Abstract:
Utilizing the phase component of a moment tensor for a seismic data signal, isolated from the amplitude component, by automatically detecting polarity changes that occur over a focal mechanism of the seismic event, and correcting for such polarity reversals. Transforming seismic (including microseismic) signals as recorded by one or more seismic detectors to enhance detection of arrivals. The transforms enable the generation of an image, or map, representative of the likelihood that there was a source of seismic energy occurring at a given point in time at a particular point in time.

Description:
CROSS RELATED APPLICATIONS 
       [0001]    This application is related to and claims priority from the following U.S. Provisional patent applications: 
         [0002]    Application Ser. No. 61/663,403 filed on 22 Jun. 2012, (Atty. Docket Number IS12.2232-1), titled “Seismic data processing using a phase weighted N th  root stack”; 
         [0003]    Application Ser. No. 61/663,416 filed on 22 Jun. 2012, (Atty. Docket Number IS12.2232-2), titled “Detecting and correcting changes in signal polarity for seismic data processing”; and 
         [0004]    Application Ser. No. 61/663,449 filed on 22 Jun. 2012, (Atty. Docket Number IS12.2232-3), titled “Seismic data processing by nonlinear stacking methods”; the disclosures of which are incorporated by reference herein in their entirety for all purposes. 
     
    
     BACKGROUND 
       [0005]    Reservoir characterization may be accomplished in a variety of ways for modeling behavior of fluids within a reservoir under different sets of circumstances and for finding optimal production techniques to maximize production. Seismic and microseismic surveys may be used for many applications, including for characterizing: structure, lithology, fractures, and fluid distribution in a reservoir. One example of an application for seismic or microseismic surveying is in hydraulic fracturing operations, wherein microseismic monitoring can be used to track the propagation of a hydraulic fracture through a formation. Seismic events can be detected, located and used to detect propagation of fluids/fractures) in a formation. Software may provide modeling, survey design, microseismic event detection and location (which may be optionally automated), uncertainty analysis, data integration, and visualization for interpretation. 
         [0006]    Seismic events are acoustic events generated by a force, such as a force generated by airguns, vibroseis systems, dynamite, etc. Microseismic events are elastic events generated by rock movement. Microseismic events may be generated during hydraulic fracturing of a formation as well as during other oilfield operations such as fluid production; water, gas or steam flooding; or formation compaction. 
         [0007]    In seismic surveys, a seismic source may be used to induce seismic waves in the earth. By contrast, in a microseismic survey, the sources may be natural subterranean events or induced subterranean events, such as propagation of hydraulics induced fractures through an earth formation. In both cases, the seismic waves may propagate through the earth and may be transmitted, reflected, and diffracted by formations or discontinuities in the earth. The seismic waves may be detected by a plurality of sensors that may be positioned at the surface or within the earth, i.e., in shallow pilot wells or down boreholes in the earth. Each sensor may be used to monitor and record the seismic wavefield. The data received and recorded by a sensor is collectively referred to as a trace. The collection of traces from one or more sensors may be processed to gain information about the earth&#39;s subsurface or stored for later processing. 
         [0008]    Seismic and microseismic events, both naturally occurring and induced, can be characterized by a moment tensor that describes a unique radiation pattern having a polarity component and an amplitude component of the compressional and shear seismic energy radiated from the source of the seismic event. A large-aperture seismic array may be useful to observe changes in polarity and amplitude of the energy radiated. Inversion of seismic moment tensors can provide a way to characterize microseismic events to gain an understanding of stresses and strains in a subterranean field, including an understanding of the orientation and propagation of fractures in the field. 
         [0009]    Non-linear event location methods may involve selection and time picking of discrete microseismic arrivals for each of a plurality of seismic detectors and mapping to visually locate the source of the measured microseismic energy. However, to successfully and accurately locate the microseismic event, the discrete time picks for each seismic detector must correspond to the same arrival of either a “P” or “S” wave and measure an arrival originating from a unique microseismic event. 
         [0010]    Imaging approaches relating to detection and location of seismic events may involve summing the signals recorded by a seismic array. However, when there are changes in the polarity of the moment tensor, signals having opposing polarity cancel each other out during stacking computations, rather than summing constructively. As such, in a summing technique information may be lost due to polarity changes. 
         [0011]    Feedback on seismic events occurring in the formation can be used to plan various stages of wellsite operations. Feedback on seismic events determined in real-time enables operators of wellsite procedures to intervene, direct or redirect the operations during the process to optimize the procedure and/or avoid undesired results. 
         [0012]    Some feedback methods involve processing microseismic event locations by mapping microseismic arrival times and polarization information into three-dimensional space through the use of modeled travel times and/or ray paths. Travel time look-up tables may be generated by modeling seismic data/an earth formation for a given velocity model. One mapping method for seismic/microseismic interpretation is commonly known as the “Non-Linear Event Location” method. Non-linear event location has also been used to locate macroseismic events such as earthquakes. Additional information on the topic can be found in U.S. Pat. No. 7,391,675 to Drew, incorporated herein in its entirety for all purposes, and the references listed therein. 
       SUMMARY 
       [0013]    This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. 
         [0014]    In an embodiment, a method is disclosed for seismic data processing by nonlinear stacking methods. The method can include receiving a seismic data signal comprising a plurality of traces; deriving a non-linear stack as a function of the seismic data signal; and detecting a polarity reversal in at least one of the plurality of traces based on the non-linear stack. 
         [0015]    In another embodiment, a method is disclosed where method can include disposing a sensor network in a seismic survey geometry; obtaining seismic survey data with the sensor network; correcting for move-out for a given horizon in the seismic survey data; segmenting the seismic survey data into a plurality of local groups; calculating a non-linear stack from the seismic survey data for each one of the local groups; locating a polarity reversal in the seismic survey data within the non-linear stack for each local group based on the non-linear stack for the particular group; and reversing the phase for the located polarity reversal in the seismic survey data within the non-linear stack for each local group. 
         [0016]    In one embodiment, a system is disclosed for acquiring and processing the seismic data. The system can include a seismic acquisition network of seismic sensors configured to acquire a seismic survey comprising: a plurality of data traces and a data processing apparatus. The data processing apparatus receives the plurality of data traces acquired in a formation from the seismic acquisition apparatus; computes a non-linear stack as a function of the seismic data signal; detects a polarity reversal in at least one of the plurality of traces based on the non-linear stack; and outputs a phase reversal to correct the trace in which the polarity reversal is detected. 
         [0017]    In yet another embodiment, a system is disclosed for acquiring seismic data and processing the seismic data. The system can include a data processing apparatus and a seismic acquisition network of seismic sensors configured to acquire a seismic survey. The data processing apparatus having a processor and a data storage device can perform a data processing method disclosed above for polarity detection and correction. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    Embodiments of a method and system for seismic data processing for detecting and correcting changes in signal polarity are described with reference to the following figures. Like numbers are used throughout the figures to reference like features and components. 
           [0019]      FIG. 1  illustrates a wellsite system, in accordance with one or more implementations of various techniques described herein. 
           [0020]      FIG. 2  shows a first seismic data processing method work flow, in accordance with one or more implementations of various techniques described herein. 
           [0021]      FIG. 3  shows a plot of a gathered seismic signal of eight seismic data traces, i.e., a synthetic signal plus real noise, on 9 channels, plotted versus time (milliseconds). 
           [0022]      FIG. 4  shows a plot of the seismic signal of  FIG. 3  with specific quantities of interest before a first iteration of the processing method of the present disclosure. 
           [0023]      FIG. 5  shows a plot of the seismic signal of  FIG. 3  with specific quantities of interest after three iterations. 
           [0024]      FIG. 6  shows the data traces of  FIG. 3  windowed by the AGCed STA/LTA of the phase-weighted stack, where “AGCed STA/LTA” stands for Automatic Gain Controlled ratio of the short term average (STA) to the long term average (LTA). 
           [0025]      FIG. 7  shows plots of correlation coefficients between channels  1 - 8  and the AGCed STA/LTA of the phase-weighted stack of the seismic data of  FIG. 3 . 
           [0026]      FIG. 8  shows a plot of a final phase-weighted stack after three iterations of processing are complete. 
           [0027]      FIG. 9  shows a plot of the seismic data as a function of the AGCed STA/LTA of the final phase-weighted stack after three iterations are complete. 
           [0028]      FIG. 10  shows a plot of the correlation coefficients by channel after four iterations are complete. 
           [0029]      FIG. 11  shows a seismic data processing method work flow, in accordance with one or more implementations of various techniques described herein. 
           [0030]      FIGS. 12A and 12B  show plots of a gathered seismic signal of many seismic data traces, i.e., a synthetic signal plus real noise. For illustrating the present method,  FIG. 12A  shows the synthetic signal with added noise whereas  FIG. 12B  shows the synthetic signal isolated from the noise. 
           [0031]      FIG. 13  shows a magnified view of all the traces from the area highlighted in a rectangle on  FIG. 12 . For illustrating the method of  FIG. 11 ,  FIG. 13A  shows the highlighted portion of synthetic signal with added noise whereas  FIG. 13B  shows the highlighted portion of the synthetic signal isolated from the noise. 
           [0032]      FIG. 14  shows a further magnified view of all the traces from the area highlighted in a rectangle on  FIG. 13 . For illustrating the method of  FIG. 11 ,  FIG. 14A  shows the further magnified portion of the synthetic signal with added noise while  FIG. 14B  shows the further magnified portion of the synthetic signal isolated from the noise. 
           [0033]      FIG. 15A  shows a plot of ideal correlation coefficients for representative groups of traces for the signal of  FIG. 12  while  FIG. 15B  shows a plot of the actual correlation coefficients computed for the same representative groups. 
           [0034]      FIG. 16  illustrates a computer network into which implementations of various technologies described herein may be implemented. 
       
    
    
     DETAILED DESCRIPTION 
       [0035]    In the following description, numerous details are set forth to provide an understanding of the present disclosure. However, it will be understood by those skilled in the art that the present disclosure may be practiced without these details and that numerous variations or modifications from the described embodiments are possible. 
         [0036]    Specific details are given in the following description to provide a thorough understanding of the embodiments. However, it will be understood by one of ordinary skill in the art that the embodiments maybe practiced without these specific details. For example, circuits may be shown in block diagrams in order not to obscure the embodiments in unnecessary detail. In other instances, well-known circuits, processes, algorithms, structures, and techniques may be shown without unnecessary detail in order to avoid obscuring the embodiments. 
         [0037]    Also, it is noted that the embodiments may be described as a process which is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. Although a flowchart may describe the operations as a sequential process, many of the operations can be performed in parallel or concurrently. In addition, the order of the operations may be re-arranged. A process is terminated when its operations are completed, but could have additional steps not included in the figure. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, its termination corresponds to a return of the function to the calling function or the main function. 
         [0038]    Moreover, as disclosed herein, the term “storage medium” may represent one or more devices for storing data, including read only memory (ROM), random access memory (RAM), magnetic RAM, core memory, magnetic disk storage mediums, optical storage mediums, flash memory devices and/or other machine readable mediums for storing information. The term “computer-readable medium” includes, but is not limited to portable or fixed storage devices, optical storage devices, wireless channels and various other mediums capable of storing, containing or carrying instruction(s) and/or data. 
         [0039]    Furthermore, embodiments may be implemented by hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware or microcode, the program code or code segments to perform the necessary tasks may be stored in a machine readable medium such as storage medium. A processor(s) may perform the necessary tasks. A code segment may represent a procedure, a function, a subprogram, a program, a routine, a subroutine, a module, a software package, a class, or any combination of instructions, data structures, or program statements. A code segment may be coupled to another code segment or a hardware circuit by passing and/or receiving information, data, arguments, parameters, or memory contents. Information, arguments, parameters, data, etc. may be passed, forwarded, or transmitted via any suitable means including memory sharing, message passing, token passing, network transmission, etc. 
         [0040]    The disclosure relates to methods for data processing seismic survey data; including, but not limited to, microseismic data. Various methods utilize the amplitude component of acquired seismic survey data, including, but not limited to, stacking, migration, velocity analysis and attribute analysis. Various methods utilize the amplitude component of microseismic survey data; see, e.g., utilizing the energy onset SPE 95513, entitled “Automated Microseismic Event Detection and Location by Continuous Spatial Mapping,” Drew et al, 2005, and utilizing signal envelope, “The Source-Scanning Algorithm: Mapping the Distribution of Seismic Sources in Time and Space,” Kao, H., et al, 2004, Geophys. J. Int., 157, 589-594. A semblance migration, or other stacking method, stacks the entire signal, inclusive of both amplitude and phase. The present disclosure is directed to methods utilizing, by comparison, various non-linear stacking methods and systems that can be used for detecting and correcting signal polarity changes. This may be of use, for instance, in detecting polarity changes that occur over a focal mechanism of the seismic event, detecting polarity changes that occur within a seismic offset gather due to AVO (amplitude versus offset) variations, detecting polarity changes that occur in the recording system, or detecting polarity changes attributed to other reasons, and correcting for such polarity reversals. 
         [0041]      FIG. 1  illustrates a wellsite system  100  in accordance with one or more implementations of various techniques described herein. The operation may also be referred to herein as the hydraulic fracturing operation, though various additional production operations are contemplated herein as well. In the wellsite system  100 , the operation may be conducted in concert with an active seismic survey in order to improve the effectiveness of the operation. The wellsite system  100  may optionally include an operations mechanism  102  for applying an operation such as pumping a fluid (such as a fracturing fluid or proppant) into or applying pressure or seismic forces to a well bore  104  disposed in a hydrocarbon reservoir  108 . The wellsite system  100  may also include a surface seismic array  112 , a buried seismic array  116 , a borehole seismic array  118 , or any combination thereof. A seismic source  114  may be included in the system  100 . 
         [0042]    The hydrocarbon reservoir  108  may be within a subsurface formation  110 , such as one of sandstone, carbonate, or chalk. Fractures  106  caused by, for example, the operation may be present in the formation  110 . The fractures  106  may improve the flow of hydrocarbons to the wellbore  104 . 
         [0043]    Receivers (i.e., geophones) may be used to collect seismic/microseismic, monitoring data; and can be deployed in a number of ways: inserted near the depth of investigation (i.e., at the depth of a fracture) in a borehole (either the well being monitored or a nearby well); placed on the surface; buried relatively shallowly compared to formation depths (for example, at a range of about 1 to 300 feet); and any combination thereof. 
         [0044]    The surface seismic array  112 , the buried seismic array  116 , and the borehole seismic array  118  may include standard seismic receiver arrays used in seismic surveying and may include geophones, receivers, or other seismic sensing equipment configured to acquire seismic or microseismic data. The surface seismic array  112  may be positioned on the surface as a network of sensors. The buried seismic array  116  may be buried at any depth. In an embodiment, the buried seismic array  116  may be buried at a depth that is shallow relative to the depth of the formation  110  such as, but not limited to, from a range of about 1 to 300 feet. The borehole seismic array  118  may be placed permanently in the borehole, for example, or conveyed to any depth via a wireline cable, coiled tubing or the like. 
         [0045]    The seismic source  114  may be a standard seismic source used in seismic surveying, such as a vibroseis or dynamite. The seismic source  114  may be located on the surface or in a borehole. The seismic source  114 , the surface seismic array  112 , the buried seismic array  116  and/or the borehole seismic array  118  may be used to perform a seismic survey during the operation. 
         [0046]    The wellsite system  100  may also include a data processing apparatus  120  in a truck (or other convenient location, for instance, such as a vehicle, shelter or building) with computer equipment, discussed further below, to receive data acquired during a seismic survey by the surface seismic array  112 , the buried seismic array  116 , the borehole seismic array  118 , or any combination thereof according to a survey geometry. A data connection may be present between the surface seismic array  112 , the buried seismic array  116 , the borehole seismic array  118  and the data processing apparatus  120 ; and the data connection may be a wired connection or a wireless connection. 
         [0047]    Alternatively, for data processing at a data processing location remote to the wellsite, a satellite  122  may be included, providing a wireless data connection between the surface seismic array  112 , the buried seismic array  116 , and the borehole seismic array  118  (or any combination thereof) to computer equipment, discussed further below, located at the data processing location. The manner of telemetry between the various system components is intended to be inclusive of all wired and wireless communications known and developed in the future; it is not the focus of the present disclosure. 
         [0048]    In an embodiment, the data from the surface seismic array  112 , the buried seismic array  116 , and/or the borehole seismic array  118  may be pre-processed (for example, by the data processing apparatus  120 ) before the methods described in this patent are applied to the data. The pre-processing might include any one or more of the following steps in any order: filtering, transforming, interpolating, combinations of 3-component signals (for instance XYZ sensors), and modifying the time-index; the steps can be applied to either a single or several traces together, either deterministic or data-dependent. The specific individual processes may include, but are not limited to, frequency filtering, time resampling, deconvolution, signal rotation or re-orientation, noise-attenuation, FK filtering, tau-p filtering, time-variant move-out corrections, static-time corrections, modelled-time corrections, interpolation of traces, interpolation of sample values, and the like. Thus, the data as processed according to the methods described herein may be pre-processed upon receipt from the surface seismic array  112 , the buried seismic array  116 , and the borehole seismic array  118 . 
         [0049]    In one implementation, a seismic survey may be used to improve the effectiveness of a fracturing operation. For example, by performing a seismic survey during the fracturing operation, it may be possible to identify where in the formation  110  the fractures  106  are induced. In other implementations, seismic surveys may be used to improve the effectiveness of a fluid production operation; the effectiveness of a water, gas or steam flooding operation; and the effectiveness of a formation compaction operation. 
         [0050]      FIG. 2  shows a seismic data processing method work flow  250 , in accordance with one or more implementations of various techniques described herein. The method  250  begins with receiving a seismic data signal comprising a plurality of data traces at  200 . The method proceeds with computing a non-linear stack based on the seismic data signal at  202 . Though examples presented below are directed to using a phase-weighted stack, for practical purposes, any non-linear or linear stacking method could be applied in accordance with the present processing method, including: phase normalized stack, an N th  root stack, double-phase-weighted stack, double-phase-weighted N th  root stack, real phasor stack, squared real phasor stack, or some combination of these and other non-linear stacks; some of which are described in an application filed concurrently herewith as “Methods and Systems for Seismic Data Processing by Nonlinear Stacking Methods” (Atty. Docket Number IS12.2232.1). Some of the non-linear stacks are described briefly below: N th  Root Stack 
         [0051]    For example, in a non-linear stacking method referred to as the N th  root stack, a product may be calculated by an equation according to the form: 
         [0000]        y   NR ( t,n )= sgn[u ( t,n )]| u ( t,n )| n   eq. 1
 
         [0000]    where sgn({circumflex over (x)} n (t)) is the sign or signum function (preserving the sign of x n (t) when the N th  power is applied), and the summation or Nth root stack (see, e.g., Kanasewich et al., 1973) may be calculated by an equation according to the following form: 
         [0000]    
       
         
           
             
               
                 
                   
                     u 
                      
                     
                       ( 
                       
                         t 
                         , 
                         n 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       L 
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         L 
                       
                        
                       
                         
                           sgn 
                            
                           
                             [ 
                             
                               
                                 x 
                                 i 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             ] 
                           
                         
                          
                         
                           
                              
                             
                               
                                 x 
                                 i 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                           
                           
                             1 
                              
                             
                               / 
                             
                              
                             n 
                           
                         
                       
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   2 
                 
               
             
           
         
       
     
         [0000]    wherein subscript i denotes the different receiver signals in the data, sgn[x i (t)] represents the sign or signum function (preserving the sign of x i (t) when the N th  power is applied), L is the number of traces used in the stack, and the power n is a number larger than or equal to 1 that amplifies relatively small amplitude signals. For example, calculating an N th  root stack with n=1 results in a linear stack, and n&gt;1 leads to a reduction in the signal variance. 
       Phase-Weighted Stack 
       [0052]    In another embodiment, a phase-weighted stack, see, e.g., Schimmel and Paulssen, 1997, can be calculated according to the form: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         y 
                         PW 
                       
                        
                       
                         ( 
                         
                           t 
                           , 
                           m 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           [ 
                           
                             
                               y 
                               P 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ] 
                         
                         m 
                       
                        
                       
                         1 
                         L 
                       
                        
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           L 
                         
                          
                         
                           
                             x 
                             i 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   3 
                 
               
             
             
               
                 
                   
                     
                       y 
                       P 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       L 
                     
                      
                     
                        
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           L 
                         
                          
                         
                           exp 
                            
                           
                             { 
                             
                               j 
                                
                               
                                   
                               
                                
                               
                                 
                                   ∅ 
                                   
                                     x 
                                     , 
                                     i 
                                   
                                 
                                  
                                 
                                   ( 
                                   t 
                                   ) 
                                 
                               
                             
                             } 
                           
                         
                       
                        
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   4 
                 
               
             
           
         
       
     
         [0000]    is the phase stack derived from the phase of the analytical signal 
         [0000]        x   A ( t )= x ( t )+ j             {x ( t )}=| x   A ( t )|exp{ jφ   x ( t )},  eq, 5
 
         [0000]    wherein          {x(t)} is defined as a Hilbert transform of the signal. A Hilbert transform is an analytical transform discussed in further detail in U.S. Pat. No. 6,748,330, which is hereby incorporated in its entirety by reference for all purposes. The stack may be referred to as “phase weighted” as each sample of the linear stack will be weighted by the coherency of its instantaneous phases. 
       Phase Weighted Nth Root Stack 
       [0053]    As described in the related application filed concurrently herewith cited above (Atty. Docket Number IS12.2232.1), the phase weighted Nth root stack may be derived according to an equation of the form: 
         [0000]        y   PWNR ( t,m,n )=[ y   P ( t )] m   y   NR ( t,n )  eq. 6
 
         [0000]    where y P (t) is the phase stack derived in  202  and y NR (t,n) is the n th  root stack derived in  204 ; the resulting phase weighted Nth root stack y PWNR (t) is a product of the two. 
       Double Phase-Weighted Stack 
       [0054]    Also described in the related application filed concurrently herewith cited above (Atty. Docket Number IS12.2232.1), and analogous to the phase weighted stack described above, a double-phase-weighted stack may be governed by a function of the form: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         y 
                         DPW 
                       
                        
                       
                         ( 
                         
                           t 
                           , 
                           m 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           [ 
                           
                             
                               y 
                               DP 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           ] 
                         
                         m 
                       
                        
                       
                         1 
                         L 
                       
                        
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           L 
                         
                          
                         
                           
                             x 
                             i 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   where 
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   7 
                 
               
             
             
               
                 
                   
                     
                       
                         y 
                         DP 
                       
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         L 
                       
                        
                       
                          
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               1 
                             
                             L 
                           
                            
                           
                             exp 
                              
                             
                               { 
                               
                                 j2 
                                  
                                 
                                     
                                 
                                  
                                 
                                   
                                     ∅ 
                                     
                                       x 
                                       , 
                                       i 
                                     
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                               } 
                             
                           
                         
                          
                       
                     
                   
                   , 
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
         [0000]    is the double-phase stack derived from the phase of the analytical signal of eq. 5. 
       Double Phase Weighted Nth Root Stack 
       [0055]    Also described in the related application filed concurrently herewith cited above (Atty. Docket Number IS12.2232.1), and analogous to the phase weighted stack described above, a double-phase-weighted Nth root stack may be governed by an equation of the form: 
         [0000]        y   DPWNR ( t,m,n )=[ y   DP ( t )] m   y   NR ( t,n )  eq. 9
 
         [0000]    where y DP (t) is the double phase stack and y NR (t,n) is the n th  root stack; the result represents a product of the two. 
       Real Phasor and Squared Real Phasor Stacks 
       [0056]    The normalized data may be referred to as real-phasor (RP) x RP (t). The real-phasor (RP) and the envelope function |x A (t)|, in this context, can be derived from an analytic signal x A (t), defined as in eq. 5, or: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       x 
                       RP 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       x 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     
                        
                       
                         
                           x 
                           A 
                         
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                        
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   10 
                 
               
             
             
               
                 
                   
                     
                       x 
                       RP 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         x 
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                       
                          
                         
                           
                             x 
                             A 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                          
                       
                     
                     = 
                     
                       cos 
                        
                       
                         ( 
                         
                           
                             φ 
                             x 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   11 
                 
               
             
           
         
       
     
         [0000]    where x A (t) and φ x (t) are defined in eq. 5. Eq. 10 is a definition of real-phasor, while Eq. 11 shows an identity or an alternative definition, which is defined by a phase function only. Depending on the data availability, the real-phasor may be computed by eq. 10 or 11. 
         [0057]    From real phasor, we may define several more non-linear stacks; mathematically, the stacked functions may be described by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       y 
                       RP 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       L 
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         L 
                       
                        
                       
                         
                           x 
                           
                             RP 
                             , 
                             i 
                           
                         
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   12 
                 
               
             
             
               
                 
                   
                     
                       y 
                       SRP 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       L 
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         L 
                       
                        
                       
                         [ 
                         
                           
                             
                               x 
                               
                                 RP 
                                 , 
                                 i 
                               
                               2 
                             
                              
                             
                               ( 
                               t 
                               ) 
                             
                           
                           - 
                           
                             1 
                             2 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   13 
                 
               
             
           
         
       
     
         [0000]    where subscript i denotes the different receiver signals in the data and x RP (t) represents the normalized signal in the manner described above. These non-linear stacks in eq. 12 and 13 are referred to as real-phasor and squared real-phasor stacks, respectively. 
         [0058]    In yet another non-linear stack, referred to as a double phase weighted squared real-phasor stack, the transformed signal can be represented by a function of the form: 
         [0000]        y   DPWSRP ( t,m )=[ y   DP ( t )] m   y   SRR ( t )  eq. 14
 
         [0000]    where y DPWSRP (t,m), y DP (t), and y SRP (t) are defined above. 
       Linear Stack 
       [0059]    The linear stack has the form of: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       y 
                       Lin 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       L 
                     
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         L 
                       
                        
                       
                         
                           x 
                           i 
                         
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   15 
                 
               
             
           
         
       
     
         [0000]    wherein Lin is the number of folds in the linear stack. It is included here for comparison. 
         [0060]    In an embodiment, the method proceeds with computing a function that emphasises, or “detects,” a particular time interval (or time window) containing a signal, such as the “short term average long term average ratio” (referred to herein as STA/LTA) of the non-linear stack (which was computed in  202 ) at  204 . Various known methods for detection such as computation of the STA/LTA may be employed, and the details of which are not related to present novelty. In an embodiment, mathematically, y i  can represent the non-linear stack from  202 . The number of points in a short-term window can be represented as ns, and the number of points in a long-term window can be represented as nl, with nl&gt;ns. Then, the average energies in the short and long term windows preceding the time index i can be represented in the form: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       STA 
                        
                       
                         ( 
                         
                           y 
                           , 
                           t 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         ns 
                       
                        
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             
                               i 
                               - 
                               ns 
                             
                           
                           i 
                         
                          
                         
                           y 
                           j 
                           2 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   and 
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   16 
                 
               
             
             
               
                 
                   
                     
                       LTA 
                        
                       
                         ( 
                         
                           y 
                           , 
                           t 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         1 
                         nl 
                       
                        
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             
                               i 
                               - 
                               nl 
                             
                           
                           i 
                         
                          
                         
                           y 
                           j 
                           2 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   17 
                 
               
             
           
         
       
     
         [0000]    from which the ratio STA/LTA can be directly calculated. The method of detection of the signal itself is not the focus of the present disclosure, however, as there are many detection methods, there are many forms of STA/LTA in different references and in common use (e.g., in the definition of the sum limits). In the present disclosure we use the detection function to illustrate certain time windows that may be most likely to contain signal. The STA/LTA function or other detection function can, for instance, be used in a cross multiplication for each time sample with the stacked function, represented by an expression such as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       w 
                        
                       
                         ( 
                         t 
                         ) 
                       
                     
                     = 
                     
                       
                         
                           STA 
                            
                           
                             ( 
                             
                               y 
                               , 
                               t 
                             
                             ) 
                           
                         
                         
                           LTA 
                            
                           
                             ( 
                             
                               y 
                               , 
                               t 
                             
                             ) 
                           
                         
                       
                        
                       
                         y 
                          
                         
                           ( 
                           t 
                           ) 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                    
                   18 
                 
               
             
           
         
       
     
         [0000]    where the STA/LTA ratio is from stacked function y(t) and can be replaced by any detection function and any non-linear stacking function, as described above. The detection function increases in value for time windows containing coherent signal in the stacked function; and provides a further enhancement of the stacked signals by multiplication of the functions when compared to the background noise. The window containing the signal could also be defined by calculation, prediction, or inspection of the data. 
         [0061]    In an embodiment, the method proceeds with defining a window about each input trace (from  200 ) using the STA/LTA at  206 , or other detection method. In an embodiment, the STA/LTA may also be processed by automatic gain control and applied to define a window framing about each trace. 
         [0062]    The method proceeds with cross-correlating the windowed input traces (from  206 ) with the non-linear stack (from  204 ) at  208 . 
         [0063]    The method proceeds with detecting, or locating, the trace amongst the cross-correlated traces that contains the largest correlation error and reversing the polarity of the trace having the largest correlation error at  210 , such that upon stacking (or summing), portions with reversed polarity do not cancel, but constructively add, resulting in more accurate detection of the seismic signal amongst the noise. 
         [0064]    The method iterates at 212 to repeat blocks  202  through  210  for each of the plurality of traces until polarity reversals in the plurality of traces have been detected, or until the channels for the plurality of traces correlate to within a target error threshold. 
         [0065]    Not all the steps in the above example  250  are necessary. For example, the linear or non-linear stacking ( 202 ) is used when the signal-to-noise ratio is low in many seismic surveys. But if the acquired data is of high quality and the SNR is above a desired threshold, then the stacking step ( 202 ) may be skipped and a polarity detection function (e.g.  204 ) may applied to the data. 
         [0066]      FIG. 3  illustrates an example, showing a plot of a seismic signal of eight seismic data traces, i.e., a synthetic signal plus real noise, on 9 channels, plotted versus time (milliseconds). The SNR is −8 dB. Four of the eight channels have had their signal components reversed in polarity for the purpose of illustrating the method of  FIG. 2 . As shown in  FIG. 3 , channels  2 ,  4 ,  5 , and  6  specifically show a polarity reversal. 
         [0067]      FIG. 4  shows a plot of the seismic signal of  FIG. 3  with specific quantities of interest before a first iteration of the processing method of  FIG. 2  is applied. Channel − 1  shows the total data signal (i.e., the synthetic signal combined with a real noise signal), plotted as a function of time. Channel  0  shows the synthetic signal, isolated for clarity, as a function of time. Channel  1  shows one form of non-linear stack, specifically, the phase stack, as a function of time. Channel  2  shows a linear stack of the eight channels. Channel  3  shows the phase-weighted stack (such as may be computed in block  202  of  FIG. 2 ) and Channel  4  shows the STA/LTA of the phase-weighted stack (such as the one computed in block  204  of  FIG. 2 ). 
         [0068]      FIG. 5  shows a plot of the seismic signal of  FIG. 3  with the quantities of interest shown in  FIG. 4  after three iterations. Channel − 1  shows the total data signal (i.e., the synthetic signal combined with a real noise signal), plotted as a function of time. Channel  0  shows the synthetic signal, isolated for clarity, as a function of time. Channel  1  shows one form of non-linear stack, that is, the phase stack, as a function of time after 3 iterations of the process of  FIG. 2 . Channel  2  shows a linear stack of the signal of Channel − 1  as a function of time after 3 iterations of the process of  FIG. 2 . Channel  3  shows the phase-weighted stack (such as the one computed in block  202  of  FIG. 2 ) after 3 iterations of the process of  FIG. 2 , and Channel  4  shows the STA/LTA of the phase-weighted stack (such as the one computed in block  204  of  FIG. 2 ) after 3 iterations of the process of  FIG. 2 . The result of 3 iterations through the method is that the SNR improves and the stack results are more similar to the synthetic data signal. Specifically, the polarity reversals in channels  2 ,  4 , and  5  have been detected and switched relative to the polarities shown in  FIG. 3 . 
         [0069]      FIG. 6  shows various data traces windowed by the automatic gain controlled (AGCed) STA/LTA (channel  4  from  FIG. 5 ) after 3 iterations of processing according to a method of the present disclosure. Channels  1 - 8  show the windowed input traces, and channel  9  shows the windowed phase-weighted stack (that is, a product of channel  3  and channel  4  from  FIG. 5 ). As shown, of the four channels with reversed polarities originally, only channel  6  remains reversed, while the other 3 channels with polarity reversals have been reversed upon detection of the polarity reversal within each channel. 
         [0070]      FIG. 7  shows plots of correlation coefficients between channels  1 - 8  and the AGCed STA/LTA of the phase-weighted stack of the seismic data of  FIG. 3 , confirming that only channel  6  still has reversed polarity after 3 iterations of the process of  FIG. 2 , because each of the other channels (which have been corrected) correlates positively with the synthetic signal. 
         [0071]      FIG. 8  shows a plot of a final phase-weighted stack after four iterations of processing are complete; all four polarity reversals as corrected by the process are shown. Channel − 1  shows the total data signal (i.e., the synthetic signal combined with a real noise signal) plotted over time. Channel  0  shows the synthetic signal isolated for clarity over time. Channel  1  shows one form of non-linear stack, that is, the phase stack, as a function of time, after all iterations of the process of  FIG. 2 , such that all four polarity reversals have been detected. Channel  2  shows a linear stack of all eight channels as a function of time after 4 iterations of the process of  FIG. 2 . Channel  3  shows the phase-weighted stack (such as that computed in block  202  of  FIG. 2 ) after 4 iterations of the process of  FIG. 2 , and Channel  4  shows the STA/LTA of the phase-weighted stack (such as that computed in block  204  of  FIG. 2 ) after 4 iterations of the process of  FIG. 2 . The result of all four iterations through the method is that the SNR improves further, still, and the stack results are more closely correlated to the synthetic data signal. 
         [0072]      FIG. 9  shows a plot of the seismic data as a function of the automatic gain controlled STA/LTA of the final phase-weighted stack after four iterations are complete. Specifically, the polarity reversal present for channel  6  in  FIG. 6  is now corrected (having been detected). 
         [0073]      FIG. 10  shows a plot of the correlation coefficients by channel after four iterations are complete. All have positive values and confirms that the non-linear stack positively correlates to the original synthetic signal for all channels. 
         [0074]    The method shown in  FIG. 2  can automatically detect polarity changes in traces and reverse them. Once the polarity reversals are detected and corrected, weak microseimic events may be more effectively detected. As mentioned above, even though the example was generated using phase-weighted stack, any other non-linear stacks may also be used. 
         [0075]    Once the polarity changes in traces are detected and corrected, the traces may be further processed using any desired processes. For example, the data may be processed for determining a parameter for a subterranean property. The data may be used for detecting or determining a microseismic event in a production operation. The microseismicity gives rise to an event, such as a fracturing operation; or a water, gas or steam flooding operation; may also be evaluated. The data with much improved SNR may also be used for creating an image of a subterranean structure. 
         [0076]      FIG. 11  shows another seismic data processing method work flow in accordance with one or more implementations of various techniques described herein. This method may be used to detect polarity reversals along a seismic horizon under poor SNR conditions. This method may be used as an automatic fault plane solution (e.g. beach ball diagram) on surface arrays; or automatic polarity reversal correction to enable semblance-based processing. 
         [0077]    The method begins with disposing a sensor network in a seismic survey geometry and dividing data from a surface sensor network into local groups at  1100 , such that data may be stacked within the local groups to increase the signal to noise ratio. The particular group size may in some embodiments be a parameter set by the user, and may depend on the particular problem. In an embodiment, the particular group size may be selected in such a way, based on data signal polarities, that the data in each group has signal that can be stacked constructively, added, or combined in some manner. The method includes obtaining seismic survey data with the sensor network at  1101 . 
         [0078]    The method further includes segmenting the seismic survey data a second time at  1102  into segments. Segmenting, here, refers to associating specific portions of the seismic data (or seismic gather) to one of the two polarities that exist. In other words, segmenting can refer to labeling each trace (or part of each trace around a seismic horizon) with a positive polarity or a negative polarity. There can be 2 or more segments depending on the nature of the data. In an embodiment, the segment size may be as small as one. 
         [0079]    The method further includes selecting a horizon among the obtained seismic survey data at  1103 . 
         [0080]    Moveout can be defined as relating to the difference in the arrival times or travel times of a wave measured by receivers at two different offset locations. One form of moveout is caused by the separation between the source and the receiver. The method proceeds with correcting for move-out for the selected horizon in the seismic survey data at  1104 . Various techniques of correcting for move-out are known, and any of such techniques could be employed at  1104 . 
         [0081]    The method proceeds with calculating a non-linear stack of the data associated with the horizon, which has been corrected for move-out at  1106  for each local group. The method proceeds with locating a polarity reversal in the seismic survey data based on the non-linear stack (calculated in  1106  for each local group) at  1108 , which may be performed using the LTA/STA (as described above) or any other detection method. The method further includes correcting the polarity of at least one segment of the seismic survey data according to the location of the polarity reversal at  1110 . 
         [0082]      FIG. 12A  shows a plot of a gathered seismic signal of many seismic data traces, i.e., a synthetic signal plus real noise. We arbitrarily show only one trace in  5  from a large range of traces and display them at a convenient trace spacing to show the variation in traces, amplitude, and plotting offset (in meters) versus time (milliseconds). The signal to noise ratio is −18 dB.  FIG. 12B  shows the synthetic signal isolated from noise, with the polarity reversed along certain segments, plotting offset (in meters) versus time (in milliseconds). A first polarity reversal occurs at just before 900 m and a second polarity reversal occurs at roughly 1200 m, and a third at 1650 m, shown in  FIG. 12B . A rectangle highlights the section containing several polarity changes, aligning with where the local groups of the sensor network are and with the manner in which the data are segmented into local groups and stacked within the local groups, as described above with reference to  FIG. 11 .  FIGS. 13A  and B show magnified views of all the traces from the areas highlighted in a rectangle on  FIGS. 12A and 12B  in order to highlight a single polarity reversal. Whereas,  FIG. 13A  shows the synthetic signal with noise added, and  FIG. 13B  shows the synthetic signal isolated from noise. In turn,  FIGS. 14A and 14B  show a further magnified view of the area highlighted in the rectangle on  FIG. 13 , showing just the one segment of data containing the polarity reversal at about 880 m.  FIG. 14B  shows the synthetic signal with noise added, and  FIG. 14A  shows the synthetic signal without the noise added. 
         [0083]      FIG. 15A  shows a plot of ideal correlation coefficients for representative groups of traces for the signal of  FIG. 12A , whereas  FIG. 15B  shows a plot of the actual correlation coefficients computed for the same representative groups. The data is segmented into local groups (as described above), phase-weighted N th  root stack applied and the cross-correlation computed according to the method of  FIG. 11 . By not only detecting polarity changes, but correctly identifying wherein the data the polarity changes occur, the polarity can be handled so that the non-linear stack is cumulatively added, and polarity reversals do not mathematically cancel out portions of the data. 
         [0084]      FIG. 16  illustrates a computing system  1600 , into which implementations of various technologies described herein may be implemented. The computing system  1600  may include one or more system computers (processors)  1630 , which may be implemented as any conventional personal computer or server. However, those skilled in the art will appreciate that implementations of various technologies described herein may be practiced in other computer system configurations, including hypertext transfer protocol (HTTP) servers, hand-held devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, and the like. 
         [0085]    The system computer  1630  may be in communication with disk storage devices  1629 ,  1631 , and  1633 , which may be external hard disk storage devices. It is contemplated that disk storage devices  1629 ,  1631 , and  1633  are conventional hard disk drives, and as such, will be implemented by way of a local area network or by remote access. Of course, while disk storage devices  1629 ,  1631 , and  1633  are illustrated as separate devices, a single disk storage device may be used to store any and all the program instructions, measurement data, and results as desired. 
         [0086]    In one implementation, seismic data from the receivers may be stored in disk storage device  1631 . The system computer  1630  may retrieve the appropriate data from the disk storage device  1631  to process seismic data according to program instructions that correspond to implementations of various technologies described herein. The program instructions may be written in a computer programming language, such as C++, Java and the like. The program instructions may be stored in a computer-readable medium, such as program disk storage device  1633 . Such computer-readable media may include computer storage media and communication media. Computer storage media may include volatile and non-volatile media, and removable and non-removable media implemented in any method or technology for storage of information, such as computer-readable instructions, data structures, program modules or other data. Computer storage media may further include RAM, ROM, erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other solid state memory technology, CD-ROM, digital versatile disks (DVD), or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the system computer  1630 . 
         [0087]    Communication media may embody computer-readable instructions, data structures, program modules or other data in a modulated data signal, such as a carrier wave or other transport mechanism. It may include any information delivery media. The term “modulated data signal” may mean a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media may include wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Combinations of any of the above may also be included within the scope of computer readable media. 
         [0088]    In one implementation, the system computer  1630  may present output primarily onto graphics display  1627 , or alternatively via printer  1628 . The system computer  1630  may store the results of the methods described above on disk storage  1629 , for later use and further analysis. The keyboard  1626  and the pointing device (e.g., a mouse, trackball, or the like)  1625  may be provided with the system computer  1630  to enable interactive operation. 
         [0089]    The system computer  1630  may be located at a data center remote from the survey region. The system computer  1630  may be in communication with the receivers (either directly or via a recording unit, not shown), to receive signals indicative of the reflected seismic energy. These signals, after conventional formatting and other initial processing, may be stored by the system computer  1630  as digital data in the disk storage  1631  for subsequent retrieval and processing in the manner described above. While  FIG. 16  illustrates the disk storage  1631  as directly connected to the system computer  1630 , it is also contemplated that the disk storage device  1631  may be accessible through a local area network or by remote access. Furthermore, while disk storage devices  1629 ,  1631  are illustrated as separate devices for storing input seismic data and analysis results, the disk storage devices  1629 ,  1631  may be implemented within a single disk drive (either together with or separately from program disk storage device  1633 ), or in any other conventional manner as will be fully understood by one of skill in the art having reference to this specification. 
         [0090]    Note that while the present disclosure describes the concepts as applied to a time domain representation of the signal, it is intended that the same principals apply if treating the signal in other forms including complex wavelets. Complex wavelets are a more general way to describe the signal, and encompasses both the complex time domain representation (wavelet is a “delta function” in time domain), frequency domain representation (wavelet is a “sine wave” in time domain) and other classes of “wavelets” that to a greater or lesser degree are compact in the time domain or frequency domain. In all cases the concept of the complex “wavelet” representation of the signal includes the concept of amplitude and phase. 
         [0091]    Additionally, the methods and systems of the present disclosure may be fully automated and able to operate continuously in time for monitoring, detecting, and locating seismic and microseismic events from on or multiple seismic detectors. Methods of the present invention utilize the contributions from one or multiple seismic detectors. 
         [0092]    While the disclosure has been disclosed with respect to a limited number of embodiments, those skilled in the art, having the benefit of this disclosure, will appreciate numerous modifications and variations therefrom. While the disclosure has been described in the context of applications in downhole tools, the apparatus of the disclosure can be used in many applications. 
         [0093]    Although a few example embodiments have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the example embodiments without materially departing from this disclosure. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims. In the claims, means-plus-function clauses are intended to cover the structures described herein as performing the recited function and not simply structural equivalents, but also equivalent structures. Thus, although a nail and a screw may not be structural equivalents in that a nail employs a cylindrical surface to secure wooden parts together, whereas a screw employs a helical surface, in the environment of fastening wooden parts, a nail and a screw may be equivalent structures. It is the express intention of the applicant not to invoke 35 U.S.C. §112, paragraph 6 for any limitations of any of the claims herein, except for those in which the claim expressly uses the words ‘means for’ together with an associated function. 
         [0094]    The preferred aspects and embodiments were chosen and described in order to best explain the principles of the invention and its practical application. The preceding description is intended to enable others skilled in the art to best utilize the invention in various aspects and embodiments and with various modifications as are suited to the particular use contemplated. The description may be implemented in any seismic or microseismic measurement system, and particularly for microseismic for hydraulic fracture monitoring. In addition, the methods may be programmed and saved as a set of instructions, that, when executed, perform the methods described herein. It is intended that the scope of the invention be defined by the following claims.