Effective sampling in tomographic current mapping using two moving vehicles

Moving vehicle tomography (MVT) is a promising method for obtaining a high-resolution, nearly synoptic ocean image. To map ocean currents efficiently, this study proposes a sampling strategy using the integral data of the field in the xy plane along a set of lines connected by two moving vehicles. In a Radon transform, the line integral data are a function of (u, theta) of the line equation in a form of u = x cox theta + y sin theta. The integral function in the u theta plane is uniformly sampled for designing vehicles' trajectories. To reconstruct the current field perfectly, about 810 projection lines are obtained with a line spacing of 200 m and an angular spacing of 2 degrees. Considering the time required to obtain those projections, a subset of the projection lines in the u theta plane are selected to extract the important features corresponding to low wavenumbers. It results in only 22 ray paths in the xy plane. In the tomographic current inversion using a relatively small number of differential travel times (DTTs), the open-boundary modal analysis (OMA) is applied to obtain the coast-fitting modes that efficiently represent the incompressible and irrotational flows. The OMA-inverted current field reveals a circulation inside and southeastward flow outside the bay. The estimated currents agree with the measurements obtained using acoustic Doppler current profilers (ADCPs) deployed on the moving vehicles. Furthermore, an estimator for combing DTT and ADCP measurements reduces the uncertainties in the inverted currents.