Kanai-Tajimi Power Spectrum - Trigonometric Series Method for Simulating Artificial Seismic Waves

This program utilizes the Kanai-Tajimi power spectrum combined with the trigonometric series method to simulate artificial seismic waves. The implementation incorporates Du Xiuli's modifications for both high-frequency and low-frequency components, adding two adjustment parameters (ad1 and ad2) in MATLAB to enhance the simulation accuracy. The Kanai-Tajimi power spectrum is a widely used method for seismic wave simulation that decomposes seismic signals into trigonometric waves of different frequencies. The algorithm adjusts these components based on the frequency characteristics of the Kanai-Tajimi spectrum to generate realistic artificial seismic waves. The trigonometric series method serves as a mathematical foundation, representing any periodic signal as a series of trigonometric functions through Fourier decomposition. Du Xiuli's modifications specifically target the high-frequency and low-frequency components to improve simulation precision and realism. The high-frequency adjustments better capture rapid variations and detailed features of seismic waves, while the low-frequency modifications enhance the representation of overall waveform characteristics and long-period vibrations. In MATLAB implementation, these adjustments are typically achieved through frequency-domain filtering and amplitude scaling operations. The ad1 and ad2 parameters added in the MATLAB code represent algorithmic optimizations that may include: ad1 potentially controlling high-frequency damping coefficients or spectral decay rates, while ad2 might adjust low-frequency amplification factors or baseline corrections. These parameters likely involve optimization techniques such as spectral shaping, parameter tuning, or numerical stability improvements to enhance computational performance and accuracy. The MATLAB implementation likely involves key functions such as: - Frequency domain decomposition using FFT algorithms - Power spectrum scaling based on Kanai-Tajimi parameters - Trigonometric series reconstruction with phase randomization - Parameter optimization loops for ad1/ad2 adjustments Through these enhancements, the program achieves improved simulation of artificial seismic waves with better performance characteristics and accuracy. The modifications demonstrate practical applications of spectral modification techniques in seismic engineering simulations.