The In Situ Evaluation of the SEIS Noise Model

Abstract

Mimoun et al. (Space Sci Rev 211(1–4):383–428, 2017) developed a pre-landing noise model of the Martian seismometer package SEIS onboard InSight that analysed all the external and internal noise sources. We updated the environmental and instrumental parameters of the model as well as the ground properties with InSight mission data. We compared the output of the in situ noise model to the actual noise measured during the full mission for each individual noise source as well as for the full noise model. We evaluate in detail the efficiency of the model to fit the measured data and discuss the transient noise and other sources that were not included in the model. The main noise sources in the seismic bandwidth are the pressure noise and the lander noise, which is increased from the pre-landing model and overestimated when compared to the data; the magnetic field noise was overestimated in the pre-landing model and is now found to be negligible. The conclusions and models from this study could benefit future space missions.

Appendices

Appendix A: Minor Contributors Unchanged from Mimoun et al. (2017)

The self noise and the acquisition noise are modelled the same way as in (Mimoun et al. 2017). They are shown on Fig. 18 for the self noise and Fig. 19 for the acquisition noise. Some of the noise at night is at the self noise level.

Fig. 18

Self noise model, printed over the measured seismic noise, shown as a Probabilistic Amplitude Spectral Density, divided into day (6 a.m. - 6 p.m. LTST, a, b) and night (6 p.m. - 6 a.m. LTST, c, d) and horizontal (a, c) and vertical (b, d) components. The color indicates the probability density of the mission noise over the selected (vertical) frequency bin; the red color corresponds to a 1.5% probability density, while the dark blue is a 0% probability density. The self noise model is shown in a solid white line

Fig. 19

Acquisition noise model, printed over the measured seismic noise, shown as a Probabilistic Amplitude Spectral Density, divided into day (6 a.m. - 6 p.m. LTST, a, b) and night (6 p.m. - 6 a.m. LTST, c, d) and horizontal (a, c) and vertical (b, d) components. The color indicates the probability density of the mission noise over the selected (vertical) frequency bin; the red color corresponds to a 1.5% probability density, while the dark blue is a 0% probability density. The acquisition noise model is shown in a solid white line

Appendix B: Comparison Between Environment Assumptions from Mimoun et al. (2017) and Measurements

This appendix compares the actual environment characteristics spectral measurements by InSight to the models of Mimoun et al. (2017). The magnetic field assumptions are shown on Fig. 20, the wind speed squared on Fig. 21 and the temperature inside the WTS is shown on Fig. 22.

Fig. 20

Comparison between the measured magnetic field (background, in color) and the assumptions from Mimoun et al. (2017) in white lines. For this figure and the following ones, the solid line is for the median model, the dashed one is for the $1\sigma$ model, and the dotted line show the $3\sigma$ model

Fig. 21

Comparison between the measured wind speed squared (background, in color) and the assumptions from Mimoun et al. (2017) in white lines

Fig. 22

Comparison between the SCIT, which measures the temperature inside the WTS (background, in color) and the assumptions from Mimoun et al. (2017) in white lines

The differences between the SCIT and the assumptions from Mimoun et al. (2017) can be explained by Fig. 23, which shows that the first order low-pass filter model of the WTS is insufficient. In particular, the slope and amplitude of the SCIT is not fitted well by the atmospheric temperature filtered by a modelled WTS.

Fig. 23

Atmospheric temperature ASD (blue), and atmospheric temperature filtered by the WTS first-order lowpass filter model (dashed yellow), compared to the ASD of the SCIT (red)

Appendix C: Environment Parameters Detailed Assumptions

3.1 C.1 Wind Probabilistic ASD

The ASD of the wind speed squared is computed for all the mission duration (using TWINS data at 1 sample per second, via a Welch’s power spectral density estimate algorithm with a 10-minute long Hamming window and $50\%$ overlap, see Sect. 2). A bimodal Gaussian distribution is fitted to the data, for each frequency bin. Figure 24 shows a vertical cut through the probabilistic ASD of Fig. 6, at frequency $4.4\times10^{-2} \text{ Hz}$, i.e. the distribution of the wind speed squared ASD values for the frequency bin at $4.4\times10^{-2} \text{ Hz}$.

Fig. 24

Distribution of the wind speed squared ASD, for day (a) and for night (b), and fits with a bimodal distribution. The frequency for this plot is $4.4\times10^{-2} \text{ Hz}$ (see text for details)

3.2 C.2 Wind Speed

The wind speed on Mars is often modelled with a Weibull distribution (Lorenz 1996). Figure 25 shows the statistics of the wind speed as measured by the TWINS instrument, and the fitted Weibull distribution for day and night, with the median and $\pm 1 \sigma$ values. The parameters of the fitted Weibull distribution are coherent with those found by Viúdez-Moreiras et al. (2022), as shown in Table 9. The differences are most likely due to the different datasets used (different start and end times and data selection), but the overall values and evolution with local time remain consistent.

Fig. 25

Distribution of the wind speed, for day (a) and for night (b), and fits with a Weibull distribution

Table 9 Values of the shape and scale parameters of the Weibull distributions for the wind speed between several local times; values for Viúdez-Moreiras et al. (2022) compared to values found in this work

3.3 C.3 Wind Direction

Figure 26 shows the statistics of the wind direction as measured by the TWINS instrument. The highest peak has been chosen for each period for the lander noise calculation. A more complex model could take into account the variation of angle with each hour and throughout the year, but this was not included in this work since it is more advanced than what was done in Mimoun et al. (2017).

Fig. 26

Distribution of the wind direction, for day (a) and for night (b)

3.4 C.4 Ground Structure and Compliance

Figure 27 shows the ground structure used for the modelling of the pressure noise and the lander noise. The structure below the surface is extracted from Carrasco et al. (2023). From this structure, we model the horizontal and vertical compliance below, as well as the tilt compliance entering in the computation of the horizontal pressure noise (Fig. 28).

Fig. 27

Ground structure below InSight. The crosses at 0 m depth are the HP³ hammering experiment measurements at the surface, used for the lander noise

Fig. 28

Compliance modelled from the ground structure

Appendix D: Probability Distributions of the Measured Noise and Some Noise Sources at 0.1 Hz and 0.9 Hz

In order to have a better picture of the measured noise and the modelled noise, we plot a vertical cut through the probabilistic ASD of Fig. 2 for two frequencies, showing the probability distribution of the noise sources and the histogram of the noise. The two selected frequencies are 0.1 Hz and 0.9 Hz (and not 1 Hz to avoid the tick noise). We model the noise sources as Gaussian distributions, but this is only an approximation: the computations in the model only estimate the median and $\pm 1 \sigma$ for each noise source, not the full distribution. We show the results in Figs. 29, 30, 31 and 32 for each component and day and night.

Fig. 29

Histogram of the horizontal daytime measured noise in grey bars for two frequencies, 0.1 Hz (left) and 0.9 Hz (right). This corresponds to a vertical cut through the probabilistic ASD of Fig. 2. Over the histogram are shown the models of some noise sources and the full noise at the frequencies studied. The distributions chosen there are Gaussian distributions with the same median and $\pm 1 \sigma$ as the modelled noise, although it only is an approximation of the actual noise distribution. The probability density has been normalized to a maximum of 1 for each noise for clarity. Values of ASD below $10^{-10}~\text{m}\,\text{s}^{-2}\,\text{Hz}^{-0.5}$ are shown to include the magnetic field noise but are non-physical because they are below the acquisition noise

Fig. 30

Histogram of the horizontal nighttime measured noise in grey bars for two frequencies, 0.1 Hz (left) and 0.9 Hz (right). This corresponds to a vertical cut through the probabilistic ASD of Fig. 2. Over the histogram are shown the models of some noise sources and the full noise at the frequencies studied. The distributions chosen there are Gaussian distributions with the same median and $\pm 1 \sigma$ as the modelled noise, although it only is an approximation of the actual noise distribution. The probability density has been normalized to a maximum of 1 for each noise for clarity. Values of ASD below $10^{-10}~\text{m}\,\text{s}^{-2}\,\text{Hz}^{-0.5}$ are shown to include the magnetic field noise but are non-physical because they are below the acquisition noise

Fig. 31

Histogram of the vertical daytime measured noise in grey bars for two frequencies, 0.1 Hz (left) and 0.9 Hz (right). This corresponds to a vertical cut through the probabilistic ASD of Fig. 2. Over the histogram are shown the models of some noise sources and the full noise at the frequencies studied. The distributions chosen there are Gaussian distributions with the same median and $\pm 1 \sigma$ as the modelled noise, although it only is an approximation of the actual noise distribution. The probability density has been normalized to a maximum of 1 for each noise for clarity. Values of ASD below $10^{-10}~\text{m}\,\text{s}^{-2}\,\text{Hz}^{-0.5}$ are shown to include the magnetic field noise but are non-physical because they are below the acquisition noise

Fig. 32

Histogram of the vertical nighttime measured noise in grey bars for two frequencies, 0.1 Hz (left) and 0.9 Hz (right). This corresponds to a vertical cut through the probabilistic ASD of Fig. 2. Over the histogram are shown the models of some noise sources and the full noise at the frequencies studied. The distributions chosen there are Gaussian distributions with the same median and $\pm 1 \sigma$ as the modelled noise, although it only is an approximation of the actual noise distribution. The probability density has been normalized to a maximum of 1 for each noise for clarity. Values of ASD below $10^{-10}~\text{m}\,\text{s}^{-2}\,\text{Hz}^{-0.5}$ are shown to include the magnetic field noise but are non-physical because they are below the acquisition noise

Appendix E: Noise Before Deployment of the Wind and Thermal Shield

The VBB measurements before the deployment of the Wind and Thermal Shield allow to characterise the noise without the WTS, and therefore generated by the wind drag on the seismometer. There are a few caveats to the comparison to the noise for the full mission which has been done on Fig. 33: first of all, the different instrument mode used (the instrument is in engineering mode before the WTS installation and scientific mode after that, with a different self noise); also, there are fewer data before the installation of the WTS, and the data are not continuously recorded throughout the day.

Fig. 33

Noise measured before the deployment of the Wind and Thermal Shield, as measured by the VBBs in Engineering mode. The day and night noise have been merged. The noise during the day after the deployment of the WTS is shown in white lines (solid lines for the mean noise, dashed lines for $\pm 1 \sigma$. (a) shows the noise on the horizontal components and (b) the noise on the vertical. The drop at frequencies lower than $10^{-2}\text{ Hz}$ is due to filtering in post-processing