# Corrected Tilt Calculation for Atmospheric Pressure-Induced Seismic Noise
## 4 Discussion  
A thorough review of literature which cites [PERSON] [3] using SCOPUS and Google Scholar was performed and the literature studied to see if the use of the incomplete expression for tilt had a significant impact on the published results. The majority of the papers do not involve detailed calculations of the tilt contribution below the surface. These papers are divided into five classes which are analyzed in the following paragraphs:  
Many papers just quote [PERSON] [3] for the existence of horizontal and vertical displacements due to atmospheric pressure fluctuations on the earth's surface [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49]. The correction has no effect on the results of these papers. A second set of papers refers to [PERSON]'s [3] prediction of the exponential attenuation of the vertical and tilt contributions as a means of reducing noise on geophones, but do not perform any calculations with the equations [13; 18; 21; 25; 33; 38; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62]. Again, the details of the tilt decay with depth are inconsequential to the validity of these papers. Note that some of these papers are also included in the first set. Figure 4: Ratio of total horizontal displacement (solid line) to vertical displacement at surface and vertical displacement (dotted line) to vertical displacement at surface at different depths for period of (**a**) 1 s, (**b**) 5 s, (**c**) 10 s, (**d**) 20 s, and (**e**) 40 s for model parameter with \(\frac{\lambda+2\mu}{\lambda+\mu}=1.5\). A third set of papers are concerned with seismic surface noise on other planets [63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78]. The constraints of planetary exploration limit the placement of the seismometers to the surface where [PERSON]'s [3] tilt calculation is correct; these are not affected by the correction discussed in this paper. An interesting extension of [PERSON]'s principles to dust devil detection is investigated in [57, 63, 69, 75]. A smaller set of papers is those that reference [PERSON] [3] but investigate phenomena outside the range of significance of the tilt correction. Included in this set are Ref. [1] and [2] which investigate seismic wind noise above 1 Hz. At the other extreme are papers [79, 80, 81, 82, 83, 84] which investigate pressure effects on the ground displacement and tilt at very low frequencies (f \(<\) 10\({}^{-3}\) Hz) where the parameter \(\omega\)z/c is negligible even for sensors employed at depths of hundreds of meters. In addition, the gravitational effect of the increased air mass above the sensor dominates the direct vertical displacement at these low frequencies. Four papers adapt [PERSON]'s [3] calculations to sound coupling into the ground. The phase speed of the pressure fluctuations due to sound is on the order of the speed of sound at approximately 330 m/s or higher. For these cases the parameter \(\omega\)z/c will be small, even for moderate frequencies and depths, so the horizontal tilt contribution is approximately the surface value. [PERSON] [85] adapts [PERSON]'s [3] mathematical model to the problem of sonic boom coupling into the ground. [PERSON] [86] studied ambient infrasonic waves and corresponding seismic signals with borehole and surface sensors. [PERSON] [87] used seismic recordings to estimate volcanic explosivity from the infrasound levels inferred from the seismic measurements. [PERSON], [PERSON], and [PERSON] [88] studied ground coupling of atmospheric gravity waves into the ground using [PERSON]'s [3] results for vertical displacement, but did not study any horizontal components. [PERSON]'s own papers subsequent to Ref. [3] do not correct the use of the single gradient instead of the curl for the tilt angle.