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Wave equation techniques have been an integral part of geophysical imaging workflows to investigate the Earth's subsurface. Least-squares reverse time migration (LSRTM) is a linearized inversion problem that iteratively minimizes a misfit…

A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…

We present different computational approaches for the rapid extraction of the signal parameters of discretely sampled damped sinusoidal signals. We compare time- and frequency-domain-based computational approaches in terms of their accuracy…

Real-time water-level monitoring across many locations is vital for flood response, infrastructure management, and environmental forecasting. Yet many sensing methods rely on fixed instruments - acoustic, radar, camera, or pressure probes -…

We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…

A fundamental challenge in ocean dynamics is disentangling balanced motions and internal waves. Extracting internal tidal (IT) imprints from surface data is a central part of this challenge. Traditional harmonic analysis can fail under…

Reconstructions of sea level prior to the satellite altimeter era are usually derived from tide gauge records; however most algorithms for this assume that modes of sea level variability are stationary which is not true over several…

We perform a statistical analysis of measured time series of sea levels at various coastal locations in the UK, measured at time differences of 15 minutes over the past 20 years. When the astronomical tide and other deterministic components…

Accurate prediction of shallow water flows relies on precise bottom topography data, yet direct bathymetric surveys are expensive and time-consuming. In contrast, remote sensing platforms such as radar or satellite altimetry provide…

Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming and expensive.…

The present work deals with the rational model order reduction method based on the single-point Least-Square (LS) Pad\'e approximation technique introduced in [3]. Algorithmical aspects concerning the construction of the rational LS-Pad\'e…

We apply state-of-the-art computational geometry methods to the problem of reconstructing a time-varying sea surface from tide gauge records. Our work builds on a recent article by Nitzke et al.~(Computers \& Geosciences, 157:104920, 2021)…

Along-track wavenumber spectral densities of sea surface height (SSH) are estimated from Jason-2 altimetry data as a function of spatial location and calendar month, to understand the seasonality of meso- and submesoscale balanced dynamics…

MAGAL lays the foundations for a future constellation of small satellites carrying radar altimeters aiming to improve the understanding of ocean circulation variability at local, regional, and global scales. All necessary tools will be…

Satellite radar altimeters are a key source of observation of ocean surface dynamics. However, current sensor technology and mapping techniques do not yet allow to systematically resolve scales smaller than 100km. With their new sensors,…

This paper presents the first scientific application of local time-stepping (LTS) schemes in the Model for Prediction Across Scales-Ocean (MPAS-O). We use LTS schemes in a single-layer, global ocean model that predicts the storm surge…

When a mechanical wavemaker at one end of a water-wave tank oscillates with a frequency, $\omega_0$, time series of downstream surface waves typically include the dominant frequency (or first harmonic), $\omega_0$, along with the second,…

The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with…

We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…

We propose a Bayesian, noisy-input, spatial-temporal generalised additive model to examine regional relative sea-level (RSL) changes over time. The model provides probabilistic estimates of component drivers of regional RSL change via the…