In a triaxial seismometer such as the Streckeisen STS2 (Fig. 13), transfer functions in a strict sense can only be attributed to the individual U,V,W sensors, not to the X,Y,Z outputs. Formally, the response of a triaxial seismometer to arbitrary ground motions is described by a nearly diagonal 3 x 3 matrix of transfer functions relating the X,Y,Z output signals to the X,Y,Z ground motions. (This is also true for conventional three-component sets if they are not perfectly aligned; only the composition of the matrix is slightly different.) If the U,V,W sensors are reasonably well matched, the effective transfer functions of the X,Y,Z channels have the traditional form and their parameters are weighted averages of those of the U,V,W sensors. The X,Y,Z outputs can therefore be calibrated as usual. For the simulation of horizontal and vertical ground accelerations via the calibration coils, each sensor must receive an appropriate portion of the calibration current. For the vertical component this is approximately accomplished by connecting the three calibration coils in parallel. For the horizontal components and also for a more precise excitation of the vertical, the calibration current or voltage must be split into three individually adjustable and invertible U,V,W components. These are then adjusted so that the test signal appears only at the desired output of the seismometer.
It is also possible to calibrate the U, V, and W sensors separately - the Z output may be used for this purpose - and then to average the U, V, W transfer functions (or parameters) with a matrix whose elements are the squares of those of the matrix in Eq. (35):
Eqs. (35) and (40) are only approximate since they assume the mechanical alignment to be perfect. Actually the resistor network that determines the matrix in Eq. (35) is adjusted in each instrument so as to compensate for slight misalignments of the U, V and W sensors. The difference between the nominal and the actual matrix can however be ignored in the context of calibration.