# Method of Suppressing Rayleigh Waves Based on the Technology of Time-Domain Differential Detection
## 1 Introduction  
Seismic exploration relies on the differences in elasticity and density of subsurface media. The physical properties and geometric states of subterranean media are determined by analyzing seismic response signals from artificially induced seismic waves. Seismic exploration broadly covers traditional oil and gas exploration, engineering seismic exploration, and ultrasonic non-destructive testing of solid-phase media. Although the principles of elastic wave propagation and diffusion, along with signal extraction and processing methods, remain similar, each application targets specific objectives. For reflection or scattering engineering seismic exploration, a critical step in subsequent signal processinginvolves separating or selectively suppressing Rayleigh waves and reflected wave signals near the free interface [1; 2]. Previous studies have proposed three effective methods for suppressing Rayleigh waves. The first method, combined detection, includes spatial geometric combined detection [3; 4] and time-domain numerical combined detection technology [5]. The interference mechanism of this technology is well understood, with numerous successful applications [6]. However, a geophone array is essentially a coherent stacking method based on zero correction or static correction. Its capacity to suppress Rayleigh waves in near-source shot records is limited, potentially affecting the time-frequency attributes of reflected wave signals and making it challenging to mitigate these effects in the following stages. Hence, the associated combination operation methods are indirect and passive. The second method involves transformation domain numerical filtering technology for extensive common shot records. This approach utilizes the disparities in energy, frequency bands, and phase velocities between effective reflected and interfering waves, such as Rayleigh, direct, and refracted waves, to suppress Rayleigh waves. Algorithms have evolved from one-dimensional filtering in the frequency domain to variable velocity filtering [7; 8], progressing from traditional \(\tau-p\) transformations to advanced multi-transformation domain filtering [9; 10; 11]. Transformation domain filtering addresses both the macroscopic and microscopic characteristics of shot records. The algorithms used in practice primarily include wavelet transforms [12; 13; 14; 15], curvelet transformations [16; 17; 18; 19], ridgelet transformations [20; 21], S-transforms [22; 23], adaptive nonsubsampled shearlet transforms [24], and the unsupervised learning method [25]. Although transformation domain filtering strategies have effectively unified the macroscopic and microscopic aspects in suppressing Rayleigh waves in shot records, achieving this balance is often complex. This complexity arises because, whether in shallow or deep seismic exploration, the coupling environment of various independent detectors and the mechanical parameters of near-surface media often exhibit significant variability in both vertical and horizontal directions. This dispersion results in distinct Rayleigh wave characteristics in each shot record or at individual recording points in the time-space or frequency domain, making it challenging to implement a unified strategy. The third method for suppressing Rayleigh waves employs seismic interferometry, utilizing Green's function extraction. Through the applications and research efforts of scientists, techniques such as seismic interferometry [26; 27; 28], super-virtual interferometry [29; 30], and adaptive weighted super-virtual interferometry [31; 32; 33] have progressively refined the technology for suppressing Rayleigh wave interference, considering the dispersion characteristics of different detection points and achieving relatively ideal outcomes. Based on previous studies, subsequent application reports are relatively scarce, possibly due to the need for further investigation and elaboration on specific engineering application details and improving its practical operability.