Multiple echo train inversion

Abstract

A method for inversion of multiple echo trains with different wait times uses a cutoff times for each of the echo trains for full polarization. Simultaneous inversion is carried out for T 2 bins where full polarization exists

1 . A method of characterizing an earth formation, the method comprising: 
 (a) obtaining a plurality of nuclear magnetic resonance (NMR) echo trains,    (b) defining a plurality of bins of a T 2  distribution of the earth formation; and    (c) determining a value associated with each of the plurality of echo trains by simultaneously inverting the plurality of echo trains.    
   
   
       2 . The method of  claim 1  wherein at least one of NMR echo trains is a fully polarized echo train.  
   
   
       3 . The method of  claim 1  wherein the plurality of echo trains are selected from the group consisting of (i) a fully polarized echo train, (ii) a CBW echo train, and, (iii) a BVI echo train.  
   
   
       4 . The method of  claim 27  wherein each of the associated cutoff times is determined from a wait time of an associated pulse sequence and a maximum longitudinal relaxation time of the earth formation.  
   
   
       5 . The method of  claim 1  wherein determining the value associated with each of the plurality of bins further comprises performing a least squares inversion.  
   
   
       6 . The method of  claim 5  wherein the inversion comprises a weighted inversion.  
   
   
       7 . The method of  claim 1  wherein determining the value associated with each of the plurality of bins further comprises a simultaneous fitting over each of the echo trains for a bin that is fully polarized for each of the plurality of echo trains.  
   
   
       8 . The method of  claim 1  wherein determining the value associated with each of the plurality of bins further comprises a simultaneous fitting of a subset of the echo trains for a bin that is fully polarized for the subset of echo trains.  
   
   
       9 . The method of  claim 2  wherein determining the value associated with each of the plurality of bins further comprises defining a vector that includes bins associated with the fully polarized echo train.  
   
   
       10 . The method of  claim 1  further comprising determining at least one characteristic of the earth formation selected from (i) clay bound water, (ii) bulk volume irreducible, and, (iii) porosity.  
   
   
       11 . An apparatus for characterizing an earth formation, the apparatus comprising: 
 (a) a nuclear magnetic resonance (NMR) tool conveyed in a borehole in the earth formation, the NMR tool pulsing the earth formation with a plurality of radio frequency (RF) magnetic pulse sequences and receiving a plurality of associated echo trains;    (b) a processor which determines from the plurality of echo trains a value associated with each of a plurality of bins of a T 2  distribution based at least in Dar be simultaneously inverting the echo trains.    
   
   
       12 . The apparatus of  claim 11  wherein the plurality of echo trains are selected from the group consisting of (i) a fully polarized echo train, (ii) a CBW echo train, and, (iii) a BVI echo train.  
   
   
       13 . The apparatus of  claim 29  wherein each of the associated cutoff times is determined from a wait time of the associated pulse sequence and a maximum longitudinal relaxation time of the earth formation.  
   
   
       14 . (canceled)  
   
   
       15 . The apparatus of  claim 11  wherein the inversion comprises a weighted inversion.  
   
   
       16 . The apparatus of  claim 11  wherein the processor determines the value associated with each of the plurality of bins by performing a simultaneous fitting over each of the echo trains for a bin that is fully polarized for each of the plurality of echo trains.  
   
   
       17 . The apparatus of  claim 11  wherein the processor determines the value associated with each of the plurality of bins by performing a simultaneous fitting of a subset of the echo trains for a bin that is folly polarized for the subset of echo trains.  
   
   
       18 . The apparatus of  claim 11  wherein the processor determines the value associated with each of the plurality of bins by defining a vector that includes bins associated with a fully polarized echo train.  
   
   
       19 . The apparatus of  claim 11  wherein a location of the processor is selected from the group consisting of (i) a surface location, (ii) a downhole location, and, (iii) a remote location.  
   
   
       20 . The apparatus of  claim 11  further comprising a conveyance device for the NMR tool, the conveyance device selected from the group consisting of: (i) a wireline, (ii) a drillstring, and, (iii) coiled tubing.  
   
   
       21 . The apparatus of  claim 11  wherein the processor further determines a characteristic of the earth formation selected from (i) clay bound water, (ii) bound volume irreducible, and, (iii) porosity.  
   
   
       22 . A machine readable medium for use with an apparatus for characterizing an earth formation, the apparatus comprising 
 (a) a nuclear magnetic resonance (NMR) tool conveyed in a borehole in the earth formation to acquire a plurality of echo trains, each of the echo trains resulting from pulsing of the earth formation with an associated pulse sequence having an associated wait time;    the medium comprising instructions which enable a processor to:    (b) simultaneously invert the plurality of echo trains and determine a value associated with each of a plurality of bins of a T 2  distribution.    
   
   
       23 . The machine readable medium of  claim 22  wherein instructions further comprise enabling the processor to process echo trains are selected from the group consisting of (i) a fully polarized echo train, (ii) a CBW echo train, and, (iii) a BVI echo train.  
   
   
       24 . (canceled)  
   
   
       25 . The machine readable medium of  claim 22  wherein the medium is selected from the group consisting of (i) ROMs, (ii) EPROMs, (iii) EAROMs, (iv) Flash Memories, and, (v) Optical disks.  
   
   
       26 . The machine readable medium of  claim 22  wherein the medium further comprises instructions for determining a characteristic of the formation selected from (i) clay bound water, (ii) bulk volume irreducible, and, (iii) porosity.  
   
   
       27 . The method of  claim 1  wherein inverting the plurality of echo trains further comprises: 
 (i) for each of the plurality of echo trains, determining an associated cutoff time for full polarization, and    (ii) determining the value associated with each of the plurality of bins based at least in part on the associated cutoff time.    
   
   
       28 . The method of  claim 1  wherein each of the echo trains results from pulsing of the earth formation with an associated pulse sequence having an associated wait time.  
   
   
       29 . The apparatus of  claim 11  wherein the processor inverts the plurality of echo trains by further: 
 (i) determining a cutoff time for full polarization of each of the plurality of echo trains, and    (ii) determining the value associated with each of the plurality of bins using the associated cut off time.