Methods of correcting accelerometer and magnetometer measurements

1. A method of correcting accelerometer and magnetometer measurements made in a well, comprising:

making a series of triaxial magnetometer measurements (Mx, My, Mz) and a series of triaxial accelerometer measurements (Ax, Av, Az) at N positions in an interval of the well to derive measured values of gravitational acceleration g, magnetic field intensity B and the sine of a magnetic inclination sinI; obtaining known values of g, B and sinI for each measured position N in the interval; determining a accelerometer measurement offset ΔA and a magnetometer measurement offset ΔM to be applied across the measured interval of the well, wherein ΔA comprises three accelerometer corrections (ΔAx, ΔAy, ΔAz) and ΔM comprises three magnetometer corrections (ΔMx, ΔMy, ΔMz), by simultaneously minimizing the root-mean-square difference between the series of measured values of g, B and sinI and the known values of g, B and sinI across all measured positions N in the interval; and applying the accelerometer measurement offset ΔA and the magnetometer measurement offset ΔM across the measured interval of the well to determine in situ corrected accelerometer and magnetometer measurements, wherein the corrected accelerometer and magnetometer measurements are given by

A′=A−ΔA =( A x −ΔA x ,A y −ΔA y ,A z −ΔA z ),

M′=M−ΔM= ( M x −ΔM x ,M y −ΔM y ,M z −ΔM z ),

and the measured values of g, B and sinI by

IA′I =√( A′ x 2 +A′ y 2 +A′ z 2 ),

IM′I=√ ( M′ x 2 +M′ y 2 +M′ z 2 ), and

A′·M′/IA′IIM′I,

the method comprising determining offsets ΔA=(ΔAx, ΔAy, ΔAz) and ΔM=(ΔMx, ΔMy, ΔMz) that will simultaneously minimize the root-mean-square difference between the measured and known values of g, B and sinI, wherein the offsets ΔA and ΔM are obtained by minimizing the cost function:

χ=σ* g 2 +σ* B 2 +σ sinI 2 +Λ A 2 +Λ M 2

where

σ* g =√[Σ(1 −|A′|/g ) 2 /N],

σ* B =√[Σ(1 −|M′|/B ) 2 /N],

σ sinI =√[Σ(sin I−A′·M′/|A′||M ′|) 2 /N],

(Σ represents a sum over N depth levels)

are the standard deviation of the measured g, B and sinI and * indicates that the values are expressed as fractions of the reference values, and the terms:

Λ 2 A =( a g σ* g Theoretical /σ* g ) 2 |ΔA| 2 /g 2 ,

and

Λ 2 M =( a B σ* B Theoretical /σ* B ) 2 |ΔM| 2 /B 2

are used so that if two solutions give the same fit in the absence of these terms, the one whose offset vector has the smaller magnitude is preferred.