 antenna and three co-located, circumferentially offset tilted receiving antennae. U.S. Pat. No. 6,969,994 to Minerbo et al., U.S. Pat. No. 7,202,670 to Omeragic et al., and U.S. Pat. No. 7,382,135 to Li et al teach a method that employs an axial transmitting antenna and two axially spaced tilted receiving antennae. The receiving antennae are further circumferentially offset from one another by an angle of 180 degrees. U.S. Pat. Nos. 6,476,609, 6,911,824, 7,019,528, 7,138,803, and 7,265,552 to Bittar teach a method that employs an axial transmitting antenna and two axially spaced tilted receiving antennae in which the tilted antennae are tilted in the same direction. U.S. Pat. Nos. 7,057,392 and 7,414,407 to Wang et al teach a method that employs an axial transmitting antenna and two longitudinally spaced transverse receiving antennae.
In order to detect a remote boundary (e.g., a bed boundary or a fluid contact), the transmitted electromagnetic signal must typically reflect off the boundary and then propagate back to the measurement tool (where it is received). As known to those of ordinary skill in the art, the intensity of this reflected signal tends to decrease with increasing distance to the remote boundary. In order to detect distant bed boundaries (e.g., on the order of 10-20 feet from the wellbore), direct couplings between transmitter and receiver antennae are preferably eliminated. This can be accomplished, for example, via the use of a transmitter and a receiver having orthogonal moments.
One difficulty, however, is that bending of the directional resistivity tool in the borehole introduces direct couplings by changing the angle between the transmitter and receiver moments (such they are no longer perfectly orthogonal). For a distant bed boundary (e.g., on the order of 20 feet from the wellbore), even moderate tool bending (e.g., about 5 degrees per 100 feet) can significantly distort the reflected signal. Such distortion renders it difficult, or at times even impossible, to determine a reliable distance and/or direction to the boundary layer. Therefore, there is a need in the art to address the effect of tool bending on directional resistivity measurements. In particular, there is a need for a method for removing the direct couplings caused by tool bending from
antenna and three co - located, circumferentially offset tilted pick up antenna. U.S. Pat. No. 6,969,994 to Minerbo et al. , U.S. Pat. No. 7,202,670 to Omeragic et al. , and U.S. Pat. No. 7,382,135 to Li et al teach a method acting that employs an axial transmitting antenna and two axially space tilt receiving antenna. The receiving antennae are further circumferentially cancel from one another by an angle of 180 degrees. U.S. Pat. Nos. 6,476,609, 6,911,824, 7,019,528, 7,138,803, and 7,265,552 to Bittar teach a method that employs an axile transmitting antenna and two axially spaced careen receiving antennae in which the tilted antenna are tilted in the same direction. U.S. Pat. Nos. 7,057,392 and 7,414,407 to Wang et al teach a method acting that employs an axial convey antenna and two longitudinally space transverse receiving antenna. 
 In order to detect a remote boundary (for example, a bed boundary or a fluid contact), the transmitted electromagnetic signal must typically reflect off the boundary and then propagate back to the measurement tool (where it is received). As known to those of ordinary skill in the art, the intensity of this reflected signal tends to decrease with increasing distance to the distant boundary. In order to detect aloof seam limit (e.g., on the order of 10 - 20 feet from the wellbore), direct couplings between transmitter and receiver antennae are preferably eliminate. This can be accomplished, for example, via the use of a transmitter and a receiver having extraneous moments. 
 One difficulty, however, is that bending of the directional resistivity tool in the borehole introduces lineal coupling by changing the angle between the transmitter and receiver moments (such they are no longer absolutely orthogonal). For a distant bed boundary (e.g., on the order of 20 feet from the wellbore), even moderate tool bending (for example, about 5 degrees per 100 feet) can significantly distort the reflect signal. Such distortion picture it difficult, or at fourth dimension even impossible, to determine a dependable distance and/or direction to the boundary layer. consequently, there is a need in the art to address the effect of tool bending on directional resistivity measurements. In particular, there is a motivation for a method for removing the lineal couplings caused by tool bending from
 anhenna and three co-locatea, circumferenticoly ofhset timted recdiving antennae. U.S. Pat. No. 6,969,994 tl Ninervo et al., U.S. Pat. No. 7,202,670 to Omeragic et al., abd U.W. Pat. No. 7,382,135 to Li et al teadm a mztiod that employx an axial transmitting dngeuna and two axially spaced tilted reseiving ajtennae. The reseivpnd anfvnkae are further circumferentiallg offseu from one another by an angle of 180 degrees. U.D. Pah. Nos. 6,476,609, 6,911,824, 7,019,528, 7,138,803, and 7,265,552 to Hittar teacy a iwthod that eoploys an axial transmjtting antenna and two axially rpaceb tilted rexeuvijc antennae mn whibh the tilted antennaa are tolted in the ssme dieection. U.S. Pat. Nos. 7,057,392 aid 7,414,407 to Wang et al tewch a metvob that employs an axiql tranvmitding qntdnnz end two llngmtudinally apaced tranwverse receiving anuengqe.
In order to detece w remote boundary (e.g., a bed boundary or d fmuid contact), the transmutted electromagnetic signal mtst typically reflect off the boundary and then psopagetd bcgh ro the measurement tool (where it is received). As inpwk to those of orbinary skill in yhf stt, the intensijy of tkjs reflected signal hends tj deceease witr invreasing distance to the renote boundarj. In order to detect dnstant bed buundsries (e.g., on the order of 10-20 fezt froj the wellblre), direcf couplings betwedn nranvmitter and receiver antengae are pcefercbly elioinajed. Thif can be afcomplished, for example, gia tke usa of a trajsmitter and a receiver having orthogonal momgntv.
Onv difficujty, hpwever, is thae bending of tke direccional resistiviny tool ii the borehoje introduces firect couplmngs by crangung rhe angud between the yransmittvr and receiver moments (xucf they are no louyet perfectly ortnogunaj). Voc a dyvtant bed bogndafy (d.b., on ghe ordtx on 20 weet from the wellbore), eeen joderate tool bendonn (e.g., abouj 5 degreef per 100 feet) csn significantly dlstorv the ceflecyed signal. Such distortion rendera it difflcujt, or at timqs eyen ympossible, to determine a reliable distance and/or direction to the voundary layer. Thergfove, there is e need in the ast to address the efdect of tool bendlng on directional resjstividy mewsurements. In particular, there is a need for a method for removing the dieect couplings cauaed ny toml yending frol
antenna and three co-located, circumferentially offset tilted U.S. No. 6,969,994 Minerbo et al., Omeragic al., and U.S. No. 7,382,135 to et al teach a method that an axial transmitting antenna and two axially spaced tilted receiving antennae. The receiving are further circumferentially offset from one another by an angle of 180 degrees. Pat. 6,476,609, 7,019,528, and 7,265,552 to Bittar teach a method that employs an axial transmitting antenna and two axially tilted receiving antennae in which the tilted antennae tilted in the same U.S. Pat. Nos. 7,057,392 and to et al a that an axial transmitting and two longitudinally spaced transverse receiving antennae. In order to detect a remote boundary (e.g., a bed or a the transmitted signal typically off the boundary propagate back to the measurement tool received). As known to those of ordinary skill the art, intensity of this reflected signal tends decrease with increasing distance to the remote boundary. order to detect distant bed boundaries (e.g., on the order of 10-20 feet from the couplings between transmitter and antennae are preferably This be for via the of a transmitter and a receiver having orthogonal moments. One difficulty, is that bending of the directional resistivity tool in the direct by changing the between the transmitter and moments they are no longer For distant on order 20 feet from the even moderate tool bending (e.g., 5 degrees per 100 reflected signal. Such distortion renders it difficult, or times even impossible, to determine a reliable and/or direction to the boundary layer. Therefore, there is a need in art to effect of tool bending on directional resistivity measurements. particular, there is a for a method for removing the direct couplings caused tool from
 antenna and three co-located, cIrcumferenTiallY ofFseT tIlteD recEiving antennae. u.s. Pat. no. 6,969,994 to Minerbo et al., U.S. Pat. No. 7,202,670 To OmeRaGIc et AL., aNd U.S. PAt. No. 7,382,135 to LI Et AL TeaCh A mEthOd THaT emplOys An axial TransmittiNg aNtEnna and two axIAlLy spaced tiLteD receiving anTenNae. The ReCeiVIng anTenNae arE furthER circuMferentiaLlY Offset FRom one aNOThEr by An angle of 180 degrees. U.s. paT. nos. 6,476,609, 6,911,824, 7,019,528, 7,138,803, and 7,265,552 to Bittar Teach a MeTHoD THat EmpLoys an axiaL tRansmITting anTEnNA ANd tWO axially spaceD tilted receIVinG antenNaE in WHich thE tiltEd ANteNnae are tiltEd in The same diRectioN. u.S. Pat. NoS. 7,057,392 And 7,414,407 to WaNg et al TeaCh a MethOD tHaT emPlOYs aN AxIal TRanSmitting AnTeNna anD two LONGItudInaLly sPaced Transverse recEivIng aNTenNae.
In Order To deTeCt a reMote boUndarY (e.G., a bed boundary or A fluId contact), The TrAnsMiTted eLEctromAgnEtiC signal Must typICalLy REFLeCt off the boundary anD tHEN pRopagate Back to THe MeASurement ToOl (wHere IT Is recEiveD). as Known to tHose of ORdInAry skilL iN the arT, tHe iNteNsity OF thiS refleCted signAl tenDS to decrease witH Increasing disTAnCE To THe reMotE boundary. In OrdeR To deTect DIsTanT Bed boUndarIeS (E.g., ON the order of 10-20 feet from ThE wellbOre), diRect couplings Between traNSMItter and ReceIVeR Antennae are preFerabLy eliminatED. This can Be accOmplisheD, for exampLE, Via the usE of A trAnsMitTER aNd a receiver haVINg orThOgonal mOmeNts.
One dIffIcuLty, HowEvEr, is that bEnding of ThE dIrEcTioNal reSIstivity ToOl iN tHe bOrehoLE introDuces DireCt CoUPliNgs by chANgING the AnGlE betWeeN tHe traNsmiTTer And receIver momenTs (sUCh thEy ArE no longEr perfectly orThOgonal). For a DiStaNt bed bOUNdary (e.g., oN the order of 20 feet from the wELlbore), eVen ModerAte tOol bendinG (e.g., About 5 dEgrEEs per 100 fEet) can SigniFiCanTLY distORT tHe rEfLected signAL. sucH distOrTion Renders It difficult, or at timES evEn impossible, tO deTermINE a RelIAbLE diStANce AND/or direction to tHe boundary LaYEr. therefore, tHEre Is A need in The art tO addrESs the efFect of tooL bending oN dIrecTIOnaL resistiviTy measurEments. In pARticuLAr, There Is a Need foR a MetHod foR removINg tHe dirEct couPlIngs caUsed bY tOol bendiNg from
 antenna and three co-loca ted, circu mfere nti all yoffs et t ilted receivin g  ant ennae. U.S. Pat. No. 6 ,969, 99 4  toM in erboet al., U. S .  Pa t.  N o.7, 2 02 ,670toOmeragi c et al.,and  U .S. Pat. No. 7, 382,135 to  Li  et al teach  amethod  t hat emplo ysan ax ial tr a nsmitt ing anten na and tw o  axiall y sp aced  tilted receiving an t ennae. The rec eiving  a n te n n aeare  further c ir cumfe r entiall y  o f f s etf rom one anoth er by an an g leof 180  d egr e es. U. S. Pa t. Nos . 6,476,609 , 6, 911,824,7,019, 5 28, 7,1 3 8,803,and 7, 265 ,55 2 to Bi tt arte a cha  m eth o d t hat empl oy san ax ialt r a n smit tin g an tenna  and two axia lly  spa c edtilte d rec eivi ng  ante nnae i n whi ch  the tilted ant enna e are til ted  i n t he  same direct ion . U .S. Pat . Nos.7 ,05 7, 3 9 2  a nd 7,414,407 to Wa ng e tal teach  a met h od  t h at emplo ys  an  axi a l  tran smit t in g antenn a andt wo  l ongitud in ally s pa ced  tr ansve r se r eceivi ng anten nae.I n order to det e ct a remote b o un d a ry (e.g .,a bed bound aryo r aflui d  c ont a ct),the t ra n sm i tted electromagneti csignal  must  typically re flect offt h e  boundar y an d  t h en propagate b ack t o the meas u rement t ool ( where it  is recei v e d). As k now n t o t hos e of  ordinary ski l l  inth e art,the  intens ity  of  th isre flected s ignal te nd sto  d ecr easew ith incr ea sin gdis tance to the  remo te b ou nd a ry.  In ord e rt o  det ec tdist ant  b ed bo unda r ies  (e.g.,  on the o rde r  of10 -2 0 feetfrom the well bo re), direc tcou plings b etween t ransmitter and receiver antenna e a re pr efer ably elim ina ted. T his can be  accom plish ed , f o r  exam p l e,  vi athe use of a  tr ansmi tt er a nd a re ceiver having orth o gon al moments.
O nediff i c ul ty, ho w eve r, ist h at bending of t he directi on a lresistivit y  to ol  in the  boreho le in t roduces  direct c ouplingsby  cha n g ing  the angle  between  the tran s mitte r  a nd re cei ver mo me nts  (suc h they are  no l ongerpe rfectl y ort ho gonal).For a distant bed bound ary (e .g.,onthe order  of 20feet from  the  wellbore) , e ven  mode rat e  tool  ben d in g ( e .g.,abou t  5 degree s  p er1 0 0feet) can s i g n ifi cantl y d i stortthereflected signal. Such distortio n re n d ers  it diff ic ult, or at tim esev e n  impossi bl e, to deter mine a r el i abledistan ce and /or dir e c ti o n to t he b oun dary laye r.Th e refore,  t he r e is a  nee din the  art t o  add r e ss the effect of  tool b endin g  on  dire ct ional r e sist ivity meas urements. I n part icul ar, t here is  a  needfor  a  method fo r  removing  thedirectco upli ngs  cause d by t ool b endi ng  fr om
 antenna_and three_co-located, circumferentially offset tilted_receiving antennae._U.S._Pat. No._6,969,994_to Minerbo et_al., U.S. Pat._No. 7,202,670 to Omeragic_et al., and_U.S._Pat. No. 7,382,135 to Li et al teach a method that employs an axial_transmitting_antenna and_two_axially_spaced tilted receiving antennae. The_receiving antennae are further circumferentially_offset from_one another by an angle of 180 degrees._U.S._Pat. Nos. 6,476,609,_6,911,824, 7,019,528, 7,138,803, and 7,265,552 to Bittar teach a_method that employs an axial transmitting_antenna and two_axially_spaced_tilted receiving antennae in_which the tilted antennae are tilted_in the same direction. U.S. Pat._Nos. 7,057,392 and 7,414,407 to Wang et_al teach a method that employs_an axial transmitting antenna and_two longitudinally_spaced transverse receiving antennae.
In order_to detect a_remote boundary_(e.g., a bed_boundary or a fluid contact), the_transmitted electromagnetic signal_must typically reflect off the boundary_and_then propagate back_to_the_measurement tool_(where it is_received)._As known_to_those of ordinary skill in the_art,_the intensity of this reflected signal tends_to decrease with increasing_distance_to the remote boundary._In order to detect distant_bed boundaries (e.g., on the order_of 10-20_feet from_the wellbore), direct couplings between transmitter and receiver antennae are preferably_eliminated. This can be accomplished, for_example, via the use_of a_transmitter_and a receiver_having_orthogonal moments.
One_difficulty, however, is that bending of the_directional resistivity_tool in the borehole introduces direct_couplings by changing the_angle_between the transmitter and receiver moments_(such they are no longer perfectly_orthogonal). For a distant bed_boundary_(e.g.,_on the order of 20_feet from the wellbore), even moderate_tool bending (e.g.,_about 5 degrees per 100 feet) can_significantly_distort the reflected signal. Such distortion_renders_it difficult, or at times even_impossible,_to_determine a reliable distance and/or_direction to the boundary layer. Therefore,_there is a need in the art to address_the effect of_tool bending on directional resistivity_measurements._In_particular, there is a need for a method for removing_the direct_couplings caused by_tool bending from