Geodetic observations provide a measure of surface deformation caused by underground geophysical processes. GPS and InSAR are the most two widely used geodetic techniques, and are often combined because of their complementary advantages. This dissertation presents several methods and study cases to detect and model transient deformation recorded by GPS and InSAR measurements.A time-dependent inversion filter based on the unscented Kalman filter is developed to combine InSAR and GPS measurements for volcano deformation modeling. The InSAR and GPS data at Okmok since the 2008 eruption shows a shallow magma system to be sill-like structure at ̃0.9 km and a Mogi source at ̃3.2 km depth. The shallow sill structure was not seen before the 2008 eruption. Five inflation episodes have been observed from 2008 to 2019, each decaying exponentially in time. A hydraulic model with the episodically increasing pressure of the deep magma reservoir and increasing influx from deep to shallow sources volcano is discussed to explain consecutive inflation events.Most of the available InSAR and GPS data, including campaign GPS, continuous GPS, single InSAR and InSAR times series, are used to recover the magma supply history of Akutan, Makushin and Westdahl volcano over the past 20-25 years since the first geodetic measurements were made there. The time-dependent volume changes show diverse temporal patterns across the three volcanoes. A small residual velocity signal is extracted by comparing the estimated regional velocity to the current block models. Two possible coupling models are tested to explain the residual velocity signal as a result of slip deficit on the megathrust.A sequence-to-sequence ML method is proposed to detect the transient signals in GPS time series. The model is trained using synthetic data time series that are relatively short in length but can be applied to time series of arbitrary length. The model is validated by being applied to some real-world datasets containing transient signals with various characteristics. By decimating a time series to a lower data rate to effectively compress time, the model is able to recognize long-duration transients even when it has been trained only on short-duration transients. This indicates the similarity in nature between the short and long transients.
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