Correction for misalignment and cross axis sensitivity of strong earthquake motion recorded by sma-1 accelerographs, 1995

Two procedures are presented, one for correction of strong earthquake accelerations recorded on film for transducers' cross-axis sensitivity and misalignment, and another one for determining the misalignment angles from field tests. Misalignment refers to imperfections in the alignment of the penduli of the three transducers, and is typically of the order of few degrees. It results in the transducers recording motion in directions other than along the nominal sensitivity axis. Cross-axis sensitivity is the phenomenon of a transducer recording components of motion in directions other than its sensitivity axis, even when the transducer pendulum is perfectly aligned. This effect is pronounced for large amplitude recordings (peak acceleration close to 1g). The two effects are coupled. Correction for these effects was presented in the mid 1970's, and applied to the Pacoima dam accelerogram (San Fernando, 1971 California earthquake). Not until the 1994 Northridge, California, earthquake, so many large accelerations were recorded during one strong motion event.; The correction for these two effects, after the misalignment angles have been determined, is performed by expressing the motion along the ideal position of the sensitivity axes in terms of the motions in the actual directions of the penduli. This involves several successive coordinate transformations. The misalignment angles are determined by solving a generalized inverse problem. Namely, the deflection of the trace on the film caused by known forces (a component of the weight of the pendulum) is measured very accurately, and then an overdetermined system of equations is solved by a least squares procedure. The misalignment angles and the sensitivities are the only unknowns. A special tilt is used in the field, and the film record with static deflections of the traces is digitized by a scanner and a PC, to get the input for the inverse problem.; Distribution of teh values of the misalignment angles is presented for the 80 stations of the Los Angeles Strong Motion Network. These angels are typically of the order of 1° to 1.5°, but in few cases are as large as 3° to 4°. Also, results are presented illustrating the significance of these two effects for several recordings of the Northridge, 1994, earthquake (e.g., the record at the Rinaldi Receiving Station of the Department of Water and Power, City of Los Angeles). The results show that, for zero misalignment angles, the cross-axis sensitivity does not influence the record significantly. However, when coupled with misalignment, the effects are significant. The peak accelerations change by up to 3% for 1.5°, and by up to 7% for 3° misalignment angles. The misalignment and cross-axis sensitivity affect not only the peak values, but also the Fourier and Response spectra of the record, and their phase.; The largest systematic errors are associated with the limitation of the simple tilt test procedure. We show that the sensitivities specified by the manufacturer are larger than the estimates by our algorithm by 3% to 5% on average, and in most cases less than 10%. Coupled with the effects of cross-axis sensitivity and misalignment, this will result in errors in the computed accelerations which may approach about 15%.; The study concludes that correction of strong motion recordings by SMA-1 accelerographs for misalignment and cross-axis sensitivity effects is significant for large recorded accelerations, especially for some applications such as source inversion from displacements of recorded ground motion, and structural system identification procedures.

本文提出了两种处理流程：其一用于校正胶片记录的强地震加速度数据中传感器的轴间灵敏度与轴不对准误差；其二用于通过现场试验确定轴不对准角。轴不对准指的是三台传感器的摆体对准存在偏差，其量级通常为数度。该偏差会导致传感器记录的运动方向并非其标称灵敏度轴方向。轴间灵敏度则是指即便传感器摆体完全对准，传感器仍会记录非灵敏度轴方向的运动分量的现象。该效应在大振幅记录（峰值加速度接近1g）中尤为显著。上述两种效应存在耦合关系。针对这两类效应的校正方法于20世纪70年代中期被提出，并被应用于帕科伊马大坝加速度记录（1971年加利福尼亚圣费尔南多地震）。直至1994年加利福尼亚北岭地震，单次强震动事件才首次记录到如此多的大振幅加速度数据。
在确定轴不对准角后，可通过将灵敏度轴理想位置处的运动转换为摆体实际方向上的运动分量，完成上述两种效应的校正。该过程涉及多次连续的坐标变换。轴不对准角的求解需通过广义逆问题实现：首先精准测量已知力（摆体重力分量）引起的胶片记录轨迹偏移量，随后通过最小二乘法求解超定方程组，其中未知量仅为轴不对准角与传感器灵敏度。现场试验中采用专用倾角装置，通过扫描仪与个人计算机将带有静态轨迹偏移的胶片记录数字化，以此作为逆问题的输入数据。
本文给出了洛杉矶强震动台网80个台站的轴不对准角分布情况。该类角度通常介于1°~1.5°之间，少数案例中可达3°~4°。此外，本文还针对1994年北岭地震的多段记录分析了两类效应的影响显著性，例如洛杉矶市水电部门里纳利接收站的加速度记录。研究结果表明，当轴不对准角为零时，轴间灵敏度对记录的影响并不显著；但当与轴不对准误差耦合时，其影响则较为显著。对于1.5°的不对准角，峰值加速度可产生最高3%的变化；而对于3°的不对准角，该变化可达7%。轴不对准与轴间灵敏度不仅会影响记录的峰值，还会改变记录的傅里叶谱、反应谱及其相位。
最大的系统误差源于简易倾角试验流程的局限性。研究表明，厂商标称的传感器灵敏度平均比本算法的估算值高出3%~5%，多数情况下偏差不超过10%。结合轴间灵敏度与轴不对准误差的影响，该偏差将导致加速度计算误差可达约15%。
本研究最终得出结论：针对SMA-1型加速度记录仪的强震动记录进行轴不对准与轴间灵敏度校正，对于大振幅记录而言具有重要意义，尤其适用于基于地面运动位移的震源反演、结构系统识别等应用场景。