Soil liquefaction is one of the significant factors affecting soil stability, among them, seabed soil liquefaction is a harmful marine geological disaster, which has attracted widespread attention from domestic and foreign geotechnical engineering and coastal engineering communities. Under the continuous erosion and scouring of waves, fine particles on the surface soil of the seabed migrate out and escape along the pores of the coarse particles, thereby forming larger pores in the soil (Dassanayake et al., 2022). This can destroy the structural integrity of the soil, and weaken the hydraulic properties (Jia et al., 2014) and engineering characteristics (Liu et al., 2013) of the soil, which may induce soil liquefaction under cyclic loading (Bachrach et al., 2001), causing damage to offshore structures such as submarine pipelines (Sumer et al., 1999; Zhou et al., 2013), offshore platforms (Sumer, 2014; Zhang et al., 2017), and breakwaters (Jeng, 2001; Zhao and Jeng, 2015). The Yellow River Delta is a typical rapidly deposited delta, and also the place with the densest offshore structures on the south coast of the Bohai Bay. The fine-grained soils such as silt and silty sand are widely developed in the Yellow River Delta, with weaker permeability and poorer water stability, which makes them more prone to unstable failure of soil such as liquefaction (Ren et al., 2020; Wang et al., 2022; Liu et al., 2023; Zhang et al., 2023). For this reason, accurately assessing the seabed liquefaction has become an essential part of disaster prevention and mitigation in the construction of the Yellow River Delta.

At present, there are three primary methods for assessing soil liquefaction: in-situ tests (Fergany and Omar, 2017), laboratory tests (Kumar et al., 2020), and numerical simulation (Ye et al., 2016; Zhao et al., 2018). These methods have been maturely applied in the study of liquefaction in sandy soils due to their safety and reliability (Amini and Qi, 2000; Dobry and Abdoun, 2017; Ye et al., 2018). However, for seabed soil, sampling measurements and laboratory tests can only obtain the physical and mechanical properties of shallow soil layers (Meng et al., 2018), and cannot guarantee the natural structure and stress state of seabed soil, resulting in failure to reflect the real dynamic response of soil. Numerical simulation can provide guidance for experimental research and theoretical analysis, but the simplification of boundary conditions and material properties in the numerical simulation process with a certain degree of randomness can lead to affect the reliability of the results. Furthermore, invasive in-situ tests such as standard penetration test (SPT) (Seed et al., 1983) and cone penetration test (CPT) (Boumpoulis et al., 2021; Geyin and Maurer, 2021) are complex and expensive, making them unsuitable for large-scale seabed measurements. Submarine acoustic exploration technology uses the acoustic properties of the compression waves (P-waves) and the shear waves (S-waves) to investigate the engineering properties of seabed soils. This method can effectively avoid measuring errors caused by disturbances, which is becoming a prominent means for studying the properties of seabed soils (Gorgas et al., 2002; Hou et al., 2018). Compared with the results of SPT and CPT testing, shear wave velocity (V_s ) is closely related to liquefaction resistance, and is influenced by factors such as porosity ratio, stress state, relative density, and soil type (Hardin and Drnevich, 1972; Tokimatsu and Uchida, 1990; Xu et al., 2015). Moreover, V_s is one of the fundamental mechanical properties of soils, which can characterize the shear stiffness under small strain conditions and soil-structure interaction, and has potential application prospects in assessing soil liquefaction (Qin et al., 2020; Lin et al., 2021). Nevertheless, traditional shear wave velocity testing requires placing shear wave sensors in surface or underground boreholes, making it difficult to conduct measurements in the seabed. Moreover, the harsh seafloor environment and complex sediment structure seriously affect the measurement accuracy, and the high cost and limited measurement range restrict the development of submarine acoustic exploration technology.

There exist weak and low-amplitude vibration in the natural environment, known as ambient noise, which are commonly considered as an interference signal in geophysics. Over the past few decades, researchers have gradually discovered that ambient noise can be used to prospect subsurface structures (Aki, 1957; Toksoz, 1964). The composition of different body and surface waves in ambient noise is highly complex (Bonnefoy-Claudet et al., 2006). Nakamura (Nakamura, 1989; Nakamura, 2008; Nakamura, 2009) proposed the horizontal to vertical spectral ratio method (HVSR), which normalizes the amplification effects of the horizontal and vertical components of ambient noise, calculates the Fourier spectrum ratio of the horizontal and vertical components of noise, and evaluates the ground response characteristics of soft sediment caused by multiple reflections of shear waves (Nakamura, 2000; Nakamura, 2019). The HVSR curve is closely related to the properties of the soil (Field et al., 1990; Field and Jacob, 1993) and is considered as a “transfer function” of the vertically incident shear wave in the strata (Nakamura, 1989; Nakamura, 2008). Kawase et al. (2011) proved that the horizontal-to-vertical spectral ratios match the ratios estimated from 1D shear wave velocity model using the simple theory of diffuse field. Therefore, based on the fundamental resonant frequency and spectral amplitude on the HVSR curve, the shear wave velocity can be estimated using an inversion algorithm (forward modeling routine and Monte Carlo method) and an empirical relationship between shear wave velocity and depth, such as the quarter-wavelength theory (Joyner et al., 1981; Boore, 2003; Edwards et al., 2011). The ambient noise on land is mainly caused by industrial machinery, vehicles, and other human activities, which is predominantly composed of high-frequency and short-wavelength noise (Bonnefoy-Claudet et al., 2006). In contrast, ocean ambient noise is mainly caused by the action of waves on the seabed (Hasselmann, 1963; Bromirski et al., 2005), and it is a broad-band vibration with low-frequency and long-wavelength characteristics, which ensures that ocean ambient noise exploration has a greater detection depth and sufficient resolution.yao

The structure of this study is as follows: Firstly, we introduce the feasibility analysis for assessing the liquefaction potential of seabed soils based on shear wave velocities obtained by inverting ocean ambient noise. Secondly, we present the geological overview of the study area (the coastal zone of the Yellow River Delta). Third, we describe the inversion method and strategy of ocean ambient noise. Fourth, we discuss the characteristics of ocean ambient noise and the accuracy of inversion results, respectively. In addition, we propose and validate the shear wave velocity threshold that can be used for fine-grained soil liquefaction assessment based on statistical analysis. Finally, we conclude this study by discussing and concluding the effectiveness, limitations and potential for assessing the liquefaction of seabed soils by the shear wave velocity obtained by the inversion of ocean ambient noise.

The Yellow River Delta is located on the southern coast of Bohai, and the Yellow River Delta Plain is a fluvial plain formed by the long-term siltation and continuous sea reclamation of high-concentration sediment carried by the Yellow River. We selected the northern coastal zone of the Yellow River Delta as our study area ( Figure 1 ), which has an overall flat topography and gentle slope. The thickness of the Quaternary strata is about 26 m, with a horizontal distribution. Due to the special deposition pattern, silty soils are commonly developed in the surface sediments, with predominantly silt, fine sand and small amounts of clay (Zhao et al., 2013), showing the engineering characteristics of a high water content, poor grading, low bearing capacity, and high compressibility. In addition, thin-layered soft soil layers are widely developed in the stratum, with a thickness of about 1-5 m, which are interspersed with the sedimentary layers in a finger-like way. The engineering geological environment of the Yellow River Delta region is controlled by the sedimentary dynamic environment, which is mainly determined by the muddy and sandy nature of the Yellow River and its frequent siltation and migration. Owing to the migration of the Yellow River Estuary, the sediment supply has been interrupted. In the northern coastal zone, under the action of long-term differential hydrodynamic forces, the structural integrity of the surface soil of the tidal flats are destroyed, leading to a decrease in strength and gradual erosion, which has formed a drop of nearly 1 m between the tidal flats and the embankment. Thus, the study of the engineering characteristics of seabed soil under dynamic action would be helpful to maintain the safety of marine buildings.

In this paper, the OpenHVSR-inversion program (Bignardi et al., 2018) is used to invert the HVSR curves of ocean ambient noise and obtain the shear wave velocity. This program can be used to model and invert HVSR dataset simultaneously, obtaining the distribution of shear wave velocity in different depth layers to construct 2-D or 3-D subsurface models. The forward modeling is based on the method proposed by Tsai and Housner (1970), which calculates the theoretical transfer function of the layered subsurface model. The inversion strategy is based on the Monte Carlo method, where a randomly perturbed version of the best fitting model is generated in each iteration, and used to compute a set of simulated curves for comparison with experimental curves. The generation of many trial models allows exploring the parameters space while searching for a new and better fitting model.

Several in-situ ambient noise recordings were carried out in the Yellow River Delta, and the observed distribution of fundamental frequency is shown in Figure 2 , which is mainly concentrated in the range of 0.8-9.8 Hz (Meng et al., 2023). As a result, we set the frequency band for inversion from 0.6 to10 Hz. The inversion was divided into three stages. In the first stage, the inversion was started with a simple 4-layer subsurface model ( Table 1 ), limiting the frequency band to 0.6-4 Hz. Successively, when the best-fit model was found, the result was saved as a new project and the subsurface model was edited, dividing the deeper layer in three sublayers, while the total thickness of the layer remains unchanged. Then, set the frequency band for the second stage to 0.6-8 Hz and continue with the next, with the shallower layer dividing in four sublayers, and so on. The frequency band for the third stage was set at 0.6-10 Hz, with a total of 10 layers.

In each stage of the inversion, firstly, the longitudinal wave velocity, shear wave velocity, and thickness were allowed a 5% perturbation for 3000 iterations of global inversion. Secondly, the best-fitting model of the HVSR curve for each station was locally optimized, allowing a 15% perturbation of the parameters for 5000 iterations. Finally, 10000 iterations were performed with 20% lateral constraint perturbations. In order to provide a more intuitive description of the inversion results, an example of the inversion of the ocean ambient noise in the Yellow River Delta is given in Figure 3 . Figure 3A illustrates the HVSR curve of the measured noise (black), the standard deviation (gray), the best-fitting curve obtained by Monte Carlo inversion (red), and the fitting curve generated by the last iteration of Monte Carlo inversion (blue). It can be seen that peaks are observed in the HVSR curve at both 1.9 Hz and 10 Hz in Figure 3A . According to the method for identifying the fundamental frequency proposed by Meng et al. (2023), the fundamental frequency of the soil at this station is 1.9 Hz, not 10 Hz, and the peak at 10 Hz was caused by the fundamental Rayleigh waves (Nakamura, 2008). The Figure 3A also shown the good consistency among the best-fit curve and the fitted curve generated by the last iteration with the HVSR curve. Figure 3B represents the shear wave velocity structure of the observation station obtained by inversion of the ocean ambient noise.

To evaluate the accuracy of the inversion, we used two concepts: global misfit and local misfit. Local misfit refers to the normalized misfit between the simulated and experimental curve at each station. For the global misfit, we introduced the objective function (Bignardi et al., 2018):

Where M(m) represents the misfit between the simulated and experimental curves; S(m) represents the fitting degree of the simulated and experimental curves at the peaks; and R_j (m) represents the regularization term. The constants a and b in above Equation are used to balance the relative weight of the M(m) and S(m) terms. Based on the objective function, we define the global misfit as aM(m) + bS(m).

Figure 4A shows the global misfit of the inversion results. As can be seen from the figure that the global misfit between the inversion results and experimental data is 0.1, and the fitting degree at the peak of the experimental curve and simulated curve is around 0.9. The normalized misfit between the experimental data and simulated data at each station is shown in Figure 4B , and it can be seen that there are 52 stations with a local misfit of less than 0.1; 6 stations with a local misfit between 0.1 to 0.2; and only 6 stations have a local misfit exceeding 0.2.

The purpose of this paper is to obtain the shear wave velocity of seabed soils by inversion of ocean ambient noise for rapid assessment of seabed soil liquefaction. In-situ noise recording and analysis were performed in the northern coast of the Yellow River Delta using the HVSR method to obtain the shear wave velocity of the seabed soil. Based on statistical analysis of liquefaction investigation data, a shear wave velocity threshold was proposed for assessing the liquefaction potential, and the location of liquefiable soil was identified in the light of 1-D shear wave velocity structure and 2-D shear wave velocity profile. In summary, the following results were obtained:

1. Ocean ambient noise has the characteristics of low-frequency, long-wavelength, and wide bandwidth. Therefore, in-situ observations of ocean ambient noise can not only obtain the physical and mechanical properties of the seabed soil in a deeper range depending on the propagation characteristics of noise in the seabed sediment, but also monitor the deformation and stability of the seabed soil, provide the necessary support for the design and construction of marine engineering, and are of great significance for risk assessment and the early warning of marine geology disasters.

2. Shear wave velocities of seabed soils were obtained by inversing the HVSR dataset of oceanic ambient noise. The stratigraphic distribution of the shear wave velocity obtained by inversion is broadly consistent with existing research results, which indicates that the results have a certain degree of accuracy and that the method for inverting ocean ambient noise is quite feasible.

3. The application of a shear wave velocity threshold of 200 m/s in assessing the liquefaction potential of fine-grained soils in the Yellow River Delta yielded consistent results with traditional methods. The assessment showed the liquefaction potential of soil in depths of 0-10 m, and indicated that this threshold is reasonable for liquefaction assessment of seabed soil in the Yellow River Delta. Accordingly, the stability problems of the soil in the tidal flat area should be taken into sufficient consideration during engineering construction. It is necessary to adopt measures such as replacement methods and dynamic consolidation for foundation treatment to ensure the safety of engineering construction and use.

4. The HVSR-based ocean ambient noise prospecting method has the advantages of being convenient, economical, environment-independent, and deeper detection depth. It can provide services for disaster prevention and mitigation of marine engineering construction, and has good practical application. In addition, in the actual application process, combining this method with other geotechnical tests (such as drilling, in-situ tests, or laboratory tests, etc.) can more accurately determine the engineering characteristics of soil, and further classify the liquefaction hazard of soil, which is crucial for coastal protection and marine engineering construction.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Conceptualization & methodology, YL, QM and SW. Formal analysis, YL and WW. Data curation, YL and YC. Writing—original draft preparation, YL. Writing—review & editing, YL and QM. Visualization, YC and SW. Project administration, YL and WW. Funding acquisition, QM. All authors contributed to the article and approved the submitted version.