Prediction of Acoustic Impedance of Submarine Sediments in the Middle Area of the South Yellow Sea Using on a Random Forest Algorithm

Abstract

This study investigates the prediction of the acoustic impedance of submarine sediments in the middle area of the South Yellow Sea using the Random Forest (RF) model algorithm. A predictive model for the acoustic impedance of submarine sediments was established using a Random Forest algorithm based on six characteristic factors, including density, porosity, liquid limit, moisture content, plasticity index, and median particle size. The results indicate that the highest prediction accuracy and lowest error were achieved when n_estimator was set to 27, max_depth to 8, and min_samples_leaf to 7. The model significantly outperformed traditional single-parameter regression equations. The coefficient of determination (R²) of the test set reached 0.991 after model training, the mean absolute error (MAE) was 23.14 × 10³ kg/(m²·s), and the mean absolute percentage error (MAPE) was 0.90%. This paper provides an in-depth analysis of the relationship between acoustic impedance and various physical and mechanical properties, providing valuable guidance for advancing the prediction of acoustic impedance of submarine sediments.

1. Introduction

Shallow seafloor sediments, as the interface between seawater and the seabed, are an essential component of the marine acoustic environment and are indispensable for marine resource investigations [1]. The relationship between the acoustic properties of seafloor sediments and their physical and mechanical properties has long been a primary focus of marine acoustics research: Hamilton et al. [2] obtained extensive sediment acoustic parameters through measurements of sediment core samples in laboratory, establishing correlations between sound speed, sound attenuation factors, porosity, density, grain size, and other physical parameters in multiple marine sediment regions. Orsi et al. [3] also established sound speed prediction equations based on porosity through statistical fitting of measured data. Lu et al. [4], Zou et al. [5], and Kan et al. [6] combined acoustic measurement data of seafloor sediments in continental shelves near the South China Sea, East China Sea, and Yellow Sea, establishing empirical formulas for sound speed and physical parameters. In addition to sound speed, acoustic attenuation coefficient, and shear wave velocity, acoustic impedance is also an important acoustic parameter of seafloor sediments that is usually used for determining and calculating the seabed reflection and transmission coefficients. The empirical regression equation between sediment acoustic impedance and sediment physical property parameters is often used to remotely measure and invert sediment physical properties such as porosity, permeability, bulk density, and particle size. Zhou et al. [7] inverted the porosity and bulk density of seafloor sediment based on the reflection coefficient of the seafloor, which was calculated from the acoustic impedance. Lu et al. [8] developed a PSO-BP neural network approach for inverting sediment sound speed from reflection coefficients of the seafloor calculated from the acoustic impedance obtained based on chirp sonar data. Many researchers conducted studies on the acoustic impedance of seafloor sediment. Kan et al. [9] established single-parameter empirical regression equations between acoustic impedance and physical–mechanical parameters in the middle area of the South China Sea. Jackson and Richardson [10] provided the regression formulas between acoustic impedance and sediment physical parameters, including the porosity, density, and median grain size of siliceous clastic and carbonate sediments. Chen et al. [11], Hou et al. [12], and Chen et al. [13,14] applied machine learning algorithms to predict submarine sediment sound speed, achieving promising results in experiments.

However, research on seafloor sediment acoustic impedance in the middle area of the South Yellow Sea remains limited. To address this research gap, this paper proposes a machine learning approach for submarine sediment acoustic impedance based on the Random Forest algorithm. As an ensemble learning algorithm, Random Forest concurrently trains multiple decision trees on the dataset and derives the final prediction results through a voting mechanism or averaging method. This approach effectively enhances prediction accuracy while handling high-dimensional data and assessing feature importance. To date, no study has applied the Random Forest model to predict acoustic impedance of seafloor sediments in the middle area of the South Yellow Sea. In this research, we preprocess laboratory test data of sediment samples from the middle area of the South Yellow Sea, select significant feature elements based on feature importance assessment results, conduct model training and validation, and compare the proposed model with traditional prediction equations in this study area using test data from the same study area.

2. Study Area and Data Sources

2.1. Study Area Location

The study area is situated in the middle area of the South Yellow Sea (33°46′26.4″ N–36°20′46.8″ N, 121°30′51″ E–123°48′55.8″ E), with water depths ranging from 17 to 83 m [14,15]. The topography is characterized by shallower depths in the southwest and deeper depths in the northeast. The sedimentary environment in this area is complex, with diverse sources of materials, which have resulted in distinct regional distribution characteristics and the formation of five types of seabed sediments: silt sand, sandy silt, silt, clayey silt, and silty clay [16]. The southwestern part of the survey area, near the shoal region off the northern Jiangsu coast, is primarily composed of silt and fine sand. The northwestern substrate mainly consists of silty sand, while the eastern and central parts are dominated by clayey silt and silty clay sediments.

2.2. Data Sources

Sediment core samples used in this study were collected from 287 stations in the middle area of the South Yellow Sea. Following the survey, all collected samples were transported to a temperature- and humidity-controlled sample repository for subsequent acoustic parameter and physical–mechanical property measurements.

During laboratory testing, the samples underwent initial processing through cutting according to actual conditions. Subsequently, the sediment samples were placed on a measurement platform, and the sound speed of the sediment samples was measured using a WSD-3 digital acoustic wave instrument produced by Chongqing Benteng Numerical Control Technology Research Institute Co., Ltd. (Chongqing, China) [17].

The samples were extruded from polyvinyl chloride (PVC) tubes after sound speed measurement and subjected to physical–mechanical property measurement of sediments, including density, moisture content, porosity, void ratio, median particle size, sand content, clay content, liquid limit, plastic limit, plasticity index, compression coefficient, and shear strength [9]. Acoustic impedance is defined as the product of sediment sound speed and density, and it can be calculated as follows:

$$Z_a={\rho V}_P$$

(1)

where Z_a is the sediment acoustic impedance, in kg/(m²·s) or (Pa·s)/m, ρ is the density of sediment, in kg/m³, and V_p is the sound speed of sediment, in m/s. This study utilized a dataset consisting of 287 samples of 100 kHz measurement data, which not only provides sufficient samples but also exhibits strong representativeness [9]. Furthermore, this dataset enables further comparison with the research findings of other scholars studying the same study area.

The sediment in the study area mainly includes five types: silty sand, sandy silt, silt, clayey silt, and silty clay. According to

Table 1. Physical–mechanical parameters of sediments and acoustic impedance.

Parameter	Max	Min	Ave
$\mathsf{\rho }$ (g/cm3)	2.02	1.399	1.686
$\mathrm{w}$ (%) *	127.54	27.03	66.12
$\mathrm{n}$ (%) *	77.3	41.4	60.76
d50 (mm) *	0.067	0.001	0.014
${\mathrm{w}}_{\mathrm{s}}$ (%)	53.9	0	10.04
${\mathrm{w}}_{\mathrm{c}}$ (%)	91.4	4.6	39.45
${\mathrm{w}}_{\mathrm{l}}$ (%) *	75	23.2	44
${\mathrm{w}}_{\mathrm{p}}$ (%) *	44.3	12.8	24
${\mathrm{I}}_{\mathrm{p}}$ (%) *	42.6	6	20.01
${\mathsf{\alpha }}_{\mathsf{\nu }}$ (MPa) *	6.73	0.28	1.71
$\mathrm{S}$ (kPa) *	10.54	0.24	2.36
${\mathrm{V}}_{\mathrm{P}}$ (m/s)	1654.1	1359.4	1529.5
${\mathrm{Z}}_{\mathrm{a}}$ (103 kg/(m2·s))	3326.99	2065.14	2590.38

* d₅₀ is the median particle size; $\mathrm{w}$ is the moisture content; $\mathrm{n}$ is the porosity; ${\mathrm{w}}_{\mathrm{l}}$ is the liquid limit; ${\mathrm{w}}_{\mathrm{p}}$ is the plastic limit; ${\mathrm{I}}_{\mathrm{p}}$ is the plasticity index; ${\mathsf{\alpha }}_{\mathsf{\nu }}$ is the compression coefficient; and $\mathrm{s}$ is the shear strength.

, at a measurement frequency of 100 kHz, the maximum acoustic impedance obtained is 3326.99 × 103 kg/(m²·s), corresponding to the silty sand sediment type, while the minimum acoustic impedance is 2065.14 × 103 kg/(m²·s), corresponding to the silty clay sediment type. The overall average acoustic impedance is 2590.38 × 103 kg/(m²·s).

3. Principle and Implementation of the Random Forest Model

Random Forest is an ensemble algorithm based on the Bagging algorithm aimed at addressing potential issues, such as high variance and overfitting, that are commonly associated with individual decision trees [18]. The core idea of this algorithm is to combine multiple different decision trees to reduce the bias and inaccuracies that a single decision tree may lead to. Building upon their foundation, Random Forest improves the construction of decision trees. Unlike traditional decision tree algorithms that select the optimal feature from all sample features at a node, Random Forest randomly selects a subset of sample features at a node to split the decision tree into left and right subtrees, thereby further enhancing the model’s generalization ability.

3.1. Data Preprocessing

3.1.1. Data Cleaning

Data cleaning aims to remove noisy data and retain valid samples to ensure the accuracy and reliability of subsequent analysis and modeling. During data collection, the original data are often affected by marine environmental disturbances, resulting in a large amount of noisy data, which may contain missing or anomalous values. Therefore, we first exclude missing values and then utilize box plots to detect and remove outliers as abnormal data. Such operations not only reduce analysis bias caused by data errors but also improve the accuracy and reliability of the overall model. The 253 data samples were selected from 287 samples of 100 kHz measurement data after data cleaning.

3.1.2. Feature Extraction

By organizing cruise reports and laboratory measurement data of sediment samples, a total of 18 data attributes were collected, including (1) sound speed, acoustic impedance, sampling site longitude, and latitude; (2) basic physical properties: porosity, void ratio, density, and moisture content; (3) grain size parameters: median particle size, sand content, clay content, and silt content; (4) mechanical properties: compression coefficient, shear strength, and cohesion; and (5) consistency limit parameters: plastic limit, liquid limit, plasticity index, and liquidity index.

To ensure that the model considers various influencing factors on acoustic impedance as much as possible while reducing model complexity, in this study, initial selection for Pearson correlation coefficient calculation encompassed porosity, density, moisture content, median particle size, sand content, clay content, plastic limit, liquid limit, and plasticity index. These parameters were chosen from the basic physical properties, grain size parameters, mechanical properties, and consistency limit parameters.

The Pearson correlation coefficient is mainly used to measure the strength and direction of the correlation between two variables. Through quantitative description, it helps us accurately understand and interpret the relationships between variables. Its calculation formula is as follows:

$$\mathsf{\tau }={\displaystyle \frac{\sum _{i=1}^n\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)}{\sqrt{{\sum _{i=1}^n\left(X_i-\overline{X}\right)}^2}\sqrt{\sum _{i=1}^n{\left(Y_i-\overline{Y}\right)}^2}}}$$

(2)

where τ indicates the strength of correlation between two variables. When the correlation coefficient is close to 1, it indicates that there is a linear positive correlation between the two variables. A value close to −1 indicates that there is a linear negative correlation, and a value near 0 indicates that there is no linear relationship.

As shown in Figure 1, sediment acoustic impedance exhibits a strong association with the basic physical properties of sediment. Specifically, density exhibits an extremely strong positive correlation with a correlation coefficient exceeding 0.95, while porosity and moisture content show a strong negative correlation with absolute correlation coefficients also exceeding 0.95. In contrast, the correlation between sediment acoustic impedance and grain size parameters is relatively weak: the correlation coefficient with median particle size is slightly above 0.75, and those of sand content and clay content are lower, approaching or below 0.70. The correlation between sediment acoustic impedance and consistency limit parameters is moderate, with correlation coefficients around 0.90.

Based on the above analysis, to ensure that the Random Forest model achieves predictive accuracy close to the expective value, feature elements with absolute correlation coefficients near 1 should be selected as input parameters. To balance model complexity and feature diversity, we exclude sand content, clay content, and plastic limit. Ultimately, we determine that the feature parameters involved in model training are density, median particle size, moisture content, liquid limit, plasticity index, and porosity. Among these feature parameters, density and median particle size exhibit a positive correlation with acoustic impedance, while moisture content, liquid limit, plasticity index, and porosity are negatively correlated with acoustic impedance.

3.1.3. Data Partitioning

The 253 data samples were divided into training, validation and test sets. The random forest model randomly selected 177 samples for the training set, 46 samples for the validation set, and 30 samples for the test set. During model training, the training set data were used to construct the model, while the validation set data were employed to effectively valuate the model’s generalization ability on unseen data. The independent test set helps prevent the random forest model from overfitting the characteristics of the training set while more accurately evaluating the model’s performance and objectivity on real data. Subsequently, 30 test samples were used for comparison with other models.

3.2. Model Training and Parameter Tuning

To effectively mitigate potential underfitting or overfitting during the training process of the random forest model, it is necessary to optimize hyperparameters that affect the model training accuracy, including the number of leaf nodes, the number of decision trees, and the tree depth. In this study, 5-Fold Cross-Validation was employed to optimize the model performance. The implementation of 5-Fold Cross-Validation involved dividing the dataset into five equal parts, with each part alternately serving as the validation set while the remaining four parts serve as the training set. By repeating this process with different validation sets each time while keeping the training set constant, the average accuracy of five experiments was obtained to evaluate the predictive performance of the model. A dataset containing 177 training samples was utilized to train the random forest model, and the remaining 46 validation samples were used to assist in determining the optimal number of decision trees, tree depth, and number of leaf nodes.

The randomness of the random forest is reflected in two aspects: the random selection of training samples for each tree and the random selection of classification attributes for each node in the tree. This study focused on improving the model by tuning three hyperparameters. (1) n_estimators: the number of decision trees. As the number of decision trees increases, the generalization error of Random Forest reduces. However, once the number of decision trees reaches a certain threshold, further performance improvement becomes less significant and may even lead to overfitting and increased computation time. In this study, we set the number of trees within the range from 2 to 100 (2) max_depth: the maximum depth of the tree, controlling the complexity of a single decision tree. In this study, we set the tree depth within the range from 1 to 10. (3) min_samples_leaf: minimum number of samples required for a leaf node used to prevent overfitting. In this study, we set the number of leaf nodes within the range from 1 to 10. As shown in Figure 2, Figure 3, and Figure 4, the n_estimators, max_depth, and min_samples_leaf were determined as 27, 8 and 7, respectively. At this point, the determination coefficient R² of the model on the validation set after training reached 0.991, with an MAE of 23.14 × 103 kg/(m²·s) and an MAPE of 0.90%.

3.3. Model Interpretation

The random forest model has the ability to evaluate the importance of each feature for sample classification, which is crucial for feature selection and ranking. During modeling, each decision tree quantifies the total reduction in impurity by comparing the Gini impurity or information gain before and after node splitting at each node. Subsequently, the importance of each feature in each decision tree is weighted and averaged to obtain a comprehensive assessment of the feature importance in the overall model. This method effectively measures the contribution of each feature to the predictive performance and provides reliable support for practical applications.

As shown in Figure 5, the six feature elements used for model training are ranked in descending order of importance: density, porosity, liquid limit, moisture content, plasticity index, and median particle size. This ranking is consistent with the Pearson correlation coefficients presented in Figure 1. In the following section, we construct models to predict seafloor sediment acoustic impedance based on different categories of feature elements. This step deepens the understanding of the impact of each feature element on acoustic impedance prediction and provides more accurate guidance for model construction.

4. Discussion

4.1. Single-Parameter Models

In order to investigate the relationships between seafloor sediment acoustic impedance and physical properties, Kan et al. [9] employed the regression analysis to establish single-parameter models for acoustic impedance and parameters such as density, moisture content, porosity ratio, porosity, liquid limit, plastic limit, plasticity index, sand content, clay content, median particle size, compression coefficient, and shear strength in the study area. Their results indicate that the acoustic impedance of seafloor sediments in the study area has a strong correlation with sediment density, moisture content, and porosity, with coefficient of determination (R²) exceeding 0.95. Liquid limit, plasticity index, and compression coefficient exhibit strong moderate correlations, with R² value around 0.90, while the correlation with shear strength was very poor (R² < 0.4).

In seafloor sediments, the solid-phase materials are primarily composed of mineral particles, and the density of these particles directly affects the propagation speed of sound waves in the medium. Conversely, an increase in moisture content in sediments will increase the number and area of water–solid phase interfaces, leading to enhanced reflection and transmission of sound waves at these interfaces and reducing the contact area between solid-phase particles. Therefore, acoustic impedance of sediments exhibits a positive correlation with density and compression coefficient and a negative correlation with moisture content, porosity, liquid limit, and plasticity index.

In this study, 30 samples were randomly selected for error analysis comparing the RF model with traditional single-parameter empirical regression equations. Since the input feature elements of the RF model are density, moisture content, porosity, median grain size, liquid limit, and plasticity index, the error analysis was also conducted on these six physical quantities. As shown in

Table 2. Error analysis of the RF model and traditional single-parameter empirical regression models.

Prediction Model	Tolerance Range (×103 kg/(m2·s))	MAE (×103 kg/(m2·s))	MAPE (%)
$\rho$	−58.94~98.76	24.18	0.91
$w$	−175.49~170.11	62.17	2.32
$n$	−86.60~64.45	30.50	1.18
$w_l$	−285.21~143.66	72.06	2.72
$I_p$	43.54~453.27	290.78	12.00
$d_{50}$	−475.49~241.36	127.27	5.08
RF	−72.36~50.40	23.15	0.90

Note: Tolerance range refers to the minimum to maximum range of prediction errors.

, the accuracy of acoustic impedance predicted using the RF model established in this study is the highest, with a mean absolute error (MAE) of 23.15 × 103 kg/(m²·s) and a mean absolute percentage error (MAPE) of 0.90%, followed by the single-parameter model in terms of density, porosity, moisture content, liquid limit, and plastic limit index. Compared with the single-parameter empirical regression equations, the random forest model reduced the average absolute error (MAE) by 1.03 to 267.63 × 103 kg/(m²·s) and the mean absolute percentage error (MAPE) by 0.01 to 11.1%, demonstrating a substantial improvement in prediction accuracy. Wang et al. (2025) applied Random Forest, Support Vector Regression (SVR), and Convolutional Neural Network (CNN) algorithms to predict acoustic attenuation coefficients in seafloor sediments, and the result similarly indicates that the Random Forest model exhibited the lowest prediction error among the three algorithms, which aligns with our findings and strengthens the evidence for RF’s effectiveness in sediment acoustic parameter prediction [19].

4.2. Acoustic Impedance and Physical–Mechanical Parameter Models

To further analyze the relationship between acoustic impedance and physical properties, this study categorizes porosity, density, moisture content, median grain size, sand content, clay content, compression coefficient, shear strength, plastic limit, liquid limit, and plasticity index into four categories: basic physical properties, grain size parameters, mechanical properties, and consistency limits. Among them, the basic physical properties are divided into two categories: with density and without density. As shown in Figure 6, the predicted acoustic impedance based on the grain size parameters and mechanical properties shows larger deviations from the true value of acoustic impedance, while the predicted acoustic impedance based on basic physical properties fits the true value best.

4.2.1. Acoustic Impedance and Sediment Basic Physical Parameter Models

According to formula (2), acoustic impedance can be expressed as the product of sediment density and sound speed. Whether using a random forest model or a single-parameter regression equation, density exhibits the highest correlation, greatest contribution, and smallest error in relation to acoustic impedance. Therefore, this study discusses the cases with and without density separately.

As shown in

Table 3. Error analysis of the predicted result of the RF model based on density–moisture content–porosity.

Parameter of Feature	Importance of Feature	MAE (×103 kg/(m2·s))	R2
$\mathsf{\rho }$	0.908	0.30	0.992
$\mathrm{w}$	0.866
$\mathrm{n}$	0.870

and

Table 4. Error analysis of the predicted result of the RF model based on moisture content–porosity.

Parameter of Feature	Importance of Feature	MAE (×103 kg/(m2·s))	R2
$\mathrm{w}$	1.308	0.55	0.974
$\mathrm{n}$	1.289

, density has the most significant contribution to the model, while porosity and moisture content contribute similarly. Compared to models without density features, inclusion of density reduces the average absolute error (MAE) by 0.25 × 103 kg/(m²·s) and increases the coefficient of determination (R²) by 0.018, which has a positive effect on predictive accuracy. The model based on acoustic impedance, density, porosity, and moisture content shows the best performance among the models constructed using these basic physical parameters. Even without density, the model still performs remarkably well. Therefore, these three parameters, whether used in combination or individually, are highly valuable for acoustic impedance prediction.

4.2.2. Acoustic Impedance and Sediment Particle Size Parameter Models

The median particle size, sand content, and clay content reflect the particle composition and structural characteristics of sediment. The median particle size reflects the average size of particles, the sand content indicates the proportion of sand particles in the sediment, and the clay content represents the amount of clay particles. The acoustic impedance is mainly influenced by sound speed, solid phase material density, and moisture content, which are not directly related to particle composition and structure. This leads to relatively poor correlations between acoustic impedance and median particle size, sand content, and clay content. As shown in

Table 5. Error analysis of the predicted result of the RF model based on median grain size–sand content–clay content.

Parameter of Feature	Importance of Feature	MAE (×103 kg/(m2·s))	R2
d50	1.711	2.16	0.643
${\mathrm{w}}_{\mathrm{s}}$	1.211
${\mathrm{w}}_{\mathrm{c}}$	0.841

, the performance of the RF model constructed based on particle size parameters alone performs poorly. Although median particle size contributes more than sand or clay content, the model’s coefficient of determination (R²) is still less than 0.7. Therefore, particle size parameters cannot be used as sole predictors for acoustic impedance models.

4.2.3. Acoustic Impedance and Sediment Mechanical Property Models

The compression coefficient is typically used to describe the response and deformation characteristics of a medium under sound waves, while shear strength is primarily used to assess the stability and deformation capacity of the medium under stress. Shear strength refers to the resistance of a medium to shear stress, which is related to friction and bonding forces between solid particles. The physical mechanism of acoustic impedance related to sound wave propagation differs from shear strength. The compression of sediment to some extent determines the variation in sound speed, thus also affecting the variation in acoustic impedance [20].

As shown in

Table 6. Error analysis of the predicted result of the RF model based on the compression coefficient and shear strength.

Parameter of Feature	Importance of Feature	MAE (×103 kg/(m2·s))	R2
${\mathsf{\alpha }}_{\mathsf{\nu }}$	2.504	1.09	0.905
$\mathrm{s}$	0.812

, it is evident that the compression coefficient contributes significantly more to the model compared to shear strength, showing the largest difference among the four categories of mechanical parameter models. Due to the strong correlation between the compression coefficient and acoustic impedance, the model coefficient of determination (R²) reaches 0.905, indicating reasonably high predictive accuracy.

4.2.4. Acoustic Impedance and Sediment Consistency Boundary Model

The liquid limit and plastic limit reflect the moisture content in seafloor sediments, with higher values usually being associated with increased moisture content. The plasticity index, defined as the difference between the plastic limit and liquid limit, reflects the strength of sediment plasticity. As shown in

Table 7. Error analysis of the predicted result of the RF model based on liquid limit–plastic limit–plasticity index model.

Parameter of Feature	Importance of Feature	MAE (×103 kg/(m2·s))	R2
${\mathrm{w}}_{\mathrm{l}}$	0.859	1.08	0.895
${\mathrm{w}}_{\mathrm{p}}$	0.881
${\mathrm{I}}_{\mathrm{p}}$	0.860

, acoustic impedance exhibits a good negative correlation with liquid limit, plastic limit, and plasticity index. In this model, the contributions of these three factors are approximately equal, and this model also demonstrates good predictive accuracy.

5. Conclusions

This study focuses on predicting acoustic impedance of seabed sediments in the central–western Yellow Sea using the random forest model algorithm. By analyzing different feature elements, this study provides deeper insights into the impact of each feature on prediction accuracy. The main conclusions of this study are as follows:

(1)

The Random Forest model exhibits superior predictive performance compared to traditional single-parameter empirical regression equations. Both MAE and MAPE are substantially lower, indicating a marked improvement in prediction accuracy. The six feature elements used for model training are ranked in descending order of importance: density, porosity, liquid limit, moisture content, plasticity index, and median particle size. This ranking is consistent with the Pearson correlation coefficient analysis.

(2)

Acoustic impedance is strongly correlated with basic physical properties such as density, moisture content, and porosity, but poorly correlated with shear strength. Further analysis reveals that basic physical properties and mechanical properties significantly influence acoustic impedance, whereas grain size parameters contribute less effectively. The compression coefficient shows substantial predictive value, and there is a strong negative correlation between acoustic impedance and consistency limits (liquid limit, plastic limit, and plasticity index), leading to higher prediction accuracy.

In addition, it is well known that acoustic impedance is frequency dependent. In this study, the acoustic impedance only at the frequency of 100 kHz is discussed, but the predictive performance of the model at other frequencies has not been evaluated and needs to be investigated further.