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Geoexplorution, 28 (1991) 91-106 Elsevier Science Publishers B.V., Amsterdam 91 Porosity interpretation through seismics C.H. Mehta and B.M. Verma Geoscience Research Division, K.D. Malviya Institutefor Petroleum Exploration, Oil and Natural Gas Commission, Dehradun, India (Received May 4, 1990; accepted after revision July 30, 1990) ABSTRACT Mehta, C.H. and Verma, B.M., 199 1. Porosity interpretation through seismics. Geoexploration, 28: 91-106. This paper describes a procedure for porosity interpretation from seismic data (POISE) by exploit- ing merits of several recent advances in seismic data processing and interpretation. Briefly, the procedure is as follows: starting from NM0 corrected CDP gathers of P-wave data and applying amplitude versus offset (AVO) analysis, one can separate out zero offset “P-wave” and “S- wave” stacks both as a function of P-wave time. Here the term “S-wave” refers to a stack that we would have obtained if we had carried out an S-wave survey and displayed the data in P-wave travel- time. Application of maximum likelihood deconvolution/modelling technique on stacks leads to models for P-wave and S-wave reflection coefficients. Finally, inverting the reflection coefficients for interval transit time, a section can be prepared to display AT,-AT,, the difference in slowness of the S-wave and P-wave as a function of the P-wave traveltime. The final output of POISE for AT,-AT,, is particularly useful for studying variations in lithology and porosity within a formation. The interpretation is founded on an empirical observation by Ikwuakor that AT,-AT, from character logs for a large number of carbonate and sandstone samples, is propor- tional to the core porosity (for a given rock type). The utility of POISE is illustrated with a field example in a carbonate reservoir. INTRODUCTION For a variety of reasons, conventional approach to seismic data processing and interpretation is often inadequate in deciphering the subtle stratigraphic situations such as detection of weak or closely spaced reflectors in a sand- shale configuration, porosity variation in carbonates, porosity in fractured basement, reefal bodies, etc. During the last few years, several new seismic technologies have emerged which attempt to tackle such subtle objectives. Among them, three most promising and significant technologies are ( 1) am- plitude versus offset (AVO) analysis (Ostrander, 1984; Chacko, 1989; Ruth- erford and Williams, 1989)) (2) use of shear wave (S-wave) properties along with compressional wave (P-wave) (Tatham, 1982; Eastwood and Castagna, 1983; Domenico, 1984), and (3) model based parametric inversions of se- 0016-7142/91/$03.50 0 199 1 - Elsevier Science Publishers B.V.

Porosity interpretation through seismics

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Geoexplorution, 28 (1991) 91-106 Elsevier Science Publishers B.V., Amsterdam

91

Porosity interpretation through seismics

C.H. Mehta and B.M. Verma Geoscience Research Division, K.D. Malviya Institutefor Petroleum Exploration, Oil and Natural Gas

Commission, Dehradun, India

(Received May 4, 1990; accepted after revision July 30, 1990)

ABSTRACT

Mehta, C.H. and Verma, B.M., 199 1. Porosity interpretation through seismics. Geoexploration, 28: 91-106.

This paper describes a procedure for porosity interpretation from seismic data (POISE) by exploit- ing merits of several recent advances in seismic data processing and interpretation.

Briefly, the procedure is as follows: starting from NM0 corrected CDP gathers of P-wave data and applying amplitude versus offset (AVO) analysis, one can separate out zero offset “P-wave” and “S- wave” stacks both as a function of P-wave time. Here the term “S-wave” refers to a stack that we would have obtained if we had carried out an S-wave survey and displayed the data in P-wave travel- time. Application of maximum likelihood deconvolution/modelling technique on stacks leads to models for P-wave and S-wave reflection coefficients. Finally, inverting the reflection coefficients for interval transit time, a section can be prepared to display AT,-AT,, the difference in slowness of the S-wave and P-wave as a function of the P-wave traveltime.

The final output of POISE for AT,-AT,, is particularly useful for studying variations in lithology and porosity within a formation. The interpretation is founded on an empirical observation by Ikwuakor that AT,-AT, from character logs for a large number of carbonate and sandstone samples, is propor- tional to the core porosity (for a given rock type).

The utility of POISE is illustrated with a field example in a carbonate reservoir.

INTRODUCTION

For a variety of reasons, conventional approach to seismic data processing and interpretation is often inadequate in deciphering the subtle stratigraphic situations such as detection of weak or closely spaced reflectors in a sand- shale configuration, porosity variation in carbonates, porosity in fractured basement, reefal bodies, etc. During the last few years, several new seismic technologies have emerged which attempt to tackle such subtle objectives. Among them, three most promising and significant technologies are ( 1) am- plitude versus offset (AVO) analysis (Ostrander, 1984; Chacko, 1989; Ruth- erford and Williams, 1989)) (2) use of shear wave (S-wave) properties along with compressional wave (P-wave) (Tatham, 1982; Eastwood and Castagna, 1983; Domenico, 1984), and (3) model based parametric inversions of se-

0016-7142/91/$03.50 0 199 1 - Elsevier Science Publishers B.V.

92 C.H. MEHTA AND B.M. VERMA

ismic data using techniques such as maximum likelihood deconvolution/mo- delling (MLD/MLM) (Chi et al., 1984) or seismic lithologic modelling (SLIM) (Gelfand and Larner, 1984).

In this paper, we present a procedure which we call POISE (porosity inter- pretation from seismics), to exploit the merits of the three technologies men- tioned above. The final output of POISE is a section for the difference in the slowness of the S-wave and P-wave, which is directly interpretable in terms of lithological and porosity variations within a formation.

We illustrate the utility of POISE by analysing an exploration paradox en- countered in an offshore field. Figure 1 shows a seismic section along an E- W line where a well (# 1) was drilled in the western part and oil was struck in the Middle Eocene limestone in the time window ( 1420- 1544 ms). In the eastern part of the line, a well (# 2) was drilled but the formation proved to be water bearing even though it is at a structurally higher position than well # 1. Our findings using POISE as depicted in Fig. 9 reveal the existence of a compact zone between wells # 1 and # 2 which might have acted as a barrier for updip migration of hydrocarbons.

THEORETICAL BACKGROUND OF POISE

AVO analysis

Provided the percentage changes in elastic properties are small, the ampli- tude R,( 0) for P-wave reflection from a planar interface at time t is given approximately by Aki and Richards ( 1980) as

-4( VJV,)’ sin20AVs/Vs. (1)

Assuming VP/ V,= 2, the expression simplifies to

&(@)=$(I-sin28)&/p+~(l+tan20)AV,/V~-sin28AV,/V, (2)

=t(Ap/p+AVp/V,)+~(-Ap/p+AV,,/Vp-2AVS/VS)sin28

+ t (tan20-sin*@)AVJ V,. (3)

The third term is of the order of @ and, therefore, for small angles of inci- dence 8 (0~ 30” ), expression (3) can be simplified. The result is linear in sin20:

R,(0)=P,+G,sin28 (4)

where (dropping the subscript t henceforth ) :

POROSlTYINTERPRETATIONTHROLJGHSEISMlCS 93

c ._

I

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h z ._ z ._ .f #

94 C.H. MEHTA AND B.M. VERMA

VP, V, and p are the averages of the P-wave velocity, S-wave velocity and bulk density, respectively, of the media on either side of the reflecting interface, and AI’,, Al’, and Ap are the differences between these quantities across the interface.

We remark in passing that the fact that R, ( 8) depends linearly on sin*@ for small 8 also follows from the reciprocity theorem: if the source and receiver are interchanged, then the ray paths are unaltered, and barring the source and receiver angular response, R,( 8) = R,( - 8). R,(S) can, therefore have only even powers in sin 8.

For NM0 corrected common midpoint (CMP) gather, the linear lit of am- plitude versus sin28 at each time sample t, yields two new kinds of seismic traces. One is the trace constructed from the zero offset intercept (P) . This so-called zero-offset stack or “P-wave stack” represents the response to changes in acoustic impedance across reflecting boundaries. The second is the trace constructed from slope (G). This “gradient stack” represents a response to changes in S-wave velocity, P-wave velocity and bulk density.

The difference between the P-wave trace and gradient trace is given by

f(P-G)=~(40/p+AV,/I/,)~S. (7)

Expression (7) is formally similar to expression (5 ) with V,, replaced by I’, and, therefore, it can be interpreted as an “S-wave stack”. It is obtained from AVO analysis on P-wave data alone and no measurement of S-wave and/or converted waves is required. This is a particular advantage of AVO analysis and is applicable for offshore data also. It is assumed, however, that measure- ment noise is random and free from any trend in 8.

The conventional CMP stack is influenced by the systematic amplitude variations with offset, and hence is not a good approximation to the zero- offset data. The P-wave stack obtained from AVO, on the other hand, re- moves this systematic amplitude variation with offset and is, in general, a better approximation to the zero-offset P-wave section. It is, therefore, also more appropriate for any subsequent inversion process. Interpretation of the P-wave stack is along the same lines as that of conventional CMP stack.

The S-wave stack gives the result that we would have obtained if we had carried out an S-wave survey and displayed the data in P-wave traveltime. Alternatively, S-wave stack can be thought of as a P-wave stack section in which P-wave wave reflection coefficients in the subsurface have been re- placed by normal incidence S-wave reflection coefficients extracted through AVO. A peak indicates an increase in the S-wave impedance, a trough repre-

POROSITY INTERPRETATION THROUGH SEISMICS 95

sents a decrease in the normal polarity display with compression recorded as positive number.

While qualitative assessment of the similarities and differences between these various types of stacks is of potential value to an interpreter, the value of these different data is enhanced by simultaneous use of V, and V, which can be extracted from the P-wave stack and S-wave stack.

Ikwuakor ( 1988) provided a state-of-the-art discussion of the relevance of V, and V, for interpreting lithology and porosity.

From an analysis of a large number of data on V, and I’, for different rocks, Ikwuakor concluded that V,/ V, is not a good indicator of lithology or varia- tions in lithology and porosity. The ratio I’,/ V, is linearly related with V, and increases with V, for limestone, but decreases with increasing I’, for sandstone.

In contrast to I’,/ V, the difference between AT, and AT, is linearly related with porosity:

AT,- AT,= (AT,,,,-AT,,) + (B,-B,)@ (8)

where CD is the porosity and subscripts p and s refer to P-wave and S-wave, respectively, AT, is the transit time of the matrix material and B is a constant dependent on lithology, effective stress, and grain contact area or grain struc-

. .:. . . . l .* .

. l l ;. . . . . . . . . .

89.8 0.. a. . . . . . . . . . l 0 .

” . . .

1: 4 6 8 lo 12 ’ Core porosity

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Fig. 2. AT,--AT, versus core porosity for limestone samples. AT,-AT, from character log, po- rosity from core. AT, = reciprocal shear wave velocity; AT,= reciprocal compressional wave ve- locity. (Courtesy: World Oil. )

96 C.H. MEHTA AND B.M. VERMA

ture. The straight line regression fit for AT,-AT, versus core porosity illus- trated by Ikwuakor for various types of carbonates is shown in Fig. 2.

Application of MLDMLM

P-wave stack and S-wave stack contain wavelets. On the other hand, the velocity inversion programs invariably assume that the input is a reflectivity section. Such a reflectivity section can be constructed from a stack section using a suitable technique for wavelet deconvolution combined with modell- ing e.g. MLD/MLM. Essentially this technique extracts a wavelet and a sparse reflection coefficient model iteratively for each seismic trace until the likeli- hood of realising the given input trace becomes maximum. The process is repeated for each trace of the input. No assumption is made regarding the phase characteristics of the wavelet.

POISE

The objective of POISE is to extract from P-wave data a section for the difference in the slowness of S-waves and P-waves. The procedure is briefly as follows:

First, starting from NM0 corrected gathers and using AVO analysis, a P- wave stack and an S-wave stack are prepared. Next, using the MLM/MLD techniques, we get the models for the P-wave reflection coefficient. These models are then inverted for obtaining the so-called seislogs displaying the velocities I’, and V, as function of P-wave traveltime. The low-frequency ramps required for preparation of seislogs should ideally be derived from well informations. However, frequently, only P-wave velocities are available from a well. In such a case, S-wave ramp (at P-wave traveltime) has to be esti- mated from P-wave velocities by assigning V,/ V, ratios appropriate to differ- ent lithologies in the area. Finally, by subtracting the transit times for P-wave from that of S-waves we get the POISE display of AT,-AT, versus P-wave traveltime.

The quality and reliability of POISE depend on how well the data have been conditioned from acquisition through processing. AVO requires good control of the amplitude, accurate velocity analysis and suppression of mul- tiples. MLM/MLD requires, in addition to the above, good S/N ratio and conscious avoiding of processes such as steep filters, Q-compensation and spectral balancing.

The utility of POISE is founded on the empirical observation that AT, - AT, is directly proportional to porosity for a given lithology (Fig. 2 ). We illustrate this with an example in the next section.

POROSITY INTERPRETATION THROUGH SEISMIC’S 97

FIELD ILLUSTRATION OF POISE

Figure 1 shows a part of a seismic section along an E-W dip line over a producing field in Indian offshore with a carbonate reservoir. During the pro- cess of development of the field well # 1 and, later, well # 2 were drilled at places marked on the section. In well # 1 on the western side, oil was struck in Middle Eocene limestone (B zone) in the interval corresponding to 1420 to 1544 ms on the seismic section. The same formation in well # 2 proved to be water bearing, although with as good a porosity as in well #l and structur- ally higher than in well # 1.

The paradox is further accentuated by the fact that, according to the geo- chemical analysis, it is believed that the oil was generated not in situ in the limestone but from terrestrial organic matter derived from elastics (shale) deposited further west toward the basin and downdip of the section shown in Fig. 1.

The conventional stack in Fig. 1 provides little help in resolving this para- dox. The data were, therefore, reprocessed through the POISE procedure. Comparison of Figs. 1, 3 and 4 show that as we proceed from conventional stack to P-wave stack and the corresponding maximum likelihood model for reflectivity, the quality of the seismic section improves in terms of clarity and resolution of events. For instance, on conventional stack (Fig. 1) it is not possible to resolve the top and bottom of the “A” zone viz. limestone of Early Oligocene age. However, on MLM output (Fig. 4) top and bottom of the A zone are clearly resolved i.e., 20ms apart. (The B interface between the Late Eocene elastics and middle Eocene limestone is weak/transitional as per the CVL and is, therefore, not visible separately even on MLM).

The S-wave stack (at P-wave time) and S-wave reflectivity model are dis- played in Figs. 5 and 6. Compared to the P-wave sections (Fig. 3) the S-wave sections show more changes in the quality of reflections.

For instance, the A reflector is more continuous on P-wave sections than on S-wave sections. This is due to the fact that S-wave velocity for elastics and limestone increases/decreases faster than the P-wave velocity does with de- crease/increase in porosity. Consequently, lateral variations in the porosity of Oligocene elastics above A or in the Oligocene limestone below A have stronger effect on the variation in the velocities of the S-wave than that of the P-wave.

As a result of such sensitivity of S-wave velocity to variations in the lithol- ogy, the S-wave section is better suited for identifying faults than the P-wave section provided of course that the S-wave section is generated with the same reliability as the P-wave section.

The seislog for P-wave is displayed in Fig. 7. For obtaining the seislog a low-frequency ramp for velocity is required. This was obtained from CVL in well # 1 and superposed on the seislog.

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POROSITY INTERPRETATION THROUGH SEISMICS 101

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POROSITY INTERPRETATION THROUGH SEISMICS 105

Figure 8 displays a seislog prepared from the S-wave stack after MLD/ MLM. The velocity ramp of the S-wave (not shown) was obtained from the corresponding P-wave ramp assuming I’,/ I’, = 2.0 for elastics and V,/ I’, = 1.7 for carbonates.

Figure 9 is the POISE display of AT,- AT, at P-wave time. This section is prepared using I’,, and I’, (Figs. 7 and 8 ). As found empirically (Ikwuakor, 1988 ), AT,- AT, is directly proportional to the porosity within a formation. Such a section is therefore very useful for studying variation in porosity or lithology within a formation. The numerical ranges of AT,-AT,, obtained for limestone in this study are much higher than those found by Ikwuakor for carbonates. This is probably due to differences in the log and seismic frequen- cies and to uncertainty in the V,/ V, ratio used for generating S-wave ramp from P-wave well data. The display shows that Middle Eocene limestone be- low the B marker does have porosity both on the eastern side as on the west- ern side. The presence of oil in well # 1 and its absence in well # 2 (structur- ally higher) is possibly due to a very low porosity (and hence permeability) zone around CDPs 355 to 377 along the migration path. The decrease in po- rosity could have come about because of diagenetic recrystallisation along the fault plane which, in turn, would also have decreased the value for the differ- ence in slowness AT,, - AT_, for the rock matrix.

CONCLUSION

The procedure POISE, which exploits the merits of amplitude versus offset analysis, maximum likelihood deconvolution/modelling, and linear depen- dence of AT,- AT, (the difference in slowness of shear and pressure waves) on porosity, is useful for studying porosity/lithological variation in a forma- tion using seismic data.

ACKNOWLEDGEMENTS

The authors wish to acknowledge useful discussions with Dr. G.C. Agarwal, General Manager (Geology), ONGC. The authors are also grateful to Mr. P.K. Chandra, Vice Chairman, ONGC for permission to publish this work.

The views expressed in this paper are those of the authors and not neces- sarily of the organisation in which they are working.

REFERENCES

Aki, K. and Richards, P., 1980. Quantitative Seismology. Theory and Methods, Vol. 1. Free- man, San Francisco, 158 pp.

Chacko, S., 1989. Porosity identification usingamplitude variations with offset: examples from south Sumatra. Geophysics, 54( 8): 942-951.

106 C.H. MEHTA AND B.M. VERMA

Chi, Cheng-Yung, Mendel, J.M. and Hampson, D., 1984. A computationally fast approach to MLD. Geophysics, 49( 5) 550-565.

Domenico, S.N., 1984. Rock lithology and porosity determination from shear and compres- sional wave velocity. Geophysics, 49: 1188-l 195.

Eastwood, L.R. and Castagna, J.P., 1983. Basis for interpretation of V,,/ V, ratios in complex lithologies. Trans. SPWLA 24th Annual Logging Symposium, Calgary, Alta., Canada, June 27-30. Sot. Prof. Well Log Analysts, Houston, TX.

Gelfand, V. and Larner, K., 1984. Seismic lithologic modelling. The Leading Edge, 3: 30-35. lkwuakor, K.C., 1988. VP/V, revisited: pitfalls and new interpretation techniques. World Oil, 9:

41-46. Ostrander, W.J., 1984. Plane wave reflection co-efticients for gas sands at non-normal angles of

incidence. Geophysics, 49: 1637- 1648. Rutherford, S.R. and Williams, R.H., 1989. Amplitude vs. offset in gas sands. Geophysics, 54( 6):

680-685. Tatham, R.H., 1982. VP/V, and lithology. Geophysics, 47: 0366-0344.