Patent Application: US-201414461193-A

Abstract:
method for using a non - stationary , multi - scale domain transformation to combine multiple geophysical data sources , for example seismic data and well log data , into one coherent reservoir model . the seismic data are inverted to obtain one or more geophysical properties which are converted using petrophysical relationships to a subsurface model of a reservoir property such as porosity or shale volume fraction . the well log data are used to generate a geostatistical forward model of the reservoir property . both models of the reservoir property are transformed to a joint space / scale domain , of order & gt ; 1 , where processing is applied to merge the models into a coherent way into a single model before inverse transforming back to the space domain . the transform is a non - stationary multi - scale transform such as a wavelet , ridgelet , or curvelet transform . the processing may be by , for example , information theory or convex combination .

Description:
non - stationary multi - scale transforms use higher domain order ( order & gt ; 1 ) joint representations of data . here , an example is given that uses a joint representation of “ scale ” and “ space ” to perform reservoir modeling activity , where “ scale and “ space ” are domains . a geostatistical forward model is one example of a reservoir model . reservoir models may also be created by surfaces forming an enclosed object ( s ) and populating the properties by processing local coordinate fields within the object ( s ) in order to match input statistics . bortoli ( 1993 ) uses a method that performs the processing in the space domain only , domain order = 1 ( fig5 ). calvert et al . ( 2001 ) covers the use of a representation that represents “ scale ” or “ space ”, one or the other but not both jointly ; thus , domain order = 1 ( fig6 ). in the calvert publication , the fourier transform is used to accomplish the representation and perform stationary reservoir modeling in the scale , i . e . frequency , domain . ( frequency is the scale when the measurement is time .) the fourier transform decomposes a signal into a global summation of sine and cosine bases at certain frequencies . it relies on constructive and deconstructive interference of these globally specified frequencies to localize events in the signal . thus , it has no direct local control on what is happening and where . the representation of the signal in this domain is therefore not sparse , but rather full , complicated , and cumbersome to use in spatial modeling . the addition of the joint representation of both “ scale ” and “ space ” enables the modeler to handle not only scale dependency but also non - stationarity . here , stationarity is referring to signals that happen globally in the model , whereas non - stationarity refers to locally varying spatial signals . if a multi - scale transform is non - stationary it allows the modeler to incorporate a given frequency of variation at a particular location in space , or in the model . the stationary methods allow only global specification of the frequency content . the present invention uses this non - stationary , multi - scale representation to combine multiple data sources into one coherent reservoir model . certain types of data are frequency band limited and thus the multi - scale nature of the transforms are utilized to honor them appropriately . likewise , other data types are spatially localized , and thus the non - stationary nature of these transforms can be exploited to honor these data types . additionally , this representation can be used to extract meaningful trends and patterns from a third co - located data source . this third set of data can be used in the processing responsible for the merging of the two primary data sources . algorithms can also be expressed to operate in this non - stationary multi - scale representation of domains that combine many data types or create new data from the existing data . the following non - exhaustive list contains some examples of non - stationary multi - scale transforms : all of these transforms may be generalized to n - dimensional analysis , and are typically used in 1 , 2 , 3 , or 4 dimensions . a method for processing data with these representations can take the form of an equation , an algorithm or a heuristic . after the reservoir modeling processing has been completed within this joint representation of domains the transform back is performed with the given transform inverse . this inverse transform yields the final reservoir model . the present inventive method also includes the use of fast versions of these algorithms . the fast versions use computational methods to compute the equivalent results of the transforms with some efficient computational method . an example is the use of filter banks for the fast discrete wavelet transform . likewise , the present invention also includes the use of a single scale version of the transform being used in reservoir modeling to accomplish the desired result . any processing method in the joint representation space may be used . one example uses heuristics based on information theory to determine how to combine data within the transformed domain . a second example uses a convex combination with a weighting coefficient determined by a third input volume . alternatively , any other user - defined method of processing may be used . although the drawings discussed previously may indicate use of the wavelet transform ( debauchies 1992 ), the curvelet transform ( candes and donoho 2004 ) or the ridgelet transform ( candes 1998 ) may be substituted . fig1 - 16 outline examples using the curvelet transform . information entropy can be defined as many types of entropy , for example the shannon entropy : h ( x )= e [ i ( x )]= e [− 1 n ( p ( x ))]= σ i − p ( x i ) log b p ( x i ) ( 1 ) where i is the number of samples in x and b is a base of the logarithm . common values of b include 2 , euler &# 39 ; s number e , and 10 . entropy , as defined in ( 1 ), can be understood as a measure of disorder or uncertainty . it is used here at each resolution level to determine which data source within the joint representation space to choose at each discretization for the merged data output . a heuristic , such as “ choose the data source with the maximum entropy ” or “ choose the data source with the minimum entropy ” may be used to abstract the choosing to a quantitative logical operation . examples of this are illustrated in fig7 and 8 . a third co - located data source may be used to indicate how to combine the two other primary data sources , the reservoir model ( e . g ., geostatistical model ) and the seismic data . this data source may be transformed into the joint representation domain along with the two primary data sources as outlined in fig9 . it is used with the joint representation to provide a parameter α to a merging equation : equation ( 2 ) is a convex combination of two data types ; it can be extended to be applicable to any number of data types : the only requirement is that all the weighting coefficients sum to one : ∀∝ i & gt ; 0 and ∝ 1 +∝ 2 +∝ 3 + . . . +∝ n − 1 ( 4 ) this equation is evaluated at every resolution level within the multi - resolution data structure created by the transform . here , α may be based on any arbitrary collocated data , and when it is transformed into the joint representation space , the values are normalized to lie between zero and one for each resolution level . the foregoing description is directed to particular embodiments of the present invention for the purpose of illustrating it . it will be apparent , however , to one skilled in the art , that many modifications and variations to the embodiments described herein are possible . all such modifications and variations are intended to be within the scope of the present invention , as defined by the appended claims . all references cited in this document are incorporated herein by reference in those jurisdictions that allow it , to the extent they are not inconsistent with the disclosures herein . bortoli , l . j ., albert , f ., haas , a ., journel , a . g ., “ constraining stochastic images to seismic data ”, geostatistics , troia , quantitative geology and geostatistics 1 , 325 - 338 ( 1992 ). calvert , c . s ., bishop , g . w ., ma , y . z ., yao , t ., foreman , j . l ., sullivan , k . b ., dawson , d . c ., jones , t . a ., u . s . pat . no . 7 , 415 , 401 ( 2001 ). candes , e . j ., donoho , d . l ., “ new tight frames of curvelets and optimal representations of objects with c 2 singularities ,” communications on pure and applied mathematics 57 , 219 - 266 ( 2004 ). connolly , p ., “ elastic impedance ,” the leading edge 18 , 438 - 452 ( 1999 ). donoho , d . l ., hou , x ., “ beamlets and multiscale image analysis ,” multiscale and multiresolution methods , lecture notes in computational science and engineering 20 , 149 - 196 ( 2002 ). haas , a ., and o . dubrule , “ geostatistical inversion — a sequential method of stochastic reservoir modeling constrained by seismic data ,” first break 12 , 561 - 569 ( 1994 ). isaaks , e . h . and srivastava , r . m ., applied geostatistics , oxford university press , new york , particularly pages 40 - 65 ( 1989 ). journel , a ., “ geostatistics : roadblocks and challenges ,” geostatistics , troia &# 39 ; 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