Changsoo Shin

We present a recursive-derivative model of consciousness in which mental dynamics are governed by wave-like propagation over a multidimensional delay (memory) space. By embedding threshold-based transitions within a hierarchical recursive structure, the current state of awareness emerges as a compressed summary of layered episodic pasts. This formulation yields a nonlinear wave equation for mental potential, where cross-derivative terms capture memory interaction and recall. Higher-order derivatives correspond to the stability and salience of mental states, enabling a unified interpretation of attention, forgetting, and decision-making. Our results suggest that consciousness may operate not through spatial neural propagation, but through dynamical optimization across structured memory space.

Studying seismic wave propagation through complex media is crucial to numerous aspects of geophysics and engineering including seismic hazard assessment. In particular, small-scale structure such as sedimentary basins and their edges can have significant effects on high-frequency earthquake ground motion, which is the main cause for the damage to buildings and infrastructure. However, such structural effects are poorly understood due to limitations in numerical and analytical methods. To overcome this challenge, for the first time, we utilize the 3D printing technique to build a scaled-down physical representation of geological structure and perform lab-scale seismic experiments on it. Specifically, a physical model based on the Los Angeles Basin is printed and used as synthetic medium to propagate ultrasonic waves, to mimic seismic wave propagation from local earthquakes. Our results show clear body and surface waves recorded at expected time and locations, as well as waves that are scattered from the basin edges. We find that high-frequency energies are significantly reduced at the basin, which is at odds with the conventional view of basins as ground motion amplifiers. This novel waveform modeling approach with 3D printed Earth models is largely automated and provides an effective means to tackle geophysical problems of significance.

Numerical modeling of the 3D acoustic wave equation regularly faces a trade‐off between accuracy and efficiency. Usually, an improved computational efficiency leads to a compromised numerical accuracy, in which the numerical dispersion error increases. Such a trade‐off is commonly reported for the finite difference methods, and the consistent, lumped, eclectic finite element matrices, and the high‐order spectral element methods. Therefore, we present a methodology that simultaneously optimizes both the accuracy and the computational efficiency of the finite element method for modeling the 3D acoustic wave equation in the frequency domain. The numerical dispersion objective function is derived and minimized for a tri‐linear interpolation function of a cube element in terms of the mass and the stiffness matrices. With four grid points per wavelength sampling, for less than 0.5% error in velocities, the optimized modeled solutions outperform the results from extant approaches. Numerical experiments with the homogeneous, 3D unbounded 2‐layer and the 3D Society of Exploration Geophysicists salt velocity models reveal that the optimized accuracy is persistent across all source‐receiver offsets, a performance observably absent from other finite element matrices. The optimized matrices are not only useful for numerical modeling, but are also readily available for accurate computation of the sensitivity matrices of the density and the bulk modulus parameters for the multi‐parameterization inversion.

In the frequency domain, we optimize the entries of the element stiffness matrix computed on a square element with the purpose of approximating the 2D acoustic wave equation with the second spatial order. The optimized matrices are computed from the minimization of the normalized phase velocity as a function of propagation angle and the number of grid points per wavelength, leading to a remarkable reduction in the numerical error. The optimized number of 4.1 sample points in a wavelength, with a maximum error in velocities <0.3%, offering the simulation of large-scale realistic models. The superior performance of the optimized matrices to those from the lumped, consistent and eclectic matrices, is evident from the numerical examples presented, with consequent reduction not only in the numerical dispersion/anisotropy but also in an improved resolution. It is noteworthy that optimized matrices give modeling results with better accuracy than models from the high-order spectral element method. Our methodology is easily extendable to the accurate discretizing of the general 3D elastic wave equation that optimizes the bandwidth of the impedance matrix, availing computational resources for accurately modeling the compressional and shear wave velocities, density, as well as multi-parameter inversion.

We propose seismic elastic full-waveform inversion (EFWI) using both the multiparametric approximate Hessian and the discrete cosine transform (DCT). EFWI is a promising technology for obtaining physical parameters. EFWI using the multiparametric approximate Hessian can suppress crosstalk artifacts for each physical parameter, but the computational burden increases as the number of physical parameters considered increases. In this study, to reduce the computational burden, DCT was used to compress the model parameters and accelerate EFWI in the truncated DCT domain. EFWI using DCT is possible to increase the calculation efficiency by reducing the total number of unknown variables. We implemented EFWI using monoparametric Hessian and multiparametric Hessian, which reduced the computational burden using DCT and conducted tests through numerical experiments using each Hessian. In numerical result, despite using a small number of DCT coefficients, we confirmed that contamination due to crosstalk artifacts was suppressed when EFWI was performed using the multiparametric approximate Hessian.

We have developed compact implicit finite-difference (FD) schemes in the time-space domain based on the second-order FD approximation for accurate solution of the acoustic wave equation in 1D, 2D, and 3D. Our method is based on the weighted linear combination of the second-order FD operators with different spatial orientations to mitigate numerical error anisotropy and the weighted averaging of the mass acceleration term over the grid points of the second-order FD stencil to reduce the overall numerical dispersion error. We have developed a derivation of the schemes for 1D, 2D, and 3D cases. We obtain their corresponding dispersion equations, then we find the optimum weights by optimization of the time-space domain dispersion function, and finally we tabulate the optimized weights for each case. We analyze the numerical dispersion, stability, and convergence rates of our schemes and compare their numerical dispersion characteristics with the standard high-order ones. We also discuss the efficient solution of the system of equations associated with our implicit schemes using the conjugate-gradient method. The comparison of dispersion curves and the numerical solutions with the analytical and the pseudospectral solutions reveals that our schemes have better performance than the standard spatial high-order schemes and remain stable for relatively large time steps.

A numerical technique is developed for dispersion optimization in frequency-domain acoustic wave modeling. The optimization is performed using the null space of the modeling operator, which reduces the dispersion error during modeling with a high wavenumber. Approximation of the modeling operator and optimization of the dispersion error can be applied to arbitrarily positioned nodes. To obtain an optimal wave operator, flexible approximation is used, and its degrees of freedom are fully functional with the basis for the nullspace of the operator. A dispersion-optimized operator based on this approach yields an improved reduction in the numerical dispersion error. Numerical examples are evaluated to demonstrate the effectiveness of the developed method, compared with those of the existing finite-difference and finite-element schemes. We have found that the developed approach can produce more accurate results for frequency-domain wave modeling with regular and irregular grids.