Seepage identification of Sidoarjo mud embankment via 2D resistivity and self-potential methods

Assessment of embankment stability is one of the ways to discover the embankment condition. Several factors can affect the strength of the embankment body including seepage, leakage, deformation (vertical and horizontal), and overtopping. Hence, identification of seepage in the subsurface of the embankment is important to provide early information about the threat of embankment failures. Sidoarjo mud (LUSI) embankment has been collapsed several times since it built in 2006. Most of the failures are mainly caused by the existing water seepage in the subsurface of the embankment. To identify the seepage pathways of the embankment body, two non-destructive geo-electricity methods were applied in the LUSI embankment. Direct current resistivity (DCR) and self-potential (SP) methods were carried out to reconstruct subsurface conditions at lines P76-P79. Therefore, seepage interpretation was conducted to identify the presence of water flows through the embankment body. 2D tomography of resistivity data revealed the indication of water seepage in some measurement areas. This information was strengthened by the numerical interpretation of self-potential data, recognizing water seepage through the embankment body in each line.


Introduction
Mud volcano is a phenomenon where fluids such as hydrocarbons and methane are released to the earth's surface.This phenomenon commonly appears on the earth's surface through fractures underground.Hot mudflow in the Porong, Sidoarjo, East Java initially appeared on May 29, 2006.The presence of two fault systems (Siring and Watukosek) across the LUSI area becomes the channel to spout the materials out to the surface [1].The active crater erupts liquid mud with a volume rate reaching 5000 m 3 /day.Previous research done by Mazzini point out that the volume of extrusion increased from 120.000 m 3 /day to 180.000 m 3 /day after some earthquakes in 2006 [2].Eruption materials contain water vapor, CO 2 , gas, and CH 4 .The type of fluid that comes out with the mud has a salinity of ~20 g/kg which is lower than the salinity of seawater (~35 g/kg).This composition indicates 1250 (2023) 012017 IOP Publishing doi:10.1088/1755-1315/1250/1/012017 2 the presence of dilution and modification of seawater under LUSI.The research also provides information on the existence of several factors that influence the volume eruption such as volcanic activity, earthquakes, as well as the formation of subsurface seawater to the continuous LUSI eruption.
To prevent the widespread impact of the LUSI eruption, an embankment was built around the overflowing mud to control the surrounding area [3].This embankment dam becomes a hot mud pool before the dredging process to the Porong River.The embankments were constructed using soil-based material and fine-grained rock to meet a flexible design as a mud retainer.However, the design cannot solve the three main problems in the field, that is the shear strength of the soil, subsidence, and mud pressure.The embankment was constructed using soft clay materials so that the strength of the soil is quite low [4].In addition, excess pore pressure due to fluids emerging from the Kalibeng Formation increases the vulnerability to embankment failure [2].
Since it was built, the embankment has collapsed several times due to the accumulation of mud that increases continuously, resulting in a large amount of hydrostatic pressure on the embankment body.The high moisture content of the mud indicates that mud has a low viscosity.Therefore, the mud tends to spread to the side and applied some pressure on the embankment which eventually induces it to collapse [1].
Monitoring an embankment was very important to ensure the stability of its structure.The geotechnical and hydraulic properties of materials in various types of dams were different, so it is necessary to analyze the stability according to their characteristics.In general, embankment failure is caused by several types of mechanisms.The mechanism of embankment failure can occur due to structural or hydraulic factors.The seepage failure rate reached 40% of all the embankment failure cases [5].Seepage that accumulates in the body of the embankment can be one of the causes of embankment failure [6].The flow rate of the fluid in the soil which induces embankment failure can be expressed as an empirical equation by Darcy's law:  = .. (1) where  represents the water flow rate (discharge), A is stands for the cross-section area of the medium,  and  are Darcy coefficients of permeability and hydraulic gradient, respectively.Some embankments can withstand the presence of seepage to some extent.However, the rate and quantity of the seepage should be controlled.If the water seepage was uncontrolled, it would erode fine soil material from the downstream slope and continue to move towards the upstream slope to form a piping system which often leads to the complete failure of the embankment [5].

2D Resistivity Method
The resistivity of a rock ideally will not change even though the potential difference or electric current changes.Resistivity depends on the type of material used [7].The characteristics of a rock to resist electric current can be quantified by resistivity.Another factor that affects the resistivity value is the porosity and saturation of the fluid.Assuming the rock pores are filled with fluid, the rock resistivity tends to decrease if the porosity value increases.The relationship between resistivity and porosity can be described by the Archie equation (1942), namely: ) where   is the effective resistivity of rock,   ,, represents water resistivity, porosity, and water saturation, respectively, m, n, and a is constant with the value are 0.5 ≤  ≤ 2.5, 1.3 ≤  ≤ 2.5, and  ≈ 2. The ratio of the effective resistivity of rock and resistivity of water can be referred to as the formation factor.

Data acquisition of 2D-resistivity
Electrical current injected into the homogeneous soil at a certain point on the surface will propagate radially to form a hemisphere.The voltage between two different points below the surface will decrease in the direction the electric current travels.The line connecting points that have the same potential value is called the equipotential.This equipotential line will pass through points with the same electric current in a homogeneous medium.The potential difference gradient on a homogeneous soil that forms a hemisphere due to a single source of electric current can be described mathematically by the equation: (3) where , , and  are the electric potential, current, and area of the half surface of the sphere, respectively.Then,  represents the rock resistivity.For current propagation using two current electrodes that have a certain distance, the electric potential that appears around the measurement point will be influenced by the two electrodes.
The configuration used for data collection is Wenner-Schlumberger.This method was conducted by plugging the first electrode into the track with a distance between the electrodes of 3 meters.Thus, the cable is connected to each electrode and resistivity meter and battery.The rest of the measurement was carried out automatically, according to the resistivity meter device settings.Then the voltage and electric current are measured automatically by the resistivity meter.Since the maximum resistivity mapping target is approximately 15 meters, the measurement space was set in short and each measurement path needs to be dispart as shown in Figure 1.

Data processing of 2D-resistivity
The measurement data were analyzed to obtain the 2D apparent resistivity value.The resulting resistivity value indicates the apparent resistivity.Therefore, the data inversion process should be carried out to produce the real resistivity value.In this inversion process, the constrained Gauss-Newton Method was used to minimize the objective function which is a combination of misfit and constraint.The result of this inversion process is the 2D resistivity value.Resistivity data is processed using Earth Imager 2D Software applied the Least-Square Smoothness Constraint algorithm.

Self-Potential Method
Self-potential is a passive geophysical method that uses the principle of measuring the earth's natural potential difference due to electrochemical, electrokinetics, and thermoelectric fields which occur under the earth's surface.The measured potential values are generated by electrochemical processes, which involve reduction and oxidation, which occur when ore or metallic materials interact with rock or groundwater [8].Electrochemical processes generally cause strong SP anomalies (up to hundreds of millivolts).In addition, the mobility of anions and cations due to different concentrations of solutions might trigger potential differences.This type of potential is called diffusion potential.There is another mechanism that caused natural potential known as streaming potential, which generally has an amplitude of a few millivolts to hundreds of millivolts.Streaming potential appears because of the 4 movement of groundwater in porous rocks caused by a pore pressure gradient [9].In this case, groundwater plays an important role by acting as an electrolyte [10].Self-potential methods have some advantages such as relatively straightforward measurement, fast, and suitable for shallow subsurface analysis [10] [11].

Data acquisition of self-potential
Self-potential measurements are carried out at a set of measurement points or commonly known as self-potential stations.The equipment used in the SP method of measurement is quite simple, that requires a pair of electrodes (porous pot) which is connected by a cable to a voltmeter.The value of the natural potential difference is measured by burying a pair of non-polarizing electrodes connected to a voltmeter.Non-polarizing electrodes are formed from metals immersed in a saturated solution of their salts.The electrode and its saturated solution used in this research are Cu in CuSO 4 .The purpose of using non-polarizing electrodes was to overcome the appearance of apparent potentials that might arise due to contact of metal materials with the ground.The measured electrical potential difference between the two electrodes has a high sensitivity of at least 0.1 mV [10] and is generally less than 100 mV [11].
Configuration setting of SP field measurement is divided into two types of procedure.The first is the leapfrog method, also called as gradient method, which used a pair of electrodes to be placed in a fixed space, then the two electrodes are moved alternately along the survey line.Spacing between two electrodes with a distance of 2 meters is usually good enough for the majority of applications [12].Another type of configuration for data acquisition is a fixed-based method.This method is carried out by setting a fixed electrode at the base station and one electrode moves along the track.Normal polarity occurs when the base electrode is connected to the negative input of the multimeter and the switching electrode is connected to the positive input of the multimeter.By using this method, a long cable is needed to cover the entire measurement area.However, the advantage of this method provides better data quality because of the smaller cumulative error compared to the leapfrog method [10].In this research, there are two lines as the object of data measurement, which are lines P75-P67 and P76-P77 as shown in Figure 2. The length of each measurement line is 440 and 330 m, respectively.

Data processing of self-potential
Environmental conditions during the measurement process cause the measurement data unavoidable from noise.These data inherently not represented the actual subsurface conditions.Therefore, correction and filtering data are important to reduce the effect of noise on data measurement [12].Reference correction is performed when the reference electrode was moved.The reference point was transferred due to the limitation of cable which links the porous pot and multimeter.In the next measurement, the moving electrode changes its role as a new reference electrode and the previous reference electrode is used as a moving electrode for the next measurement.Reference correction is done by adding up the potential value at the new reference point into all the potential difference values in subsequent measurements [13].
In addition, a filter process might be applied to reduce noise contained in the data.Empirical Mode Decomposition (EMD) is used to separate and reduce the noise during the measurement process.This method was introduced to analyze non-linear or non-stationary data and then decompose it into several modes known as Intrinsic Mode Functions (IMF) [14].EMD works by decomposing complex signals into several oscillatory components modulated in amplitude and frequency called IMFs [15].However, the output of the EMD filter is quite prone to mode-mixing.Mode-mixing happens when similar modes appear in some IMF or it might come up as one mode was distributed to several parts of the IMF [16].To overcome this problem, another filtering method that is Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) was proposed [17].CEEMDAN filter was decomposed signal () as expressed below: () =  =1    () + () (4) In the SP method, the filter is worthwhile to eliminate the linear trend of the data which is generally correlated with electrode deviation and the slope of the measurement area.In addition, this method could also reduce high-frequency noise which reflects the telluric effect associated with shallow subsurface heterogeneous conditions [9].
Then, filtered data should be inverted to obtain the model parameter of SP data.The inversion was performed using Ensemble Kalman Inversion (EKI).Ensemble Kalman Filter (EnKF) is an algorithm used to analyze and determine the model parameters of data [18].The initial process that needs to be done is to determine the number of ensembles (Ne) and the initials of the model parameters (as many as the number of ensemble members).The next step is to calculate the objective function of the ensemble model.The objective function for each ensemble of the model parameters X is calculated using the following equation [19]: where   is data obtained from field measurement and (  ) denotes forward modeling function.
The model parameter depends on the assumption used in forward modeling.To obtain a more quantitative distribution of subsurface physical properties, it is generally done through modeling.The model is a representation of the subsurface geological condition by anomalous objects with certain physical and geometric quantities [20].The geometry of subsurface structures can be illustrated in the form of spheres, horizontal and vertical cylinders, and inclined sheet structures [8].In the case of LUSI, seepage in the embankment can be assumed by modeling the SP anomaly in the form of spherical or cylindrical geometry.The general equation for the anomaly SP (  ) at any point P in the measurement lines is denoted as: where ,  0 , ℎ   and for polarization magnitude, the center position of the anomaly source, depth of the center anomaly, and polarization angle, respectively [21].Then  denote a shape factor of the anomaly.The shape factors of a sphere (3-D), horizontal cylinder (2-D), and vertical cylinder (2-D) are 1.5, 1.0, and 0.5, respectively [22].

Interpretation of 2D-Resistivity
The results of the inversion process of resistivity data at lines P67-P75 are shown in Figure 3.These three figures depict the apparent resistivity of the measured data (Figure 3a), the apparent resistivity of the calculation (Figure 3b), and the 2D resistivity model (Figure 3c).Generally, the results of the inversion contain Root Mean Square (RMS) error information that describes the fitting value between the apparent resistivity measurement data and the calculation result.At this location, the RMS error is 23.47%.Determination of the "best" model can be done in two ways, namely through an assessment of the uncertainty of the model parameters and the suitability of the model results compared to geological conditions during the data measurement.Furthermore, the 2D resistivity model resulting from this inversion can be interpreted to identify seepage on the Sidoarjo mud embankment.The resistivity value of the LUSI embankment might be higher than the foundation rock (the embankment and foundation are bounded by a black dotted line), then the low resistivity value in the embankment layer may be caused by saturation of the fluid through the embankment (in Figure 4 and Figure 5 is marked with a dotted red line).Fluid saturation in this embankment contained of rainwater combined with the eruption material, which forms 40% liquid (containing Ca, Li, Sr, with high salinity or NaCl dominant content), and the rest are solids material.The solid material might contribute to inducing excess pore pressure on the embankment.
The LUSI embankment was constructed by compacted expansive material which is able to be saturated by fluids (Sungkono et al., 2018).According to Schön (1998), porous rocks or fractures when filled with air (dry) have high resistivity (> 104 ), while rocks whose pores or cracks are filled with water (wet) will have low resistivity (conductive).Therefore, embankments that contain fluid through the body and pores saturated with mud fluids tend to have low resistivity values.Thus, a low resistivity value on the inversion results indicates the position of the fluid saturation on the embankment.The red dotted lines in Figure 4 and Figure 5 indicate an anomaly because it has a lower resistivity value (high conductivity) (0.1 -1.3Ωm) than the resistivity value of the surrounding area.Low resistivity anomaly in the embankment body might occur due to fluid saturation through the porous material or fracture of the embankment.Figure 4 show a fracture which is interpreted as a black line.The areas A1 and B1 in Figure 4 indicates that the soil was contaminated by a saturated fluid due to the fracture.Figure 5 also shows an indication of crack passes through the embankment at line D, where a distance of 54-72 meters, and line E at a distance of 72-90 meters.That area expressed a low resistivity value surrounding the crack line of the embankment.The result of seepage at lines P76-P77 is greater than at lines P67-P75.This situation might occur due to geological conditions effect on the time of measurement which shows large vertical deformation at lines P76-P77.The 2D resistivity method is sufficient to identify seepage below the ground surface.The results of the interpretation of this method can be used as a reference in monitoring the LUSI Embankment to prevent collapse and failures of the embankment.

Interpretation of SP anomaly
The inversion process was applied using the number of EKI ensembles (  ) is equal to 50, covariance noise to the data of   = 0.02 d obs , and the maximum number of iterations is 500 times.The results of the inversion process show a good fit between the observed data and the calculation result on P75-P67 (misfit 3.8%), as shown in Figure 6.Data at a distance of 0 to 300 meters show a tendency for the SP value to be relatively small compared to the SP value measured above 300 to 420 meters.The upper side of Figure 6 shows the difference in the amplitude of the SP value, where the polarization amplitude in the end area of the path is greater than the previous areas.The presence of seepage accumulation with a larger amount at 300 to 420 meters can affect the magnitude of the measured potential value.The results of inversion at lines P75-P67 interpret four sources of anomaly which indicate the presence of fluid accumulation in a certain area (lower side of Figure 6).This signifies an anomaly was detected at a relatively shallow subsurface.The solution of the model parameters obtained through the inversion process is listed in Table 1.
Table 1 The table also shows the value of the geometry factor of the anomaly source.All four anomalies have a geometric factor value greater than 0.5.Embankment failure can be modeled through the interpretation of SP data with several geometric shapes [23].The spherical geometry factor ( = 1.4) represents the fluid accumulation in a certain area.The source of the anomaly with spherical geometry was detected at a distance of 211 meters with a depth of 5 meters.This indicates an anomaly in the located in quite shallow from the ground surface which occur in the middle of the measurement line.This phenomenon can interpret as water seepage under the measurement area.On the other hand, the inversion of Lines P76-P77 successfully interprets nine subsurface anomalies in the embankment as shown in Figure 7. From this figure, we can observe that the source of the SP anomaly has varying depths.In addition, the geometry factor value from the anomaly modeling also shows varying results.There are three anomalies modeled as vertical cylindrical geometry ( ≤ 0.5) at a distance of 28, 104, and 138 meters.While the other six anomalies are shown as horizontal cylinder and spherical geometries.Based on the inversion data shown in Table 2, at a distance of 104 meters from the starting point of the measurement there is an anomaly source at a depth of 10 meters.This data provides information on the location of the source of the anomaly that is inferred to be found in the structure of the embankment body.Considering the data from the results of the inversion process, an anomaly with spherical geometry is described at a distance of 51 meters and 168 meters.The spherical geometry factor in the SP anomaly can be used to indicate the presence of internal erosion inside soil particles.Internal erosion occurring in the embankment body would induce structural damage to the embankment.

Conclusion
Seepage or seepage of mud fluid on the LUSI embankment paths P67-75 and P76-77 can be identified through the inversion of the 2D resistivity data method which is indicated by a lower resistivity value than the environmental resistivity value.The correlation between the results of the inversion and the conditions in the field shows that seepage in the two paths of the embankment occurs due to water from the saturated pond to the embankment body through the pores of the embankment or cracks, which is characterized by low resistivity values.In general, the low resistivity anomaly with a value range of 0.1 -1.3 m on the embankment body is found at a depth range of 1 -15 meters below the surface of the embankment.
Figure 1 shows that line P75-P67 is divided into three measuring sections (with A-C notation) thus the total length of the line is 495 meters (3 x 165m).Meanwhile, at line P76 -P77, 2 measurements were taken (with the D-E notation) resulting in a total track length of 330 meters (2 x 165m).2D resistivity measurements of Tracks P67-P75 (A-C) and Tracks P76-P77(D-E) using a set of AGI Super Sting RI IP/Multi-channel resistivity meter equipment.The measured data for Track P67-P75(A-C) yields 452-454 datums, while Tracks P76-P77(D-E) produces 437-455 datums.

Figure 4 (
Figure 4 (A-C) and Figure 5 (D-E) show the results of the 2D resistivity inversion on the P67-P75 embankment and the P76-P77, respectively.The distribution of resistivity values for each line varies and some of them have low resistivity values, which indicates the anomaly.The resistivity value is influenced by the resistivity of rock constituents, porosity, fluid saturation level, and fluid resistivity, which is empirically formulated as: ∇((, )∇(, , ) = −( −   )( −   ) (7) where  represents the Dirac Delta function,  denotes the conductivity,,  and  are represent the potential and electric current, respectively.The resistivity value of the LUSI embankment might be higher than the foundation rock (the embankment and foundation are bounded by a black dotted line), then the low resistivity value in the embankment layer may be caused by saturation of the fluid through the embankment (in Figure4and Figure5is marked with a dotted red line).Fluid saturation in this embankment contained of rainwater combined with the eruption material, which forms 40% liquid (containing Ca, Li, Sr, with high salinity or NaCl dominant content), and the rest are solids material.The solid material might contribute to inducing excess pore pressure on the embankment.The LUSI embankment was constructed by compacted expansive material which is able to be saturated by fluids(Sungkono et al., 2018).According to Schön (1998), porous rocks or fractures when filled with air (dry) have high resistivity (> 104 ), while rocks whose pores or cracks are filled with water (wet) will have low resistivity (conductive).Therefore, embankments that contain fluid through the body and pores saturated with mud fluids tend to have low resistivity values.Thus, a low resistivity value on the inversion results indicates the position of the fluid saturation on the embankment.The red dotted lines in Figure4and Figure5indicate an anomaly because it has a lower resistivity value (high conductivity) (0.1 -1.3Ωm) than the resistivity value of the surrounding area.

.
Parameter model of SP anomaly at Line P75-P67

Table 2 .
Parameter model of SP anomaly at Line P76-P77