Real time surveying while drilling

A method for drilling a subterranean wellbore, the method comprising:

• (a) drilling the subterranean wellbore via rotating a drill string therein, the drill string including a drill bit, a triaxial accelerometer set, and a triaxial magnetometer set;
• (b) causing the triaxial accelerometer set and the triaxial magnetometer set to make corresponding analog triaxial accelerometer measurements and analog triaxial magnetometer measurements while drilling in (a);
• (c) filtering the triaxial magnetometer measurements made in (b) using a first analog circuit located in the drill string to obtain filtered triaxial magnetometer measurements;
• (d) filtering the triaxial accelerometer measurements made in (b) using a second analog circuit located in the drill string to obtain filtered triaxial accelerometer measurements;
• (e) digitizing the filtered triaxial magnetometer measurements obtained in (c) and the filtered triaxial accelerometer measurements obtained in (d) to obtain digitized triaxial magnetometer measurements and digitized triaxial accelerometer measurements;
• (f) processing the digitized magnetometer measurements to remove a first time lag and thereby obtain compensated magnetometer measurement;
• (g) processing the digitized accelerometer measurements to remove a second time lag and thereby obtain compensated accelerometer measurements;
• and
• (h) processing the compensated magnetometer measurements and the compensated accelerometer measurements to compute an inclination and an azimuth of the subterranean wellbore while drilling in (a).

A system for drilling a subterranean wellbore, the system comprising:

• a bottom hole assembly configured to drill the subterranean wellbore via rotating therein on a drill string;
• a triaxial magnetometer set and a triaxial accelerometer set deployed in the bottom hole assembly, the triaxial magnetometer set in electrical communication with a first analog circuit and the triaxial accelerometer set in electrical communication with a second analog circuit;
• the first analog circuit and the second analog circuit in electrical communication with an analog to digital converter, the analog to digital converter configured to digitize signals received from the first analog circuit and the second analog circuit;
• the analog to digital converter in electronic communication with a digital signal processor, the digital signal processor configured to (i) process digitized magnetometer measurements to remove a first time lag induced by the first analog circuit and thereby obtain compensated magnetometer measurements, (ii) process digitized accelerometer measurements to remove a second time lag induced by the second analog circuit and thereby obtain compensated accelerometer measurements, and (iii) process the compensated magnetometer measurements and the compensated accelerometer measurements to compute an inclination and an azimuth of the subterranean wellbore while drilling.