Full Dispersion Spectrum Inversion (FDSI) reconstructs near-surface velocity structures by directly minimizing the misfit of energy spectra in the dispersion domain. By avoiding the error-prone process of dispersion-curve picking, it enables the joint use of multi-mode information for high-resolution imaging. Different objective functions offer complementary advantages in initial-model robustness and reconstruction resolution, often motivating staged inversion strategies. Neural reparametrization offers an alternative means of improving inversion robustness without switching objective functions, but existing methods often converge slowly and struggle to recover fine-scale details. In addition, static positional encoding (SPE) may introduce high-frequency instability if improperly configured. To address this limitation, we propose an Adaptive Neural Reparametrization Dispersion Spectrum Inversion (ANR-DSI) method. The subsurface velocity model is reparametrized by a coordinate-based multilayer perceptron (MLP), and an adaptive positional encoding (APE) mechanism is incorporated whose frequency weights are updated through gradients propagated from the physical forward operator. By promoting a coarse-to-fine optimization trajectory, this dynamic mechanism enhances inversion robustness by stabilizing large-scale structures first, while simultaneously accelerating the learning of fine-scale features. Experimental results demonstrate that the proposed method effectively mitigates the inversion’s dependence on the initial model, accelerates convergence relative to standard neural reparametrization, and maintains stable performance under noisy conditions. Furthermore, application to a real-world urban distributed acoustic sensing (DAS) dataset confirms its immense potential for near-surface imaging in practical scenarios.
Summary The flow in the liquid core of the Earth is controlled by the interplay between buoyancy and the Coriolis force due to planetary rotation. Fast rotation imposes the Taylor-Proudman Constraint (TPC) that opposes fluid motion across an imaginary cylindrical surface called the Tangent Cylinder (TC) obtained by extruding the equatorial perimeter of the solid inner core along the rotation direction, and up to the core-mantle boundary (CMB). Because this boundary is imaginary, however, mass and heat transfer through the TC, as well as the regimes of convection within the TC may differ from those inside a solid cylinder with well-defined boundary conditions. How to best model this peculiar boundary is to date unclear, and so is how its influence on the flow inside and outside the TC differs from that of canonical boundary conditions. This impedes our understanding of the flow in the polar regions of the core. To clarify this question, we mimic the TC geometry experimentally in the Little Earth Experiment 2 (LEE2), where the CMB is modelled as a cold, cylindrical vessel filled with water, with a hot cylinder inside it acting as the inner solid core. The vessel is filled with water so as to optically map the velocity field in regimes of supercriticality and rotational constraint consistent with those of the Earth (Rayleigh number up to $\widetilde{R\!a}=191$ times critical and ratio of inertial to Coriolis forces in the range 10−3 to 10−1). We find that although the regimes of convection within the TC broadly resemble those within a cylinder with solid impermeable insulating walls (CSIIW), the TC boundary introduces differences of particular significance in the context of the Earth’s core. The main new mechanism arises out of the baroclinicity near the cold lateral boundary of the vessel, which drives inertia at the outer boundary of the TC, as convection in the equatorial regions of the Earth’s core does. The baroclinicity just outside the TC suppresses the classical wall modes found in CSIIW and the inertia there causes an early breakdown of the TPC at the TC boundary. The breakdown appears locally at low supercriticality $\widetilde{R\!a}\simeq 3$ and then over the entire TC surface at $\widetilde{R\!a}\simeq 36$. The flow remains dominated by the Coriolis force even up to $\widetilde{R\!a}=191$, but inertia near the TC boundary drives a transition to geostrophic turbulence around $\widetilde{R\!a}\simeq 36$. It also promotes the emergence of a few large structures, of similar topology to the flux patches observed in geomagnetic data. The heat flux escapes increasingly through the TC boundary as the TPC there becomes weaker. It eventually bypasses the axial heat flux and homogenises temperature laterally. This translates into a diffusivity-free scaling expressed in terms of the diffusivity-free counterparts of the Nusselt and flux-based Rayleigh numbers as $N\!u^*\sim (R\!a_q^*)^{1/3}$, that is independent of rotation. Hence inertia driven by baroclinicity outside the TC provides a convenient route to geostrophic turbulence, which is otherwise difficult to reach in experiments. These results also highlight a process whereby the convection outside the TC may control turbulence inside it and bypass the axial heat transfer. We finally discuss how Earth’s conditions, especially its magnetic field may change how this process acts within the Earth’s core.
Summary Classical full waveform inversion (FWI) is sensitive to kinematic inaccuracies in the initial velocity model, converging to local minima due to cycle skipping when low-frequency data are absent. The recently developed deep-learning-matching FWI (DLM-FWI) framework mitigates this by dynamically bridging the phase gap between synthetic and observed data, utilizing a convolutional neural network (CNN) within the inversion loop as a robust kinematic preconditioner. However, because standard deep learning (DL) automatic differentiation (AD) engines scale poorly to large-scale wave equations, deploying DLM-FWI on practical field-scale data has been computationally prohibitive. To overcome this, we introduce a memory-efficient, hybrid computational workflow that interfaces the Flux machine-learning ecosystem with the Julia Devito Inversion framework (JUDI) finite-difference library. By decoupling the network’s AD graph from the physical solver and evaluating the chain rule strictly in the data domain, we avoid storing massive spatiotemporal wavefield histories. After verifying that this decoupled architecture maintains resilience to source-wavelet mismatch and ambient noise on the Marmousi2 synthetic model, we apply the workflow to the Mobil AVO Viking Graben Line 12 marine dataset to evaluate its practical scalability. Compared to classical L-BFGS FWI, the field-scale DLM-FWI results exhibit robust convergence, mitigation of shallow cycle-skipped artifacts, and geologically coherent structural continuity. This study addresses the gap between small-scale synthetic DL studies and field-scale 2D implementations, demonstrating that physics-guided matching strategies can be deployed in practice to improve FWI robustness on complex field datasets.
Summary Before inverting the Moho topography, the Parker-Oldenburg method requires the determination of appropriate inversion parameters, exponential term and low-pass filtering, in order to minimise the artificial smoothing introduced by these factors, which would suppress the genuine short-wavelength undulations of Moho topography. Previous research has tended to focus on addressing the individual impact of a single factor, whilst neglecting other factors. To address this, we proposed the PO-PSO method. This method builds upon the Parker-Oldenburg method, employing a particle swarm optimisation to determine the correction terms of Moho topography, thereby restoring the high-frequency features within the Moho topography. Synthetic tests show that, compared with the Parker-Oldenburg method, the Moho topography obtained by PO-PSO is closer to the synthetic model under both noise-free and noisy conditions, with an improvement in accuracy of 30∼32%. In practice, we utilised PO-PSO to invert the Moho topography of South China Sea. The results reveal that the Moho topography in the study area ranges from 4.59 to 27.85 km. When compared against multiple seismic profiles, the root mean square error of final model was 1.57 km. This represents an 11.8% improvement in accuracy compared to the initial model.
Summary It is shown how the equations of magnetohydrodynamics within an aspherical body diffeomorphic to a ball may be posed with respect to a fixed spherical reference domain. Transforming the equations onto this computational domain produces what we term “referential” equations, which are more algebraically complicated than their physical cousins; on the other hand, the computational gain of this approach is to permit the use of powerful spectral representations of scalar fields on the unit ball, representations that are not readily available in aspherical geometries. The referential equations are derived and schematic discussion is given regarding aspects of their numerical solution. A numerical proof of concept then compares the proposed referential approach with body-fitted spectral-element calculations. For small and moderate departures from spherical symmetry the former is substantially cheaper at fixed accuracy, while its advantage diminishes as the deformation grows. The remaining numerical issues involved in extending this approach to full time-dependent MHD are then discussed.
