Part I. Near-source acoustic coupling between the atmosphere and the solid earth during volcanic eruptions. Part II. Nearfield normal mode amplitude anomalies of the Landers earthquake

This thesis consists of two parts. In the first part, the normal mode theory of a spherical Earth model is extended to include the atmosphere. Harmonic ground motions were observed worldwide during the eruption of Mt. Pinatubo in 1991 with distinct periods at 230 s and 270 s. During the eruption of Mt. St. Helens, barographic pressure change with a period of 300 s was recorded. The normal mode theory is applied to understand the mechanism of the air-ground acoustic coupling during volcanic eruptions, and to construct synthetic ground motions. Long-horizontal wavelength acoustic modes can couple to the fundamental mode Rayleigh waves at two distinct periods of 270 and 230 sec. Those waves are the gravest mode and the first over tone acoustic mode of the Earth's atmosphere. The wave with a period 300 s is the gravity mode trapped in the stratosphere and does not couple to the ground efficiently. We estimated the total energy release from the 1991 Mt. Pinatubo eruption to excite the atmospheric waves at about 10{dollar}sp{lcub}19{rcub}{dollar} J.; In the second part, the fully developed normal mode theory for 3D Earth models is applied to understand the nearfield amplitude anomalies of the 1992 Landers earthquake. Large spheroidal mode amplitude anomalies, up to 600 s, are observed in Southern California after the waves traveled around the Earth. The synthetic seismograms for the recently-available three dimensional seismic global Earth models are constructed using the variational method, and can explain the large nearfield normal mode amplitude anomalies of spheroidal modes observed for the Landers earthquake in Southern California. The vertical component seismogram, that is located near the epicenter of an earthquake with a vertical strike source mechanism, is very sensitive to the shallow large scale lateral heterogeneity with angular order 2, such as global variations of crustal thickness and upper mantle seismic velocity lateral heterogeneity. The contribution from the crustal structure to the amplitude anomalies is as large as those from the whole mantle structure. However, for a thrust or normal fault type source mechanism, the waveforms near the epicenter are explained well with an 1D Earth model.