Abstract:
Representative embodiments provide for a computer including a program code configured to cause a processor to invert and thereafter calibrate first and second data sets, subtract the inverted second data set from the inverted first data set to derive a time-lapse data set, calculate a model including a plurality of parametric values, sort the plurality of parametric values into a plurality of bins, select, map and calibrate a plurality of optimal parametric values from the plurality of bins, and plot the plurality of calibrated optimal parametric values to represent at least one physical characteristic of a subterranean reservoir of hydrocarbons. The method includes deriving a time-lapse data set from a first seismic data set and a second seismic data set, deriving a model, sorting the plurality of values into bins, selecting, mapping and calibrating a plurality of optimal values from the bins, and plotting the calibrated values.

Description:
BACKGROUND  
       [0001]     The use of seismic data in the analysis and modeling of subterranean reservoirs containing hydrocarbons and other fluids is known. Typically, such data are gathered through the use of a source of seismic energy and one or more receivers respectively located on a ground or water surface over a subterranean region of interest. The source is used to produce a seismic pulse, burst, or similar energy which travels generally downward and away from the source, into the subterranean material of the region under examination.  
         [0002]     As the seismic pulse encounters a change in material properties, most notably at an interface between one type of subterranean material and another, some of the seismic pulse energy is reflected back toward the surface. The receiver or receivers detect this reflected pulse energy and record corresponding data, often with respect to other parameters of interest such as linear distance from the particular receiver to the source, time-of-flight (i.e., time between emission of source pulse and detected reflection), amplitude of the detected reflection, angle of incidence of the detected reflection relative to the ground (or water) surface plane or some other datum, etc. Thus, the presence of the interface can be detected through later analysis of the detected and recorded pulse reflection data.  
         [0003]     Generally, such pulse reflection and associated parameter data have been used to model, or estimate, the depths of these subterranean material interfaces and to present this information in the form of a cross-sectional elevation plot of the subterranean region of interest. However, such a plot often fails to provide other desirable information regarding the present physical state of a subterranean reservoir containing hydrocarbons or other fluids.  
         [0004]     Therefore, it is desirable to provide a method and apparatus for modeling various other subterranean physical parameters, and to present that model in the form of planar view representation (as well as 3D view presentation) of the subterranean region of interest.  
       SUMMARY  
       [0005]     One embodiment of the present invention provides for a method of modeling seismic data. The method includes deriving a time-lapse data set from a first seismic data set and a second seismic data set, and deriving a forward-modeled time-lapse data set including a plurality of values. The method further includes sorting the plurality of values into a plurality of bins corresponding to the forward-modeled time-lapse data set, selecting a plurality of optimal values from the plurality of bins, and then mapping the plurality of optimal values using the time lapse data set. The method also includes calibrating the plurality of optimal values. The method further includes plotting the plurality of calibrated optimal values.  
         [0006]     Another embodiment provides for a method of modeling seismic data corresponding to a subterranean reservoir containing hydrocarbons. The method includes calibrating a first seismic data set and a second seismic data set, and then subtracting the calibrated second seismic data set from the calibrated first seismic data set to derive a time-lapse data set. The method further includes deriving a forward- modeled time-lapse data set including a plurality of physical parametric values, sorting the plurality of physical parametric values into a plurality of bins corresponding to the forward-modeled time-lapse data set, and selecting a plurality of optimal physical parametric values from the plurality of bins of physical parametric values. The method also includes mapping the plurality of optimal physical parametric values to a corresponding plurality of subterranean locations using the time-lapse data set, and calibrating the plurality of optimal physical parametric values. The method also includes plotting the plurality of calibrated optimal physical parametric values as a visual representation of the subterranean reservoir containing hydrocarbons.  
         [0007]     Yet another embodiment provides for a computer which includes a processor and a computer-readable storage medium coupled in data communication with the processor. The computer-readable storage medium stores a first data set and a second data set and a plurality of rock physics relationships and a program code. The program code is configured to cause the processor to calibrate each of the first and second data sets, and then to subtract the calibrated second data set from the calibrated first data set to derive a time-lapse data set. The program code is further configured to cause the processor to calculate a forward-modeled time-lapse data set including a plurality of parametric values using selected ones of the plurality of rock physics relationships. The program code is still further configured to sort the plurality of parametric values into a plurality of bins corresponding to the forward-modeled time-lapse data set, and to select a plurality of optimal parametric values from the plurality of parametric values sorted into the plurality of bins. The program code is further configured to cause the processor to map the plurality of optimal parametric values to a corresponding plurality of subterranean locations using the time-lapse data set, calibrate the plurality of optimal parametric values, and to plot the plurality of calibrated optimal parametric values to visually represent at least one spatially distributed physical characteristic of a subterranean reservoir of hydrocarbons.  
         [0008]     These and other aspects and embodiments will now be described in detail with reference to the accompanying drawings, wherein: 
     
    
     DESCRIPTION OF THE DRAWINGS  
       [0009]     The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.  
         [0010]      FIG. 1  is a side elevation sectional view depicting a field seismology arrangement in accordance with an embodiment of the present invention.  
         [0011]      FIG. 2  is a flowchart depicting a method of modeling seismic data in accordance with another embodiment of the present invention.  
         [0012]      FIG. 3  is a mapping diagram referring to exemplary data plots  3 A- 3 D in accordance with the present invention.  
         [0013]      FIGS. 3A through 3D  are data plots depicting exemplary P-wave and S-wave seismic data collected at times T1 and T2 in accordance with the present invention.  
         [0014]      FIG. 4  is a mapping diagram referring to exemplary data plots  4 A- 4 B in accordance with the present invention.  
         [0015]      FIGS. 4A and 4B  are data plots depicting exemplary inverted time-lapse P-wave and S-wave seismic data in accordance with the present invention.  
         [0016]      FIG. 5  is a block diagram depicting a data cube in accordance with an embodiment of the present invention.  
         [0017]      FIG. 6  is a block diagram depicting the data cube of  FIG. 5  and a corresponding data array in accordance with an embodiment of the present invention.  
         [0018]      FIG. 7  is a locus plot in accordance with an embodiment of the present invention.  
         [0019]      FIG. 8  is a block diagram depicting data mapping in accordance with an embodiment of the present invention.  
         [0020]      FIG. 9  is a mapping diagram referring to exemplary data plots  9 A- 9 D in accordance with the present invention.  FIGS. 9A through 9D  are data plots depicting exemplary calibrated and actual (true) saturation and pore pressure values in accordance with the present invention.  
         [0021]      FIG. 10  is a block diagram depicting a data acquisition and processing system in accordance with yet another embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION  
       [0022]     In representative embodiments, the present teachings provide methods and apparatus for acquiring and processing seismic data corresponding to a subterranean region of interest, typically containing hydrocarbons, and to plot a final processed data set as a graphic representation of time-lapse changes to various selected physical parameters of the subterranean region of interest.  
         [0023]     Turning now to  FIG. 1 , a side elevation sectional view depicts a field seismology arrangement  100  in accordance with an embodiment of the present invention. The arrangement  100  includes a source (i.e., emitter) of seismic energy  102 . The source  102  is located on a ground surface  104  over a subterranean region  106 . The source  102  can be defined by any suitable apparatus capable of producing a seismic (acoustic) pulse or vibrational energy which is directed generally into the subterranean region  106 .  
         [0024]     The field seismology arrangement  100  further includes a pair of seismic detectors  108  and  110 , respectively (also known as “receivers”, as for example geophones, or hydrophones when the surface  104  is underwater). Each of the seismic detectors  108  and  110  rests on the ground surface  104 , and is spaced apart from the source  102  by an offset distance  112  or  114 , respectively. Each of the seismic detectors  108  and  110  can be defined by any detection device suitable for detecting and recording seismic energy pulses or reflections (described in detail hereafter) that arrive at the detectors  108  and  110  after passing through the subterranean region  106 .  
         [0025]     The subterranean region  106  includes three different material strata designated as  116 ,  118  and  120 , respectively. Each of the material strata  116 ,  118  and  120  is respectively defined by a depth D 1 , D 2  and D 3 . Furthermore, the region  106  includes an interface  122  between the material strata  116  and  118 , an interface  124  between the material strata  118  and  120 , and an interface  126  between the material strata  120  and an underlying region  121 . It is assumed that each of the strata  116 ,  118  and  120  includes a respective average material incompressibility, fluid content (or lack thereof), and other physical parameters that distinguish it from the other respective material strata.  
         [0026]     Typical operation of the field seismology arrangement  100  is as follows: the source  102  produces a source seismic pulse P 1  of known amplitude A 1 . The source pulse P 1  is directed into the subterranean region  106  and proceeds initially through the material strata  116 , striking the interface  122  at angle of incidence AN 1 . A portion of the energy of pulse P 1  is reflected from the interface  122  back toward the surface  104 , as reflection pulse P 2 , at an angle of reflection AN 1 . The pulse P 2  arrives at surface  104  within detectable vicinity to the seismic detector  108 , having amplitude A 2  upon arrival.  
         [0027]     The seismic detector  108  records data corresponding to the detection of the reflection pulse P 2 . This recorded data can include, for example, a detected amplitude corresponding to amplitude A 2  of the pulse P 2 , the detected angle of reflection (i.e., incidence) AN 1  of the pulse P 2 , the offset distance  112 , the arrival time of the detected pulse P 2  relative to the (known) time of emission of the source pulse P 1 , etc. It will be appreciated that the seismic detector  108  only transitorily “records” data, and that in fact the detector  108  transmits the data to a permanent recording station (not shown) for recording on computer readable media such as a magnetic tape or a hard disk drive.  
         [0028]     As the source pulse P 1  continues into the subterranean region  106 , similar reflection pulses P 3  and P 4  are reflected from interfaces  124  and  126 , respectively. The reflection pulse P 3  is initially reflected from the interface  124  back toward the surface  104  at an angle of AN 2 , and is then refracted at the interface  122  to a new angle of incidence AN 1 . Thus, the reflection pulses P 3  and P 4  arrive at the surface  104  within detectable vicinity of the seismic detectors  108  and  110 , respectively. The seismic detectors  108  and  110  then record data corresponding to the reflected pulses P 3  and P 4 . This recorded data can include any or all of the various characteristics described above in regard to the pulse P 2 .  
         [0029]     The data thus received by the seismic detectors  108  and  110  are recorded and then communicated to a suitable analytical apparatus (i.e., a computer) for analysis by way of the method of the present invention, described in detail hereafter.  
         [0030]     It is to be understood that the field seismology arrangement  100  of  FIG. 1  is intended to convey conceptual information regarding the acquisition of seismic data as used in the methods of the present invention, and that a similar field seismology arrangement (not shown) can include any suitable number of seismic energy sources (i.e., source  102 ) and seismic detectors (i.e., detector  108 ) arranged in a linear or matrix pattern on a ground surface (i.e., surface  104 ) or on a water surface in the case where the ground surface  104  is submerged under water. Thus, the field seismology arrangement  100  of  FIG. 1  is exemplary of the data acquisition of the present invention and does not represent the only type of such arrangement that can be used, nor does it represent the only type of field conditions under which data acquisition can be performed within the context of the present invention.  
         [0031]      FIG. 2  is a flowchart depicting a method  200  in accordance with the present invention. Simultaneous reference shall be made, as directed, to  FIGS. 1 and 3  through  9 D, during the description of the method  200  of  FIG. 2 .  
         [0032]     In step  202 , amplitude-versus-offset (hereafter, AVO) field seismic data are acquired through the use of field seismology (e.g., the field seismology arrangement  100  of  FIG. 1 ). These AVO data are acquired at a first time T1 and at a later time T2, and are generally collected over a subterranean region of interest such that an area at a given depth (i.e., stratum) is represented. AVO data for both generally planar and volumetric regions of interest can be suitably acquired.  
         [0033]     In step  204 , the AVO data are inverted to seismic impedance data using standard mathematical techniques. As a typical AVO data set is relatively vast, such inversion is generally done by way of electronic computer (see  FIG. 10 ). The inverted data sets include P-wave pseudo impedance data (hereafter, IP&#39;) and S-wave pseudo impedance data (hereafter, IS&#39;), and are referred to as IP&#39;(T1), IS&#39;(T1), IP&#39;(T2), and IS&#39;(T2).  
         [0034]     In step  205 , the P-wave and S-wave pseudo impedance data IP&#39;(T1), IS&#39;(T1), IP&#39;(T2), and IS&#39;(T2) are calibrated so as to correspond more closely with actual field conditions. This calibration can be performed in a number of different ways; non-limiting examples include: calibrating the pseudo values against like kinds of data (i.e., P-wave and S-wave impedance data) measured at selected well bores; or modeling the pseudo values using rock physics relationships (properties). Combinations of these or other calibration methods can also be used.  
         [0035]     It is to be understood that such calibration is not necessarily linear in nature. In any case, the calibration method yields calibrated P-wave and S-wave impedance data IP (T1), IS (T1), IP(T2), and IS(T2) for the subterranean region under consideration.  
         [0036]     Exemplary plots of such calibrated data IP(T1), IS(T1), IP(T2), and IS(T2) are respectively depicted in  FIGS. 3A, 3B ,  3 C, and  3 D. Within  FIGS. 3A-3D , color is indicative of the signal or seismic wave impedance, with red indicative of seismic wave impedance values at the lower end of the represented scale, and blue used to indicate seismic impedance values at the higher end of the represented scale. The color white (or colorless) is used to indicate mid-scale seismic impedance values.  
         [0037]     As such,  FIGS. 3C and 3D  each depict the presence of two spot locations where a generally distinct decrease in seismic wave impedance has occurred, relative to the same locations in  FIGS. 3A and 3B . These spot decreases (i.e., changes) in seismic wave impedance correspond to physical changes within the subterranean region of interest, such as, for example, changes in porosity, pore pressure, saturation, etc.  
         [0038]     In step  206 , the inverted AVO data matrices derived in step  204  are subtracted in accordance with the two following formulas, thus providing the indicated time-lapse data (i.e., recorded field data): 
        1) TL(IP) =[IP(T2)- IP(T1)]     2) TL(IS) =[IS(T2)- IS(T1)] It is important to note that time-lapse data required by this embodiment of the present invention need not be seismic impedance (i.e., inverted AVO) data as described above for step  204 . Any time lapse data that can be forward-modeled from a set of physical parameters within the context of the present invention can potentially be used in step  206 . Thus, in another embodiment (not shown) of the present invention, a method using appropriate AVO data acquired in step  202  can dispense with (i.e., skip over) the inverting of step  204  above and proceed directly to the calibrating of step  205  above. Other methods (not shown) in accordance with other embodiments of the present invention can also be used.        
 
         [0041]     Exemplary plots of such time-lapse data are respectively depicted in  FIGS. 4A and 4B . As described above, color is indicative of (i.e., in correspondence to) seismic wave impedance value within  FIGS. 4A and 4B . The time-lapse data TL(IP) and TL(IS) derived within step  206  result in a generally more pronounced and distinct indication of physical changes within the subterranean region. As shown in  FIGS. 4A and 4B , the two spot locations described above are clearly pronounced, and are assumed to be indicative of a subterranean physical change of interest (i.e., porosity, saturation, etc.), or a combination of such changes.  
         [0042]     In step  208 , selected known rock physics relationships and corresponding formulas are used to compute forward-modeled time-lapse data (i.e., synthetic data) FMTL(lp) and FMTL(ls). Typically, these relationships include such physical parameters as pore pressure, fluid saturation, and rock porosity. Such calculations can be generally represented by the two following formulas: 
        3) FMTL(IP) =F 1 [TL(Saturation), TL(Pore Pressure), TL(Porosity)]     4) FMTL(IS) =F 2 [TL(Saturation), TL(Pore Pressure), TL(Porosity)] where F1 and F2 are selected rock physics relationships (i.e., formulas) that are functions of the desired physical parameters of porosity, saturation, and pore pressure. Other physical parameters, by way of their associated formulas, can also be considered such as, for example, temperature, salinity, gas-to-oil ratio (GOR), gas gravity, overburden pressure, etc.        
 
         [0045]     Reference is now made to  FIG. 5 . These rock physics calculations are generally used to construct a data cube  300  of the three exemplary parameter types, respectively depicted as TL pore pressure  302 , TL saturation  304 , and TL porosity  306 . The data cube  300  thus includes a plurality of three-dimensional cells  308 , which respectively contain the forward-modeled time-lapse data FMTL(IP) and FMTL(IS) pair values corresponding to the coordinates (i.e., parametric values) of the particular cell  308 . An exemplary cell  310  of the plurality of cells  308  is depicted, which includes corresponding FMTL(IP) and FMTL(IS) data pair contents  312 . The data cube  300  therefore represents a three-dimensional data model of the subterranean region of interest. It is to be understood that if other physical parameters are considered, a corresponding data cube (not shown) can have four or more dimensions.  
         [0046]     It is important to note that any given forward-modeled time-lapse data pair FMTL(IP) and FMTL(IS) can result from more than one corresponding set of physical parameters—that is, more than one cell  308  within the data cube  300 . Typically, any given time-lapse data pair (for example, data pair  312 ) results from several corresponding sets of physical parameters, which can be visualized as rays or arcs of adjacent or near-adjacent, associated cells  308  within the data cube  300 .  
         [0047]     In step  210 , the forward-modeled time-lapse physics data within data cube  300  is sorted. Reference is now made to  FIG. 6 . A two-dimensional array  314  including a plurality of data bins  316  is constructed, with each data bin  316  defined by coordinates corresponding to the values of a particular forward-modeled time-lapse data pair (i.e., FMTL(IP) and FMTL(IS)). As described above, any particular forward-modeled time-lapse data pair can correspond to a plurality of derived physical parameters, and therefore several associated physical parameter sets, or vectors, can be sorted into any particular data bin  316  of the array  314 . As depicted in  FIG. 6 , an exemplary data bin  318  of the plurality of data bins  316  is depicted, which contains (i.e., includes) an associated physical parameter vector  320 . As depicted in  FIG. 6 , Pp&#39; refers to pseudo pore pressure, Sw&#39; refers to pseudo water saturation, and φ (phi) refers to porosity.  
         [0048]     The sorting process is conducted in an exhaustive fashion until all the physical parameter vectors (i.e.,  320 ) have been sorted into their respective data bins  316  within the array  314 .  
         [0049]     In step  212 , the contents of each data bin  316  within the array  314  are compared (i.e., searched) to a predetermined, selected parameter value, so as to determine which particular physical parameter vector represents the “optimal” such vector within each data bin  316 . For example, one approach for conducting this search is to compare each of the physical parameter vectors with an average or sample porosity value for the subterranean region under consideration. This comparison value can be predetermined, say, by use of appropriate field instrumentation deployed within a borehole or similar arrangement (not shown). Other search and comparison techniques can be used.  
         [0050]     Reference is now made to  FIG. 7 , which is a plot  330  depicting the contents of the data bins  316  of the array  314 , and is provided to assist in an understanding of the optimal value search operation of step  212  of the method  200 . The plot  330  is formatted with a horizontal axis scaled to represent time-lapse pressure values  332 , and a vertical axis scaled to represent time-lapse saturation values  334 . Each of the data bins  316  of the array  314  has its physical parameter vectors plotted as a single locus  336  of values on the plot  330  (that is, there is one plotted locus  336  for each data bin  316 ).  
         [0051]     Within each locus  336  is a selected optimum parameter pair (i.e., vector) value  338 , including corresponding pressure  332  and saturation  334  values, as determined by the comparative search described above. The optimum pressure  332  and saturation  334  parameter pairs  338  are extracted for further use as described hereafter.  
         [0052]     In step  214 , the optimum parameter pairs  338  are mapped to their corresponding locations within the subterranean area under consideration. Steps  210 - 214  are generally referred to as inversion. Reference is now made to  FIG. 8 , which depicts a parameter mapping schema  350  in accordance with the present invention. To begin, the time-lapse data pair TL(IP) and TL(IS) from step  206  for each location within the subterranean region under consideration is isolated, one data pair at a time. The data bin  316  within the array  314  that corresponds to the values of an isolated time-lapse data pair is then referenced, and its parameter vector contents considered. The optimal parameter vector  338  within that data bin  316 , as determined in step  212  above, is then extracted from the data bin  316 .  
         [0053]     The desired discrete physical parameters within the optimal parameter vector  338  are then associated with the subterranean location of the original time-lapse data pair TL(IP) and TL(IS). As depicted in  FIG. 8 , the time-lapse data pair  312  is associated with a location  352  within the subterranean region corresponding to the original AVO data. Therefore, the particular optimal parameter vector  338 , depicted as a vector  354 , is also associated with the same location  352 . As particularly depicted in  FIG. 8 , a pore pressure parameter  356  and a saturation parameter  358  of the vector  354  are associated with the location  352 . These mapped, optimal parameters (i.e., pore pressure  356  and saturation  358 ) are also referred to as pseudo values, and are designated in  FIG. 8  as TL Press&#39; and TL Sat&#39;, respectively.  
         [0054]     The mapping process of step  214  is generally repeated as described above, until optimal physical parameters are associated with each location within the subterranean region corresponding to the original AVO data.  
         [0055]     In step  216 , the pseudo values (i.e., TL Press&#39;  356  and TL Sat&#39;  358 ) mapped in step  214  above are calibrated so as to correspond more closely with actual field conditions. This calibration can be performed in a number of different ways; non-limiting examples include: calibrating the pseudo values against like kinds of data (i.e., pore pressures and saturations) measured at selected well bores; calibrating the pseudo values against a flow model of the subterranean region of consideration; or modeling the pseudo values against rock physics relationships (properties) in which only pore pressure changes or saturation changes. Combinations of these or other calibration methods can also be used. It is to be understood that such calibration is not necessarily linear in nature. In any case, the calibration method yields calibrated pore pressure and saturation data for the subterranean region under consideration.  
         [0056]     In step  218 , the calibrated data from step  216  above are plotted to provide a 2-dimensional representation of the subterranean region under consideration. Reference is now made to  FIGS. 9A-9D . This plot represents the time-lapse change in the physical parameters derived and calibrated as described above in regard to steps  202 - 216  of the method  200 .  FIGS. 9A and 9B  represent the calibrated saturation and pore pressure data from step  216  above, respectively.  FIGS. 9C and 9D  represent the actual (true) saturation and pore pressure data, respectively. Once again, the colors red and blue are used to indicate parameter value within the  FIGS. 9A-9D . Once the data plotting of step  218  is performed, performance of the method  200  is complete.  
         [0057]     It is to be understood that the method  200  of  FIG. 2  represents one embodiment of the present invention, and that other methods (not shown) corresponding to other embodiments of the present invention can also be used. For example, the methods and teachings of the present invention can be used with other kinds of AVO data that can be forward-modeled from a set of physical parameters. The impedance data exemplified in method  200  represents just one of several possible approaches. As described above, under another embodiment of the present invention, for example, the inversion of step  204  described above would be optional.  
         [0058]     Furthermore, other embodiments of the present invention can provide corresponding methods in which the certain steps or operations are performed substantially in parallel with (i.e., concurrent to) other certain steps. For example, another embodiment (not shown; see  FIG. 2 ) can provide for the performing of steps  202  through  206  above substantially in parallel with the performing of steps  208  through  212  above, wherein the respective results of these substantially parallel operations (e.g., the time-lapse data set TL(IP) and TL(IS), and the optimum parameter pairs  338 ) are then used to perform steps  214  through  218 . Other methods and other embodiments of the present invention are also possible.  
         [0059]      FIG. 10  is a block diagram depicting a data acquisition and processing system (hereafter, system)  400  in accordance with yet another embodiment of the present invention. The system  400  includes a field seismology arrangement  402 . As depicted in  FIG. 10 , the field seismology arrangement  402  includes a plurality of seismic detectors (i.e., receivers)  408 ,  410 , and  412 , respectively. The field seismology arrangement  402  is assumed to include at least one source of seismic energy (not shown), and any other elements as required and configured to acquire desired seismic (i.e., AVO or AVA, where AVA is amplitude-versus-angle type seismic data) data corresponding to a subterranean region  414  underlying the field seismology arrangement  402 . The field seismology arrangement  402  is further configured to provide one or more acquired seismic data bundles  416  for processing with the balance of the system  400  as described hereafter.  
         [0060]     The system  400  also includes a computer  418 . The computer  418  includes a processor  420  coupled in data communication with a computer-accessible memory  422 . The memory  422  stores a first seismic data set  424  and a second seismic data set  426 . The first seismic data set  424  is assumed to be received by the computer  418  and stored in the memory  422 , prior to the computer  418  receiving and storing the second seismic data set  426 . It will be appreciated that the data sets  424  and  426  can also be stored in a remote memory device which is accessible by the computer  418 .  
         [0061]     Both the first and second seismic data sets  424  and  426  are delivered to the computer  418  as corresponding seismic data bundles  416 , and can be delivered to the computer  418  by way of any satisfactory means. Non-limiting examples of such delivery means (not shown) can include data cable coupling, transferal by way of optical or magnetic storage media, radio telemetry linking, etc. Those of skill in the instrumentation and related arts can appreciate that any number of satisfactory seismic data  416  delivery means can be utilized within the scope of the present invention, and that further elaboration is not required for purposes herein. The memory  422  further stores a program code  428  that is executable by the processor  420 . The program code  428  is configured to cause to the processor  420  to substantially perform the method  200  of  FIG. 2  as described above. The memory  422  also stores a plurality of rock physics relationships  430 , which are selectively accessed and used by the processor  420  during execution of the program code  428 .  
         [0062]     The system  400  also includes a monitor  432  that is coupled in signal communication with the computer  418 . The monitor is configured to provide a user visible data plot  434  under the control of the processor  420  during execution of the program code  428 . The system  400  further includes a printer  436  coupled in signal communication with the computer  418 . The printer  418  is configured to provide a hardcopy data plot  438  under the control of the processor  420  during execution of the program code  428 .  
         [0063]     The computer  418  is further understood to include a plurality of other elements as desired and/or required for normal operation, which are not shown in  FIG. 10 . Such elements (not shown) can include, for example, a user keyboard, a user mouse, a power supply, etc. One of skill in the computing arts can appreciate that such elements can be respectively included with the computer  418  and configured as desired, and that further elaboration is not required for an understanding of the present invention.  
         [0064]     Typical normal operation of the system  400  is as follows: The field seismology arrangement  402  acquires the first seismic data set  424 , and at some predetermined period of time thereafter, the field seismology arrangement  402  acquires the second seismic data set  426 . The first and second seismic data sets  424  and  426  are delivered to the computer  418  as respective seismic data bundles  416 , which stores them accordingly within the memory  422 .  
         [0065]     Next, execution of the program code  428  by the processor  420  is initiated by a user (for example, by way of a user keyboard or mouse, not shown). The program code  428  then causes the processor  420  to selectively access the first and second seismic data sets  424  and  426 , as well as the rock physics relationships  430 , which are respectively stored in the memory  422 . The processor  420  then uses the data sets  424  and  426  and the rock physics relationships  430  to carry out (i.e., perform) the method  200  of  FIG. 2  substantially as described above, thus deriving a calibrated physical parameter data set corresponding to the first and second seismic data sets  424  and  426  provided by the field seismology arrangement  402 .  
         [0066]     The program code  428  then causes the processor  420  to plot the calibrated physical parameter data set using the monitor  432  and/or the printer  436 , resulting in the visible data plot  434  and/or the hardcopy data plot  438 , respectively. The plot  434  and/or  438  thus provides a visible representation of the selected time-lapse physical characteristics (i.e., porosity, pressure and/or saturation, etc.) of the subterranean region  414 .  
         [0067]     In this way, the system  400  of  FIG. 10  provides a substantially automated data acquisition and processing system that performs the method of the present invention and provides resulting 2-dimensional data plots  434  and/or  438 . The system  400  is particularly suitable for use in monitoring and analyzing time-lapse changes in various physical parameters of subterranean regions (i.e., region  414 ) that contain hydrocarbons such as crude oil, natural gas, etc, or other fluids such as water. It is to be understood that three-dimensional volumetric plots (not shown) corresponding to a case of three- dimensional inversion can also be provided under the present invention.  
         [0068]     Furthermore, it is to be understood that while the methods of the present invention described above consider first and second AVO data sets, any number of suitable data sets can also be considered within corresponding other embodiments (hot shown) of the present invention. Within such embodiments (not shown), the methods and teachings of the present invention would typically be applied to any two suitable data sets at a time.  
         [0069]     While the above methods and apparatus have been described in language more or less specific as to structural and methodical features, it is to be understood, however, that they are not limited to the specific features shown and described, since the means herein disclosed comprise preferred forms of putting the invention into effect. The methods and apparatus are, therefore, claimed in any of their forms or modifications within the proper scope of the appended claims appropriately interpreted in accordance with the doctrine of equivalents.