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Virtual-source surface wave responses can be retrieved using the crosscorrelation (CC) of wavefields observed at two receivers. Higher mode surface waves cannot be properly retrieved when there is a lack of subsurface sources that excite these wavefields, as is often the case. In this paper, we present a multidimensional-deconvolution (MDD) scheme that is based on an approximate convolution theorem. The scheme introduces an additional processing step in which the CC result is deconvolved by a so-called point-spread tensor. The involved point-spread functions capture the imprint of the lack of subsurface sources and possible anelastic effects, and quantify the associated spatial and temporal smearing of the virtual-source components that leads to the poor surface wave retrieval. The functions can be calculated from the same wavefields as used in the CC method. For a 2-D example that is representative of the envisaged applications, we show that the deconvolution partially corrects for the smearing. The retrieved virtual-source response only has some amplitude error in the ideal situation of having the depth of the required vertical array equal to the depth penetration of the surface waves. The error is due to ignored cross-mode terms in the approximate convolution theorem. Shorter arrays are also possible. In the limit case of only a single surface receiver, the retrieved virtual-source response is still more accurate than the CC result. The MDD scheme is valid for horizontally layered media that are laterally invariant, and includes exclusively multicomponent point-force responses (rather than their spatial derivatives) and multicomponent observations. The improved retrieval of multimode surface waves can facilitate dispersion analyses in shallow-subsurface inversion problems and monitoring, and surface wave removal algorithms. [ABSTRACT FROM AUTHOR]

To meet the political goals regarding renewable energy production, offshore wind keeps expanding to waters with larger depths and harsher conditions, while the turbine size continues to grow and ever-larger foundation structures are required. This development can only be successful if further cuts in the levelized cost of energy are established. Regarding the design of the foundation structures, a particular challenge in this respect relates to the reduction of the total computational time required for the design. For both practical and commercial reasons, the decoupled modelling of offshore wind support structures finds a common application, especially during the preliminary design stage. This modelling approach aims at capturing the relevant characteristics of the different environment-structure interactions, while reducing the complexity as much as possible. This paper presents a comprehensive review of the state-of-the-art modelling approaches of environmental interactions with offshore wind support structures. In this respect, the primary focus is on the monopile foundation, as this concept is expected to remain the prominent solution in the years to come. Current challenges in the field are identified, considering as well the engineering practice and the insights obtained from code comparison studies and experimental validations. It is concluded that the decoupled analysis provides valuable modelling perspectives, in particular for the preliminary design stage. In the further development of the different modelling strategies, however, the trade-off with computational costs should always be kept in mind. [ABSTRACT FROM AUTHOR]