# A High-Resolution Spectral Analysis Method Based on Fast Iterative Least Squares Constraints
## 1 Introduction
Traditional seismic processing and interpretation techniques are influenced by seismic resolution; for faults smaller than 5 m, the verification rate is low. Using spectrum decomposition technology can effectively overcome the limitations of seismic resolution [13; 14; 15], better highlighting geological anomalies. At the same time, spectrum decomposition technology aids in displaying rock layer morphology, significantly enhancing the recognition of complex geological bodies [16]. Various algorithms are commonly employed to achieve spectral decomposition. Short-time Fourier transform (STFT) could be one of the most computationally cost-effective methods for spectral decomposition; however, a key challenge lies in selecting an appropriate window length that maintains both time and frequency resolution in the output. Another widely used spectral decomposition method is Continuous Wavelet Transform (CWT). The CWT method decomposes seismic traces into different frequency components using child wavelets with varying scales, effectively performing bandpass filtering in the time domain [17; 18]. Compared to STFT, the CWT method is less affected by the choice of time window, as the spectral dictionary inherently incorporates frequency-related windows. It is important to note that the wavelets used in CWT must be orthogonal, and its output can also be obtained using STFT with an appropriate window function. Another class of spectral decomposition methods involves user-defined wavelet dictionaries. These methods typically yield results with high temporal and spectral resolution, but they come with significant computational costs. Due to their high-resolution advantages, many researchers are focused on improving their efficiency. Additionally, there are various other methods for decomposing seismic data into the time-frequency domain, each with its own advantages and potential effectiveness in specific situations [19]. STFT offers fixed time-frequency localization, but wavelet transform provides more flexible localization. For different frequency ranges, wavelets adjust the window size, which gives better time localization for high frequencies but poorer frequency resolution for low frequencies. While wavelet transform offers better time localization for non-stationary signals, particularly at high frequencies, it sacrifices frequency resolution, especially at low frequencies. This is why wavelet transform's time-frequency resolution is often lower than that of STFT, especially in the low-frequency range. In summary, wavelet transform has more adaptive time-frequency localization but at the cost of frequency resolution, especially at lower frequencies, making its overall resolution sometimes lower than that of fixed-resolution STFT. In comparison, STFT provides a fixed frequency resolution for a given window size. This results in a more balanced time-frequency resolution across the entire spectrum. However, the fixed window in STFT does not adapt like wavelet transform, meaning the time-frequency trade-off is more uniform. Currently, signal processing methods based on inversion concepts can enhance resolution or signal-to-noise ratio through iterative processes [20; 21; 22; 23; 24; 25; 26]. Similarly, inversion-based spectral decomposition methods are among the most effective techniques. The constrained least squares spectral analysis (CLSSA) proposed by [27] is a highly specialized spectral decomposition method that can handle both narrowband and broadband seismic data. The CLSSA method significantly reduces distortion caused by the window function effect by directly optimizing the L2-regularized least squares fitting function to solve for the Fourier coefficients. Ref. [27] demonstrated that the CLSSA method can accurately predict the Fourier spectrum even with very short window lengths [27]. [PERSON] et al. (2014) applied [PERSON]'s inversion method to braided river and reservoir characterization, achieving favorable results [28].