AN ACR RPTS COMPASS PROBS AFTER DEP FROM RWY 13 AT LGA; NY.

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OUR FLT XXX DEPARTED RWY 13 AT LGA AT XA05 ON THE LGA 9 DEP; WHITESTONE CLB. NORMAL OPS AND INST INDICATIONS THROUGH THE INITIAL CLB DURING TURN TO 180 DEGS. DURING THE R TURN; ATC HANDED US OFF TO DEP CTL. DEP CTL ASSIGNED US TO CLB TO 15000 FT. THE FO (PNF) READ IT BACK TO THE CTLR AND BOTH PLTS CONFIRMED ALT CLRNC AS SELECTED IN THE ALT READOUT OF THE PFD. REACHING THE 2.5 DME LGA; I BEGAN MY L TURN TO A HDG OF 040 DEGS AS DEPICTED ON THE SID. SHORTLY AFTER STARTING THE TURN TO THE L; ATC CLRED US TO MAKE A TIGHT R TURN TO A HDG OF 040 DEGS. I STOPPED THE L TURN AND BEGAN TO ROLL INTO A TURN TO THE R AND INSTRUCTED THE PNF TO QUERY ATC AND CONFIRM A R TURN. FLT DIRECTOR FAIL FLAGS ON BOTH PFD'S ILLUMINATED AT THIS TIME. AUTOPLT WAS OFF. ATC INQUIRED AS TO WHETHER WE WERE FLYING THE WHITESTONE CLB; WHICH WE REPLIED YES. ATC THEN STATED 'YOU SHOULD TRY READING IT FIRST NEXT TIME.' AS WE WERE TURNING TO THE R; ATC CLRED US TO TURN IN THE SHORTEST DIRECTION TO A HDG OF 040 DEGS. I INSTRUCTED THE FO TO CLARIFY THE DIRECTION OF TURN AS I ROLLED BACK TO THE L TOWARD A HDG OF 040 DEGS. MY HSI INDICATED THE SHORTEST DIRECTION WAS TO THE L. AT THIS TIME AN EFIS COMPASS MONITOR CAUTION MESSAGE POSTED. ATC THEN QUERIED US AS TO OUR HDG. I BELIEVE THE INDICATED HDG AT THE TIME WAS 090 DEGS IN THE L TURN. ATC ADVISED US THAT THE HDG WAS SIGNIFICANTLY OFF TRACK AND THAT HE WAS GIVING US 'NO GYRO VECTORS.' ATC ISSUED A FURTHER CLRNC TO INITIATE A L TURN. AT THIS TIME WE COMPARED THE WET COMPASS TO THE HSI'S (BOTH) AND THEY DID NOT AGREE. I TOOK COMMAND OF THE RADIO AND INSTRUCTED THE PNF TO INITIATE THE QRH PROCS FOR THE FLT DIRECTOR FAIL AND THE EFIS COMPASS MONITOR. I ADVISED ATC THAT BOTH COMPASSES WERE INOP; WE WERE IN A L TURN; AND TO ADVISE WHEN TO STOP TURN. AFTER ATC CLRED US TO STOP TURNING; I INSTRUCTED THE PNF TO SWITCH BOTH AHRS UNITS TO THE DIRECTIONAL GYRO MODE AND SLEW THE HDG TO MATCH THE WET COMPASS. ESTABLISHED NOW ON A HDG AND STILL CLBING TO THE ASSIGNED ALT; THE FLT DIRECTOR FAIL AND EFIS COMPASS MONITOR MESSAGES HAD EXTINGUISHED. HSI INDICATIONS IN THE DIRECTIONAL GYRO MODE APPEARED NORMAL; SO I INSTRUCTED THE PNF TO SELECT THE R HSI TO MAGNETIC MODE SO WE COULD MONITOR BOTH MODES TO DETERMINE IF THE MAGNETIC MODE WAS OPERATING CORRECTLY NOW. ATC THEN CLRED US DIRECT PARKE INTXN. WE SEQUENCED THE FMS AND SELECTED NAV. THE FLT DIRECTORS APPEARED TO BE STEERING CORRECTLY AND WE CONFIRMED THAT WITH ATC. A MOMENT LATER WE GOT ANOTHER EFIS COMPASS MONITOR CAUTION MESSAGE. WHILE WE WERE REFERRING TO THE QRH AGAIN CLBING THROUGH 12300 FT; ATC ADVISED US THAT WE WERE TO MAINTAIN 12000 FT. I STOPPED THE CLB IMMEDIATELY; LEVELED OFF AT 12500 FT AND DSNDED TO 12000 FT. ESTABLISHED LEVEL AT 12000 FT; I INSTRUCTED THE PNF TO SWITCH THE L AHRS BACK TO MAGNETIC MODE AND THE EFIS COMPASS MONITOR MESSAGE EXTINGUISHED. APCHING THE PARKE INTXN; I ADVISED ATC THAT OUR COMPASS SYS WERE OPERATIONAL. ATC THEN CLRED US TO CHANGE FREQS. NO FURTHER DIFFICULTIES FOR THE REMAINDER OF THE FLT. IN SUMMARY; I SUSPECT THAT THE CONCRETE AND STEEL PIER THAT SUPPORTS THE END OF RWY 13 AT LGA DISABLED OUR FLUX COMPASS SYS TO A DEG THAT WHEN WE INITIATED THE TURN TO A HDG OF 180 DEGS THAT THE HSI WAS TURNING SLOWER THAN THE ACTUAL RATE OF TURN. THIS RESULTED IN OUR ACTUAL HDG BEING SIGNIFICANTLY MORE TO THE R THAN INDICATED. THE PIER NORMALLY CAUSES FLUX COMPASS ERRORS AND ASSOCIATED WARNING FLAGS AS YOU APCH RWY 13 ON TXWYS G AND P. THESE COMPASS ERRORS STOP WHEN YOU TAXI ONTO THE RWY. THE STANDARD PROC IS TO START YOUR TKOF ROLL A FEW HUNDRED FT FORWARD OF TXWY P; HOLD SHORT LINE TO REDUCE THE EFFECT OF TH STEEL IN THE PIER THERE IS A LIGHTED SIGN SHORT OF RWY 13 THAT CAUTIONS PLTS TO CHK HDG WHEN IN POS. I DID THAT AND NOTED NO ABNORMAL HDG INDICATIONS. IN THE FUTURE; I PLAN TO USE THE DIRECTIONAL GYRO MODE DURING DEPS FROM LGA'S RWYS 13 AND 22 BECAUSE THEY ARE BOTH ON STEEL PIERS. THIS SHOULD ELIMINATE ANY FLUX COMPASS ERRORS DURING THE INITIAL DEP.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR INDICATED THAT HE HAS COME TO THE CONCLUSION THAT THE PROB IS WITH THE ARPT RATHER THAN ANY PARTICULAR PROB WITH THE ACFT. HE INDICATED THAT THE CTLRS INVOLVED SEEMED TO BE QUITE FAMILIAR WITH THE PROB. SINCE MAKING THE RPT HE HAS HEARD WHAT APPEARED TO BE VERY SIMILAR INCIDENTS WHILE MONITORING THE TWR AND DEP FREQS THAT ATC SEEMED TO BE WATCHING FOR AND HANDLED IN A SIMILAR FASHION TO HIS EXPERIENCE.