Process for directly detecting the presence of hydrocarbons in a rock formation

A process for directly detecting the presence of hydrocarbons in a rock formation includes generating a plurality of seismic rays at spaced intervals from one another above or within the surface of the rock formation being surveyed to form a normal move-out corrected common mid-point gather; determining an approximate angle of incidence for each seismic ray; applying predetermined weighting factors to time samples of each of the reflected rays before stacking the time samples to form a trace; extracting the reflectivity of compressional longitudinal waves (p-waves) and shear waves (s-waves) of each sample; determining the p-wave reflectivity as a function of the s-wave reflectivity; and subtracting the p-wave reflectivity so determined from the extracted p-wave reflectivity thereby to define a fluid factor which gives a direct indication of the presence of hydrocarbons in the rock formation being surveyed.

FIELD OF INVENTION 
THIS INVENTION relates to a process of detection. More particularly, the 
invention relates to a process for directly detecting the presence of 
hydrocarbons in a rock formation. 
BACKGROUND TO THE INVENTION 
The Applicants are aware of various models which have been proposed for 
facilitating the detection of hydrocarbons in a rock formation. So, for 
example, in U.S. Pat. No. 4,534,019 to Wiggins, et al and corresponding 
European Patent Application No. 83300227.2, a method is proposed for 
determining the reflectivities of shear waves (s-waves), of geologic 
formations. However, a problem with this method is that data 
representative of the presence of hydrocarbons in the geologic formation 
cannot be obtained directly. 
Also, in recent times, variation of amplitudes of reflected compressional 
longitudinal waves (p-waves) as a function of the angles of incidence (or 
offset) has received much attention. The majority of recent publications 
on this subject have included some form of forward modelling in which the 
amplitudes of reflections in a common mid-point (CMP) gather are compared 
to those predicted by a model (see, for example, in this regard Ostrander, 
W.J.; "Plane-wave Reflection Coefficients for Gas Sands at Nonnormal 
Angles of Incidence"; Geophysics, Volume 49, 1984, pp1637-1648; Gassaway, 
G.S., and Richgels, H.J., SAMPLE: "Seismic Amplitude Measurement for 
Primary Lithology Estimation": 53rd Annual International SEG Meeting, 
September 1983, Las Vagas; Abstract Book, pp610-613; Yu, G., 
"Offset-amplitude Variation and Controlled-Amplitude Processing" 
Geophysics, Volume 50, 1985, pp2697-2708.). The modelling is generally 
done using the Zoeppritz equations or some simplified version thereof. 
However, a problem with this system is that it is very time-consuming and 
complicated. Also it does not give a direct indication of the presence of 
hydrocarbons in the rock formation. 
An alternative approach is to use curve fitting techniques to invert the 
seismic traces to a physical model directly. The principle of this method 
is outlined by Stolt, R.H., and Weglein, A.B.; "Migration and Inversion of 
Seismic Data", Geophysics, Volume 50, 1985 pp2458-2472. Stolt and Weglein 
use wave equation analysis to show that the extraction of elastic 
parameter changes from reflection seismic data is obtained by a set of 
weighted stacks. However, the shortcoming of this paper is that no mention 
is made of how the weighting factors are obtained. 
SUMMARY OF THE INVENTION 
According to the invention, there is provided a process for directly 
detecting the presence of hydrocarbons in a rock formation which includes 
generating a plurality of seismic rays at spaced intervals from one another 
above or within the surface of the rock formation being surveyed to form a 
normal move-out corrected common mid-point gather; 
determining an approximate angle of incidence for each seismic ray; 
applying predetermined weighting factors to time samples of each of the 
reflected rays before stacking the time samples to form a trace; 
extracting the reflectivity of compressional longitudinal waves (p-waves) 
and shear waves (s-waves) of each sample; 
determining the p-wave reflectivity as a function of the s-wave 
reflectivity; and 
subtracting the p-wave reflectivity so determined from the extracted p-wave 
reflectivity thereby to define a fluid factor which gives a direct 
indication of the presence of hydrocarbons in the rock formation being 
surveyed. 
The process may include initially determining the average velocities of the 
seismic rays through the rock formation. 
The process may include determining the average velocities from stacking 
velocities or borehole information. From the average velocities, the 
process may include extracting p-wave interval velocities of the rays 
between interfaces of layers constituting the rock formation. 
To determine the approximate angles of incidence, a smooth velocity 
function is required. Hence, the process may include utilising 
curve-fitting techniques to generate a smooth interval velocity function 
from the p-wave interval velocities. The curve-fitting techniques utilised 
may be cubic splines curves. 
Once the interval velocity function is known, the process may include 
determining the approximate angles of incidence of each ray using 
iterative ray tracing. 
The process may then include determining the ratio of p-wave velocities and 
s-wave velocities by means of an empirical relationship. The empirical 
relationship may be either a universal or local relationship depending on 
the lithology of the rock formation being surveyed. When a local 
relationship is used, the process may include deriving the relationship 
from cross-plots of borehole measurements using a conventional s-wave 
logging technique. 
The process may also include determining the density of the layers of the 
rock formation in terms of the velocities of the rays. 
The weighting factors to be applied to the samples may be both time and 
offset variant and are dependent on the determined interval velocity 
function, the ratio of p-wave velocities to s-wave velocities, and an 
offset pattern of the common mid-point gather, including a mute pattern. 
The weighting factors may include both positive and negative values. 
The process may then include displaying the outputs of the weighted stacks 
so formed as traces representing the p-wave reflectivity and s-wave 
reflectivity, both of which have a time scale of a normal seismogram, such 
a time scale being representative of depth. 
The process may include determining the p-wave reflectivity as a function 
of the s-wave reflectivity by using the relationship employed to determine 
the ratio of p-wave velocities to s-wave velocities. Instead the process 
may include determining the p-wave reflectivity as a function of the 
s-wave reflectivity by comparing amplitudes of the traces representing the 
p-wave reflectivity and the s-wave reflectivity. 
The fluid factor formed by substracting the determined p-wave reflectivity 
from the extracted p-wave reflectivity should be close to zero for all 
water-bearing rock, but will be negative at the top of a gas sand and 
positive at the bottom. Hence, the process may include representing the 
fluid factor in the form of a normal seismogram, such fluid factor having 
approximately zero deflection except where gas is present.

DETAILED DESCRIPTION OF THE INVENTION 
Referring to FIG. 1, a schematic diagram of the path of a transmitted 
seismic ray 10 is shown. At an interface 12 between layers of a rock 
formation being surveyed, a portion of the transmitted ray 10 is reflected 
as a reflected ray 14 and a portion of the ray 10 is transmitted or 
refracted as a refracted ray 16. 
The Zoeppritz equations can be used to provide reflection co-efficients of 
a reflected seismic ray. The Zoeppritz equations describe the 
relationships between incident, reflected and transmitted or refracted 
compressional longitudinal waves hereinafter referred to as p-waves) and 
shear waves ((hereinafter referred to as s-waves) on both sides of the 
interface 12. 
From Aki, K.I. and Richards, P.G., Quantitative Seismology; W.H. Freemand 
and Co., 1979, p153; a simplified form of the Zoeppritz equation can be 
written as 
##EQU1## 
where R=reflection co-efficient of p-waves 
W=average of s-wave velocities across the interface 12 
V=average of p-wave velocities 
.rho.=average of density 
.theta.=average of angles of incidence and 
angles of transmission of the p-wave 
.DELTA.V=change in V across the interface 12 
.DELTA.W=change in W across the interface 12; 
.DELTA..rho.=change in .rho. across the interface 12. 
For most reflection seismic surveys, it is reasonable to assume that the 
relative changes of property, ie (.DELTA.V/V), (.DELTA.W/W), and 
(.DELTA..rho./.rho.), are sufficiently small that second order terms can 
be neglected and that the average angle of incidence does not approach 
90.degree.. 
In terms of the identity: 
##EQU2## 
equation (1) can be rearranged to give: 
##EQU3## 
The terms can be rearranged so that the co-efficients become increasingly 
important towards the right side of the equation with increasing angles of 
incidence. Hence, following Shuey, R.T., "A Simplification of the 
Zoeppritz Equations": Geophysics, Volume 50, 1985, pp609-614, equation (2) 
can be written as follows: 
##EQU4## 
To be able to find the terms (.DELTA.V/V), (.DELTA.W/W) and 
(.DELTA..rho./.rho.) in the above equation, it is necessary firstly to 
determine the angles of incidence and the factor (W/V), ie the ratio of 
s-wave velocity to p-wave velocity. 
To determine the angle of incidence of each sample in a normal move-out 
common mid-point (CMP) gather, an iterative ray tracing technique can be 
employed. Before ray tracing can be carried out, it is necessary to 
specify a p-wave interval velocity function, ie. the velocity of the 
p-wave between interfaces of layers constituting the rock formation. The 
interval velocities can be obtained from the average velocity of the 
p-wave through the rock formation. This average velocity can be determined 
from stacking velocities, borehole information if available, or the like. 
The interval velocities determined from the average velocities are not well 
known in detail as shown in FIG. 2, in which reference numeral 18 shows 
the interval velocities derived from a vertical seismic profile, and 
reference numeral 20 shows the interval velocities derived from stacking 
velocities. By using a curve fitting technique such as a cubic splines 
curve fitting method a smooth interval velocity function can be obtained 
as shown by line 22 in FIG. 2. An assumption is made that there is 
horizontal layering, ie. no dip in the layers of the rock formation, and 
then with the determined smooth interval velocity function, iterative ray 
tracing can be carried out to determine the angles of incidence. 
It is now necessary to determine the factor (W/V) in equation (2). Since a 
seismic trace only give reflectivities and not actual values of W and V, 
it is necessary to make some assumptions about (W/V). Castagna, J.P., 
Batzle, M.L., and Eastwood, R.L. "Relationships Between Compressional Wave 
and Shear Wave Velocities in Clastic Silicate Rocks". Geophysics, Volume 
50, 1985 pp571-581 gives a relationship between V and W which has been 
derived for water-saturated clastic silicate rocks in the form: 
EQU V=1360+1,16 W (velocities in metres per second) (4) 
This relationship, together with the smooth p-wave interval velocity 
function as shown in FIG. 2 can be used to provide a value of (W/V) for 
each time sample of the CMP gather. 
The above equation may not appropriate for other types of rocks and other 
relationships may have to be used. Such other relationships may be derived 
from cross-plots of borehole measurements, using one of the s-wave logging 
techniques currently available. 
It would now appear that, with the determined angles of incidence, .theta., 
and the ratio of the velocities, (W/V), equation (2) could be fitted to 
amplitudes of the seismic traces for each time sample of the CMP gather to 
yield the co-efficients of the equation, and hence the reflectivities 
(.DELTA.V/V), (.DELTA.W/W) and (.DELTA..rho./.rho.). However a good 
estimate of all three is difficult to obtain. In equation (2) we have a 
co-efficient of sin.sup.2 .theta. and tan.sup.2 .theta.. For moderate 
angles of incidence the shapes of a sin.sup.2 .theta. curve and a 
tan.sup.2 .theta. curve are very similar, and therefore only slight 
inaccuracies in the data could result in a wrong distribution between the 
two terms. This is also apparent from equation (3), with the last term 
only becoming effective at large angles of incidence, and will be 
determined very inaccurately. 
It is thus necessary to make a further assumption. An assumption can be 
made regarding the relationship between p-wave velocity and density. From 
Gardner, G.H.F., Gardner, L.W., and Gregory, A.R., "Formation Velocity and 
Density--the Diagnostic Basics for Stratigraphic Traps": Geophysics, 
Volume 38, 1974, pp770-780, a relationship is given for water-saturated 
rocks excluding evaporites, as density being proportional to the 4th root 
of velocities. This leads to the equation: 
##EQU5## 
Substituting equation (5) into equation (2) gives: 
##EQU6## 
By curve fitting to seismic data, the reflectivities (.DELTA.V/V) and 
(.DELTA.W/W) can be determined. Curve fitting to the amplitudes across the 
CMP gather is equivalent to a weighted stack. Weighting factors can thus 
be applied to each sample of the CMP gather. The weighting factors to be 
applied are both offset and time variant, and depend on the p-wave 
interval velocity function, the relationship used to determine the ratio 
of the p-wave velocity to s-wave velocity, and the offset geometry of the 
CMP gather including a mute pattern. Once the weighting factors have been 
determined, weighted stacks can be formed. The outputs of the weighted 
stacks will be traces representing the p-wave reflectivity, (.DELTA.V/V), 
and the s-wave reflectivity, (.DELTA.W/W), both with the time scale of a 
normal seismogram, ie. related to depth by the p-wave velocity, as shown 
in FIGS. 3 and 4 respectively. 
To obtain the weighting factors to be applied, equation 6 can be rewritten 
in the form: 
##EQU7## 
for i=1 . . . n where n is the number of traces contributing to the normal 
move out corrected CMP gather at the particular time sample under 
consideration. It will be noted that A.sub.i and B.sub.i are functions 
only of the p-wave velocity model and the (W/V) model, and not of the 
data. 
If the actual amplitude of each offset sample is a.sub.i then the mean 
square error of all amplitudes compared with the model curve is given by: 
##EQU8## 
(.DELTA.V/V) and (.DELTA.W/W) must be varied so that the error is 
minimized. Hence, taking partial derivatives of the error with respect to 
(.DELTA.V/V) and (.DELTA.W/W), 
##EQU9## 
Setting equations (12) and (13) to zero results in the two simultaneous 
equations: 
##EQU10## 
Solving for (.DELTA.V/V) and (.DELTA.W/W) gives 
##EQU11## 
Equations (15) and (16) are written in this form to show that the right 
hand side of each is a weighted stack, with the weighting factors to be 
applied to each sample being the term in square brackets. 
To determine the lithological, or fluid content of the rock formation, 
Poisson's ratio can be investigated, (cf Shuey 1985 (supra) and Koefoed, 
O., "On the Effect of Poisson's Ratio of Rock Strata on the Reflection 
Coefficients of Plane Waves", Geophys. Prosp., 1955 pp281-387). However, 
it is more convenient to determine the ratio of (V/W) which is related to 
Poisson's ratio by: 
##EQU12## 
where .rho. is Poisson's ratio. 
Defining the ratio (V/W) as q, then the quantity (.DELTA.q/q) can be 
considered. The quantity (.DELTA.q/q) is referred to as the 
"pseudo-Poisson's ratio reflectivity". The quantity (.DELTA.q/q) is the 
difference between the p-wave reflectivity and the s-wave reflectivity, 
ie. 
##EQU13## 
A (.DELTA.q/q) trace can be formed by subtracting the (.DELTA.W/W) trace 
from the (.DELTA.V/V) trace, the (.DELTA.q/q) trace having a form as shown 
in FIG. 5. 
Alternatively, the weights applied to the s-wave reflectivity trace can be 
subtracted from the weights applied to the p-wave reflectivity trace to 
arrive at a new set of weights to give (.DELTA.q/q) directly. 
Now, to determine the presence of gas, reference again must be made to 
equation (4). Substitution of gas for water in water-bearing clastic 
silicates causes a reduction of the p-wave velocity while the s-wave 
velocity remains largely unaffected since a gas cannot support shear. 
Hence, a fluid factor, .DELTA.F, can be defined. 
From equation (4), by differentiation, 
EQU .DELTA.V.apprxeq.1.multidot.16.DELTA.W (19) 
and 
##EQU14## 
.DELTA.F can then be defined as the difference between the extracted p-wave 
reflectivity and the reflectivity of the p-wave as deduced from the 
reflectivity of the s-wave, ie. equation (20). Hence, 
##EQU15## 
.DELTA.F can also be constructed by equalizing the amplitudes of the 
(.DELTA.V/V) and (.DELTA.W/W) traces with a smooth gain function, and then 
subtracting the traces to give a .DELTA.F trace with generally low 
amplitudes. 
The fluid factor .DELTA.F can be represented as a normal seismogram as 
shown in FIGS. 6. .DELTA.F will be close to zero for all water bearing 
rocks, but will be negative at the top of a gas sand and positive at the 
bottom thereof. From FIG. 6, it will be noted that there are almost no 
perturbations on the traces except at approximately 2 seconds where a 
"bright spot" appears, the "bright spot" signalling the presence of gas. 
Referring now to FIG. 7, synthetic data is given. All the layers relate to 
the relationship given by equation (4), except at approximately 2.2 
seconds where the high s-wave velocity relative to the p-wave velocity is 
an indication of the presence of gas. FIG. 8 shows a CMP gather using the 
exact Zoeppritz equation with ray tracing through the exact model. 
Applying weighted stacks to the gather of FIG. 8 gives the reflectivities 
as shown in FIG. 9. The values of the reflectivities derived using the 
data of FIG. 7 are shown in FIG. 10. 
From FIG. 9 it is clear that the only significant perturbations in the 
.DELTA.F trace are where gas is present. 
It will be seen from FIGS. 6 and 9 that the presence of gas in a rock 
formation can be directly detected using the process as described above. 
Hence, it is an advantage of the invention that the need for drilling to 
detect gas can largely be obviated. The only borehole data used in the 
above process was that to determine the average velocities, from which the 
interval velocities can be derived. The average velocities can, however, 
be determined by stacking velocities, and hence no borehole data at all 
are necessary.