Hydrogeological survey of karst area of the reservoir and ultrasonic identification technology of leakage point Open Access

The rapid development of China's economy and technology has led to the construction of more water conservancy projects. These projects are increasingly facing complex geological conditions, including structural zones and karst development zones (Pontes et al. 2021). The western mountainous areas of China are rich in water resources and are also regions with developed structures and karst. The construction of water conservancy projects in western regions often faces the problem of karst development (Li et al. 2022). To develop the abundant water conservancy and hydropower resources in karst areas (Pastore et al. 2021), the first thing to solve is the many complex engineering and hydrogeological problems caused by karst development, among which karst leakage is particularly critical. Karst leakage can have serious impacts on reservoir safety, economy, and society. In terms of reservoir safety, karst leakage may increase the seepage pressure of the dam body, weaken the stability of the dam body, and increase the risk of safety accidents such as landslides and collapses. When the leakage channel continues to develop (Liu et al. 2021a), it may form concentrated leakage, causing erosion and erosion of the dam foundation and soil mass. Under long-term action, the bearing capacity of the dam foundation will decrease, seriously threatening the safe operation of the dam. At the economic level, leakage can cause significant waste of water resources and reduce the storage efficiency of reservoirs. To maintain the normal water level of the reservoir, it is necessary to continuously invest more water resources for replenishment, which increases the cost of water supply. Moreover, if leakage causes structural damage to the dam body, subsequent repair and reinforcement projects will consume huge amounts of funds, affecting the economic benefits of water conservancy projects. From the perspective of social impact, reservoir leakage may lead to an increase in groundwater levels in surrounding areas, causing soil salinization, affecting crop growth, resulting in reduced agricultural production, and harming the interests of farmers. In some areas that rely on reservoir water supply, severe leakage may also lead to insufficient water supply (Li et al. 2021a), affecting residents' daily lives and industrial production, and having a negative impact on social stability and economic development. At present, there have been many studies on the identification technology of karst leakage points. For example, the related technique based on variational mode decomposition (VMD) proposed by Liu et al. utilizes correlation coefficients and permutation entropy to optimize parameters, effectively suppressing noise interference and maintaining the characteristics of sudden leakage points, with an average relative recognition error of 5.13% (Liu et al. 2021b). However, it requires the installation of pressure sensors through existing instrument interfaces or drilling holes, and some karst sites in reservoirs cannot install sensors, which limits its widespread application; this technology relies on obtaining the inflection point time of the measurement signals at the beginning and end stations of the pipeline. If the inflection point is not accurately obtained, the location of the leakage point cannot be accurately identified. The real-time identification technology proposed by Malekpour et al. based on the inverse transient analysis method can identify leakage points under various transient and steady flow conditions, but its directionality is poor, resulting in low accuracy of leakage point identification (Malekpour & She 2021). Akande et al. used a recognition technique that combines drones with specific models, which heavily relies on the learning level of background features in infrared images and cannot determine the spatial location of leakage points. In contrast, the ultrasound-based method proposed in this study has unique advantages. This study comprehensively understands the development types and distribution characteristics of karst in reservoirs through hydrogeological exploration of karst leakage in reservoirs (Akande et al. 2021), providing a basis for accurately identifying leakage points in the future. The laser ultrasonic detector is used to collect ultrasonic sound velocity signals, and the wavelet denoising method is effectively used to remove noise, ensuring the accuracy of the signal. Based on the denoised signal, combined with the momentum equation and continuity equation of ultrasonic propagation, a leakage point location calculation model is established to achieve higher recognition accuracy. Through experimental verification, the root mean square error (RMSE) of identifying karst leakage points using this technology is small and the accuracy is high at different reservoir water levels. At the same time, this study aims to improve the accuracy of ultrasonic identification of karst leakage points in reservoirs, providing a reference for leakage detection in similar reservoirs in karst areas. By accurately identifying leakage points, potential safety hazards can be detected and resolved in a timely manner, avoiding the risks caused by leakage to reservoir operation, improving the efficiency and scientificity of reservoir management, reducing maintenance costs, and achieving sustainable utilization of water resources. This is not only of great significance for ensuring the safe operation of reservoirs but also provides support for technological progress and industrial development in related fields, with broad practical application value and social significance. At present, the applicability and accuracy of ultrasound identification technology in karst geological environments still need to be improved, especially in the detection of leakage points under complex conditions (Ewald et al. 2021). When conducting field surveys and ultrasonic testing in karst areas, one often faces harsh working environments such as high temperature, high humidity, and high altitude, which increases the difficulty of on-site operations and requires higher equipment and personnel requirements. Therefore, it is necessary to carry out hydrogeological exploration of karst leakage and research on ultrasonic identification technology of leakage points to improve the ultrasonic identification effect of leakage points. Through hydrogeological investigation of karst leakage in reservoirs, understand the development types and distribution characteristics of karst in reservoirs; then, the ultrasonic velocity signal in the reservoir is collected using a laser ultrasonic detector, and the internal noise of the signal is removed using wavelet denoising method; Next, based on the denoised ultrasonic sound velocity signal, a calculation model for the location of leakage points is established, and the momentum equation and continuity equation of ultrasonic propagation are used to identify leakage points.

This study focuses on a reservoir located on a carbonate rock stratum. Since the 1970s, the county government has dedicated significant efforts to its construction. The reservoir project is a multifunctional initiative primarily focused on irrigation and flood control, while also integrating urban water supply, rural drinking water for humans and livestock, power generation, and facilitating beach reclamation and ecological improvement. The designed irrigation area is 20.12 million μ, including 1.382 million μ of newly irrigated land. The reservoir provides flood protection for 50,000 μ of farmland and a population of 30,000, supplies 9.335 million m³ of urban water and 6.3037 million m³ of rural drinking water annually, and generates 10.728 million kW·h of electricity per year. The reservoir's normal pool level is 544.45 m, the flood control high level is 547.45 m, the design and check flood level is 548.90 m, the dead water level is 505.15 m, and the total storage capacity is 35.8 million m³.

The reservoir project comprises several key components: an 80.2-m-high asphalt concrete core rockfill dam, a 16-m-wide open spillway, a 55-m-high inclined horizontal water intake tower and diversion tunnel, an 87.49-km-long irrigation canal, a 114.72-km-long branch canal, a 28.2-km-long water transmission pipeline, two power stations, and a water plant project featuring a distribution of points, lines, and surfaces.

The reservoir has a ‘Y’-shaped layout on the plane. Its two branches flow into the dam site area: one from east to west and the other from south to north, where it meets the Cenlong River at Lianghekou. Both banks within the reservoir area are characterized by middle mountain terrain, with a total length of approximately 1.55 km. The natural gradient of the river channel within the reservoir is about 1.4%. Additionally, numerous underground rivers and karst formations are present on both banks of the reservoir.

The reservoir bank can be divided into a carbonate rock bank and a clastic rock bank based on the geological environment. The valley slopes on both banks of the carbonate reservoir bank are steep, and predominantly characterized by cliffs. The river valley exhibits a ‘U’ and asymmetric ‘V’ shape, with scattered loose eluvial deposits on the valley slopes and small collapsed rock fragments at the valley bottom, all located below the reservoir's normal water level. The stability of the reservoir slope is generally good.

The clastic rock reservoir section, primarily located at the reservoir's end, features relatively gentle slopes and a transverse ‘V’-shaped river valley. A small landslide with a volume of approximately 90,000 m³ is developed on the right bank. After the reservoir impoundment, the landslide is basically submerged. Although the reservoir water submerges the landslide, the volume of landslide material is minimal. Additionally, the numerous bends between the dam and the river have no impact on dam safety or reservoir operation. Following impoundment, the overall stability of the reservoir bank remains good, with only minor localized collapses and rock falls observed in some areas.

The main water-bearing rock formations within the dam site area of the reservoir and their water abundance are shown in Table 1.

The development types and distribution characteristics of karst in reservoirs can be understood through hydrogeological exploration of karst leakage. According to the geological survey of the dam site area, the development of surface karst has been understood. To investigate the vertical development types and depth patterns of karst in the dam site area, geological drilling is first used to reveal the vertical karst development. Then, geophysical testing methods such as high-density exploration, borehole acoustic waves, and borehole television imaging are used to determine the spatial distribution of karst development.

In the research area, the dip angle of the soluble rock layer is relatively large, ranging from 53° to 65°. Due to the influence of tectonic activity, joint fissures are relatively developed. Most of the carbonate rocks in the dam site area are covered by surface red clay. Only under the action of the reverse thrust structure on the left bank ridge of the dam site area, soluble rocks are relatively exposed. Under the action of atmospheric rainfall, exposed karst is formed in the form of karst ditches, karst troughs, and karst fissures. The lithology of this area is mainly gray-white thick layer of sandy clastic limestone, with fragmented rock mass and developed fault structural planes. The width of dissolution fractures in the research area varies greatly, usually developing along the joint fracture surface, and some areas are filled with calcite. Micro cracks gradually dissolve under the long-term erosion of rainfall, forming large cracks, and the rock mass on the crack surface is relatively rough. There are many dissolution fractures with a width of 2–3 cm in the dam site area. These surface fractures and fracture development zones usually provide good channels for the movement of groundwater and are the main pathways for karst leakage.

In the dam site area, the development of karst has a significant impact on the leakage and stability of the reservoir. The interconnected karst forms such as dissolution fissures, underground river systems, dissolution zones, and caves form complex karst leakage channels, increasing the risk of reservoir leakage. Therefore, in the construction and operation of reservoirs, it is necessary to fully consider the impact of karst, take effective anti-seepage and reinforcement measures, and ensure the safe operation of reservoirs.

2.2.1. The specific characteristics, formation mechanisms, and distribution patterns of different types of karst

The characteristics of dissolution fractures in the study area are significant, with a large variation in width, generally 2–3 cm, and some areas are 1 mm level, while the width is even larger in areas with strong development. The direction of fissures is often consistent with the joint surface, and the extension direction is varied, either straight or curved. The fissure surface is rough, with pits and protrusions formed by groundwater erosion. Cracks are often filled with minerals such as calcite, and the degree of looseness of the filling material affects its hydraulic conductivity. Its formation is mainly due to the dissolution of carbonate rocks by groundwater, and the infiltration of atmospheric precipitation into the ground forms acidic water to dissolve rock components, gradually expanding cracks over time. The stress generated by tectonic movements creates cracks in rocks, providing channels for groundwater and promoting dissolution. The dissolution fractures are widely distributed in the dam site area, and the exposed areas of carbonate rocks are more concentrated. The left bank ridge is affected by tectonic activity and has dense fissures; there are few cracks at the bottom of the valley, but strong dissolution occurs near the groundwater level, resulting in large crack sizes. Vertically, dissolution fractures are mainly concentrated in shallow strata, while the development of deep strata gradually weakens.

There is an underground river system downstream of the dam site area, with a triangular entrance, about 2 m high and 1.5 m wide, and an irregular cross-section. The underground river has clear water flow and flows all year round, with a flow rate of about 8–10 L/s during the dry season. The cave wall is smooth, and karst landforms such as stalactites and stalagmites can be seen locally. The sediment at the bottom of the river contains sand and gravel, which affects water flow and quality. This system is formed during long-term geological processes, where groundwater seeps through rock fractures and pores, corrodes rocks, widens and penetrates fractures, and forms channels. After the convergence of groundwater, erosion, and dissolution intensify, gradually forming large underground rivers. Its development is controlled by the lithology, geological structure, groundwater recharge, runoff, and discharge conditions of the strata. Underground rivers mainly develop in the C1x stratum, with a strike consistent with the dip and structural line of the stratum, extending from southwest to northeast. Vertically, underground rivers are located below the groundwater level, with their tops ranging from tens to hundreds of meters deep from the surface. The underground river system is connected to the surrounding karst landforms, forming a complex karst hydrogeological network.

Geological exploration data shows that there is one dissolution zone in the valley strata of the dam site area and two on the left bank ridge. The rocks in the dissolution zone are broken, making it difficult to extract rock cores. During the drilling process, drilling tools are prone to falling off and getting stuck. The rock is gray or dark gray in color, with a loose structure and developed pores and fissures. It has high permeability and water richness, which is the result of mineral precipitation and oxidation. The dissolution zone is formed by the long-term dissolution of groundwater, especially in tectonic fracture zones. Groundwater is prone to infiltrate rock fractures for dissolution, damaging rock structures and carrying sediment and other substances for erosion and erosion, expanding the scale of the dissolution zone. The dissolution zone is distributed in a strip along the structural fracture zone, and the dissolution zone in the valley strata is parallel to the direction of the river, with a width of several meters to tens of meters; The left bank ridge dissolution zone extends along the ridge direction, with a wide range but a narrow width. In the vertical direction, the development depth of the dissolution zone can reach several hundred meters. Its distribution is closely related to changes in groundwater level. When the water level rises, the dissolution effect increases, and when the water level drops, the upper part may be filled with sediment, weakening the dissolution effect.

Drilling ZK01 and ZK02 in the research area revealed two karst caves with different shapes and scales, including circular, elliptical, and irregular polygons. The interior space is open, and some parts are formed by underground lakes or rivers. The cave walls are covered with karst landforms such as dissolution grooves, stalactites, and stalagmites, with extremely high ornamental value. The formation of karst caves originates from the development of dissolution fractures and dissolution zones. When groundwater is rich in carbon dioxide, the dissolution process is enhanced, especially at the intersection of fractures or weak rock areas, gradually forming cavities and expanding into karst caves over time. Its formation is also influenced by factors such as groundwater flow velocity, rock solubility, and geological structure. In the dam site area, karst caves are mainly distributed in carbonate rock formations, closely related to structural fault zones and dissolution zones, and mostly located in areas of rock fragmentation. Vertically, karst caves often appear near or slightly above the groundwater level due to active groundwater dissolution. On the plane, there is no obvious pattern in the distribution of karst caves, but local karst cave groups may form.

The karst development type and distribution characteristics of the reservoir were analyzed through hydrogeological exploration of karst seepage (Kasahara et al. 2022). According to the geological exploration in the dam site area, the surface karst development was characterized. To investigate the vertical karst development type and depth rule in the dam site area, geological drilling was first conducted to characterize the vertical karst development. Subsequently, the spatial distribution of karst development was identified through high-density exploration, borehole acoustic wave, borehole television imaging, and other geophysical testing methods.

In the study area, the dip angle of the soluble rock layer is significant, ranging from 53° to 65°. Joint fissures are highly developed due to tectonic activity. Most carbonate rocks in the dam site area are covered by surface red clay, except on the left bank ridge, where thrust nappe structures have exposed soluble rocks. Atmospheric rainfall has further shaped these exposed rocks into karst features such as karst ditches, karst troughs, and karst fissures.

The lithology of this area consists of gray-white thick sandy clastic limestone. The rock mass is fragmented, with highly developed fracture structural planes. Corrosion fissures, varying in width, are typically developed along joint fissure surfaces. Some areas are filled with calcite. Micro-fissures gradually expand under rainfall scouring, forming larger fissures with rough rock surfaces. In the dam site area, numerous solution cracks with widths of 2–3 cm are observed. Surface fissures and fissure development zones serve as primary pathways for groundwater migration, acting as the main channels for karst leakage.

An underground river system is formed in the lower reaches of the dam site area, primarily within the C1x stratum. The portal of the river system is triangular, with a height of 2 m, a width of 1.5 m, and an irregular cross-section. The outlet direction is S41°E. The river flows year-round, with transparent and clear groundwater. During the dry season, the flow rate ranges from 8 to 10 L/s.

According to the drilling data of geological exploration, one corrosion zone is developed in the river valley stratum in the dam site area, and two solutions are developed in the left bank ridge.

The development characteristics of the dissolution zone in the dam site area are that it is formed along structural fracture zones, often filled with clay or secondary mud. Corrosion zones exhibit two forms: strip distribution on the surface and corrosion fracture zone and cavern underground. The rock core is typically highly fragmented, and drilling progresses rapidly, with the drill tending to detach or become stuck. In terms of electrical properties, these zones exhibit low resistance, which is clearly reflected in the geophysical electric sounding profile.

Under the long-term dissolution of groundwater, the carbonate rocks in the study area form differential dissolution of limestone. Controlled by joints and fractures, the dissolution continues to expand, forming underground caves of varying sizes and shapes. In the study area, two karst caves of different sizes are identified, exposed by boreholes ZK01 and ZK02, and developed near the dam site area. Drilling data reveals that the karst caves are either empty or partially filled with a small amount of clay in the lower section (Wang et al. 2022). The drilling process is characterized by instability. Due to fault influence, the roof rock mass at the upper part of the karst cave is relatively fragmented, with tunnel diameters generally ranging from 1 to 2 m. Local collapses may occur under external forces.

The working principle of the laser ultrasonic detector is as follows: a high-energy pulse laser (Lei et al. 2021) is used as the light source. The point light source is focused into a line light source through a lens to illuminate the surface of the karst pipeline in the measured reservoir. The surface of the karst pipeline interacts with the pulse laser to generate ultrasonic waves (Alguri et al. 2021). The data acquisition unit then collects the ultrasonic sound velocity signal, which contains noise, from the detection unit. The collected signal is denoised to extract the noiseless ultrasonic sound velocity signal. This processed signal provides a more accurate basis for the subsequent ultrasonic identification of karst leakage points in the reservoir.

Compared to other ultrasonic detectors, laser ultrasonic detectors have significant advantages:

• • Non-contact measurement: It does not require direct contact with the object being measured, avoiding surface damage, and is not limited by the surface roughness or shape of the object. It is particularly suitable for detection in special shapes, vulnerable or high-temperature environments, such as complex environments like karst reservoirs.

• • High spatial resolution: The laser beam can focus on small areas, achieving precise excitation and detection of ultrasonic signals, obtaining more accurate local information, and helping to discover small karst leakage points or structural changes.

• • Fast response: The pulse laser excitation process is brief and can quickly generate and acquire ultrasonic signals, making it suitable for monitoring rapidly changing physical processes, such as real-time capture of karst leakage signals in reservoirs.

• • Remote detection capability: With the help of optical systems, remote detection can be achieved. Areas that are difficult to reach, such as karst pipelines deep in reservoirs, can be detected without the need for close proximity, improving safety and convenience.

• • Signal susceptibility to interference: During laser propagation, it is susceptible to external factors such as dust, fog, and strong light, which can cause energy attenuation or spot deformation, affecting the quality of ultrasonic signals. There are many interference factors in the field environment, which may reduce measurement accuracy.

• • High equipment cost: Involving high-precision laser emission and reception systems, complex optical focusing devices, and professional data acquisition and processing equipment, the overall cost is high, limiting large-scale applications.

• • Limited detection depth: As the detection depth increases, the attenuation of ultrasound in the medium intensifies, the signal strength weakens, limiting the detectable depth, and the detection effect of deep karst leakage may be poor.

• • Complex data analysis: Laser ultrasound signals are rich and complex in information, requiring professional knowledge and complex algorithms for processing and analysis, which requires highly technical personnel and increases the difficulty of practical application.

Using the laser ultrasonic detection system, the collected reservoir karst ultrasonic velocity signal contains a large number of noise signals, which will affect the ultrasonic identification accuracy of reservoir karst leakage points. Therefore, the wavelet denoising method is used to remove the noise in the reservoir karst ultrasonic velocity signal (Sun et al. 2023).

The selection of wavelet basis functions is crucial in wavelet denoising, as different wavelet bases have unique characteristics.

Daubechies (Db) series wavelets: Commonly used and tightly supported, with increasing vanishing moments as the order increases, capable of capturing higher-order details. Db2 is suitable for processing mutation information, while Db7 has shown excellent denoising performance in this study and can preserve signal features. Its frequency domain localization characteristics are good, but it lacks symmetry and may introduce phase distortion.

Haar wavelet: The simplest, orthogonal symmetrical, and computationally convenient. However, the frequency resolution is low and may not be precise enough when processing complex signals, making it suitable for scenarios with high computational efficiency and simple signal characteristics.

Coilet wavelet: Approximately symmetrical, with high vanishing moments, it can effectively denoise while maintaining signal shape, and performs well in dealing with denoising problems that require high signal shape and features.

Mexican Hat wavelet: Derivative of second-order Gaussian function, good directionality, and frequency selectivity, suitable for edge detection. In denoising ultrasonic sound velocity signals, edge information can be highlighted, but it may not be effective when used alone in complex background noise.

The methods for selecting wavelet basis functions and decomposition levels are as follows:

Select wavelet basis function

Consider signal stationarity: Stationary signals are suitable for using wavelet bases with good frequency domain localization characteristics, such as the Db series; non-stationary signals may be more suitable for wavelet bases with good time-frequency localization characteristics, such as Morlet wavelets. Analyzing the characteristics of signal mutation: when there is a mutation point in the signal, high vanishing moment wavelet bases (such as Db7) can better capture the mutation information and suppress noise. Pay attention to the frequency components of the signal: select a wavelet basis with appropriate frequency resolution based on the main frequency range of the signal.

Select decomposition level

According to the characteristics of noise: when high-frequency noise is strong, more decomposition layers are needed to fully separate the noise and signal; when the noise is weak, excessive decomposition layers may lead to signal distortion. Using signal autocorrelation analysis: Calculate the autocorrelation sequence of the wavelet coefficient sequence, determine whether white noise dominates at the current scale based on specific conditions, and gradually determine the appropriate decomposition level. Combining experience and experimentation: based on similar signal processing experience, preliminarily determine the range of decomposition levels, evaluate the denoising effect under different decomposition levels through experiments, and select the optimal decomposition level. In this study, multiple experiments and analyses were conducted to determine the appropriate decomposition layers for denoising ultrasonic sound velocity signals in karst reservoirs.

Among them, is the wavelet coefficient of the layer j.

Among them, is the energy distribution probability of wavelet coefficients.

Among them, is the amplitude coefficient; is the bandwidth factor; is the peak arrival time of the reservoir karst ultrasonic sound velocity signal; is the center frequency of the ultrasonic detector; is phase; t is the collection time of the reservoir karst ultrasonic sound velocity signal.

Ultrasonic velocity signals of reservoir karst collected by simulated laser ultrasonic detector ⁠, combined with the applicability of wavelet bases and determine the best wavelet base.

It can be considered that white noise is dominant at the current scale, and further wavelet decomposition of the scale function is required; otherwise, it can be considered an effective signal dominant. To prevent excessive calculation, an upper limit of decomposition layers can be established. N represents the total number of wavelet coefficient series of reservoir karst ultrasonic sound velocity signal, while M denotes the total number of autocorrelation sequences of reservoir karst ultrasonic sound velocity signals.

The noise in the reservoir karst ultrasonic sound velocity signal is mainly a white noise signal composed of circuit noise. This study introduces the concept of reference noise, which involves collecting a noise signal of equal length after the acquisition of the reservoir karst ultrasonic sound velocity signal. This approach enables the estimation of the noise component within the reservoir karst ultrasonic sound velocity signal, demonstrating robust adaptability. Both the reservoir karst ultrasonic sound velocity signal and the reference noise signal undergo wavelet transformation with an identical number of layers (Li et al. 2021c). The noise standard deviation is calculated using the wavelet coefficient of each layer of the reference noise signal because the noise in the reservoir karst ultrasonic sound velocity signal shows the characteristics of Gaussian white noise, that is, the noise meets the normal distribution, based on 3 the standard deviation of the noise is used to determine the threshold value of reservoir karst ultrasonic sound velocity signal denoising, complete noise filtering, and improve the identification accuracy of reservoir karst leakage points (Yan et al. 2021).

Among them, j is the number of decomposition layers; is in the wavelet decomposition stage of the noise signal j layer's noise energy; is the karst ultrasonic sound velocity signal of noisy reservoir of the energy of the layer j.

The specific steps for using wavelet denoising to remove noise from the reservoir karst ultrasonic velocity signal are as follows.

Step 1: Conduct the first step for the reservoir karst ultrasonic sound velocity signal j layer wavelet decomposition to get the scale coefficient and wavelet coefficient;

Step 2: Conduct white noise inspection on wavelet coefficients. If the wavelet coefficients meet the white noise characteristics ⁠, execute step 1;

Step 3: Perform wavelet decomposition of the same number of layers on the reference noise signal, calculate the standard deviation of wavelet coefficients for each layer, and determine the threshold value;

Step 4: Conduct threshold processing on each layer of wavelet coefficients of reservoir karst ultrasonic sound velocity signal, reconstruct the signal, complete the reservoir karst ultrasonic sound velocity signal denoising, and provide accurate data support for leak point identification (Ning et al. 2021).

Among them, A is the cross-sectional area of the karst pipeline in the reservoir; P is the reservoir liquid flow.

Formula (11) is another expression of the continuity equation, which represents that at any position in the pipeline, the sum of the rate of change of liquid flow rate with axial distance x and the rate of change of cross-sectional area with time t is zero, reflecting the physical meaning of mass conservation when liquid flows in the pipeline. That is to say, in the absence of a liquid source or sink, the mass of liquid flowing into a small control body is equal to the mass of liquid flowing out of that control body.

Formula (12) is a deformation of the equation of motion, which describes the force and motion state of the liquid in the pipeline. The left side of the equation represents the rate of change in momentum per unit volume of liquid, including changes over time and changes along the axis of the pipeline; The first term on the right side of the equation represents the frictional resistance experienced by liquid flow, which is related to the flow rate, density, inner diameter of the pipeline, and friction coefficient of the liquid; The second term represents the force exerted by the pressure gradient on the liquid. This equation comprehensively considers the effects of various forces on liquid flow and reflects the dynamic characteristics of liquid motion in pipelines.

Formula (11) is another expression of the continuity equation, which more intuitively shows the relationship between liquid flow rate and cross-sectional area with position and time, and also follows the law of conservation of mass. Formula (12) is a deformation of the motion equation after ignoring elevation changes, simplifying the calculation process and making it easier for subsequent analysis.

Among them, is the stable denoising ultrasonic sound velocity signal in the reservoir karst pipeline after the leakage; is the change value of acoustic velocity signal of karst ultrasonic in denoising reservoir; is the stable liquid flow value in the reservoir after leakage; is the change value of liquid flow.

These two proportional coefficients reflect the quantitative relationship between changes in ultrasonic velocity signals and changes in liquid flow velocity, as well as between changes in liquid flow rate and changes in liquid flow velocity. They play a key role in subsequent calculations and help us establish a more accurate leakage point location calculation model.

Among them, is the length of the karst pipeline of the reservoir.

The karst pipeline of the reservoir is divided into two sections. is one of the first stations; is another distance from the terminal station. When the reservoir karst pipeline leaks, the distance from the leakage point to the initial station is ⁠.

The location of the leakage point of the karst pipeline of the reservoir can be determined by using Equation (24), based on the previous series of equation derivations and transformations, the changes in ultrasonic velocity signals at the beginning and end of the pipeline, as well as the length information of the pipeline, were comprehensively considered. By measuring and calculating these parameters, the location of the leakage point in the pipeline can be accurately determined, achieving ultrasonic identification of karst leakage points in reservoirs.

During the verification process of this experiment, various resources were allocated reasonably. In terms of manpower, a multi-disciplinary collaborative team has been formed. Professional geological exploration personnel are responsible for conducting comprehensive geological surveys of karst areas in reservoirs, including detailed investigations of karst development types, distribution characteristics, and geological structures, in order to lay a solid geological foundation for subsequent ultrasonic testing. Their work runs through the key stages of the early stage of the experiment and accounts for about 30% of the total experimental time. Technicians with knowledge of ultrasonic testing technology and signal processing operate laser ultrasonic detectors to collect ultrasonic sound velocity signals and use wavelet denoising and other methods to process and analyze the signals. They continuously participate in the entire experimental process, investing about 40% of the total manpower. Researchers familiar with the construction and calculation of mathematical models establish leak point localization calculation models based on ultrasound signals and related equations and complete leak point identification work. Their work focuses on data processing and model construction in the later stage of the experiment, with an investment time of about 30% of the total experimental time.

In terms of equipment, the core equipment, laser ultrasonic detectors, requires significant investment. The equipment is expensive, equipped with high-precision laser emission and reception systems, complex optical focusing devices, and professional data acquisition and processing equipment. The purchase cost of the equipment accounts for 70% of the total investment in experimental equipment. In addition, geological drilling equipment is also equipped to reveal the vertical development of karst, as well as geophysical testing equipment such as high-density exploration, borehole acoustic waves, and borehole television imaging to determine the spatial distribution of karst. These auxiliary equipment investments account for 30% of the total experimental equipment investment. Moreover, certain resources have been allocated for the maintenance and calibration of the equipment to ensure stable operation, with maintenance costs accounting for approximately 10% of the equipment purchase cost.

In terms of materials, although the cost of auxiliary materials is relatively low compared to equipment, they are indispensable. The procurement cost of standard samples used for calibrating laser ultrasonic detectors, protective equipment, communication equipment required for field operations, and other materials account for approximately 5% of the total experimental budget.

In terms of time arrangement, geological exploration work takes a long time, including a comprehensive investigation of the reservoir area, field survey, data collection, and analysis, which accounts for about 30% of the total experimental time. Ultrasonic signal acquisition requires multiple measurements at different reservoir water levels, and the data processing, model calculation, and result analysis after measurement also require a lot of time. This part of the work accounts for about 50% of the total experimental time. The remaining 20% of the time will be used to troubleshoot and resolve equipment malfunctions, data anomalies, and other issues that may arise during the experiment, ensuring the smooth progress of the experiment.

Figure 2 illustrates that the reservoir is encompassed by mountainous terrain.

According to Figure 3, there are three karst pipelines in the reservoir, one of which is long. The experiment proves that this technology can effectively investigate the karst hydrogeology of the reservoir and understand the distribution of karst pipelines.

According to Figure 3, the reservoir contains three karst pipelines, one of which is of considerable length. The experimental results demonstrate that this technology effectively investigates the karst hydrogeology and clarifies the distribution of karst pipelines. Ultrasonic sound velocity signals were collected using this technology, and the results are presented in Figure 4.

To simulate realistic conditions, a 5 dB interference noise was superimposed on the reservoir karst ultrasonic sound velocity signal generated by the Gaussian model. To mitigate the impact of random interference, the final result was obtained by averaging the outcomes of 1,000 repeated calculations. Furthermore, the optimal wavelet base is selected using the technology in this paper to remove the internal noise of the reservoir karst ultrasonic sound velocity signal. The wavelet base selection results are shown in Table 2.

According to Table 2, the Db7 wavelet basis exhibits the highest ratio of wavelet energy to energy entropy, reaching 299.0417. A higher ratio of wavelet energy to energy entropy indicates a superior denoising effect on the reservoir karst ultrasonic sound velocity signal. Therefore, the Db7 wavelet basis was selected as the optimal choice and applied to denoise the reservoir karst ultrasonic sound velocity signal, significantly improving its noise reduction efficiency. The research results can also be applied to other similar underground engineering, such as underground engineering and tunnels, providing effective solutions for leakage problems and promoting scientific, technological, and industrial advancements in related areas. Strengthening the results and findings of the current research not only improves the technical level of identifying karst seepage points in reservoirs but also demonstrates broad practical application value and social significance. Through continuous optimization and improvement of relevant technologies, we can provide more solid technical support for the safe operation and sustainable development of the reservoir.

According to Figure 5, the technical denoising treatment proposed in this paper clearly presents the changing trend of the reservoir karst ultrasonic sound velocity signal. This improvement is conducive to improving the ultrasonic identification accuracy of the subsequent reservoir karst leakage points. From the denoised ultrasonic sound velocity data, a sudden change is observed at approximately 11 s, indicating a leakage issue in the reservoir karst pipeline at that location. The maximum and minimum ultrasonic speeds are approximately 1,527.9 and 1,526.0 m/s, respectively, resulting in a change of about 1.9 m/s. The experiment shows that the technology can effectively remove the noise of ultrasonic velocity signals in reservoir karst. As a result, it provides an effective denoising method for ultrasonic identification of karst leakage points in reservoirs. By removing noise interference, useful information from the acoustic velocity signal can be extracted more accurately, thus improving the accuracy and reliability of leakage point identification. This approach not only helps to promptly discover and repair reservoir leakage issues, ensuring safe operation but also provides solutions for leakage problems in similar geological environments. Furthermore, it promotes scientific and technological progress as well as industrial development in related fields.

According to Figure 6, the technology in this paper can effectively identify the reservoir karst leakage points. The identified locations are very close to the actual leakage points, with minimal error, indicating high identification accuracy. The experiment demonstrates that this technology can accurately identify reservoir karst leakage points. By accurately identifying the karst leakage point of the reservoir, the potential safety hazards can be found and solved in time, thereby avoiding risks to reservoir operations caused by leakage. Additionally, this approach helps improve the efficiency and science of reservoir management, reduce maintenance costs, and achieve sustainable use of water resources. By improving the identification accuracy and stability, it provides a strong guarantee for the safe operation and sustainable development of the reservoir. Furthermore, the promotion and application of this technology will also provide effective solutions for leakage problems in other fields. It will also promote scientific and technological progress as well as industrial development in related areas.

According to Figure 7, with the increase of the water level of the reservoir, the RMSE of this technology to identify the karst leakage points of the reservoir began to decline. The minimum RMSE of this technology is about 0.122, which does not exceed the RMSE threshold, indicating that this technology has high accuracy in identifying karst leakage points in reservoirs. The lower the root mean square error, the higher the recognition accuracy. Therefore, 0.122 should be the lowest value here, indicating that this technology has a smaller error and higher recognition accuracy when identifying karst leakage points in reservoirs. The experiment demonstrates that the RMSE for identifying karst leakage points using this technique is significantly low across different reservoir water levels, indicating high identification accuracy. This is attributed to the method's ability to characterize the development patterns and spatial distribution of karst through hydrogeological investigations. Subsequently, the ultrasonic velocity signals were collected using a laser ultrasonic detector, and internal noise was eliminated through wavelet denoising. Based on the denoised signals, a calculation model for leakage point localization was established, leveraging the momentum equation and continuity equation of ultrasonic propagation to accurately identify leakage points. The practical implications of these findings are substantial. This method provides an efficient and accurate approach for identifying and locating karst seepage points in reservoirs, enabling timely detection and repair of leakage issues to ensure reservoir safety. Additionally, it offers a scientific basis for reservoir management and maintenance, reducing operational costs. Furthermore, the method can also be applied to other similar geological environments, such as underground engineering and tunnels, providing effective solutions for leakage problems in these fields.

Confidence interval analysis: The width of the confidence interval at different water levels reflects the stability of the recognition results. When the water level is high, such as near the normal water level, the confidence interval width is narrow (average of 0.05 m), indicating that the identification results are stable and less affected by environmental factors. When the water level is low, the width of the confidence interval increases (averaging up to 0.1 m), indicating a high degree of dispersion in the identification results, which may be related to the instability of water flow and the complex influence of geological conditions on ultrasonic signals.

Sensitivity analysis: This study investigated the impact of input parameter changes on the identification results of leakage points. By changing the input values such as ultrasonic velocity signal, liquid flow rate, pipeline parameters, and geological parameters one by one, observe the changes in the identified location. The results showed that the change in ultrasonic velocity signal had a significant impact on the recognition results. When the velocity increased by 10%, the average deviation of the leakage point position was 0.15 m. When the inner diameter of the pipeline varies within ±5%, the relative change in the identification position is relatively small, with an average deviation of only 0.03 m. This indicates that recognition technology is sensitive to ultrasonic velocity signals, and accurate acquisition of this signal is crucial for practical applications. Meanwhile, sensitivity analysis of other parameters can also help clarify key parameters, improve the reliability and recognition accuracy of the model.

However, this technology also faces some problems in practical applications. On the one hand, the geological conditions in karst areas are extremely complex. In addition to caves and dissolution fractures, there are often multiple rock types that are alternately distributed, such as carbonate rocks, clastic rocks, and metamorphic rocks. The acoustic characteristics of different rocks vary greatly, which can interfere with the propagation and analysis of ultrasonic signals, leading to misjudgment or omission of leakage points. Moreover, the underground hydrological conditions in karst areas are complex, with varying groundwater flow rates and directions, which may cause distortion of ultrasonic signals and affect the accurate identification of leakage points. On the other hand, there are many environmental interferences in the field, and electromagnetic interference, construction noise, rainstorms, sand dust and other bad weather caused by industrial activities have an impact on the detection. Electromagnetic interference affects the operation of laser ultrasonic detectors, construction noise masks ultrasonic signals, and severe weather affects laser propagation and ultrasonic signal quality, and reduces detection accuracy. In addition, although laser ultrasonic detectors have a certain detection depth, for deep karst leakage points, the ultrasonic signal attenuation is large and the intensity is weakened, making it difficult to accurately identify their location and characteristics. The detection range of this technology is limited. When detecting large-scale karst areas in reservoirs, multiple measurements and data stitching not only require a lot of work but may also introduce errors.

Corresponding solutions can be taken to address these issues. In terms of detection methods and signal processing technology, multi-frequency ultrasonic detection technology is adopted to improve the identification ability of leakage points under complex geological conditions by utilizing the sensitivity differences of different frequency ultrasonic signals to different geological structures. At the same time, combining artificial intelligence technologies such as deep learning to improve signal processing algorithms, accurately analyze and process collected ultrasound signals, enhance signal feature extraction capabilities, and reduce misjudgments and omissions. In terms of on-site environmental adaptability, improve the laser ultrasonic detector, add anti-electromagnetic interference and noise filtering devices, and enhance the stability and reliability of the equipment in complex environments. During inclement weather, build protective shelters for equipment to reduce the impact of weather on laser propagation and ultrasonic signal acquisition. Reasonably arrange the testing time and avoid interference periods. To expand the detection depth and range, higher-power laser ultrasonic detectors are developed to increase the emission energy of ultrasonic signals and enhance the propagation ability of signals in deep media. Combining other geophysical detection methods such as ground penetrating radar (GPR) and electromagnetic methods, complement each other's advantages, expanding the detection range, and improving the detection accuracy of deep leakage points. Optimize the measurement plan, arrange measurement points reasonably, and reduce data stitching errors.

When verifying the effectiveness of this technology in identifying karst leakage points in reservoirs, only two methods were compared, which has shortcomings in the comprehensiveness of experimental design. There are many advanced or commonly used methods available for comparison in related fields. ERT (Electrical Resistivity Tomography) (direct current resistivity method) calculates the resistivity distribution of underground media by supplying direct current to the ground and measuring the potential difference. Due to the differences in resistivity among different geological bodies in karst areas, the abnormal changes in resistivity can be used to infer the development and leakage location of karst. This method is sensitive to low-resistance anomalous bodies and can quickly delineate the leakage range, providing macroscopic guidance for large-scale detection. However, ERT has relatively low resolution, making it difficult to accurately locate leakage points, and is greatly affected by terrain. It is prone to errors in areas with severe undulations and has limited detection depth. It is mainly suitable for shallow karst leakage detection; In contrast, GPR utilizes the propagation characteristics of high-frequency electromagnetic waves in underground media to infer underground structures and anomalous bodies by receiving information from reflected waves. It has high resolution and can clearly display shallow geological structures and abnormal body shapes. It has a good effect on detecting shallow karst leakage points and small caves and has a fast detection speed, which can quickly scan large areas. However, GPR detection depth is limited, and electromagnetic waves attenuate severely with increasing depth. Moreover, propagation losses are high in media with high water content, which affects the detection effect. The ultrasonic method is less affected by water content and theoretically has a deeper detection depth, which can detect karst leakage points at deeper depths; the seismic reflection law uses artificial excitation of seismic waves and reception of their reflected waves to draw reflection profiles of underground geological structures, thereby identifying karst development zones and leakage areas. This method has a large detection depth and can be used to study deep geological structures and detect karst structures in deeper areas. It has advantages in determining large karst caves and deep leakage zones. However, the resolution of the seismic reflection method is relatively low, making it difficult to accurately distinguish small leakage points and fine geological structures, and its implementation is greatly limited by site conditions. In contrast, ultrasonic methods have high resolution, a strong ability to identify small leakage points, flexible operation, and are less limited by site conditions. But in terms of detection depth, the seismic reflection method has more advantages. For example, the high-density electrical method commonly used in dam leakage detection uses measuring electrodes to collect the apparent resistivity of underground media, which is widely used in many engineering scenarios. However, in the scenario of dam leakage detection, there is a problem of poor grounding effect of media such as concrete and stone, and a longer measuring line is required to ensure the detection effect. Compared with it, this ultrasonic identification technology does not need to consider the issue of medium grounding, and there are no special requirements for the length of the measuring line. It has obvious advantages in complex geological medium conditions.

GPR is also a commonly used leakage detection method. Based on the reflection principle of high-frequency electromagnetic waves in underground media, it can achieve high-resolution detection in shallow leakage paths (<10 m) with significant differences in relative permittivity and conductivity of the media. However, in dam bodies with high moisture content, electromagnetic wave attenuation is severe, and the effective detection distance is greatly shortened, resulting in poor detection effects for deeper leakage points. The ultrasonic identification technology used in this study is not affected by moisture content and can effectively detect karst leakage points at different depths, demonstrating unique advantages in terms of detection depth and anti-interference ability.

The elastic wave CT (Computerized Tomography) method uses the transmission of elastic waves in the underground medium between boreholes to achieve CT imaging of underground medium wave velocity based on the differences in wave velocity between different media, with high accuracy. However, it belongs to the category of destructive detection technology, which requires multiple drilling holes deep to the bottom of the dam, and must ensure that the dam leakage channel is located between the drilling holes, making the application conditions more stringent. In contrast, this ultrasonic recognition technology is a non-contact detection method that does not require drilling, avoiding damage to the dam structure, and can comprehensively detect the entire karst area of the reservoir, making it more applicable.

Real-time monitoring systems face many challenges in karst areas of reservoirs, mainly including data transmission delays, equipment stability issues, difficulties in processing massive amounts of data, and system compatibility issues. To address these challenges, the following solutions can be taken:

• (1) Optimize data transmission network: Adopt advanced wireless transmission technology, set up signal relay stations, apply data compression algorithms, and reduce transmission latency.

• (2) Improve equipment stability: Select high protection level equipment, conduct regular maintenance, and adopt redundant design to ensure continuous operation of the system.

• (3) Improve data processing algorithms: Introduce big data and artificial intelligence technologies such as deep learning to quickly and accurately analyze data, establish data caching mechanisms, and improve processing efficiency.

• (4) Resolve system compatibility issues: Develop unified standards, develop data conversion interfaces, establish a system integration testing platform, and achieve data sharing and collaborative work between systems.

If the comparison with these advanced or commonly used methods is added to the experiment, it can more comprehensively and intuitively highlight the advantages of this ultrasonic recognition technology in identifying karst leakage points in reservoirs, including higher recognition accuracy, wider applicability, stronger anti-interference ability, and lower detection cost, thereby further enhancing the credibility and persuasiveness of the effectiveness verification of this technology.

When analyzing the identification accuracy of karst leakage points in reservoirs at different water levels using this technology, relying solely on RMSE is not comprehensive enough. Figure 7 shows the decreasing trend of RMSE with the rise of reservoir water level, which is influenced by multiple factors. First, the rise in water level stabilizes the water flow within the karst pipelines of the reservoir. When the water level is low, the water flow is easily affected by the complexity of the terrain and local eddies inside the pipeline, resulting in large fluctuations in the ultrasonic velocity signal and increased recognition errors. At high water levels, the water flow is relatively stable, the interference of ultrasonic signals is reduced, the recognition accuracy is improved, and the RMSE is reduced accordingly. Second, changes in water level also affect the pressure distribution within karst pipelines. When the water level is low, the pressure inside the pipeline is small, and small cracks or voids may partially close, affecting the ultrasonic propagation path and velocity. After the water level rises, the pressure increases, and cracks and cavities are opened by water pressure. The ultrasonic propagation path is more stable, and the signal characteristics are more obvious, which helps to improve recognition accuracy and reduce errors. In addition, the geological environment around the reservoir also affects the recognition accuracy with changes in water level. The rise of water level will change the saturation degree of surrounding rock and soil, and the absorption and scattering characteristics of ultrasonic signals are different between saturated and unsaturated rock and soil. When the water level is low, there are many non-saturated rock and soil masses, which have strong absorption and scattering of ultrasonic signals, severe signal attenuation, and affect recognition accuracy. When the water level is high, the saturation degree of the rock and soil mass increases and the influence on the ultrasonic signal is relatively stable, which helps to reduce the root mean square error.

In summary, the RMSE decreases regularly with the rise of water level, which is closely related to changes in water flow state, pressure distribution, and surrounding geological environment. Thoroughly exploring the causes and patterns of these error changes can help to gain a more comprehensive understanding of the performance of this technology under different operating conditions, providing solid theoretical support for practical engineering applications.

In order to further verify the effectiveness of the proposed method, the proposed method is compared with the adaptive event-triggered fuzzy positioning control based on actuator saturation hybrid attack and the method in reference (Malekpour & She 2021). The test index is recognition accuracy, and the specific comparison results are shown in Table 3.

As shown in Table 3, the proposed method achieves a recognition accuracy of 98.15%, significantly higher than the 89.36 and 87.46% accuracy of methods (Liu et al. 2021b; Malekpour & She 2021). This superior recognition accuracy indicates that the proposed method can more precisely identify the location and extent of karst leakage in reservoirs. Accurately identification of leakage points enables timely repair and reinforcement, preventing further deterioration and ensuring the safe operation of the reservoir. These capabilities are highly significant for preventing and controlling karst leakage in reservoirs.

Water conservancy projects are used to control and allocate surface water and groundwater, mitigating risks and maximizing benefits. Their operation safety is crucial to the national economy and people's livelihoods. Currently, over 36,000 large-scale artificial water conservancy projects with a height exceeding 15 m are in operation worldwide. China, with the widest distribution of karst, has seen rapid development in water conservancy projects, leading to an increasing number of reservoirs being constructed in karst areas. However, the presence of karst poses significant challenges to the structural stability of main projects during construction, foundation treatment measures, and the success of water storage during operation, potentially affecting the overall success of the project.

Research on the hydrogeological investigation of karst water temperature and leakage points, along with ultrasonic identification technology, offers direct theoretical insights and practical guidance for the design, construction, and management of practical and similar projects. The experimental results show that the maximum RMSE for karst leakage point identification using this technology is 0.122, with a minimum of 0.021, proving its correctness and effectiveness. However, the accuracy and reliability of ultrasonic recognition technology in complex karst geological environments require further improvement to meet practical engineering needs. Additionally, integrated technologies involving real-time monitoring and early warning systems are needed to better address the risks and impacts of karst seepage.

Future developments should focus on integrating multiple sensor data, imaging technologies, and geophysical detection methods to enhance the monitoring accuracy and reliability of karst leakage areas. The introduction of artificial intelligence and big data analysis technologies could enable automatic identification and real-time monitoring of karst leakage hydrogeological information. Despite some achievements in hydrogeological investigation and ultrasonic identification of leakage points, limitations remain. For instance, ultrasonic identification technology may struggle to accurately identify leakage points in complex karst morphologies and multi-media interfaces, and hydrogeological investigation methods may not be applicable in extreme climates or areas with complex terrain.

Future research should explore more suitable ultrasonic recognition technology for complex karst environment, such as multi-band or multi-mode ultrasonic detection. Develop integrated survey methods that take into account multiple geological and hydrological factors. A variety of survey technologies and identification methods are effectively integrated to form a comprehensive solution. Using the Internet of Things, cloud computing, and other technologies could enable real-time transmission and intelligent analysis of survey data.

This study did not receive any funding in any form.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.