MATLAB Code Implementation for Seismic Wave Synthesis

Seismic wave synthesis is a crucial technique in earthquake engineering and seismology research, primarily used to simulate characteristics of real ground motions. Implementing this functionality through MATLAB provides a flexible tool for scientific research and engineering design. The fundamental approach for seismic wave synthesis typically involves the following key steps: Random Phase Generation: The process begins by generating a frequency spectrum with randomized phases, which is essential for simulating the uncertainty of seismic waves. This is commonly implemented using white noise as the initial signal, followed by phase characteristic adjustments through Fourier transform operations. In MATLAB, this can be achieved using functions like `randn` for noise generation and `fft` for frequency domain transformation. Target Response Spectrum Matching: Synthetic seismic waves must satisfy specific target response spectra (such as design response spectra or spectra from actual earthquake records). This is accomplished through iterative adjustments of frequency domain amplitudes using optimization algorithms. MATLAB implementations often utilize functions like `lsqnonlin` for least-squares optimization to minimize differences between synthetic and target spectra. Baseline Correction and Non-stationary Adjustments: Seismic waves typically exhibit non-stationary characteristics where amplitudes vary over time. This is simulated by applying envelope functions (such as exponential decay or piecewise linear functions) to model energy variation during ground motion. MATLAB code commonly implements this using custom envelope functions with time-varying scaling factors. Time Domain Synthesis: The adjusted frequency spectrum is converted back to time domain signals through inverse Fourier transform, followed by necessary baseline corrections to prevent unrealistic displacement drift during integration. The MATLAB implementation typically uses `ifft` for inverse transformation and polynomial fitting functions for baseline correction. MATLAB implementation of seismic wave synthesis heavily relies on the Signal Processing Toolbox, particularly FFT (Fast Fourier Transform) algorithms and optimization techniques like least-squares methods. The code structure typically involves sequential processing modules for each step, with validation checks to ensure synthesized waves meet both statistical characteristics and engineering requirements. Key functions frequently used include spectral analysis tools, optimization solvers, and signal filtering operations to achieve accurate seismic wave simulations.