Pseudo interface waves can exist at the interface of a fluid and a fluid-saturated poroelastic solid. These waves are typically related to the pseudo-Rayleigh pole and the pseudo-Stoneley pole in the complex slowness plane. It is found that each of these two poles can contribute ͑as a residue͒ to a full transient wave motion when the corresponding Fourier integral is computed on the principal Riemann sheet. This contradicts the generally accepted explanation that a pseudo interface wave originates from a pole on a nonprincipal Riemann sheet. It is also shown that part of the physical properties of a pseudo interface wave can be captured by loop integrals along the branch cuts in the complex slowness plane. Moreover, it is observed that the pseudo-Stoneley pole is not always present on the principal Riemann sheet depending also on frequency rather than on the contrast in material parameters only. Finally, it is shown that two additional zeroes of the poroelastic Stoneley dispersion equation, which are comparable with the P -poles known in nonporous elastic solids, do have physical significance due to their residue contributions to a full point-force response.

A procedure is presented for the derivation of an effective small-strain soil stiffness governing the soil-structure interaction of large-diameter monopiles. As a first step, geophysical measurements are used to estimate the depth-dependent shear modulus G of the soil stratum. The second step is to use this modulus and an estimated Poisson's ratio and density in a 3D model, which captures the deformation of both the monopile and the soil. As a final step, a new method is proposed to use the computed 3D response for identification of a depth dependent stiffness of an effective Winkler foundation. This stiffness can be used in a 1D model, which is more fit for design purposes. The presented procedure is deemed more appropriate than the often used "p-y curve" method, which was once calibrated for slender flexible piles and for which the input is based on the large-strain cone penetration test. The three steps are demonstrated for a particular design location. It is also shown that the displacements of the 3D model are smaller and the resulting fundamental natural frequency is higher than calculated with the p-y method.

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 virtualsource 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.

Retrieving virtual source surface waves from ambient seismic noise by cross correlation assumes, among others, that the noise field is equipartitioned and the medium is lossless. Violation of these assumptions reduces the accuracy of the retrieved waves. A point‐spread function computed from the same ambient noise quantifies the associated virtual source's spatial and temporal smearing. Multidimensional deconvolution (MDD) of the retrieved surface waves by this function has been shown to improve the virtual source's focusing and the accuracy of the retrieved waves using synthetic data. We tested MDD on data recorded during the Batholiths experiment, a passive deployment of broadband seismic sensors in British Columbia, Canada. The array consisted of two approximately linear station lines. Using 4 months of recordings, we retrieved fundamental‐mode Rayleigh waves (0.05–0.27 Hz). We only used noise time windows dominated by waves that traverse the northern line before reaching the southern (2.5% of all data). Compared to the conventional cross‐correlation result based on this subset, the MDD waveforms are better localized and have significantly higher signal‐to‐noise ratio. Furthermore, MDD corrects the phase, and the spatial deconvolution fills in a spectral (f, k domain) gap between the single‐frequency and double‐frequency microseism bands. Frequency whitening of the noise also fills the gap in the cross‐correlation result, but the signal‐to‐noise ratio of the MDD result remains higher. Comparison of the extracted phase velocities shows some differences between the methods, also when all data are included in the conventional cross correlation.

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