INVERTED SEISMIC ATTRIBUTE QUALITY AND LOCAL ROCK PHYSICS CALIBRATION

Methods and processing in the field of seismic data, particularly to more accurately predict petrophysical property variables at unsampled locations beyond and between wells.

DETAILED DESCRIPTION OF THE INVENTION

A flowchart of steps that may be utilized by embodiments of the present invention illustrated inFIG. 1. Some of the blocks of the flow chart may represent a code segment or other portion of the compute program. In some alternative implementations, the functions noted in the various blocks may occur out of the order depicted inFIG. 1. For example, two blocks shown in succession inFIG. 1may in fact be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order depending upon the functionality involved.

In step100, seismic survey data is obtained.

In step200, the seismic survey data is processed to produce an image of the subsurface and necessary pre-stack data required for inversion. After processing/imaging, the pre-stack data often needs further pre-conditioning to comply with the assumptions of the forward modeling operator in the seismic inversion. In the event preconditioning is a necessary step, the pre-stack seismic data used will have any necessary pre-conditioning processing applied prior to inversion. For example, the seismic survey data may contain “multiples” which should be removed prior to inversion. Multiples are events or arrivals of seismic energy that have been reflected more than once. Processing techniques for the removal of other noise types, unwanted energy and interference are well known in the art.

In step300, elastic rock properties are determined using a pre-stack inversion algorithm. Pre-stack inversion algorithms are known in the art to simultaneously produce elastic properties like P-impedance, S-impedance and density followed by rock physics transforms to produce lithology cubes. AVO (AVA) geostatistical inversion incorporates both elastic properties in the seismic resolution and higher resolution properties from well log measurements into a single method. The output models (realizations) are consistent with well log information, AVO seismic data, and honor rock property relationships found in the wells. Because all output models are equi-probable models satisfying the data constraints, the uncertainty can be quantitatively assessed to determine the range of reservoir possibilities within the constraining data.

While any pre-stack inversion algorithm may be utilized, for explanatory purposes the pres-tack inversion algorithm presented in U.S. Pat. No. 7,072,767 entitled “Simultaneous Inversion for Source Wavelet and AVO Parameters from Prestack Seismic Data” is utilized. The inversion algorithm is formulated as:

subject to φd=||Wd(dobs−F(a,b,c,S))||2−φd*subject to amin≦a≦amaxsubject to bmin≦b≦bmaxsubject to cmin≦c≦cmaxsubject to −1≦r(a,b,c)≦1
where,
φm=the model misfit function;
φd=the data misfit function;
S(t)=the source function to be obtained from inversion;
Sref(t)=the reference model for source function, which can be any a priori model, including a null set;
φS, αa, αb, αc=the control parameters (scalar) that control the relative contribution of the source, intercept and gradient norms;
a=a(t0),b=b(t0),c=c(t0);
aref(t0)=the reference intercept model at zero offset time t0;
bref(t0)=the reference gradient model at zero offset time t0;
cref(t0)=the reference curvature model at zero offset time t0;
Wd=a data weighting matrix, essentially a diagonal matrix whose elements are the reciprocal of the standard deviation for each datum;
dobs=a vector containing the data;
F(a, b, c, S)=the forward modeling operator to generate the predicted data;
φd*=the final data misfit to be achieved after the inversion;
amin, amax, bmin, bmax, cmin, cmax=the lower and upper bounds of the AVO parameters; and
r(a, b, c, θ)=the P-wave reflection coefficient as a function of AVO parameters and the angle of incidence θ.

In step400, a seismic attribute quality is calculated. Elastic attributes derived from seismic inversion are obtained using an optimization procedure. The optimization provides a balance between consistency with the seismic reflection data, i.e., adequately fitting the geophysical data, and consistency with a prior geological model input. The seismic attribute quality (SAQ) accounts for both data misfit and model norm, defined as:

The data misfit term measures the degree to which the inverted seismic attribute quality (SAQ)satisfies the reflection data in the pre-stack domain. In regions where imaging is more difficult due to data coverage or otherwise, the data misfit term will increase and the seismic attribute quality (SAQ) will decrease.

In addition to fitting the data, the pre-stack inversion algorithm also strives for consistency with any input from a prior geological model. The prior geological model misfit is referred to as the mod el misfit or the as the model norm. The mod el misfit is expressed as a product of a regularization parameter (β) with the norm of the inverted models departure from the prior model. Large departures from the prior model increases the model misfit term and thus decreased the SAQ.

Low seismic attribute quality (SAQ) is a balance between the data misfit and the model misfit . For example, large departures from the prior (larger model misfit) usually imply the seismic attribute quality (SAQ) had to adapt more to the reflection data (smaller data misfit). Therefore, the regularization parameter plays a crucial role in balancing the data misfit and the model misfit .

In step500, the rock physics relationship is adjusted. The seismic attribute quality (SAQ) can be computed at every gather location, standardized by its maximum to lie between 0 to 1 (best quality approaches unity), and then used to locally adjust the rock physics relationship as follows:

where,
ρ=the global correlation coefficient derived from collocated pairs of the target variable and the inverted seismic attribute representing the global rock physics relationship;
SAQL=the local inverted seismic attribute quality; and
ρL=the local correlation coefficient representing the new local rock physics relationship.

This new rock physic relationship can be honored during prediction of the primary variable using geostatistical techniques such as collocated cokriging and Bayesian Updating. The implementation of the new rock physics relationship is similar to Bayesian Updating, except the influence of the secondary inverted attribute are scaled back locally according to the SAQ .

In step600, the new rock physics relationship is applied.

In closing, it should be noted that the discussion of any reference is not an admission that it is prior art to the present invention, especially any reference that may have a publication date after the priority date of this application. At the same time, each and every claim below is hereby incorporated into this detailed description or specification as a additional embodiments of the present invention.

EXAMPLE

The present inventive method was applied to actual seismic data acquired over a potential oil field. After the seismic data was acquired, the following pre-stack inversion algorithm described in Roth et al. (U.S. Pat. No. 7,072,767) was utilized:

subject to φd=||Wd(dobs−F(a,b,c,S))||2−φd*subject to amin≦a≦amaxsubject to cmin≦c≦cmaxsubject to −1≦r(a,b,c)≦1
where,
φm=the model misfit function;
φd=the data misfit function;
S(t)=the source function to be obtained from inversion;
Sref(t)=the reference model for source function, which can be any a priori model, including a null set;
αS, αa, αb, αc=the control parameters (scalar) that control the relative contribution of the source, intercept and gradient norms;
a=a(t0),b=b(t0),c=c(t0);
aref(t0)=the reference intercept model at zero offset time t0;
bref(t0)=the reference gradient model at zero offset time t0;
cref(t0)=the reference curvature model at zero offset time t0;
Wd=a data weighting matrix, essentially a diagonal matrix whose elements are the reciprocal of the standard deviation for each datum;
dobs=a vector containing the data;
F(a, b, c, S)=the forward modeling operator to generate the predicted data;
φd*=the final data misfit to be achieved after the inversion;
amin, amax, bmin, bmax, cmin, cmax=the lower and upper bounds of the AVO parameters; and
r(a,b,c,θ)=the P-wave reflection coefficient as a function of AVO parameters and the angle of incidence θ.

The model misfit, shown inFIG. 2a, was determined by utilizing the following relationship:

The data misfit, shown inFIG. 2b, was determined by utilizing the following relationship:

The total misfit, shown inFIG. 2c, was determined by utilizing the following relationship:

FIG. 2Dshows the final quality. The seismic attribute quality, shown inFIGS. 3A-3Fand4A-4H, was determined by utilizing the following relationship:

As shown in the model, data and total misfit (FIGS. 3A-3Fand4A-4H), prediction uncertainty exists. The seismic attribute quality provides a more accurate prediction, by reducing the uncertainty as.

REFERENCES

All of the references cited herein are expressly incorporated by reference. The discussion of any reference is not an admission that it is prior art to the present invention, especially any reference that may have a publication data after the priority date of this application. Incorporated references are listed again here for convenience: