1.  Field of the Invention
This invention generally relates to geologic-modeling.  More specifically, this invention relates to a three-dimensional geologic modeling technique wherein multiple frequency-passband model units are combined together to form the complete geologic model. 
2.  Description of the Prior Art
A. Geologic Modeling
As used in the context of the present invention, a geologic model is a computer-based representation of a region of the subsurface, such as a petroleum reservoir or a depositional basin.  A geologic model may take on many different forms.  Most commonly, descriptive or static geologic models built for mining or petroleum applications are in the form of a three-dimensional array of individual model units or blocks (also referred to as cells) or less commonly points.  Hereafter, geologic models will be referred to in terms of blocks.  The entire set of blocks constitutes the geologic model and represents the subsurface volume.  Each block represents a unique portion of the subsurface, so the blocks may not intercut each other.  Dimensions of the blocks should be chosen so that the rock-properties assigned to each block (e.g., lithology, porosity, acoustic impedance, permeability, and water saturation) are relatively homogeneous within a block, yet without creating an excessive number of blocks.  Most commonly, blocks are square or rectangular in plan view and have thickness that is either constant or variable, but any shape may be used. 
The geologic modeling process assigns values of the rock-properties of interest to all blocks within the geologic model, which is a process known to practitioners of geologic modeling.  The value that is to be assigned to the block is calculated using one of many estimation methods, though the most common methods used are geostatistical.  Geostatistical methods take into account spatial continuity of the rock property.  The three-dimensional continuity of a rock property may be captured by a variogram, which quantifies the spatial variability of the rock property as a function of both separation distance and direction.  Also, the model is generally constrained by stratigraphic or structural surfaces and boundaries (e.g., facies changes) that separate regions of different geologic and geophysical properties.  The geologic or geophysical data and interpretations that are integrated into the geologic model come from many different sources, including core, wireline logs, outcrop analog, and 2-D or 3-D seismic data. 
B. Geostatistical Methods of Geologic Modeling
Deterministic geostatistical methods, such as kriging, are averaging methods that assign weights to the neighboring data as a function of distance from the estimation block and the variogram model.  Stochastic geostatistical methods, such as sequential-Gaussian simulation and sequential indicator simulation, generate geologic models that honor desired heterogeneity.  The estimation process first uses a deterministic method (e.g., kriging) to produce a conditional distribution of possible values of the rock property for the block.  Monte Carlo sampling of this distribution is used to select the value of the property to assign.  Since the order in which blocks are estimated affects rock property assignment, a 3-D random path typically is used.  This process can generate a suite of geologic models for the property being modeled. 
C. Frequency-Domain Description of Data and Spatial Scales
The spatial heterogeneity of rock-properties within a petroleum reservoir has a large effect on fluid flow.  Reservoir heterogeneity can be described over a wide range of spatial scales.  Each data source that is integrated into the geologic model represents a specific scale of information.  For example, well data generally provide finer-scale information than do seismic data.  The proper integration of different data types into the geologic model should account for the scale of information represented by each type.  Because spectral frequency is a representation of scale in the space domain, it is useful to consider the frequency content of the input data when building the geologic model.  Short-range or fine-scale variability in the reservoir corresponds to high-frequency heterogeneity, whereas long-range or coarse-scale variability corresponds to low-frequency heterogeneity.  These different scales of information can be described in the frequency domain (also known as the “spectral” domain). 
It can be shown that random functions such as 1-D well log or a 3-D geologic model can be decomposed into a sum of sinusoids, each representing a different frequency and unique amplitude.  This decomposition is accomplished using the Fourier transform and results in a composite amplitude spectrum 10 (see FIG.  1) which is a plot of amplitude as a function of frequency.  A defined frequency band representing a specific spatial scale can be filtered from this composite spectrum in the frequency domain.  A typical and well-known low-pass filter is the Butterworth filter which is characterized by a cutoff frequency and a slope (frequency taper) above the cutoff frequency.  This filter is easily converted to either band-pass or highpass filter types.  The low-pass filter is specified from 0 to f1 Hz resulting in low-frequency band 12, the band-pass filter from f1 to f2 Hz resulting in mid-frequency band 14, and the high-pass from f2 to Nyquist frequency (theoretical maximum frequency for a given data sample rate) resulting in high-frequency band 16, where f1 and f2 represent user defined cutoff frequencies. 
The Fourier transformation of a random function also results in phase information.  Phase information contains data relating to the spatial distribution of values, whereas the amplitude spectrum contains information about spatial variability of values. 
D. Modeling Technologies Which Account for Variations in Spatial Scale
Several geostatistical methods known to practitioners of geologic modeling attempt to account for variations in different scales of heterogeneity.  The most basic method is termed “kriging with a trend,” by which the geologic model is represented as the sum of a trend (low-frequency) component and a residual (high-frequency) component.  The trend is generally modeled as a smoothly varying deterministic component, and the residual component is modeled as a stationary random field with zero mean. 
Factorial kriging is a method related to kriging with a trend, except that the model is represented as the sum of one or more independent stochastic components.  Each component corresponds to one structure of the variogram model specific to a certain spatial scale.  Factorial kriging can be considered as a process to decompose spatially correlated data (e.g., well log, seismic data, or a geologic model) into a number of independent components, each of which can be filtered from the original data.  Filtering occurs in the space domain (seismic time or depth) instead of the frequency domain. 
Kriging with a trend and factorial kriging demonstrate a number of deficiencies and disadvantages.  One such disadvantage is identifying components of the data.  With factorial kriging, it may be difficult to identify components that have a physical interpretation, for example, to identify the component that exactly represents the spatial scale of the seismic data.  Second, with the geostatistical methods each component is modeled deterministically.  Third, the geostatistical methods assume that each component is independent of all other components, i.e., they are modeled separately and summed together to form the complete geologic model. 
The application of the Fourier transform (or fast Fourier transform) has also been used to isolate (filter) individual spatial components so that they can be modeled individually.  The Fourier transform converts stationary data from the space domain into an amplitude spectrum in the frequency domain.  Different data sources represent different frequency ranges in the composite spectrum.  Merging spectra from different data sources can generate a composite spectrum.  The inverse Fourier transform of this composite spectrum will directly yield a version of the integrated result in the space domain (e.g. a geologic-model realization). 
For example, a Fourier transform method has been applied to integrate static information from geologic interpretations (e.g., from seismic data) with dynamic information from well tests. ( Huang and Kelkar, Integration of Dynamic Data for Reservoir Characterization in the Frequency Domain, Proceedings of the SPC Technical Conference and Exhibition, Denver, Colo., Pages 209-219, Oct. 6-9, 1996.)  This method assumes that static interpretations represent low-frequency information whereas well-test data represent high-frequency information.  This high-frequency information was optimized in the frequency domain to agree with the measured data.  With this process, an initial geologic model of permeability (generated with static data) was converted to the frequency domain using the Fourier transform.  The spectrum of a defined high-frequency component was perturbed and the composite spectrum then converted back to the space domain using the inverse Fourier transform.  Pressure and production rate were simulated for the resulting geologic model and these estimates were compared with measured values using a simulated-annealing algorithm.  If convergence was not met, the process was repeated; otherwise, it was terminated. 
Prior art technologies that apply the Fourier transform or FFT to account for spatial scales in modeling demonstrate a number of deficiencies and disadvantages.  One such disadvantage is that model perturbations are performed in the amplitude spectrum in the frequency domain.  It is much more difficult to control the effect of the perturbation when it occurs in the frequency domain than in the space domain.  In addition, the model cannot easily be conditioned to well data when perturbation occurs in the frequency domain.  Second, the process of merging spectra of different components to form a composite spectrum assumes that the individual components are independent of all other components. 
Seismic-inversion methods for characterizing a given geology must also account for spatial scale.  It is understood by practitioners of seismic inversion that information on the low-frequency spatial distribution of acoustic impedance in the subsurface is absent in frequency band-limited seismic data.  However, a low-frequency acoustic impedance component can often be obtained independently using measurements from well data or seismic stacking velocities, or possibly through inference from seismic-stratigraphic or seismic-facies interpretations.  This low-frequency component can be merged with the seismic-frequency information to provide maps or models of acoustic impedance.  For example, in studies by Pendrel and Van Riel (Estimating Porosity from 3D Seismic Inversion and 3D Geostatistics, 6th Annual International Meeting of the Society of Exploration Geophysicists, Expanded Abstracts, Pages 834-387, 1997) and Torres-Verdin et al. ( Trace-based and Geostatistical Inversion of 3D Seismic Data for Thin-Sand Delineation: An Application in San Jorge Basin, Argentina, The Leading Edge, September, 1999, Pages 1070-1077), the low-frequency component was derived by interpolation of well-impedance data filtered to an appropriate bandwidth.  The resulting low-frequency component was then merged with the seismic data that had been inverted to a model of frequency band-limited acoustic impedance. 
Seismic-inversion methods are generally deficient for purposes of geologic modeling because they result in models of acoustic impedance only and contain no information at finer resolution than seismic scale.  In addition, these methods assume that the seismic-frequency and low-frequency components are independent sources of information. 
E. Deficiencies of the Prior Art Modeling Techniques
Prior art geologic modeling technologies do not properly account for different spatial scales of multiple diverse data types.  As such, inaccuracies in the geologic model can result.  Use of an inaccurate model may be very costly, resulting in inaccurate estimates of hydrocarbon reserves, missed hydrocarbon-reservoir targets, and inappropriate reservoir-development strategies. 
Most prior art geologic-modeling technologies fail to recognize that different data types used in constructing the model contain information at different scales and frequency content.  This deficiency is particularly true when integrating seismic information into the geologic model.  Seismic-amplitude data do not contain significant low-frequency information.  As a consequence of omitting this information, seismic data do not directly measure absolute rock property values nor generally measure slowly varying trends in these properties, e.g., as a result of burial compaction.  For example, seismic data may be used to estimate porosity values within a reservoir, though these values may be strongly influenced by a slowly varying compaction trend.  Direct integration of these estimates into the model without also integrating the low-frequency information will lead to inaccuracies. 
Seismic-amplitude data also do not contain significant high-frequency information.  As a consequence of omitting this information, seismic data measures properties over volumes of the subsurface which are much coarser than that measured by well data.  For example, most prior-art geologic-modeling techniques assume that the rock-properties estimated from the seismic data and integrated into the geologic model represent a volume that is no different than that measured by the well data.  If these estimated properties are integrated directly into the geologic model, the result might not properly reflect the high-frequency heterogeneity that occurs in the reservoir and that affects simulated fluid flow. 
As previously discussed, some geologic-modeling technologies attempt to account for the different spatial scales of multiple diverse data types.  Some of these technologies construct the model in the space domain, while others construct it in the frequency domain.  Deficiencies in these methods include an inability to identify spatial components that have physical interpretations, a difficulty in controlling model perturbations, and, most notably, an assumption that the individual spatial components are independent sources of information. 
For example, if shale volume (VSH) is modeled by summing multiple spatial components, the sum of all components can never exceed 100% because this would represent a physical impossibility since the total value would exceed 100%.  If all spatial components are generated independently and summed to produce the complete geologic model, there is a good probability that shale volume will exceed 100% at several locations within the model.  Therefore, each component is not independent of all other components.