64 8.2 Identification
In addition to high-frequency signals due to on-board instruments or other sources the ACC1A data contains also the low-frequency signals due to atmospheric (thermospheric) drag, solar radiation pressure as well as albedo. For an analysis of signals with a high-frequency nature it is necessary to remove any low-frequency signal. This was realized by means of a 35 mHz high-pass filter. We made use of the official CRN-filter, which is indeed a 35 mHz low-pass filter and used in order to derive ACC1B data products. However, a 35 mHz high-pass filtered ACC1A signal can be retrieved by subtracting the 35 mHz low-pass filtered ACC1A signal. The CRN-filter is explained in detail by Wu et al. (2006).
In order to avoid known third-party induced signals as well as other possible disturbing effects the ACC1A need to be pre-processed before a successful identification of the twangs may be carried out. Known signals that may impact the results of the identification process are due to thruster activations and de-activations, heater switch events as well as current changes within the magnetic torquer rods. These signals were discussed in the previous chapter (cf. chapter 7.2, p. 50). For the signals related to magnetic torquer electric current changes model spike time-series for ACC1A per day were produced by us and were hereinafter subtracted from the ACC1A data. Analogously to this approach, model spike time series due to heater switching events corresponding to the ACC1A data computed by Jakob Flury’s group of the Institut für Erdmessung (IfE) at the Leibniz Universität Hannover were subtracted from ACC1A data. This yields ACC1A data which is free from heater and magnetic torquer induced signals.
Furthermore, thruster firing events may result in signals of large amplitude within the ACC1A data. As thruster events are indeed an actual angular or linear acceleration, no time series for a subtraction of thruster spikes from ACC1A data exist. However, due to the availability of the THR1B data files, that contain the exact time stamps for thruster activations and de-activations, the corresponding ACC1A can be neglected and hence are not regarded in the further investigation and analysis process of twangs. As the implementation of the CRN-filter consequently extends the signal due to the thruster activation-deactivation processes to an unknown extent we decided to disregard ±30 s of the ACC1A data with respect to the thruster events. This time-span was regarded as a safe amount of time in order to avoid a possible thruster induced impact. Due to the enormous amount of twangs per day and the broad availability of ACC1A data covering several years, we are left with a sufficient amount of twangs in order to carry out a successful investigation, so that this time saving approach is justified.
8.2.2 RMS-ratio detection approach
This approach was already used by Hudson (2003) in order to implement a fast tool to detect twangs within ACC1A data. The RMS-ratio detection is an automated process in order to detect a wide sample of twangs within the radial component of the ACC1A data. In principle, the RM S1 of one second interval is computed and then compared to the RM S2 of the following one second interval, described by the following equation:
RM S2
RM S1
= α, (8.1)
α > αRM S. (8.2)
αRM S is a previously arbitrary defined threshold. Ifα exceeds αRM S we flag a twang within the ACC1A data. The higher the ratio, the more likely a twang is identified by the this approach.
The threshold in our case was chosen to be 1.17. If this threshold was exceeded, the corresponding
8.2 Identification 65
Figure 8.4: Introduction of the reconstruction filter (sinc, Lanczos and Gaussian).
time ofαRM S was considered to be the start of a twang. The threshold of 1.17 was validated, as the detected signal was still clearly above noise level. If the preliminary steps described in the previous section are not carried out, however, this ratio-threshold needs to be considerably higher (approx. 1.4) in order to avoid signals due to other sources, yielding falsely detected twangs or noticeably less twangs detected. With this approach averagely 420 twangs per day could be securely identified for GRACE A, and about 270 twangs per day for GRACE B.
8.2.3 Classification with cross-correlation
After having identified a significant number of representative twangs from ACC1A data by means of the RMS-ratio approach described above it is necessary to distinguish between different types of twangs. The two main types the following studies are based upon, ‘positive’ and ‘negative’
twangs, have been previously introduced. A reliable and feasible approach in order to give evidence for the existence of two main types is using normalized cross-correlation. A normalized cross-correlation does not only detect signals with the same orientation and similar shape, but also puts emphasis onto the ratios of the different amplitudes of peaks within a twang. This means that a twang needs to be very similar in shape (such as the peak ratio), duration and amplitude in order to be found by means of a normalized cross-correlation with our model. Any twang or twang-like signal, that has been previously chosen, may serve as a model used for this approach. Naturally, it is proficient to start with a signal that might represent the majority of the twangs. The previously introduced figure 8.2 shows superimposed twangs of the same orientation, i.e. type, respectively. The time in this figure is related to the time of the reference twang and the superimposed data has been shifted in time according to the highest cross-correlation coefficient.
However, in order to determine this maximum effectively it is necessary to re-sample the signal as the nominal 10 Hz sampling of ACC1A data is too sparse. We found a re-sampling of the signal to 100 Hz to be sufficient in order to carry out the cross-correlation approach. Not only the model twang that one is intending to detect within ACC1A data needs to be reconstructed to such a higher sampling, but in fact the whole ACC1A data itself needs to be reconstructed, yielding temporary but very large volume of data. There is a range of reconstruction filters that may be applied in order to re-sample a given signal – figure 8.4 represents the three most commonly used filters in this regard, which are the sinc filter, the Lanczos filter and the Gaussian filter. Based on the experience of the heater and magnetic torquer investigations, we expect that
66 8.2 Identification
Figure 8.5: Reconstruction-filter applied to a negative twang found in radial of ACC1A of GRACE B on April 1, 2008.
a twang consists of the two main peaks as described before and that these three reconstruction filters should be sufficient to match the underlaying physics. Figure 8.5 displays these three filters applied to a twang found in the 10 Hz sampled ACC1A data. It is obvious that the sinc filter intends to restore the actual amplitude of the twang most accurately. However, the sinc filter does also enhance the 100 Hz signal with artifacts prior and post the visible twang in 10 Hz data, for which there is indeed no evidence of an actual signal within ACC1A data. The Lanczos filter is a more moderate approach, with less artifacts and a slightly under-represented amplitude considering the sinc reconstruction. We chose the Gaussian filter as a reconstruction filter, as it does not enhance the reconstructed signal with any artifacts outside the actual twang.
However, it does not fully resolve the amplitude of the twang. Yet, as we are needing the signal for a normalized cross-correlation, the absolute amplitude is not of importance, but only the restoration of the ratio of the amplitudes of the different peak of one twang. Artifacts post and prior to the signal, as they would be present by the application of the sinc and Lanczos filters, might affect the results of the cross-correlation approach and are hence less suitable to access this problem.
Figures 8.2 already made it obvious that the period of the spikes of the twangs is identical and only the amplitudes are varying. This behavior applies for both positive and negative twangs.
Approximately 90 per cent of all twangs previously detected with the RMS-ratio approach could be related to any of these two types. As for the remaining twangs, we believe that a majority of these signals may be impacted by other signals or noise, or simply appeared at a time that the sampling of the accelerometer made it impossible to represent the shape of the twang to a sufficient level.