# Numerical Modeling of Coseismic Tropospheric Disturbances Arising from the Unstable Acoustic Gravity Wave Energetics

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results

- Stable+GWs: Simulation of GWs with the stable temperature profile,
- Unstable+GWs: Simulation of GWs with the unstable temperature profile without the inclusion of CI,
- Unstable+GWs+CI: Simulation of GWs with the unstable temperature profile and the inclusion of CI

## 4. Discussion

## 5. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CTDs | Co-seismic Tropospheric Disturbances |

GNSS | Global Navigation Satellite System |

AGWs | Acoustic Gravity Waves |

GWs | Gravity Waves |

CI | Convective Instability |

TRD | Tropospheric Range Delay |

## Appendix A. Wave Equation of the Acoustic Gravity Waves

#### Appendix A.1. Governing Equations in Space

#### Appendix A.2. Governing Equations in Time

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**Figure 1.**The ground vertical velocity V${}_{\mathrm{SISM}}$ associated with the earthquake of magnitude 8 (Here the seismic waveform of 2008 Wenchuan earthquake is considered).

**Figure 2.**Ambient conditions derived from the NRLMSISE model. In (

**A**,

**B**), atmospheric density and temperature are shown. Two temperature profiles represent covectively stable and unstable troposphere.

**Figure 3.**Temperature lapse rate (${\gamma}_{e}$) in red and adiabatic lapse rate (${\gamma}_{ad}$) in green, are shown. The dashed and solid curves correspond to the stable and unstable temperature profiles.

**Figure 4.**Frequency spectrum of the amplitude ${u}_{y}$ of GWs at each 2 km in 0–20 km altitude range. The spectral amplitudes are normalized to the maximum spectral amplitude at the ground. For better visualization, the line plots are multiplied by 0.5. The black circles represent the Brunt-Vaisala periods.

**Figure 5.**Vertical Travel Time diagram above the epicenter: It shows the CTDs from the stable GWs case and unstable GWs case in (

**A**,

**B**) respectively. CTDs defined as expression (6) is plotted in two types of format: as line plot at each height and as color pixmap. For better visualization, CTDs in line plot is multiplied by factor 0.2.

**Figure 6.**Vertical Travel Time diagram above the epicenter: it shows the CTDs from the unstable GWs+CI case. CTDs defined as expression (6) is plotted in two types of format: as line plot at each height and as color pixmap. For better visualization, CTDs in line plot is multiplied by factor 0.2.

**Figure 7.**It presents snapshots of spatial distribution of CTDs as pixmaps and growth rate of CI as contours for the Unstable GWs+CI case. The growth rate increases from yellow to red colors.

**Figure 8.**It presents the time vs. pressure disturbances over the epicenter. The curves correspond to the ground pressure disturbance and mean pressure disturbance from lower tropospheric altitudes between 1 and 15 km.

**Figure 9.**It demonstrates the time vs. Residual-Refractivity and time vs. Residual-TRD over the epicenter.

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**MDPI and ACS Style**

Kherani, E.A.; Sanchez, S.A.; de Paula, E.R.
Numerical Modeling of Coseismic Tropospheric Disturbances Arising from the Unstable Acoustic Gravity Wave Energetics. *Atmosphere* **2021**, *12*, 765.
https://doi.org/10.3390/atmos12060765

**AMA Style**

Kherani EA, Sanchez SA, de Paula ER.
Numerical Modeling of Coseismic Tropospheric Disturbances Arising from the Unstable Acoustic Gravity Wave Energetics. *Atmosphere*. 2021; 12(6):765.
https://doi.org/10.3390/atmos12060765

**Chicago/Turabian Style**

Kherani, Esfhan A., Saul A. Sanchez, and Eurico R. de Paula.
2021. "Numerical Modeling of Coseismic Tropospheric Disturbances Arising from the Unstable Acoustic Gravity Wave Energetics" *Atmosphere* 12, no. 6: 765.
https://doi.org/10.3390/atmos12060765