# Corrected Tilt Calculation for Atmospheric Pressure-Induced Seismic Noise
## 4 Discussion
[PERSON], [PERSON], [PERSON], and [PERSON]'s _\"Earth motion caused by local atmospheric changes\"_[89] is an experimental study which only examines the vertical component of displacement and is unaffected by the correction of the tilt equation. [PERSON] and [PERSON]'s _\"Low-frequency earth motion generated by slowly propagating partially organized fields\"_[90] studies the transfer function between pressure fluctuations and surface displacements. The single-gradient expression given in Equation (21) of the paper is used to develop the measured horizontal displacement. This is correct for surface results, as explained in Section 2. [PERSON] and [PERSON]'s _\"Prediction of pressure-generated earth motion using optimum filters\"_[91] is an experimental paper which examines the correlation between surface pressure fluctuation and surface displacements. Our literature search has not found any correction or extension of the original paper in [PERSON]'s subsequent publications. [PERSON], [PERSON], [PERSON], and [PERSON]'s _\"Characteristics and spatial variability of wind noise on near-surface broadband seismometers\"_[92] investigates correlations between measured wind speed and seismic measurements. We note that the correlations are much shorter than those reported in other papers, but also that the measurement site has many buildings and trees to affect the fetch of the wind, and therefore its correlation properties. Table 2 of this reference displays linear fits to RMS velocity curves versus RMS wind speed measurements. For sensors near the surface, the horizontal components are much larger than the corresponding vertical components which display the results of tilt on the measurements. In contrast, the results reported at 145 m show components of the horizontal and vertical of the same order of magnitude. This may indicate that the attenuation predicted using the full expression for tilt is more realistic than the tilt correction using the single gradient. [PERSON] and [PERSON] in _\"Watching the wind: Seismic data contamination at long periods due to atmospheric pressure-field-induced tilting\"_[93] study the effect of wind-induced tilt on near-surface horizontal data. Their Figure 9 displays the attenuation versus depth of tilt contribution using [PERSON]'s [3] results. The results, using the complete expression, display a zero and a sign change in the total horizontal effective velocity, and much enhanced attenuation in the range displayed. [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] in _\"Seasonal and diurnal variations in long-period noise at SPREE stations: The influence of soil characteristics on shallow stations' performance_\" [94] analyze seismic noise using [PERSON]'s [3] results, but all measurements are near-surface and are therefore not affected by the correct tilt calculation. [PERSON] and [PERSON] in \"_Low-frequency seismic noise characteristics from the analysis of co-located seismic and pressure data_\" [95] use pressure and vertical and horizontal seismic velocity data from stations in the USArray Transportable Array to estimate the rigidity of the surface in the first few hundred meters of depth. [PERSON]'s [3] formulae are used in these calculations. The predicted depth dependence of the vertical velocity is used to argue that the measurement is only sensitive to rigidities nearer to the surface. The implication of the increased attenuation of the tilt contribution discussed in Section 2 is that the horizontal velocity should be determined by the properties closer to the surface than the vertical velocities. The most intriguing paper referencing [PERSON] [3] is [PERSON] and [PERSON]'s \"_Theory for deriving shallow elasticity structure from collocated seismic and pressure data_\" [4]. This paper uses [PERSON]'s assumptions to develop an inversion scheme for estimating ground properties as a function of depth from measurements of the vertical and horizontal seismic velocities, as well as pressure fluctuations at the ground surface.