Improved Detectivity for Detecting Gas Hydrates Using the Weighted Differential Fields of the Marine Controlled-Source Electromagnetic Data

: Gas hydrate is seen as a kind of new energy resources, yet it may also be one of the main greenhouse gases as its dissociation may release methane into the atmosphere. Furthermore, a severe hazard to offshore infrastructures may also be introduced by extensive gas hydrate dissociation associated with the stability of the geological structures after gas production. Therefore, it is essential to investigate the gas hydrate as well as its environmental impacts before drilling and extracting it. The geophysical seismic reﬂection data is usually used for exploring the gas hydrate. The gas hydrate can be effectively identiﬁed by the bottom simulating reﬂectors (BSRs) on seismic reﬂection data. However, the BSR is only for identifying the bottom boundary and it is difﬁcult to estimate its space distribution and saturation within the hydrate stability zone. The marine controlled-source electromagnetic (CSEM) data is suitable for detecting the gas hydrate as the resistivity of the seaﬂoor increases signiﬁcantly in the presence of gas hydrate or free gas. In this study, a weighted differential-ﬁeld method is applied to improve the detectivity for identifying the gas hydrate. Numerical tests show that the difference of the EM ﬁelds can effectively suppress the airwaves in shallow waters. Therefore, the detectivity given by the ﬁeld ratio between the models with and without the gas hydrate target is enhanced. differential ﬁeld is less affected by the airwave and it shows evident correspondence to the hydrate. Our results indicate that


Introduction
Gas hydrate is a kind of ice-like solid substances which is usually distributed under high pressure and low temperature conditions (e.g., [1,2]). Gas hydrate is mainly composed of water and gas and it contains large amounts of methane. It is now seen as a kind of new energy resources [3]. Furthermore, the gas hydrate may also be a kind of greenhouse gases [4]. Although some of it may be trapped under the seafloor and and consumed by some microbes [2], the hydrate could be dissociated with methane released into the atmosphere if the stability of the geological structures were destroyed after gas production. Furthermore, extensive gas hydrate dissociation may also pose a severe hazard to offshore infrastructures [5]. Therefore, it is essential to investigate and quantify the gas hydrate and access its environmental impacts before its production. There are some recently developed techniques for dealing with this issue. For example, Hassanpouryouzband et al. [6] proposed the way for the permanent geological storage of CO 2 and related methane in permafrost regions and marine sediments which could greatly reduce the cost of capturing and storing the gas hydrate.
Geophysical methods are widely used for exploring the gas hydrate [3,[7][8][9]. For example, high-resolution acoustic investigations including side-scan sonar imagery and shallow subbottom profiling of the seafloor have indicated the presence of pockmarks, acoustic maskings and seeps. Acoustic anomalies associated with the gas seepage are observable within sediments of characteristic features in the seabed [10][11][12]. The pressure coring and seafloor marine heat flux measurements are also used for its accurate borehole investigations [8]. The high-resolution seismic profiles are usually used for investigating the gas hydrate deposits before drilling [13][14][15][16][17][18]. The stable gas hydrate zone is usually buried by a layer of free gas which will cause a seismic impedance contrast called the bottom simulating reflection (BSR) (e.g., [19]). Its bottom boundary can be identified from the BSRs qualitatively. However, it is not easy for us to quantify the gas hydrate deposits by the seismic reflection method only.
The marine CSEM method usually applies a towed dipole transmitter emitting low frequency EM signals [56][57][58][59]. The receivers can be deployed on the seafloor [60] or towed behind the source [28,61]. For shallow waters where the gas hydrate is usually buried, the airwave dominates the recorded EM signals and it will mask the useful signals from the seafloor hydrate target [62][63][64][65][66]. The airwave is mainly the signals from the source which propagates upward to the sea surface, travels through the air horizontally and finally goes down into the water column to the receivers [67]. As the air and seawater have an extreme physical contrast, the critical angle for total reflection between air and seawater is almost the incidence angle [68]. The energy of the airwave is strong, especially in shallow waters of depth no more than 300 m. Thus, it is necessary to suppress the airwave before processing and interpreting the marine CSEM field data [69].
The way to suppress the airwave in shallow waters are well investigated in previous studies. For example, Amundsen et al. [67] proposed the decomposition of EM fields to retract and remove the airwave from downgoing components. One can also evaluate the airwave analytically for 1D conductivity model and then remove it [62,[70][71][72]. The 1D method is usually not suitable for the earth with topography or with complex geological structures. Løseth et al. [63] presented the weighted differences of EM fields to attenuate the airwave. The weighted differential approach is proved to be effective in suppressing the airwave and it can be utilized for dealing with both 1D and multi-dimensional (2D or 3D) data sets.
In this paper, we apply the weighted differential method proposed by Løseth et al. [63] to suppress the airwave of the marine CSEM data for identifying the gas hydrate targets. It is worth mentioning that, in our tests, the resistivity contrast between the hydrates and sediments is not as high as the hydrocarbon examples used by Løseth et al. [63]. This paper is organized as follows. First, we give the theory of computing the weighted differential fields. Then, some numerical tests are presented. Finally, a conclusion is given and future work is discussed.

Methodology
In this section, we give the principles of calculating the weighted differential EM fields. Following Li and Li [73,74], the electric and magnetic fields due to a dipole source for the layered conductivity medium can be expressed as in which the parameters used in above Equations (1) and (2) : the corresponding kernel functions for the electric field; : the corresponding kernel functions for the magnetic field. Figure 1 shows the main propagation paths of different EM waves induced by a dipole source. As mentioned before, the airwave is part of the propagating EM fields (see Equations (1) and (2)) mainly reflected from the sea surface (red line in Figure 1). The hydrate target related EM signals are the reflection wave and the guided wave, which are indicated by the yellow line and the black line, respectively.

Source Receiver
Direct wave  Figure 1. Illustration of the field events due to a dipole source in the marine environment (modified after [67]). For the 1D conductivity earth, the source induced airwave (magenta), the surface reflection wave (blue) and the direct wave (green) are mainly going upward, while the reflection wave (yellow) and the guided wave (black) related to the gas hydrate deposit are going downward.
Furthermore, in the frequency domain, for a simplified model with dual air-seafloor half-spaces and a finite-thick seawater column as the interlayer, the electric part of the airwave can be expressed as [62] E air r = P cos φe ik(z+z S ) e ik 0 r 2πσ sea r 3 where • i = √ −1: the imaginary unit; • φ: the azimuth of the dipole source, and φ is set to be 0 for a horizontal source along the eastern direction y; • ω: the angular frequency; • µ 0 : the magnetic permeability in free space; • 0 : the electric permittivity in free space; • σ sea : the conductivity of the seawater; • σ: the conductivity of the seabed; • k = iωµ 0 σ sea : the wavenumber used; : the reflection coefficient of TE mode for the seabed. From Equations (1)-(3) we can see that the horizontal electric field component of the airwave is inverse to the power of three with respect to the source-receiver horizontal offset r. We also find that the horizontal magnetic field component is inverse to the power of four with respect to r [63]. By weighting the horizontal electric field with r 3 and the horizontal magnetic field with r 4 , the airwave may be attenuated in the measured data as the EM field propagation is mainly vertical [63,75]. This quantitative relationship can also be applied to the nonuniform conductivity settings under the seafloor. Therefore, the weighted differential electric field can be expressed as [63] E r 12 = (r 2 /r 12 ) 3 E r 2 − (r 1 /r 12 ) 3 E r 1 y r 2 − y r 1 , where E r 12 is the weighted differential electric field for two receivers nearby. The receivers are along the y-axis. r 12 = (r 1 + r 2 )/2, where r 1 and r 2 are the horizontal distance between the source used and the receivers 1 and 2, respectively. Here the geometric term r 3 is considered for suppressing the airwave. Equation (4) is an example for computing weighted differences for inline electric fields of two receivers nearby. The weighted differential magnetic fields for both inline and broadside modes can be calculated similarly. We will not repeat it here for clarity.

Numerical Analysis
In this section, the numerical analysis for gas hydrate deposit models in shallow waters is shown. Our aim is to validate the weighted differential approach in suppressing the airwave for both 1D and 2D cases.

1D Test
We first test a 1D gas hydrate model modified after Constable and Weiss [76] (Figure 2). The hydrate reservoir model is composed of five layers including the air, the seawater and seafloor sediments and gas hydrate. The setting of the resistivity of the hydrate is following Goswami [4]. The air is a half-space of the resistivity 10 12 Ωm (i.e., the conductivity is 10 −12 S/m). The seawater layer is of thickness 100 m and its resistivity is 0.3 Ωm. From the depth of 1100 m, there is a gas hydrate layer of thickness 50 m and its resistivity is 15 Ωm. The background sediments are of the resistivity 1.5 Ωm. An electric dipole source is placed at (x s = 0 m, y s = 0 m, z s = 850 m). The transmitting frequencies used are 0.5 and 1.25 Hz for detecting shallow hydrate targets following Schwalenberg et al. [31]. The seafloor receivers are distributed evenly along the inline direction y from 500 m to 9500 m. The receiver interval is 100 m. We use the code given by Li and Li [73] to compute the frequency-domain 1D marine CSEM fields.  Figure 3 shows the inline electric field and its weighted differences (see solid and inverse triangles in Figure 3a) and the corresponding detectivity (see the solid line and diamonds in Figure 3b). Note that the amplitude of the inline electric field and its weighted differences for the background model (Figure 2b) is also given for comparison (see dashed line and dots in Figure 3b). The transmitting frequencies 0.5 and 1.25 Hz are indicated by gray and red, respectively.
From Figure 3a we can see that the amplitude of the weighted differential field is quite smaller than that for the original electric field. The amplitude for the original electric field ranges from 10 −8 to 10 −12 V/Am 2 , 1/m 2 , while it is 10 −9 to 10 −18 V/Am 2 , 1/m 2 for the weighted differential field. This can explained by the fact that the differential field is weighted by the geometric spreading term and it is decreased remarkably as the transmitter-receiver offset increases. When using the original electric field, the detectivity using the frequencies 0.5 and 1.25 Hz is almost unity, which indicates that the original electric field is almost of the same as its corresponding background field, i.e., the airwave dominates and it masks the useful signals from the buried hydate target. We can not use the original electric field to detect the hydrate reservoir directly (see solid lines in Figure 3b). However, the detectivity is remarkably improved when using the weighted differential field (see diamonds in Figure 3b). This indicates that by using the weighted differential field, the airwave is suppressed effectively, while the signals for the hydrates are enhanced.

2D Test
We also test a 2D model to further investigate the weighted differential method. The 2D model (Figure 4) is modified after the 1D case (Figure 2), except that its hydrate deposit is of finite horizontal length of 8000 m. The transmitter-receiver layout is the same as in the 1D test. The receivers are along the inline direction y from 500 m to 5500 m with an even interval 100 m. The code given by Li and Han [30] and Li et al. [37] is used to perform the frequency-domain 2D marine CSEM field simulation.   Figure 5 shows the results for the original electric field, the weighted differential field (Figure 5a) and their corresponding detectivity (Figure 5b). The 2D numerical results also indicate that the original field is masked by the airwave and it cannot be used for identifying the gas hydrate target, while the weighted differential field is less affected by the airwave and it shows evident correspondence to the hydrate. Our results indicate that the pre-processing of the EM field data is necessary before interpretation. For our tests, the weighted differences of the original fields are proved to be effective in removing the airwave in shallow waters with gas hydrate targets.

Conclusions
In this study, we apply the weighted differential approach to process the marine CSEM data in shallow water areas with gas hydrate targets. The weighted differential field accounts for the geometric spreading factor of the EM fields and it is effective in suppressing the airwave.
The original shallow water data cannot be used directly for investigating the hydrate as it is masked by the airwave. We conduct both 1D and 2D numerical analysis and our tests show that the detectivity of the gas hydrate deposits is significantly improved, which indicates that the airwave is effectively suppressed in the weighted differential field data. The weighted differential data shows an evident correlation with the seafloor buried hydrates and it is proved to be effective in attenuating the airwave in shallow waters.
For the future work, the 3D numerical analysis will be performed. The weighted differential field can also be extended to deal with the anisotropic data. The field data will also be tested for validating the weighted differential approach used.

Author Contributions:
This study is the result of collaborative teamwork. Conceptualization, methodology, software and investigation, G.L. and Y.L.; visualization, F.T., C.L. and W.L.; funding acquisition, G.L. and Y.L. All authors have read and agreed to the published version of the manuscript.