Methods and apparatus to calculate a distance from a borehole to a boundary of an anisotropic subterranean rock layer

Abstract

Methods and apparatus to calculate a distance from a borehole to a boundary of an anisotropic subterranean rock layer are disclosed. A disclosed example method includes transmitting a first signal from a first transmitter at a first location in a borehole traversing a subterranean formation, receiving the first signal at a first receiver after a first time period at a second location in the borehole, receiving the first signal at a second receiver after a second time period at a third location in the borehole, and calculating a first distance from the first transmitter to a first portion of a boundary of a subterranean rock layer adjacent to the borehole by compensating for an anisotropy of the subterranean rock layer based on the first time period and the second time period.

1 . A method to calculate a distance from a borehole to a boundary of an anisotropic subterranean rock layer, the method comprising:
 transmitting a first signal from a first transmitter at a first location in a borehole traversing a subterranean formation;   receiving the first signal at a first receiver after a first time period at a second location in the borehole;   receiving the first signal at a second receiver after a second time period at a third location in the borehole; and   calculating a first distance from the first transmitter to a first portion of a boundary of a subterranean rock layer adjacent to the borehole by compensating for an anisotropy of the subterranean rock layer based on the first time period and the second time period.   
     
     
         2 . A method as defined in  claim 1 , wherein the first time period starts when the first signal is transmitted by the first transmitter and stops when the first signal is received by the first receiver and the second time period starts when the first signal is transmitted by the first transmitter and stops when the first signal is received by the second receiver. 
     
     
         3 . A method as defined in  claim 1 , further comprising:
 transmitting a second signal from a second transmitter at a fourth location in the borehole;   receiving the second signal at the first receiver after a third time period;   receiving the second signal at the second receiver after a fourth time period;   calculating a second distance from the second transmitter to a second portion of the boundary of the subterranean rock layer adjacent to the borehole by compensating for the anisotropy of the subterranean rock layer based on the third time period and the fourth time period; and   determining a distance from the first transmitter to between the first portion and the second portion of the boundary of the subterranean rock layer.   
     
     
         4 . A method as defined in  claim 1 , wherein:
 a first velocity of the first signal from the first transmitter to the first receiver is a value between an orthogonal velocity perpendicular to the borehole and an inline velocity based on a first angle of propagation of the first signal relative to the first portion of the boundary; and   a second velocity of the first signal from the first transmitter to the second receiver is a value between the orthogonal velocity and the inline velocity based on a second angle of propagation of the first signal relative to the first portion of the boundary.   
     
     
         5 . A method as defined in  claim 4 , wherein compensating for the anisotropy of the subterranean rock layer includes calculating the first distance from the first transmitter to the first portion of the boundary based on at least one of the first velocity, the second velocity, first time period, the second time period, the first location of the first transmitter, the second location of the first receiver, the first distance, the second distance, or an inline velocity of the first signal along the borehole. 
     
     
         6 . A method as defined in  claim 5 , wherein the first portion of the boundary reflects the first signal based on at least one of a change in rock type from the subterranean rock layer to a second subterranean rock layer, a change in a lithology of the subterranean rock layer, a change in a fault of the subterranean rock layer, or a change in an unconformity within the subterranean rock layer. 
     
     
         7 . A method as defined in  claim 3 , wherein the first and second signals are at least one or more acoustic signals, seismic signals, sonic signals or ultrasonic signals. 
     
     
         8 . A method as defined in  claim 3 , further comprising:
 moving at least one of the first transmitter, the first receiver or the second receiver a third distance;   transmitting a third signal from the first transmitter;   receiving the third signal at the first receiver after a fifth time period;   receiving the third signal at the second receiver after a sixth time period;   calculating a fourth distance from the first transmitter to a third portion of the boundary of the subterranean rock layer by compensating for the anisotropy of the subterranean rock layer based on the fifth time period and the sixth time period; and   determining the boundary of the subterranean rock layer based on at least one of the first distance to the first portion of the boundary, the second distance to the second portion of the boundary, or the third distance to the third portion of the boundary.   
     
     
         9 . An apparatus to calculate a distance from a borehole to a boundary of an anisotropic subterranean rock layer, the apparatus comprising:
 a first transmitter at a first location to transmit a first signal within a borehole of a subterranean rock layer;   a first receiver at a second location in the borehole to receive the first signal after a first time period;   a second receiver at a third location in the borehole to receive the first signal after a second time period; and   a formation processor to calculate a first distance from the first transmitter to a first portion of the boundary of the subterranean rock layer by compensating for an anisotropy of the subterranean rock layer based on the first time period and the second time period.   
     
     
         10 . An apparatus as defined in  claim 9 , further comprising a second transmitter at a fourth location in the borehole to transmit a second signal within the borehole of the subterranean rock layer. 
     
     
         11 . An apparatus as defined in  claim 10 , wherein:
 the first receiver receives the second signal after a third time period;   the second receiver receives the second signal after a fourth time period; and   the formation processor calculates a second distance from the second transmitter to a second portion of the boundary of the subterranean rock layer adjacent to the borehole by compensating for the anisotropy of the subterranean rock layer based on the third time period and the fourth time period.   
     
     
         12 . An apparatus as defined in  claim 11 , further comprising a boundary migrator to determine a distance from the first transmitter to between the first portion and the second portion of the boundary of the subterranean rock layer. 
     
     
         13 . An apparatus as defined in  claim 11 , wherein at least one of the first transmitter, the second transmitter, the formation processor, or the boundary migrator is located at a surface. 
     
     
         14 . An apparatus as defined in  claim 9 , wherein the formation processor is to:
 determine a first velocity of the first signal from the first transmitter to the first receiver based on at least one of a value between an orthogonal velocity perpendicular to the borehole and an inline velocity or a first angle of propagation of the first signal relative to the first portion of the boundary; and   determine a second velocity of the first signal from the first transmitter to the second receiver based on at least one of the value between the orthogonal velocity and the inline velocity or a second angle of propagation of the first signal relative to the first portion of the boundary.   
     
     
         15 . An apparatus as defined in  claim 14 , wherein the formation processor compensates for the anisotropy of the subterranean rock layer by calculating the first distance from the first transmitter to the first portion of the boundary based on at least one of the first velocity, the second velocity, first time period, the second time period, the first location of the first transmitter, the second location of the first receiver, the first distance, the second distance, or an inline velocity of the first signal along the borehole. 
     
     
         16 . An apparatus as defined in  claim 9 , wherein the first receiver and the second receiver include one or more sensors positioned to receive signals from different directions. 
     
     
         17 . An apparatus as defined in  claim 16 , wherein the one or more sensors associated with the first receiver are circumferentially positioned around the first receiver and the one or more sensors associated with the second receiver are circumferentially positioned around the second receiver. 
     
     
         18 . An apparatus as defined in  claim 16 , wherein at least one of the first receiver, the second receiver, or the first transmitter is coupled to a tool located in the borehole. 
     
     
         19 . An apparatus as defined in  claim 11 , wherein:
 at least one of the first transmitter, the first receiver or the second receiver is moved a third distance;   the first transmitter transmits a third signal;   the first receiver receives the third signal after a fifth time period;   the second receiver receives the third signal after a sixth time period;   the formation processor calculates a fourth distance from the first transmitter to a third portion of the boundary of the subterranean rock layer by compensating for the anisotropy of the subterranean rock layer based on the fifth time period and the sixth time period; and   the boundary migrator determines the boundary of the subterranean rock layer based on at least one of the first distance to the first portion of the boundary, the second distance to the second portion of the boundary, or the third distance to the third portion of the boundary.   
     
     
         20 . An apparatus as defined in  claim 9 , farther comprising:
 a third receiver at a fifth location in the borehole to receive the first signal after a third time period; and   a fourth receiver at a sixth location in the borehole to receive the first signal after a fourth time period.   
     
     
         21 . An apparatus as defined in  claim 20 , wherein the formation processor calculates the first distance from the first transmitter to the first portion of the boundary of the subterranean rock layer by compensating for the anisotropy of the subterranean rock layer based on the first time period, the second time period, the third time period, and the fourth time period. 
     
     
         22 . An apparatus to calculate a distance from a borehole to a boundary of an anisotropic subterranean rock layer, the apparatus comprising a formation processor to calculate a first distance from a first transmitter to a first portion of the boundary of a subterranean rock layer by compensating for an anisotropy of the subterranean rock layer based on a first time period and a second time period corresponding to a first signal. 
     
     
         23 . An apparatus as defined in  claim 22 , wherein the formation processor is to:
 determine a first velocity of the first signal from the first transmitter to a first receiver based on at least one of a value between an orthogonal velocity perpendicular to the borehole and an inline velocity or a first angle of propagation of the first signal relative to the first portion of the boundary; and   determine a second velocity of the first signal from the first transmitter to a second receiver based on at least one of the value between the orthogonal velocity and the inline velocity or a second angle of propagation of the first signal relative to the first portion of the boundary.   
     
     
         24 . An apparatus as defined in  claim 23 , wherein the formation processor compensates for the anisotropy of the subterranean rock layer by calculating the first distance from the first transmitter to the first portion of the boundary based on at least one of the first velocity, the second velocity, the first time period, the second time period, a first location of the first transmitter, a second location of the first receiver, the first distance, or an inline velocity of the first signal along the borehole.