Inversion of 1-D Resistivity Data using RR-PSO algorithm to identify Shallow Gas in Balikpapan

. In recent years shallow gas blowouts have occurred several times in Balikpapan residential areas due to drilling activities for groundwater exploration and geological structures that play as a gas trap. It is necessary to identify structures containing shallow gas by implementing geophysical methods namely Vertical Electrical Sounding (VES). VES is an electrical resistivity method which involves the rapid measurement of variations of the ground resistivity with increasing electrode spaces. The output of this method is a 1-D resistivity model used to identify shallow gas. The 1-D resistivity model can be obtained by the inversion technique. In general, the inversion of VES data is conducted using local optimization method. However, this method has several limitations hence we need to implement a global optimization method in VES data inversion. In this work, the RR-PSO algorithm was implemented, which is a global optimization method, in VES data inversion to obtain 1-D resistivity model. First, the RR-PSO algorithm is built and tested to invert synthetic data to evaluate the algorithm's performance. In this stage, the similarity index and several statistical parameters of the inversion results were calculated. After the synthetic test, the algorithm is implemented on field data inversion. The result shows that the RR-PSO algorithm has successfully inverted both the synthetic and field data. In the synthetic test, the similarity index obtained is more than 95%. The 1-D resistivity model from field data inversion indicates at the depth of 20 – 55 m a high resistivity anomaly that is identified as shallow gas. For further study, the RR-PSO algorithm could be implemented for other VES data to construct 2-D resistivity model in the study area (Palm Hills Resident area, south Balikpapan) for imaging the shallow gas presence as a mitigation measure.


Introduction
In recent years shallow gas blowouts have occurred several times in Balikpapan residential areas due to drilling activities conducted by the locals for groundwater exploration Fig. 1.This is a unique phenomenon because this kind of geological hazard occurred in densely populated residential areas (generally it occurs in petroleum field related to production activity).This hazard could occur because Balikpapan area geologically is dominated by folded structures in the form of anticlines and synclines [1].These anticlines play as a trap allowing the accumulation of gas that is migrating from the deeper layers.Thus, when drilling activity is conducted arround the anticlines, the gas blowout could occur and will risk the surrounding area.In order to minimize the disaster risk, it is necessary to do a mitigation measure by implementing geophysical methods i.e.: Vertical Electrical Sounding (VES).Vertical Electrical Sounding (VES) is a one-dimensional electrical resistivity method that is conducted by injecting a certain intensity of direct current into the ground through two current electrodes (A and B), and then measuring the voltage using another pair of potential electrodes (M and N).In this way, variations of soil resistance will be obtained with unit depth.VES is a popular geophysical tool due to its simplicity and cost-effectiveness, and its sensitivity to fluids and gases.There are three stages in VES, namely: data acquisition, plotting of the apparent resistivity value against the electrode space, and inversion to obtain a 1-D resistivity model.Inversion is the key to modelling the resistivity structure to interpret subsurface conditions.In general inversion of VES data is conducted using local optimization method like leastsquares inversion via comercial softwares or open-source programs.However, this method has several limitations [2], [3].Therefore, the use of global optimization methods can be implemented to accomodate these imitations.The global optimization method like Particle Swarm Optimization (PSO) has been succesfully implemented in VES data inversion due to its ability in solving global optimization problem [2].In addition, this algorithm has several adventages, e.g: fast processing, easy to implement, and it can provide uncertainty model [4].
PSO have been developed rapidly in last decade, and have had several versions called The PSO family optimizers [5], [6].RR-PSO is one of PSO version with the greatest convergence rate among the others.In additions-PSO has been successfully implemented in geophysical inverse problems [7], [8] including VES data inversion [9].Therefore, RR-PSO can be used as an alternative tool in VES data inversion.
In this study, RR-PSO algorithm is implemented in VES data inversion as preliminary stage in identifying shallow gas presence at Griya Residence Sepinggan, Balikpapan, East Kalimantan, Indonesia, where the blowout had ever occurred in 2021.There are two phases in this study.Firstly, synthetic test data inversion is conducted with the aim to test the performance of RR-PSO in inverting VES data.After the algorithm pass the validity test, it will be implemented in field data (one point) for preliminary identification of shallow gas in study area.

VES Method
VES or vertical electrical sounding is one of the oldest geophysical methods intensively used for the evaluation of the subsurface structure.The subsurface investigation using VES is excellent for the area where the earth horizontally layered with minimum lateral variation.This method is implemented using four electrodes as shown in Fig. 2, with the aim to determine the resistivity variation with depth.The depth of penetration depends on the distance between the current electrodes (A-B).The VES data on the field are the variation of apparent resistivity (  ) toward electrode spaces (AB/2).The apparent resistivity values do not represent the true resistivity distribution of the subsurface.Therefore, the VES data inversion needs to be carried out.In the inversion process, it is necessary to understand the mathematical relationship between VES data and the model parameters of 1-D resistivity model e.g.: thickness (ℎ) and true resistivity ().The formula that is linked the VES data and the model parameters can be written as follows: where   are linear filter coefficients as function of measurement configuration used, () is the resistivity transform function that can be calculated by using Pakeris recursive formula as follows [10]: where n-layered model, n n T  = and ( ) 1 T  depict resistivity transform for surface.As a result, ( ) ( ) . Moreover, i  and i h indicate resistivity and thickness for i-th layer, respectively, while n denotes number of layers.Thus, in the VES method () =   , where  contains i  and i h ; i = 1, 2, …, n.

RR-PSO algorithm for VES data inversion
RR-PSO (regressive-regressive PSO) is one of PSO family's versions which is deducted from the damped mass-spring system using backward finite difference scheme for velocity and acceleration in that system [6].The RR-PSO procedure basically is not different with the conventional PSO.However, due to the fact that both are derived from diffrent approach and concept hence they have also different equations for velocity, position, and their parameters (e.g: inertia, local and global acceleration).Those factors certainly have an impact on their performance in solving global optimization problems.RR-PSO known has the greatest convergence rate among the other member of PSO family, good parameter sets, and it is fast to find global minima of an objective function [7].Those make this algorithm is a powerful tool for solving VES data inversion.The RR-PSO has the formula for velocity and position written as follows : where x denotes vectors in position, v is vector in velocities, g denotes the global position on the whole swarm, In VES data inversion, vector position contain thickness and velocity of subsurface,

=
, where i  and i h represent layer thickness and resistivity for each layer respectively, while N is the number of layerss.In order to obtain the optimum model resistivity, RR-PSO needs to minimize an objective function (the distance between observed and calculated apparent resistivity) that can be written as follows : where    and   are observed and calculated apparent resistivity respectively.Furthermore, in VES inversion RR-PSO here is designed to provide posterior distribution model to provide uncertainty analysis [7].

The Result of 1-D Resistivity data using RR-PSO inversion
In this section, there are two stages e.g.: synthetic and field data inversion.Synthetic data inversion is meant to test the RR-PSO performance in inverting VES data.Afterwards, the algorithm is used to invert VES data in the study area.

Synthetic data inversion
In synthetic data inversion, VES synthetic data is built from models that represent certain subsurface condition.These data were inverted using RR-PSO algorithm with search space ±50% from true model parameters, 200 particles and 100 iterations.There are two types of synthetic data inverted, e.g.: free noise and contaminated noise.

Free-noise synthetic data
In this section, RR-PSO was tested to invert noise-free VES data.As shown in Fig. 3 and Tab.2, the inversion result can accurately estimate the 1-D resistivity model with high similarity index and low uncertainty.

Contaminated noise data
After the performance of RR-PSO has been already tested in inverting noise-free data, it is necessary to test the algorithm in inverting data that is contaminated by noise in order to know how robust this algorithm toward noise.The result show that RR-PSO still can estimate the good 1-D resistivity model on noise-contaminated data as shown in Fig. 4 .It also shows that the RR-PSO is robust toward noise as shown by the value of similirity index which insignificantly decrease.Thus, RR-PSO can be used to invert field data.

Field data inversion
Field data was collected in study area, namely Griya Residnce Sepinggan, Balikpapan, East Kalimantan, Indonesia.Geologically, the lithology of study area consist of top soil and sandstone as shown in Fig. 6b.Fig. 6a) shows a 1-D resistivity model that depicts subsurface conditions in study area.Based on 1-D resistivity model, there is a high resistivity zone at depth of 20 -50 m.Lithologically, it is should be the same with the upper layer.However there is an anomaly with high resistivity value.It can be identified as gas that is trapped in sand.Morever, the VES point is very close to blow out point (Fig. 5).Thus, RR-PSO can be used to invert othe VES data to obtain the image of shallow gas more clearly in study area.

1  and 2 
are the random global and local acceleration constants, and  is inertia weight.

Fig. 3 .
Fig. 3.The inversion result of VES synthetic data (noise free): a.) Comparison of 1-D resistivity model between inversion (green) and true (red) along with the uncertainty; b.) Fitting curve between observed and calculated data.

Fig. 4 .
Fig. 4. The inversion result of VES synthetic data (noise-contaminated): a.) Comparison of 1-D resistivity model between inversion (green) and true (red) along with the uncertainty; b.) Fitting curve between observed and calculated data.

Fig. 5 .
Fig. 5.The map of study area with locations of VES points and blow out point.

Fig. 6 .
Fig. 6.The inversion result of field data: a.) 1-D resistivity model; b.) Lithology of study area based on drilling data.

Table 1 .
The true parameters of synthetic model with the search space.

Table 2 .
The inversion result of noise free synthetic data.

Table 3 .
The inversion result of noise-contaminated synthetic data