Sensitivity of Marine Controllable Source Electromagnetic Soundings for Identifying Plume Migration in Offshore CO_{2} Storage
https://doi.org/10.1007/s11804024006014

Abstract
Offshore carbon dioxide (CO_{2}) storage is an effective method for reducing greenhouse gas emissions. However, when using traditional seismic wave methods to monitor the migration of sequestration CO_{2} plumes, the characteristics of wave velocity changes tend to become insignificant beyond a certain limit. In contrast, the controllable source electromagnetic method (CSEM) remains highly sensitive to resistivity changes. By simulating different CO_{2} plume migration conditions, we established the relevant models and calculated the corresponding electric field response characteristic curves, allowing us to analyze the CSEM's ability to monitor CO_{2} plumes. We considered potential scenarios for the migration and diffusion of offshore CO_{2} storage, including various burial depths, vertical extension diffusion, lateral extension diffusion, multiple combinations of lateral intervals, and electric field components. We also obtained differences in resistivity inversion imaging obtained by CSEM to evaluate its feasibility in monitoring and to analyze all the electric field (E_{x}, E_{y}, and E_{z}) response characteristics. CSEM has great potential in monitoring CO_{2} plume migration in offshore saltwater reservoirs due to its high sensitivity and accuracy. Furthermore, changes in electromagnetic field response reflect the transport status of CO_{2} plumes, providing an important basis for monitoring and evaluating CO_{2} transport behavior during storage processes.Article Highlights● Experimental tests evaluate the effectiveness of CSEM in monitoring the transport process of CO_{2} plumes in various typical forms.● Experiments analyze and identify the CSEM imaging characteristics of the CO_{2} plume transport process.● This analysis examines the advantages of CSEM for monitoring CO_{2} plume and points that need further development. 
1 Introduction
Carbon capture and storage (CCS) is a promising approach to mitigating global warming, and among the available carbon sequestration technologies, geological sequestration is considered the most effective (Zhang et al., 2023). In particular, marine CO_{2} geological storage has great potential, accommodating about 40% of the CO_{2} storage capacity (Li et al., 2023). China's saline water layer is widely distributed and has a large area, with its theoretical CO_{2} storage accounting for over 95% of the geological utilization and theoretical storage capacity in the country (Li et al., 2022). However, in conducting carbon sequestration, the potential leakage risk in the CO_{2} reservoir is the most worrying problem; once it is leaked, it may have serious impacts on biodiversity, the ecological environment, and the entire marine environment (Kim and Park, 2023). Therefore, CO_{2} plume migration and potential leakage detection are important. Although leak detection can be a major risk, plume boundaries must be monitored and storage levels verified throughout the process.
Recent studies have found that the seismic wave velocity used in traditional methods does not change significantly with CO_{2} saturation upon exceeding a certain limit, posing challenges to plume migration monitoring in CO_{2} sequestration (Bhuyian et al., 2012). In the deep saline water layer, the rock layer with high porosity and high permeability is filled with saline or saline water, which increases the total resistivity of the deep saline water layer (Fawad and Mondol, 2021; Li et al., 2013). With the continuous injection of CO_{2} and the migration of supercritical CO_{2} plumes, a highresistivity response appears locally in the deep saline water layer (Fawad and Mondol, 2021). Among these, the controllable source electromagnetic method (CSEM) has a significant response to the resistivity change caused by CO_{2} saturation and has an effect on the response of medium and high saturation (Eide and Carter, 2020). As CSEM works in the frequency domain and has the advantage of having strong antiinterference ability and high signaltonoise ratio, it can analyze the resistivity distribution of submarine strata by receiving reflected and refracted electromagnetic signals from submarine strata Compared to seismic monitoring, CSEM monitoring has a lower cost and can better meet the needs of longterm monitoring and the safety, effectiveness, and economic requirements of geological carbon sequestration.
Despite its advantages in monitoring CO_{2} injection and migration, only a few studies have investigated the use of CSEM for CO_{2} sequestration monitoring. By using a modified secondary field method, one study addressed the airwave problem occurring when CSEM is applied to a target beneath a shallow sea (Kang et al., 2012). Du and Nord (2012) investigated the sensitivity of the CSEM to buried thin resistive layers that could represent CO_{2} storage reservoirs. This study first investigated the sensitivities of threedimensional (3D) CSEM data to a realistic CO_{2} storage and then analyzed the use of CSEM data for making estimates of the postinjection buildup of CO_{2} layers in the subsurface. Vilamajó et al. (2013) evaluated the ability of the CSEM to monitor CO_{2} storage at the Research Laboratory on Geological Storage of CO_{2} at Hontomín located in Burgos, Spain. The synthetic timelapse study explored the possibilities of CSEM monitoring with a deep electric source. Park et al. (2017) revisited the marine CSEM data and acquired the Sleipner CO_{2} storage to further study the dataset, demonstrating the feasibility of marine CSEM for offshore CCS monitoring. Similarly, the current study confirms that marine CSEM can be an important tool for offshore CO_{2} storage monitoring. Meanwhile, Puzyrev (2019) explored the potential of using deep learning methods for electromagnetic inversion. This method's performance was assessed using models of strong practical relevance representing an onshore controlled source electromagnetic CO_{2} monitoring scenario.
Furthermore, Ayani et al. (2020) presented a stochastic optimization method called the "ensemble smoother" to invert timelapse marinecontrolled source electromagnetic data for predicting the CO_{2} plume location. The results obtained after the inversion of electromagnetic data show that the proposed method can accurately predict CO_{2} plume location and quantify the associated uncertainties. Fawad and Mondol (2021) dealt with the CO_{2} plume delineation and saturation estimation using a combination of seismic and electromagnetic synthetic data. The results revealed that monitoring the CO_{2} plume in terms of extent and saturation is feasible either using repeated seismic and electromagnetic data or combining baseline seismic data with repeated electromagnetic data. Tveit et al. (2020) explored the application of CSEM or gravity and seismic acoustic amplitude inversion (AVO) in monitoring largescale carbon dioxide injection processes. The current version of the simulation modeling problem in CCS work has also become relatively mature. For example, the stagebased modeling capability in Sim CCS is particularly useful for optimizing the dynamic deployment of CCS projects (Ma et al., 2023), along with other simulation modeling methods, thus proving the feasibility of simulation modeling methods.
The current study evaluates the sensitivity of CSEM to monitor the process of plume transport in offshore CO_{2} storage. First, we established a numerical simulation model for CO_{2} plumes during storage and determined the geometric shape and characteristics of the monitoring area. Then, we used CSEM to numerically calculate the electromagnetic field response of the simulation model, after which we analyzed the sensitivity of different parameters to the electromagnetic field response. Doing so provides a theoretical and practical basis for further research into and the application of CSEM, which is of great significance for improving the safety and stability of offshore CO_{2} storage.
2 Identifying CO_{2} plume CSEM method
2.1 CSEM soundings
CO_{2} stored in the seabed typically exhibits higher electrical resistivity than surrounding media. Electromagnetic detection is sensitive to formation resistivity; thus, it is considered the best method for deep fluid identification. The principle of CSEM soundings is to use electromagnetic induction phenomena, in which the alternating current (AC) electric field can induce the AC magnetic field, which, in turn, can also induce the AC electric field. Therefore, energy is constantly converted in the form of electric and magnetic fields and radiates into space through the alternating radiation between the two fields. The same refraction and reflection occur when it encounters different media interfaces.
When electromagnetic fields propagate in media with different levels of resistivity, they have both similar and different characteristics. On the one hand, the similarity lies in the fact that the energy of electromagnetic waves will decrease in a geometric attenuation manner as the propagation distance increases, regardless of whether the medium has high or low resistivity. On the other hand, the difference can be attributed to the highresistivity media hardly absorbing the energy of electromagnetic waves, while lowresistivity media strongly absorb the energy of electromagnetic waves, implying the occurrence of an eddy current. Therefore, the received electromagnetic field response can be analyzed to obtain the electrical distribution of the underground medium.
In Figure 1, a 2D measurement grid consisting of multiple measurement lines can be used for 3D exploration. The ship towed a long cable with an HED transmitter near the seabed to enhance the weak response signal below. The transmitter emits lowfrequency electromagnetic waves with controllable waveforms. Waves propagate to the surrounding areas, resulting in the following: 1) penetration of the seabed strata received by the receiver (red line), 2) propagation in the seawater received by the receiver (yellow line), and 3) propagation through the seabed (blue line). If the receiver can measure a clear electromagnetic response signal of CO_{2} plumes, it can help detect the distribution of the CO_{2} plume transport.
Here, we assume that the electrical conductivities of air, seawater, submarine sediment, and HC are σ_{air}, σ_{water}, σ_{sed}, and σ_{r} respectively; the magnetic permeability in the earth is the distance of the current source from the seafloor is h_{c}, the thickness of the seawater layer is h_{w}, the depth below the seafloor of the top of HC is h_{r}, and the time factor is e^{−iωt}. Thus, the system of classical Maxwell's equations yields the following:
$$ \nabla \times \boldsymbol{E}=\mathrm{i} \omega \mu_0 \boldsymbol{H} $$ (1) $$ \nabla \times \boldsymbol{H}=(\sigma\mathrm{i} \omega \varepsilon) \boldsymbol{E}+\boldsymbol{J}_i $$ (2) where J_{i} denotes the current density of the excitation source term, ε is the dielectric constant, and ω is the angular frequency. In considering the IP effect, we should also include the polarization current term. Thus, by the derivation of Harrington (1961), Eq. (2) above can be written as follows:
$$ \nabla \times \boldsymbol{H}=\sigma_{\text {sed }} \boldsymbol{E}+\boldsymbol{J}_s+\boldsymbol{J}_i $$ (3) where J_{s} = (σ_{r} − σ_{sed}) E, and J_{s} denotes the polarization current within the target body. Taking the curl on both sides of the equal sign of Eq. (1), simultaneously, the curl of the magnetic field is substituted into Eq. (3) and then simplified to obtain the fluctuation equation containing only the electric field vector as follows:
$$ \nabla \times \nabla \times \boldsymbol{E}k_3^2 \boldsymbol{E}=\mathrm{i} \omega \mu_0\left(\boldsymbol{J}_s+\boldsymbol{J}_i\right) $$ (4) The electric field E in Eq. (4) contains the incident and scattered fields; thus, E = E_{i} + E_{s}, and from this, it can be shown that the electric field of the two parts satisfies the equation.
$$ \left\{\begin{array}{l} \nabla \times \nabla \times \boldsymbol{E}_ik_3^2 \boldsymbol{E}_i=\mathrm{i} \omega \mu_0 \boldsymbol{J}_i \\ \nabla \times \nabla \times \boldsymbol{E}_sk_3^2 \boldsymbol{E}_s=\mathrm{i} \omega \mu_0 \boldsymbol{J}_s \end{array}\right. $$ (5) In solving for the scattered field, which is deemed an ordinary current source, we refer to the theory of Dyadic Green's function (Tai, 1994). As such, integration over the target body leads to the following:
$$ \boldsymbol{E}_s(r)=\mathrm{i} \omega \mu_0\left(\sigma_r\sigma_{\text {sed }}\right) \int\limits_{V_A} \boldsymbol{G}\left(r \mid r^{\prime}\right) \cdot \boldsymbol{E}\left(r^{\prime}\right) \mathrm{d} v^{\prime} $$ (6) Based on the method of integral equations combined with the theory of DGF, the following integral equations are obtained by transforming and simplifying Eqs. (1) and (2):
$$ \boldsymbol{E}(r)=\boldsymbol{E}_i(r)+\mathrm{i} \omega \mu_0\left(\sigma_r\sigma_{\text {sed }}\right) \int\limits_{V_A} \boldsymbol{G}\left(r \mid r^{\prime}\right) \cdot \boldsymbol{E}\left(r^{\prime}\right) \mathrm{d} v^{\prime} $$ (7) where E_{i} (r) is the incident field excited by the transmitted source in accordance with the classification made by Tai (1971), and G(rr') is a categoryⅢ DGF.
Using Eq. (7) in the case where in the incident field (i.e., primary field) E_{i} (r)has been solved, it is possible to calculate the electric field at each point within the anomaly. As such, the electric field at each point in the model can then be calculated from the corresponding DGF.
The 3D target body is dissected into n small cells while assuming that the electric field inside each dissected cell is constant and equal to the electric field at its center. Hence, Eq. (3) can be written as follows:
$$ \boldsymbol{E}(r)=\boldsymbol{E}_i(r)+\mathrm{i} \omega \mu_0\left(\sigma_r\sigma_{\text {sed }}\right) \sum\limits_{n=1}^N \int\limits_{V_d} \boldsymbol{G}\left(r \mid r^{\prime}\right) \mathrm{d} v^{\prime} \cdot \boldsymbol{E}_n $$ (8) Thus, the following expression for the electric field at the center of the mth cell is obtained:
$$ \boldsymbol{E}_m=\boldsymbol{E}_m^i+\mathrm{i} \omega \mu_0\left(\sigma_r\sigma_{\mathrm{sed}}\right) \sum\limits_{n=1}^N \boldsymbol{\varGamma}_{m n} \cdot \boldsymbol{E}_n $$ (9) where $\boldsymbol{\varGamma}_{m n}=\int\limits_{V_A} \boldsymbol{G}\left(r \mid r^{\prime}\right) \mathrm{d} v^{\prime}$. Based on Eq. (9), the matrix equation is obtained as follows:
$$ \sum\limits_{n=1}^N\left[\mathrm{i} \omega \mu_0\left(\sigma_r\sigma_{\mathrm{sed}}\right) \boldsymbol{\varGamma}_{m n}\boldsymbol{\delta}_{m n}\right] \cdot \boldsymbol{E}_n=\boldsymbol{E}_m^i $$ (10) where $\boldsymbol{\delta}_{m n}= \begin{cases}\boldsymbol{I}_{m n} & m=n \\ \boldsymbol{\theta}_{m n} & m \neq n\end{cases}$, I is the unit dyadic.
Occam inversion using MARE2DEM code. The Occam inversion algorithm is a least squares method based on the regularization idea, and its objective function is to minimize the following unconstrained optimization problem:
$$ U=\mu\\boldsymbol{R} \boldsymbol{m}\^2+\\boldsymbol{W}(\boldsymbol{d}F(\boldsymbol{m}))\^2 $$ (11) where m is the ndimensional model parameter vector, R is the roughness operator, and μ is a regularization operator, which is used to balance the roughness and poor fitting of the data. If μ is larger, the inversion result tends to be smooth; otherwise, it tends to fit the data. In addition, W is the diagonal weighting matrix for the fit difference, d is the observation data vector, and F(m) is the forward response corresponding to model m.
Finally, the roughness of the model can be expressed as follows:
$$ \\boldsymbol{R} \boldsymbol{m}\^2=\left\\boldsymbol{R} \boldsymbol{m}_x\right\^2+\left\\boldsymbol{R} \boldsymbol{m}_y\right\^2+\left\\boldsymbol{R} \boldsymbol{m}_z\right\^2+\lambda\left\\boldsymbol{m}\boldsymbol{m}^{\prime}\right\^2 $$ (12) where λ is the anisotropic penalty term, $\boldsymbol{m}^{\prime}=\left[\begin{array}{lll} \boldsymbol{m}_{\boldsymbol{y}} & \boldsymbol{m}_z & \boldsymbol{m}_x \end{array}\right]^{\mathrm{T}}$.
For the kth iteration model, the iteration in which the objective function is sufficiently reduced takes the following form:
$$ \begin{aligned} \boldsymbol{m}_{k+1} & =\boldsymbol{m}_{\boldsymbol{k}}+\left[\mu \boldsymbol{R}^{\mathrm{T}} \boldsymbol{R}+\left(\boldsymbol{W} \boldsymbol{J}_k\right)^{\mathrm{T}} \boldsymbol{W} \boldsymbol{J}_k\right]^{1} \\ & \times\left[\left(\boldsymbol{W J}_k\right)^{\mathrm{T}} \boldsymbol{W} \hat{\boldsymbol{d}}\mu \boldsymbol{R}^{\mathrm{T}} \boldsymbol{R} \boldsymbol{m}_k\right] \end{aligned} $$ (13) where the difference vector is fitted $\hat{d}=\boldsymbol{d}F\left(\boldsymbol{m}_k\right)$.
In the present study, we applied the finite element unstructured mesh method to twodimensional (2D) electromagnetic fields forward modeling. We used the irregular triangular mesh instead of the traditional rectangular mesh, which is more in line with complex structural boundaries, thus saving a considerable amount of computing memory and greatly improving computing efficiency and accuracy (Wen and Benson, 2019). At the same time, the mesh with insufficient precision is refined through continuous iteration, thus ensuring calculation accuracy.
2.2 Identifying plume migration using CSEM
The migration of CO_{2} plumes in seabed geological storage refers to a special flow pattern formed in underground reservoirs as a result of the injection of carbon dioxide and the migration of underground fluids. Its characteristics include high flow velocity, large diffusion coefficient, and short transport distance. The ocean CSEM is commonly used to monitor the path and velocity of plume transport in the ocean by measuring changes in the electromagnetic field. Due to its high flow velocity and plume transport diffusion coefficient, the ocean CSEM has better sensitivity and analytical ability compared to traditional monitoring methods.
2.3 CO_{2} saturation calculation formulas
We used the Archie equation to calculate water saturation in marine sediments (Archie, 1942). In a reservoir, the filling of sedimentary layers can be approximated as the filling of CO_{2} and seawater, and this is expressed in the following equation:
$$ \rho_t=\left[\frac{a \rho_w}{\phi^m S_w^n\left(1+\frac{\rho_w}{B} Q_v S_w\right)}\right] $$ (14) where B is the equivalent cation conductance, which is dependent on temperature and salinity, and Q_{v} is the cation exchange capacity per unit volume.
Then, isolating ρ_{t}, we obtain:
$$ \rho_t=\frac{a S_w^{n} \phi^{m}}{\left[\frac{1}{\rho_w}+\frac{V_{\mathrm{sh}} \phi_{\mathrm{sh}}}{\phi}\left(\frac{a}{\rho_{\mathrm{sh}} \phi_{\mathrm{sh}}^m\frac{1}{\rho_w}}\right) S_w^{1}\right]} $$ (15) where ϕ_{sh} is the total shale porosity, and ρ_{sh} is the resistivity of the formation with 100 percent volume of shale (V_{sh}), while m and a are the cementation and tortuosity exponents for the clayrich formation, respectively.
In this paper, we assumed the following values: rock porosity (ϕ) = 0.2, cementation index (m) = 1.6, tortuosity coefficient a = 1.1, saturation index (n) = 1.8, CO_{2} saturation S_{w} = 0.5, pore fluid resistivity (ρ_{w}) = 0.2, ρ_{sh} = 0.4 Ω⋅m, seawater resistivity ρ_{w} = 0.3, and total shale porosity ϕ_{sh} = 0.3 (Harp et al., 2019; Yilo et al., 2023).
3 Experiments
Meanwhile, we have considered various potential scenarios for the migration and diffusion of offshore CO_{2} storage (Hoffman and Alessio, 2017), including various burial depths, lateral extension diffusion, vertical extension diffusion, electric field components, and multiple combinations of lateral intervals. The models include the following: 1) various lengths of lateral diffusion, 2) burial depths, 3) spacing of lateral diffusion, 4) thickness of vertical diffusion, and 5) saturation models.
Based on the formula derivation calculation, we set the resistivity of the CO_{2} model in this experiment as 100 Ω. The model parameter settings used in this study are shown in Table 1.
Name of the layered medium Layer thickness (m) Layer resistivity value (Ω) Air layer H_{1} =800 ρ_{1} =1×10^{13} Marine layer H_{2}=1 000 ρ_{2}=0.3 Submarine formation H_{3}=2 500 ρ_{3}=2.0 Basement formation H_{4}=500 ρ_{4}=1 000 3.1 Various electric field components
In this group of experiments, we conducted a comparative analysis of the difference in the response amplitudes of E_{x}, E_{y}, and E_{z} when there is no abnormal object in Model 14. Then, we compared the abnormal response characteristics under different components.
Model No. Position Y (m) Position Z (m) Length (m) Thickness (m) Burialdepth (m) 14 1 500, 6 500 2 500, 3 000 5 000 500 800 We conducted forward modeling without a CO_{2} plume and calculated the response values of each component of the electromagnetic field detected by CSEM at five different frequencies of the corresponding blank field. Next, we generated the amplitude of the difference in response between the blank field and each component under the response of the target body. Normalized anomaly amplitudes were plotted for three electric field components (E_{x}, E_{y}, and E_{z}) calculated at identical frequencies (0.25 Hz) (Figure 3).
By comparing and analyzing the normalized anomaly amplitude curves of the three electric field components in Figure 3, it can be clearly seen that the three electric field components can obtain a good anomaly response to the detection target. In particular, the E_{y} component increases with the offset, and the abnormal response characteristics of the electric field obtained are the most obvious than for the E_{x} and E_{z} components. This means that the abnormal amplitude signal obtained under the measurement of the E_{y} component is the strongest and easiest to observe, and that of the E_{z} component is the weakest; that is, the abnormal signal observed under the measurement of this component is weak and difficult to observe.
The normalized anomaly amplitudes of E_{x} electric field components at five different frequencies (0.25, 0.75, 1, 3, and 5 Hz) were also plotted (Figure 4).
By comparing and analyzing the normalized anomaly amplitude curves of the E_{y} electric field components in Figure 4, it can be clearly seen that the E_{y} component can obtain a good and stable abnormal response signal under the five measured frequencies, and the strength of the abnormal response signal changes regularly with the frequency. When the lower frequency increases from 0.25 Hz to the higher frequency of 5 Hz, the abnormal response signal obtained at the same offset is gradually weakened. In other words, the electric field abnormal response signal at 0.25 Hz is the strongest, while the relative abnormal response signal at 5 Hz is the weakest.
3.2 Various lengths of lateral diffusion
Transverse diffusion is the main mode of CO_{2} plume migration because the heterogeneity of horizontal reservoirs tends to limit the vertical migration of CO_{2} (Hoffman and Alessio, 2017), and most of the supercritical CO_{2} plumes will gather under the sealing layer and migrate in the form of thin layers with high gas saturation. Meanwhile, when the plume permeability contrast is greater than 50, supercritical CO_{2} flows only in the highly permeable layer.
In the proposed model, we adopted the simulated burial depth of 800 m based on previous studies, which reported that if the burial depth in the offshore geological storage engineering is too deep, it will increase the economic cost and implementation difficulty of the project (Guo et al., 2015). One study concluded that the burial depth of 800 m has met the temperature and pressure conditions required for CO_{2} to be a supercritical state (Zendehboudi et al., 2011). Meanwhile, we also refer to the Enping Project, the first offshore CO_{2} storage project in China, in which the point of burial is also a saltwater layer located 800 m below the sea floor.
We used models of varying lengths (Models 11, 12, 13, and 14) for the lateral diffusion of offshore CO_{2}, enabling us to evaluate the CSEM's ability to distinguish CO_{2} lateral diffusion. The corresponding CSEM resistivity imaging results are shown in Figures 5(e)–(h). As shown in the figures, the highresistivity range and high saturation range obtained from imaging are consistent with the reservoir range of the model. The model parameters are shown in Table 3.
Model No. Position Y (m) Position Z (m) Length (m) Thickness (m) Burialdepth (m) 11 1 500, 2 000 2 500, 3 000 500 500 800 12 1 500, 2 500 2 500, 3 000 1 000 500 800 13 1 500, 4 500 2 500, 3 000 3 000 500 800 14 1 500, 6 500 2 500, 3 000 5 000 500 800 The length of the highresistivity area basically corresponds to the length range of the lateral extension and diffusion of offshore CO_{2}. However, significant differences are also observed in the inversion results of offshore CO_{2} (Models 11, 12, 13, and 14) with varying ranges of lateral diffusion. In Model 11, the top inversion depth and regional range of the offshore CO_{2} storage are closest to the simulated depth and regional range. Meanwhile, in Models 12, 13, and 14, as the lateral diffusion range of offshore CO_{2} gradually lengthens, the imaging depth and regional range of the offshore CO_{2} storage gradually deviate from the simulated model. However, overall, the approximate range of the model can still be obtained to determine the approximate position of the target body.
Regarding the inversion of Model 1, the curve of the RMS misfit and roughness change with the number of iterations is shown in Figure 6.
Figures 5(a)‒(d) are schematic diagrams of Models 11, 12, 13, and 14, respectively; Figures 5(e)‒(h) represent resistivity imaging for Models 11, 12, 13, and 14, respectively. In Figures 5(a)‒(d), dark blue represents the range of offshore CO_{2} diffusion areas, light yellow represents marine sediments, and black boxes represent offshore CO_{2} reservoirs.
As shown in Figure 6, the roughness increases with the increase of iterations. Furthermore, the RMS misfit of Occam inversion converges with the increase of iterations, and the target misfit is 1. The inversion RMS misfit of the four models all reach the target misfit in the 7th iteration, there by proving that the inversion results are reliable. The comparison between the inversion data of Model 11 and the actual target body data is shown in Figure 7.
Upon comparing the error range of the inversion target body of different models under two frequencies, namely, 0.25 Hz (blue curve) and 0.75 Hz (green curve), we found certain differences between the inverse resistivity value and the real value. However, there is little difference between the inversion results of the two models and the actual object, and the error range is relatively stable.
3.3 Various burial depths
In the proposed model, we used three different burial depths of 1 000, 1 500, and 2 000 m for discussion. These represent the main burial depths of saltwater reservoir sequestration projects that have been implemented around the world. The major ones include the 1 000 m burial depth adopted by the Sleipner project in Norway (CzernichowskiLauriol et al., 2003), the 1 500 m burial depth adopted by the Ordos Project in China, and the 2 000 m burial depth by the Gorgon project in Australia (Flett et al., 2009).
Furthermore, we used various burial depth models for offshore CO_{2} plumes (Models 21, 22, and 23) to evaluate the CSEM's ability to distinguish the burial depths of offshore CO_{2} plumes. The corresponding resistivity imaging results from CSEM are shown in Figures 8(d)‒(f). The highresistivity range and high saturation range obtained from imaging are consistent with the plume range of the model. The model parameters are shown in Table 4.
Model No. Position Y (m) Position Z (m) Length (m) Thickness (m) Burial depth (m) 21 1 500, 2 500 2 600, 3 600 1 000 1 000 1 000 22 1 500, 2 500 3 100, 4 100 1 000 1 000 1 500 23 1 500, 2 500 3 600, 4 600 1 000 1 000 2 000 Figures 8(a)‒(c) are schematic diagrams of Models 21, 22, and 23, with dark blue indicating the range of offshore CO_{2} diffusion areas, light yellow indicating marine sediments, and white boxes indicating offshore CO_{2} reservoirs; Figures 8(d)‒(f) are resistivity imaging of Models 21, 22, and 23, respectively.
The inversion results in the figure all show that the four models have begun to converge to the vicinity of the real model after the 10th iteration, indicating that the inversion method is real and effective. Furthermore, the depth of the highresistivity region basically corresponds to the depth range of offshore CO_{2} storage and burial. However, the inversion results of these models are still different. Among these, the inversion depth and area range of offshore CO_{2} storage in Model 21 are the closest to the depth and area range simulated by the model. In Models 22 and 23, the inversion depth and regional range of offshore CO_{2} sequestration gradually deviate from the simulated model as the simulated depth increases. However, the overall range of the approximate model can still be determined to determine the approximate target location.
For the inversion of Model 2, the curve of the RMS misfit and roughness change with the number of iterations is shown in Figure 9.
As shown in Figure 9, roughness increases with the increase of iterations. Furthermore, the RMS misfit of Occam inversion converges with the increase of iterations, and the target misfit is 1. The inversion RMS misfit of all four models can reach the target misfit in the 6th iteration, there by proving that the inversion results are reliable. The comparison between model inversion data and actual target data is shown in Figure 9.
The curves from top to bottom correspond to Models 21, 22, and 23, respectively (Figure 10). We compared the error ranges of the inversion target body of different models at two frequencies of 0.25 Hz (blue curve) and 0.75 Hz (green curve) and found certain differences between the inverse value of the resistivity and the real value. However, the inversion results of the three models had little differences with the actual target body, and the error ranges of the inversion increased with the increase of the burial depth. Nevertheless, the margin of error is stable.
3.4 Various spacing of lateral diffusion
We used various spacing lateral diffusion models for offshore CO_{2} plumes (Models 31, 32, 33, and 34) to evaluate the CSEM's ability to distinguish the various spacing lateral diffusions of offshore CO_{2} plumes. The corresponding resistivity imaging results from CSEM are shown in Figures 11(e)‒(h). The highresistivity range and saturation range obtained from imaging are consistent with the plume range of the model. The model parameters are shown in Table 5.
Model No. Spacing (m) Length (m) Thickness (m) Burial depth (m) 31 1 000 1 000 500 1 000 32 500 1 000 500 1 000 33 300 1 000 500 1 000 34 200 1 000 500 1 000 Figures 11(a)‒(d) are schematic diagrams of Models 31, 32, 33, and 34, with dark blue indicating the range of offshore CO_{2} diffusion areas, light yellow indicating marine sediments, and white boxes indicating offshore CO_{2} reservoirs; Figures 11(e)‒(h): Electrical resistivity imaging of Models 31, 32, 33, and 34.
Although the depth of highresistivity areas basically corresponds to the burial depth range of offshore CO_{2}, reservoirs, differences can still be observed in the inversion results of the four different models (Figure 11). Among these, the inversion depth of the offshore CO_{2} storage in Model 31 is closest to the depth simulated by the model and the range and boundary of the regional target body area. In Models 32, 33, and 34, there is a slight deviation between the inversion depth and regional range of the offshore CO_{2} reservoir, along with the boundary and the simulated model, as the simulated distance between adjacent target bodies decreases. The intermediate boundary of adjacent target bodies cannot be determined based on the inversion image. However, the range of the overall model can still be determined to determine the approximate position of the target body.
For the inversion of Model 3, the curve of RMS misfit and roughness change with the number of iterations is shown in Figure 12.
As shown in Figure 12, the roughness increases with the increase of iterations. Furthermore, the RMS misfit of Occam inversion converges with the increase of iterations, and the target misfit is 1. The inversion RMS misfit of all four models can all reach the target misfit in the 7th iteration, thus proving that the inversion results are reliable. The comparison between model inversion data and actual target data is shown in Figure 13.
The curves from top to bottom correspond to Models 31, 32, and 34, respectively (Figure 13). Upon comparing the error ranges of the inversion target bodies of different models at two frequencies of 0.25 Hz (blue curve) and 0.75 Hz (green curve), we find differences between the inversion values of resistance and the real values. However, there is little difference between the inversion results of the four models and the actual target bodies. Furthermore, the error ranges of inversion also increase with the increase of spacing. Nevertheless, the margin of error is stable.
3.5 Various thicknesses of vertical diffusion
We used vertical diffusion models of offshore CO_{2} plumes with various thicknesses (Models 41, 42, 43, and 44) to evaluate the CSEM's ability to distinguish the diffusion of offshore CO_{2} plumes at various thicknesses. The corresponding resistivity imaging results from CSEM are shown in Figures 14(e)‒(h). The highresistivity range and saturation range obtained from imaging are consistent with the plume range of the model. The model parameters are shown in Table 6.
Model No. Position Y (m) Position Z (m) Length (m) Thickness (m) Burial depth (m) 41 1 500, 2 500 2 500, 2 600 1 000 100 1 000 42 1 500, 2 500 2 500, 2 800 1 000 300 1 000 43 1 500, 2 500 2 500, 3 000 1 000 1 500 1 000 Figures 14(a)‒(c) are schematic diagrams of Models 41, 42, and 43, respectively. Dark blue represents the range of offshore CO_{2} diffusion areas, light yellow represents marine sediments, and white boxes represent offshore CO_{2} reservoirs. Figures 14(d) ‒ (f) are resistivity imaging for Models 41, 42, and 43, respectively.
The length of the highresistivity area basically corresponds to the length range of the offshore CO_{2} storage. However, there are significant differences in the inversion results of offshore CO_{2} (Models 41, 42, and 43) with different longitudinal dispersion ranges. In Model 41, the inversion depth and regional range of the top of the offshore CO_{2} storage are closest to the simulated depth and regional range. In comparison, in Models 42 and 43, the inversion depth and regional range of the offshore CO_{2} storage gradually deviate from the simulated model as the vertical dispersion range of offshore CO_{2} gradually decreases. However, the approximate range of the model can still be obtained to determine the approximate position of the target body.
For the inversion of Model 4, the curve of RMS misfit and roughness change with the number of iterations is shown in Figure 15.
As shown in Figure 15, roughness increases with the increase of iterations. In addition, the RMS misfit of Occam inversion converges with the increase of iterations, and the target misfit is 1. The inversion RMS misfit of the four models all reach the target misfit in the 7th iteration, thus proving that the inversion results are reliable. The comparison between model inversion data and actual target data is shown in Figure 16.
The curves from top to bottom correspond to Models 41, 42, and 43 respectively (Figure 16). By comparing the error ranges of the inversion target bodies of different models at two frequencies of 0.25 Hz (blue curve) and 0.75 Hz (green curve), we find that the difference between the resistivity inversion values and the real values is relatively small. This means that the observed error of the inversion effect is relatively stable for target bodies of different thicknesses. The inversion results of the three models have little difference from the actual target bodies.
3.6 Various adjacent saturation models
The effects of the resistivity imaging of two offshore CO_{2} saturation models (Models 51 and 52) for offshore CO_{2} models are shown in Figure 17(c)(d), respectively. The highresistivity range and high saturation range obtained by imaging are consistent with the reservoir range of the model. Several common offshore CO_{2} adjacent saturation types that need to be compared in this group of models are shown in Table 7.
Model No. Resistivity (Ω) Interval (m) Length (m) Thickness (m) Burial depth (m) 51 100/50/20 0 1 000 500 1 000 52 100/50/20 1 000 1 000 500 1 000 Figures 17(a) and (b) are schematic diagrams of Models 51 and 52, with dark blue color indicating the extent of offshore CO_{2} dispersion area, light yellow color indicating marine sediment, and white box indicating offshore CO_{2} reservoir; Figures 17(c) and (d) are resistivity maps of Models 51 and 52.
The depth of the highresistivity area basically corresponds to the depth range of the offshore CO_{2} reservoir. However, the inversion results of the two models are still different. In particular, the inversion depth and regional area range of adjacent offshore CO_{2} reservoirs with different saturation in Model 51 are the closest to the depth and regional range of the model simulation target. In comparison, in Model 52, the adjacent distance of the target body with different saturation becomes wider, and the inverse resistivity imaging image can still clearly reflect the burial depth, regional range, and boundary of each simulated target body, thus resulting in highquality resistivity imaging. For the inversion of model 5, the curve of RMS misfit and roughness change with the number of iterations is shown in Figure 18.
As shown in Figure 18, roughness increases with the increase of iterations. In addition, the RMS misfit of Occam inversion converges with the increase of iterations, and the target misfit is 1. The inversion RMS misfit of all four models can reach the target misfit in the 7th iteration, thus proving that the inversion results are reliable. The comparison between model inversion data and actual target data is shown in Figure 19.
The curves from top to bottom correspond to Models 51 and 52, respectively (Figure 19). Upon comparing the error ranges of inversion target bodies of different models at two frequencies of 0.25 Hz (blue curve) and 0.75 Hz (green curve), we find differences between the inverse value of resistance and the real value, although the inversion results of the two models are not very different from the actual target bodies, and the error ranges are relatively stable.
4 DCharacteristics and influencing factors
4.1 Influence of operating conditions
A previous study (Yilo et al., 2023) has reported that CSEM performs well in monitoring vertical leakage and providing comprehensive assessments compared with seismic methods. In contrast, our work pays more attention to the transverse transport resolution of CO_{2}. In this work, five common migration situations were divided into the establishment of the migration model, and inversion simulation and iterative misfit analysis were carried out, thus providing a more comprehensive reference for the monitoring role of CSEM in the entire CO_{2} storage work. Furthermore, by tracking the migration situation, CO_{2} reserves could be estimated in advance, and potential leakage risks could be assessed. We also discussed the impact of the following four factors on the monitoring results.
1) Influence of offset on monitoring. When the offset is less than 3 km, the electric field characteristic curves of each model almost coincide, and the observation system basically has no response to the target. When the offset exceeds 3 km, the electric field signals collected by the observation system to monitor the CO_{2} plume begin to separate from the background. Therefore, if we want to observe more obvious signal characteristics, we should select the offset of 6–7 km, in which the electric field response characteristics at each frequency are the most obvious.
2) Influence of burial depth on monitoring response. Based on the inverse resistivity image in Figure 7, when the burial depth of the CO_{2} reservoir is 2 km, CSEM's monitoring and inversion results have begun to deviate from the actual target. This finding indicates the weak reflected signal at this depth and the lost discernability of its response amplitude. Therefore, the shallower the burial depth, the better the response characteristics obtained by CSEM monitoring. Thus, it is necessary to transmit higher power signals to identify the buried highresistance anomalous body.
3) Influence of frequency on monitoring. By comparing the response characteristics of each electric field component at five different frequencies, the offset corresponding to the inflection point of the electric field response curve at different frequencies tends to vary. The higher the frequency, the smaller the offset required for the abnormal electric field response to reach the peak value, and with the increase of the offset, the stronger the influence of the airwave. Therefore, in the CSEM monitoring work, on the premise of achieving the detection target, asmaller frequency selected translates to reduced interference. For example, 0.25 Hz in the experiment has the best electric field response under each component compared with other higher frequencies.
4) Influence of different components on monitoring. As shown in Figures 3 ‒ 4, the responses of various frequencies under the three electric field components are compared. Compared with other components, the electric field response characteristics obtained by the E_{y} component under each frequency measurement are more stable and demonstrate more regular changes. Therefore, E_{y} has a more stable monitoring capability in terms of lateral resolution.
4.2 Influence of monitoring time
The influence of monitoring time on the results mainly comes from the influence of the change in CO_{2} migration distance; thus, the length of the source and receiver must be changed. Furthermore, the longer the monitoring time, the larger the offset that needs to be laid.
4.3 The influence of uncertainty
The inversion algorithm affects the resolution of inversion results, and different inversion parameters may lead to varying inversion results. Therefore, to obtain better inversion results, more parameters must be tested.
4.4 Comparison between the seismic and electromagnetic methods
The seismic method is considered a costly and costeffective technique that can provide highresolution images of structures and formations. However, in many cases, the seismic method alone is not sufficient to distinguish between fluids and their saturation. Compared to the seismic method, CSEM is a lowcost CO_{2} monitoring technique; its resistivity has a clear response to changes in fluid type and saturation, and it can be used to estimate CO_{2} saturation (Fawad and Mondol, 2021).
5 Conclusions
1) This study investigates the sensitivity of the ocean CSEM in monitoring plume transport during offshore CO_{2} storage. Through simulation experiments and data analysis, we found that this method can effectively detect and monitor the transport path and velocity of CO_{2} in the ocean.
2) This study not only provides a reference for the study of offshore CO_{2} sequestration plume migration mechanism but also proposes a method and provides technical support for CO_{2} sequestration monitoring.
3) In future studies, the experimental model can be further optimized; multiple influencing factors, such as emission source frequency, can be integrated; and joint application with other geophysical methods can be explored to improve the accuracy of monitoring work.
Competing interest The authors have no competing interests to declare that are relevant to the content of this article. 
Table 1 General model parameter settings
Name of the layered medium Layer thickness (m) Layer resistivity value (Ω) Air layer H_{1} =800 ρ_{1} =1×10^{13} Marine layer H_{2}=1 000 ρ_{2}=0.3 Submarine formation H_{3}=2 500 ρ_{3}=2.0 Basement formation H_{4}=500 ρ_{4}=1 000 Table 2 The model parameters of comparison measurements for Model 14
Model No. Position Y (m) Position Z (m) Length (m) Thickness (m) Burialdepth (m) 14 1 500, 6 500 2 500, 3 000 5 000 500 800 Table 3 The model parameters of various lateral diffusion arrangements that need to be compared in this group for Models 11, 12, 13, and 14
Model No. Position Y (m) Position Z (m) Length (m) Thickness (m) Burialdepth (m) 11 1 500, 2 000 2 500, 3 000 500 500 800 12 1 500, 2 500 2 500, 3 000 1 000 500 800 13 1 500, 4 500 2 500, 3 000 3 000 500 800 14 1 500, 6 500 2 500, 3 000 5 000 500 800 Table 4 The model parameters of reservoir burial depths to be compared in this group for Models 21, 22, and 23
Model No. Position Y (m) Position Z (m) Length (m) Thickness (m) Burial depth (m) 21 1 500, 2 500 2 600, 3 600 1 000 1 000 1 000 22 1 500, 2 500 3 100, 4 100 1 000 1 000 1 500 23 1 500, 2 500 3 600, 4 600 1 000 1 000 2 000 Table 5 The model parameters of different saturation levels to be compared in this group for Models 31, 32, 33, and 34
Model No. Spacing (m) Length (m) Thickness (m) Burial depth (m) 31 1 000 1 000 500 1 000 32 500 1 000 500 1 000 33 300 1 000 500 1 000 34 200 1 000 500 1 000 Table 6 The model parameters of different saturation levels to be compared in this group for Models 41, 42, and 43
Model No. Position Y (m) Position Z (m) Length (m) Thickness (m) Burial depth (m) 41 1 500, 2 500 2 500, 2 600 1 000 100 1 000 42 1 500, 2 500 2 500, 2 800 1 000 300 1 000 43 1 500, 2 500 2 500, 3 000 1 000 1 500 1 000 Table 7 The model parameters of various saturation levels to be compared in this group for Models 51 and 52
Model No. Resistivity (Ω) Interval (m) Length (m) Thickness (m) Burial depth (m) 51 100/50/20 0 1 000 500 1 000 52 100/50/20 1 000 1 000 500 1 000 
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