The finite-element method can easily handle complicated geometries because of the application of unstructured meshes. Unlike the Cartesian grid used in the finite-difference method, the unstructured mesh can follow the sharp interfaces that separate two layers of different properties. Therefore, the finite-element method can provide more accurate solutions for the simulation of seismic wave propagation. Meshes of good quality are required for the finite-element simulation. However, it is not trivial to set up an appropriate mesh. First of all, the mesh should contain elements of good shapes and sizes. In addition, the sharp interfaces should coincide with the edges of the elements instead of intersecting with them. These requirements are formulated as an optimization problem with three terms, measuring the difference between the actual and prescribed scaling field, shape quality, and the area between prescribed curves and the nearest triangle edges. The solution of the optimization problem should provide the desired mesh. The mesh generator MESH2D was applied to obtain an initial mesh. The Matlab function minFunc was used to search for the minimum of the constructed objective function. Three weights balance the three terms in the objective function. When it comes to complicated models, these weights have to be chosen carefully to produce a reasonable mesh.

Marine seismic acquisition is troubled with several factors of noise that can deteriorate seismic data. Marine seismic data are recorded with towed streamers that acquire the desired upgoing wavefields containing information of the geology beneath. The upgoing wavefield will travel past the streamer/hydrophone to be reflected at the sea surface and propagate back down to be collected as undesired downgoing (ghost) wavefields, before propagating further downward as a surface related multiple. Because up- and downgoing wavefields interfere, these ghost wavefields generate peaks and notches in the recorded amplitude spectrum that compromises the bandwidth, reducing the resolution and the interpretability of the seismic data. Two classes of ghosts exist - source and receiver - that can be removed (’deghosting’) through two main approaches; utilizing different acquisition strategies and/or computer based processing algorithms. Additional measurements may prove useful in acquiring broadband data but may be hampered by high costs and limited availability. Vast amounts of 2-D single streamer legacy data exist that can still benefit from enhanced deghosting techniques. Acquisition uncertainties, such as the unknown exact depth of sources and receivers, the unknown reflectivity of the free-surfaces, and the unknown propagation velocity of seismic waves in water, lead to an increased complexity in finding a solution to the deghosting problem. In this thesis, sensitivity analysis has shown that a variability in the propagation velocity of seismic waves in water has the greatest effect on the conventional 2D receiver deghosting result. The least sensitive parameter turned out to be the water surface reflectivity. A multitude of adaptive deghosting techniques - which optimize the parameter settings through data driven optimization - have been found in literature and are summarized to identify the shortcomings. A quantitative uncertainty analysis into these methods seems to be missing. A new adaptive deghosting method based on echo-deblending is introduced that incorporates an uncertainty analysis. Results look promising for determining receiver depths, however, the water surface reflectivities results are more challenging. Recommendations for future work to improve the method are given for future students pursuing the topic.