Seismic tomography has played a crucial role in the illumination of deep Earth structure. Most existing tomographic methods are based on seismic ray theory and hence do not fully account for the true physics of wave propagation. Recent computational advances allow us to embrace the full complexity of seismic wave propagation by accurately solving the 3-D seismic wave equation numerically. This can account for effects such as wavefront healing, interference, scattering and (de)focusing, which are often ignored or not properly captured by other methods such as ray tracing. Thus, such methodologies are particularly suitable for strongly heterogeneous regions such as Southeast Asia, where large variations in elastic parameters are likely to be present. Here, an unprecedented dataset and access to sizeable computational resources allow their application to Southeast Asia for the first time.

In the first part of this thesis, a continental-scale seismic model of the lithosphere and underlying mantle beneath Southeast Asia obtained from adjoint waveform tomography (often referred to as full-waveform inversion or FWI) is presented. FWI is a non-linear imaging method, where an initial model is updated in order to minimise the difference between observed and predicted waveforms. Based on > 3,000 h of analysed waveform data gathered from  13,000 unique source-receiver pairs and filtered at periods between 20 – 150 s, isotropic P-wave velocity, radially anisotropic S-wave velocity and density are imaged via an iterative non-linear inversion that begins from a 1-D reference model. At each iteration, the full 3-D wavefield is determined through an anelastic Earth, accommodating effects of topography, bathymetry and ocean load.

SASSY21, the final model after 87 iterations, appears to be robust since it is able to explain true-amplitude data from events and receivers not included in the inversion. The new model reveals detailed anomalies down to the mantle transition zone, including multiple subduction zones. The most prominent feature is the (Indo-)Australian plate descending beneath Indonesia, which is imaged as one continuous slab along the 180  curvature of the Banda Arc. The tomography confirms the existence of a hole in the slab beneath Mount Tambora and locates a high S-wave velocity zone beneath northern Borneo that may be associated with subduction termination in the mid-late Miocene. A previously undiscovered feature beneath the east coast of Borneo is also revealed, which may be a signature of postsubduction processes, delamination or underthrusting from the formation of Sulawesi.

In the second part of this thesis, SASSY21 is used as a starting model to obtain a more refined image of the eastern Indonesian region, using seismic data filtered at periods from 15 – 150 s. In this study, the fluid ocean is accounted for explicitly by solving a coupled system of the acoustic and elastic wave equation. This is computationally more expensive but allows seismic waves within the water layer to be simulated, which becomes important at shorter periods. The effects arising from surface topography, bathymetry and the fluid ocean on synthetic waveforms become pronounced at periods $\le$ 20 s. In particular, surface elevation can result in a considerable phase advance and change in amplitude of the surface wave train, and has an effect on both horizontal and the vertical seismogram components for this simulation setup. The fluid ocean results in a phase delay as well as a change in amplitudes and duration of the surface wave train, and affects both the radial and vertical components. At periods $\le$ 20 s, accounting for the fluid ocean explicitly can lead to more realistic lithospheric velocities and a more refined image compared to the commonly used ocean load approximation, even at greater depths. Furthermore, it allows for an improved waveform match for source-receiver paths passing partially or entirely through oceanic regions.

The final model, SASSIER22, after 34 iterations reveals a convergent double-subduction along the southern segment of the Philippine Trench, which was not evident in the starting model and transitions to a divergent system in the Molucca Sea further south. A more detailed illumination of the slab beneath the North Sulawesi Trench subduction zone reveals a pronounced positive wavespeed anomaly down to  200 km depth, consistent with the maximum depth of seismicity, and a more diffuse but aseismic positive wavespeed anomaly that continues to the 410 km discontinuity.