I 1.0I- x IO 6

FIG. 3. Average values of the lithologic factor K versus the average value of the lithologicparameter L grouped by value of L show that K = CL in where n=6. Numbers above the plottedpoints show the number of thousand foot sections veraged.

Equation (9) describes statistically a velocity function including lithology.This equation represents the limit of the investigation until R, values can bedetermined. Given values of R,,, L in equation (8) can be redefined to make thatequation one form o f a spec ific velocity law. Mean while the general utility ofequations (8) or (9) can be investigated by determining their predictability forindividual velocity surveys.

A possible implication of equation (9) is that the effect of geologic time Tis lithologic. Heiland6 in discussing the effect of age on velocity stated An in-creased age merely increases the probability that it has undergone a greaterdegree of dynamometamorphism.

Possibly more surprising than the relationship of T and L is the apparentindependence of [R,] and Z. This is check ed in Table II where the average ratioof y(ZTL)6 to AZ/At is shown for the indicated number of measuremen ts ac-cording to range of depth Z. There is some tendency for the ratio to increase withdepth. In view of the present inadequate knowledge of R, variations, this couldbe explained as a variation of R,, with depth or as evidence of an incompletelyaveraged lateral variation of R,.

In defense of this latter supposition it should be pointed out that whenequation (8) is tested in individual wells in the following discussion a correction



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TABLEII. RATIOOFPREDICTEDTOMEASUREDVELOCITIES AGAINST(Average of indicated ratio for N observations classified by depth Z (feel). Thwith depth is not substantiated by other evidence.)

2 = 500 1,soo *,soo 3,5oo 4,500 5>5oo 6,504 7,500AZy(ZTL)1'6/-- 0.947 0.970 0.928 0.929 0.933 0.983 I .009 1.01qAt

N 16 38 54 60 61 55 46, 38______



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in R, for depth 2 increases the errors of prediction. [R,] is considered thereforeto be independent of Z.

Possibly the work of Gassmann7 may be helpful in explaining the inde-pendence of the Z term.Predictability

The data illustrated in Figures 2 and 3 are the average of measurements hav-ing a wide range of values. While the deviations could have been inclu:led inTables I and II, the predictability of equation (8) should be a more useful meas-ure of the errors. The evidence indicates that equation (8) represents a velocitylaw, but other variables not considered or a wide range of R, values might pro-duce such scattering of predicted versus measu red velocities as to m ake equation(8) useless. When equation (8) or (9) is used to predict velocity in individual wells,the assumption of equation (5) of the constancy of R, is no longer valid.

By a summation for each well of the time increments predicted by use ofequation (8), the equality may be written:

$r(z:)6t2 - t1) + 4 (10)whe re Z1 and Zz are respectively the shallow and deep limits of available measure-ments in a well, tl and t2 the corresponding m easured vertical times, and t theprediction error.

A group of fifty velocity surveys from the ninety-six used in the determinationof equation (8) are analyzed in this manner with the results plotted on linearcoordinates in Figure 4. The ordinate of each point is the value of the left handmember of equation (IO) and the abscissa is the corresponding (tz-tl) value. Thedeviation from the Line of Correlation is the error e. While the scattering is nottoo bad, one measured time (tz-tJ at 0.588 seconds has an E of -0.090 second.The greatest positive value o f E is 0.054 secon d and the mean value o f 1E\ is0.026 second.

If E is a function of AR,, a total variation in this function of five to one issufficient to reduce E to zero for the extreme deviations. Available measuremen ts8of R, show variations of greater than one hundred to one. Since these latter areobserved in permeable sections, the water resistivities measu red are not neces-sarily of water laid down with the formation. On occasion the water present in apermeable forma&n n-ray be -meteroiL: Kevertlreless the range of fi-ve to onenecessary to explain these ES is conceivable.

If the prediction errors may be explained as the effect of variations in R,,then

V = y(Z$ )6 (II)may be the final form of a law governing velocity where + is proportional to Rtand is a function of R,. % is analogous to or equal to F.



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IELOCITY FUNCTION INCLUDING LITHOLOGIC VARIATIOLV 281

Na4

II

NNWK0.5

0

-----ii$0 0

0

J

i

MEAN DEVIATION ,026 SECONDSMAXIMUM DEVIATION +.054 TO -.090 SECONDS

j 1.0 1.5 2.0MEASURED time (SECONDS)

FIG. 4. Scattering of predicted one way travel times versus measured travel times for fiftywells taken over a wide geographical distribution. The deviations could be explained hy a 5 to Irange in the effect of R,.

The Variation of Wa ter ResistivityThe validity of the assumption upon which equation (II) is suggested may

be verified in part by other indirect evidence . Th e values o f E show n in Figure (4)are from data taken over a wide geographical distribution with consequentvariations in depos itional environment. If sufficient data were available in a morelocalized area, the range of R, variation should be more restricted. Such a con-dition ex ists in Alberta where forty-six velocity surveys not used in the develop-ment of equation (8) represent 2 70,000 feet of additional section. All of thesesurveys include measurements of some Paleozoic section as well as younger for-mations. If the range o f ES for this gro up of surveys were considerably less thanthose of Figure 4, the argument that e=f(AR,) would be sustained in part.

The short time span over which the Alberta wells were drilled insures that



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8/IL. Y. F.4 UST

MEAN DEVIATION .0145 SECONDSMAXIMUM DEVIATION +.039 TO -.028 SECONDS

0 .5 1.0 I.5 2.0MEASURED time (SECONDS)

FIG. 5. A comparison similar to Figure 4 for forty-six Alberta wells not used in the derivationof equation (8). Variations of R, should be less in this more restricted area and the deviations aresmaller.all the electric logs used in this study represent a single phase of development.The Alberta surveys show a deviation from equation (2), (K= I) from +0.075seconds to -0.186 second with twelve of the surveys having d eviations o f afew m illiseconds from that formula. The area is therefore useful also in evaluat-ing the properties of L.

The results of the application of equation (9) to the forty-six Alberta surveysare plotted on linear coordinates in Figure 5 and sh ow e values ranging from+0.039 to -0.028 second with a mean 1~1 of 0.0145 secon d. While tendingto confirm the assum ption tha t e=j(A&), the range of the es is unsatisfactorilylarge since it is assumed that good direct measurements have an accuracy o f fivemilliseconds.

The distribution of the forty-six surveys in Alberta is show n in Figure 6.Although restricted to one general basin the dimensions of the area are approxi-mately seven hundred by two hundred miles. Some variation of R, may beexpected over that extent. A rough m easure of the assumed effect of R, variationcan be determined by indicating Ae/AZ for each well. The signed numbers inFigure 6 show this measure in milliseconds per thousand feet. G eneralized



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VELOCZTY FUNCTION INCLUDING LITHOLOGIC VARIATZ0i-v 283contours of these quantities are shown. Although possibly fortuitous, the shapeof the contours is similar to that of the epicontinental seas receding in this areathrough Mesozoic time The easternmost well shown in Figure 6 and a well(not sh own) off the south edge of the ma p were used for contour control only andare not included in the analysis. The data of Figure 5 are corrected by interpola-tion o f the contours of Figure 6 except that all values within the +g contour aretaken as +5. The results are shown in Figure 7 . The mean 1c/ is 0.0079 secondwith a range of ES from $0.020 to -0.018 second.

The wells indicated as :I through I; in Figure 6 are shown in cros s sectionLn Figure 8 where the uncorrected CS are indicateI[ c+les connected by dashed-, -- -1lines and th e ts corrected by F igure 6 are indicated by aste risks connected bysolid lines. Three of the wells, namely 11, C, and F, have corrected ES of five milli-seconds or less while the othe r three w ells have the m aximum variations ofFigure 7. Evidently no generalized recontouring of Figure 6 would improvematerially these errors, and therefore the errors shown in Figure 7 represent thelimitation of the correction for R,,..

FIG. 6. Generalizedontours of the deviations per thousand feet of the wells of Figure 5.



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284

I .5

3cl6z I.0

ZLWIr-

nWI- .5v02a

0

I>. Y. FAUST

0 .5 1.0 I.5 2.0MEASURED time (SECONDS)

FIG. 7. A comparison for the same wells as shown in Figure 5 corrected by thecontoured values of Figure 6.A B C D E Ft.050

+.040t.030+.020+ .OlO

0-.OlO-.020-.030-.040-.050

1MEAN DEVIATION ,011 SECONDS

i-MAXIMUM DEVIATION +.020 TO _I - OIB SECONDSI I I IFIG. 8. A cross section of the wells indicated A-F of Figure 6 showing the uncorrected deviations

(dashed lines) and the corrected deviations (soJid lines). The variations between adjacent wellsshow that the limit of correction for RtB as been reached.



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Since the method of determining Rt as discussed previously involved the in-troduction of some error, a more careful measurem ent should reduce the errorsif equation (8) w ere exact when corrected for R,, but would have at least equalprobability of resulting in larger ts if the law were approxim ate only. The dataof the six surveys of Figure 8 are re-evaluated by con sideration of bed thickness,mud filtrate invasion, and the use of one hundred foot or sma ller intervals ofmeasurement. The revised data are shown in Figure g, Although there is no im-provement in the uncorrected values, the corrected ES vary from +0.008 to-0.007 second with a mean It\ of 0.005 second. Two o ther wells originally

Gi +.050F +.040n +.030: +.02002 +.010a 0k -.OlO5 -. 020fi -.030> -. 040:: -.050

A B C D E F

FIG. 9. The same wells as in Figure 8 showing the deviations when Rt is determined with greateraccuracy. These corrected deviations are comparable in accuracy to direct measurement.

showing corrected c values o f -0.016 and -0.017 respectively have 6s of plusfour and plus one milliseconds by the more accurate measurements.

It would be absurd to imply that the small errors in these eight w ells are areal measure of the achievements of this study since the accumulation of moredata will alm ost certainly disclose some large departures.

It is recogn ized that the argum ents relating the prediction errors to variationof R, do not prove conclusively that this is the correct explanation. Other possi-bilities hav e not been excluded. It is demon strated howe ver that the predictionerrors are essentially systematic rather than random .

This paper has described the results of all but six surveys which h ave beenused in testing equation (8). These six surveys represent a more recent effortby the writer to test the equation against the most anomalous velocity conditions.All six have ch ecked satisfactorily. The most anom alous of this group is a deepsurvey in the Gulf C oas t called to the writers attention by 0. B. Manes. Thissurvey has a measured vertical time in excessof the predicted time from equation



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(2) by nearly three-tenths of a second. Equation (8) predicts the measured timeto twenty-one milliseconds (uncorrected).l3alllalimt of results

It is believed that equation (8) or its equivalent, equation (g), may be re-garded as a statistical law governin, 0 velocity. While the improvement in predic-tion accuracy with each refinement is evidence favoring the conclusion that ac-ceptable accuracy may be attainable, the results of the study of the Albertavelocities s hould not be generalized without further conlirmation.

Since the measured vertical time over the greatest possible depth range repre-sents usually the most accurate measurem ent of a conventional velocity survey,the predictions of equation (8) have been referred only to such measurem ents.It is arguable that in some shorter interval the predicted velocities could be themore accurate. Ii. S. Cressma n und er the general sulxrvision of the writer hasbeen successful apparently in using equation (8) in short intervals in a study ofthe composite nature of reflections. However resistivity measurements acrosssmall intervals of varying resistivity are inexact. U.hile Summ ers and Erodingreported a generally good correspondence! between five foot interval velocitylogs and resistivity, Broding has stated in his discussion of the first presentationof this paper lo that in some wells a total lack of correspondence has been observedover certain intervals.

The problem of the formulation of + in equation (II) requires considerationnot only of the errors of the velocity formula but also of those errors involvedin direct velocity measurem ent and especially of the errors in resistivity measure-ment.

The writer is not qualified to discuss the significance of this study from theviewpo int of the resistivity specialist. The wo rk of Owen in emphasizing theimportance of cementation on resistivity may have an important bearing onthis problem.

A CO-OPER ATIVE IiSVESTIGATIONTwo approaches to the practical use of these relationships seem possible. The

preparation of correction maps with present techniques could be institutedimmediately. The improvements in resistivity measurem ents and techniques fordetermining R, variations await future development.The Use of /he Presettl Techniques

Much more investigation will be required before the general accuracy of theseempirically derived formulae is ascertained. Independent work in this field isdesirable. One suggested project is an attempt to duplicate StulkenP velocitymaps in the Bakersfield region by means of electric logs, It should he mentionedhowever that the re-evaluation of the data show n in Figure 9 required the equiva-lent of one work week. It ma y be preferable therefore to institute further investi-



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gation on a cooperative basis. The confidential nature of most velocity informa-tion m ight seem to bar such a venture. The writer has available a library of morethan one thousand velocity surveys and would be willing to serve as a clearinghouse in the dissemination of non-confidential material. Corres pond ence couldbe confined to surveys available both to the writer and to the particular investi-gator. Map s of the areas of interest cou ld be prepared similar to that shown inFigure 6 . It is evident that such a correction m ap shou ld be made within eachgeneral unconformity. These correction maps , being non-confidential, could bedistributed to all collabora tors. A first requirement wou ld be an argeem ent on astandard method of measuring R1 determined preferably with the advice ofspecialists in electric logging.Improvement of the Method

Improvements in the method depend primarily on the electric logging special-ists and service companies. It would be helpful to sho w the zero deflection at b oththe start and end of a run. The deflection corresponding to one standard resistiv-ity would be desirable. The example in Figure 4 of e= -o.ogo is suspected ofbeing an error in scale since the readings were abnormally high for all depths.Lacking good evidence on this point howe ver the value was included. The clarifi-cation of the multiple scale traces would be useful. In Gulf Coas t areas of lowresistivity, a complete set of amplified curves would improve accuracy.

The newer logging devices may be expected to improve accuracy, especiallyin West Texas. However a measurement of R, for the complete section is of para-mount importance. Offers of aid in suc h a project have been received. Dr. Leen-dert de Witte has suggeste d an extension of Wyllies method for correcting forR, to a first approximation. It is hoped that it will now be possible for the writerto secure the collaboration of an electric log specialist in comparing the resultsof this suggested correction with the data of Figure 6.

ACKNOWLEDGMENTSAppreciation is expresse d to Dr. B. B. W eatherby for permission to publish

this pap er. The w riter is indebted to E. E. Finklea for information concerningresistivity measurem ents, to F. F. Campbell for his valuable aid in the writingof this paper and especially to K. &I. Lawrence and Paul Lyons for their encour-agement. The figures were prepared by the Ame rada Drafting Department.

REFERENCES(I) L. Y. Faust, Seismic Velocity as a Pwution of Depth and Geologic Time, Geophysics,XVI,

2 (1951), 192-206.(2) G. E. Archie, The Electrical Resistivity Log as an Aid in Determining Solne Reservoir Charac-

teristics, Petroleum Development and Technology, 146 (1942)~ 54-62.(3) C. B. Vogel, A Seismic Velocity Logging Melhod GeopAysics, XVII, 3 (1952)~ 586-597.(4) M. R. J. Wyllie, A Quantitahve Analysis of the Electrochemical Component of the S P Curve,

PetrOkUm Technology, I, I (1949).



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288 L. Y. FAUST

(3) Schlumberger Document Number 3.(6) C. A. Heiland, Geophysical Exploration, Prentice-Hall (1940)~ 475.(7) Fritz Gassman, Elmtic Wav es Through a Packing nf Spheres, geophysics XVI, 4 (1951),

673-685.(8) Water Resistivity Cards, A.I.M.E. Special Publication (1950).(9) G. C. Summers and R. A. Broding, Continuous Velocity Logging, Geophysics,XVII, 3 (1952),

59X-614.(IO) Presented before The Geophysical Society of Tulsa, December II, r9j2.(I I) J. E. Owen, The Resistiaity of a F&d-Filled Porous Body, Petroleum Transactions, A.I.M.E.

95 (r952), 169-174.(12) E. J. Stulken Seis& lvelotities in Tke Southeastern San Joaquin Valley of California,

geophysicsI, 4 (1941), 327-355.(13) Personal communication, December 29, 1932.

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A Velocity Function including Lithology Variation.pdf