Full time-domain waveform inversion of controlled ...

Full time-domain waveform inversion of controlled-source electromagnetic exploration of submarine massive sulphides Downloaded 06/28/18 to 200.1.118.115. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/

Naoto Imamura∗ , Tada-nori Goto, Junichi Takekawa and Hitoshi Mikada, Kyoto University SUMMARY In this study, we present a full waveform inversion method in time-domain using controlled-source electromagnetic (CSEM) method to explore submarine massive sulfides (SMS). This inversion methods, We use a Graphic Processing Unit (GPU) to accelerate the Finite-Difference Time-Domain (FDTD) simulation for forward calculation to minimize the calculation time cost. Using data from a synthetic SMS, we demonstrate that conductive anomalies around SMS could be estimated. We discussed the resolution of our CSEM inversion method, considering the orientation of the dipole of a transmitter and receivers. The synthetic inversion examples show that the upper surface of SMS is resolved appropriately with vertical directed dipoles. We also find that the thickness of SMS is resolved accurately when we use the horizontal directed dipoles. These differences of the inversion results are explained considering the electric current. From numerical results, we consider that it is efficient to employ different oriented dipoles of transmitter and receivers for accurate inversion.

INTRODUCTION Recently, controlled-source electromagnetic (CSEM) method is widely used for shallow subsurface exploration to measure resistivity structure in detail. This method is also used for surveying oil and natural gas resources in deep sea (Constable et al., 2007; Constable, 2010). Recently, theoretical and experimental attempts have been initiated to survey submarine massive sulphides (SMS) using electromagnetic method. Kowalczyk (2008) surveyed SMS using EM method with magnetic source, although the sounding depth was limited within several meters. From conventional studies about SMS, some features of SMS become clear. Nakayama et al. (2011) found that core samples of SMS showed high IP effects. Imamura et al. (2011) shows that the thickness of SMS is proportional to the attenuated rate of amplitude of electromagnetic fields. Various kinds of CSEM inversion methods in frequency domain have been developed, although this method requires solutions for each frequency in the source spectrum. In this paper, we present the implementation of time domain full waveform inversion algorithm. Full waveform inversion requires only time domain data to obtain inversion results of model parameter, so multiple frequency solutions are not required. For the full waveform inversion method, Wang et al. (1994) presented the inversion algorithm for TEM data, which originally developed for seismic wavefields by Tarantola (1984). Sanada et al. (1999) applied this algorithm to crosshole radar tomography. Ernst et al. (2007a) discussed the resolution of inversion results considering the model parameters using crosshole radar data. Ernst et al. (2007b) applied this method to the real data set and obtained high resolution permittivity and conductiv-

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ity images. In the past few years, various time-domain CSEM inversion algorithms have been presented. Maaø (2007) and Støren et al. (2008) described the fast finite-difference timedomain modeling for CSEM inversion. Employing Hessianbased optimization, Zach et al. (2008) developed time-domain inversion using CSEM method. Black et al. (2010) presented 3D inversion of time-lapse CSEM data for synthetic reservoir data. In this paper, we present the implementation of a 2D timedomain full waveform inversion algorithm for synthetic marine CSEM data to explore SMS. We used a conjugate gradient method to compute the distribution of conductivity iteratively. When we simulate electromagnetic field in time domain with low frequency transmitter, enormous time step is needed. A Graphic Processing Unit (GPU) is used to accelerate the calculation speed via Computer Unified Device Architecture (CUDA), which is the computing architecture in NVIDIA GPUs (Owens et al., 2008). In the CSEM methods, the orientation of dipoles such as inline or broadside are important. We discussed our results in terms of the resolution of the inversion images and found out that the combination of the orientations of the transmitter and receivers above on the SMS is a key to determine the resolution.

METHOD

Figure 1: Flow chart for full waveform inversion. For wave propagation in the 2D Cartesian coordinates, we used the transverse electric modes of Maxwell equation. This equation is solved using FDTD simulation based on staggered-grid finite-difference operators that are second-order accurate. We used perfectly matched layer (PML) for absorbing boundaries to decrease the artificial reflections at the edges of the model space. Our inversion flow is shown in Figure 1. The spatial distribution of conductivity σ and permittivity ε that minimize

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Full time-domain waveform inversion of CSEM exploration of SMS SYNTHETIC MODEL GEOMETRY

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a function of the form is computed as follows, 1 Fd = [ecal (rtrn , rrec ,t, σ , ε) − eobs (rtrn , rrec ,t, σtrue , εtrue )]2 2 (1) where rtrn and rrec are vectors that identify the transmitter and receiver positions, ecal and eobs are the computed and observed electric fields at the receiver locations. Fd is minimized using a conjugate gradient method. Small perturbation of Fd is computed from Taylor expansion

Z δ Fd = Fd (p + δ p) − Fd (p) =

γ(r0 ) · δ p(r0 )dr0

(2)

V

where p show model parameters σ and ε, V is the region where the model is allowed to vary. The gradients γσ and γε are computed dividing partial derivatives of the error function Fd by the model parameter. δ Fd δp

γp =

(3)

Considering the model change like p’ = p + δ p, we obtain the gradients γσ and γε . The resulting gradient steps of σ and ε are obtained as follows, γσ = −

XZ

T

dt0

0

trn

∂e 0 0 (r ,t ) · eb (r0 ,t 0 |δ e0 ) ∂t

(4)

∂ e 0 0 ∂ eb 0 0 (r ,t ) · (r ,t |δ e0 ) ∂t ∂t

(5)

dt0

0

trn

γε =

T

XZ

where eb (r0 ,t 0 |δ e0 ) =

XZ

T

dt0 Gz (r0 ,t 0 |ri ,t) · δ e0 (rt ,t)

(6)

0

rec

is the back-propagated field. The reversal of the time order is implicit in the definition of the Green dyadic. In conjugate gradient method, the search direction is determined by the gradient of Fd and the previous search direction as p(k+1) = p(k) + α p b(k)

(7)

where α p is the step length of model parameters and b(k) = −γ (k) + β (k) b(k−1)

(8) β (k)

is the search direction. The scalar parameter can be updated as < γ (k) , γ (k) − γ (k−1) > β (k) = (9) < γ (k−1) , γ (k−1) > The step length is determined by simple method such as the step length is gradually attenuated with respect to the data error. To confirm the convergence of the inversion, we calculate the normalized data error En as

qP En =

trn

RT 2 rec 0 (e0 − e) dt

P

qP

trn

(10)

RT

2 rec 0 e0 dt

P

To obtain high performance computation, Nvidia Geforce GTX 590 is used as a GPU board. We computed forward simulation with single precision. We implemented Computer Unified Device Architecture (CUDA) for FDTD simulation (Nagaoka, 2011).

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Figure 2: Simulation model for inversion. Electric current is transmitted from each transmitter at a time. We change the orientation of transmitter and receivers Many explorations were conducted to survey SMS around the world, but any detailed cross-sectional structure and model parameters that includes SMS has not been completely provided yet. In this study, we assume SMS to be a simple rectangular block in sediments shown in Figure 2. We also assume model parameters to be shown in Table 1. A transmitter and nine receivers are arranged above the anomaly. Electric current is transmitted while the transmitter moves to nine positions. Totally, the forward calculation is performed nine times to calculate one gradient in each iteration. We set the waveform as ricker wavelet and the center frequency as 100 kHz . We also set the grid size as 0.2 m and the number of grid is 256 in both directions. The distance from the transmitter to seafloor is arranged to be 0.8 m and from the receivers to seafloor is arranged to be 0.4 m. Each of receiver is arranged at intervals of 1.6 m. Although these parameters are for compact scale for CSEM method exploring hydrocarbon, we regard this model as a miniature model considering the skin depth. To test our 2D inversion algorithm, we apply it to a simple model shown in Figure 2. When the model parameters are updated, we used the masking method (Zach et al., 2008) considering the footprints of receiver. Employing this method, we fixed the model parameters of the top five grid cells. When the model parameters are updated, it is possible that conductivity becomes less than zero. We set the minimum value of conductivity as 0.0001 S/m. The starting model used in inversion was a 0.45 S/m half-space. In this model, we set the initial step length as 0.8 for conductivity and as 4.0 for relative permittivity.

Sea water Basalt SMS

Conductivity [S/m]

Relative permittivity

3.3 0.45 5.0

81.0 20.0 100.0

Table 1: Model parameters used in this model

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Full time-domain waveform inversion of CSEM exploration of SMS

(a)

Figure 3: Comparison of the inverted waveform and the waveform of synthetic model shown in Figure 2. Each of trace shows the received vertical electric field. In this figure, the transmitted trace is No.5. The amplitude of trace is set to relative for each trace number, considering the attenuation of electromagnetic field. Red line shows the inverted waveform. Blue line shows the waveform of synthetic model shown in Figure 2.

RESULTS AND DISCUSSIONS The effect of using different orientation of dipoles We show numerical results in Figure 4(a) and Figure 4(b) that are inversion results. In these results, we set the orientations of transmitter and receivers as vertical direction in Figure 4(a) and as horizontal direction, which is often called inline, in Figure 4(b). In each figure, a dotted rectangle shows the existence area of conductive anomaly. We also show the example result of inverted waveform in Figure 3 with vertical dipoles. Figure 3 show that the inverted waveform is recovered to the waveform obtained from the model in Figure 2. As shown in Figure 4(b) and Figure 4(a), the resolution of the inversion results with conductive anomaly is different. In case of Figure 4(a), the vertical position of anomaly is resolved precisely comparing with Figure 4(b). Figure 4(a) also shows that the upper surface position of SMS is detected accurately, although a lower surface position of SMS isn’t resolved clearly. On the other hand, in case of Figure 4(b), the thickness of anomaly is well resolved comparing with Figure 4(a). These differences of the inversion results are explained considering distribution of electric current. In case of Figure 4(a), the vertical flow of an electric current around the anomaly is dominant. The upper surface of the anomaly is resolved accurately because the electric current flows vertically. After the electric current goes through the conductive anomaly, the amplitude of electric current is attenuated because of the loss term of Maxwell equation. Because of the attenuated electric current, the lower surface of the anomaly isn’t detected clearly. The lateral side of anomaly isn’t resolved properly because the attenuated electric current goes horizontally around the lateral

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(b)

(c)

Figure 4: Comparison of inversion results changing the orientations of transmitter and receivers. The contour color depict the conductivity. (a) The transmitter and receivers are directed to vertical axis. (b) The transmitter and receivers are directed to horizontal axis. (c) The transmitter and receivers are directed to horizontal axis. Considering the inversion result of (a), the gradient muting is applied from the seafloor to upper surface of SMS.

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Full time-domain waveform inversion of CSEM exploration of SMS 8

horizontally directed dipoles and vertically directed dipoles, considering the gradient muting range. As a result, the resolution of the anomaly is improved for upper surface and thickness of SMS. We also find that the observed inversion results may be affected considerably by attenuated electric current.

Numerical model Figure 3(a) Figure 3(b) Figure 3(c)

7

conductivity (S/m)

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6 5 4 3 2 1 0 120

130

140

150

160

170

grid number

Figure 5: Inversion results of conductivity with regard to vertical position on the grid of y=128. The line of ”Numerical model” shows the synthetic model in the vertical plane. Other lines shows the inversion results of Figure 4(a), Figure 4(b), Figure 4(c) in the vertical plane.

Through all numerical calculations, we would like to conclude that it is efficient to implement this CSEM method for SMS exploration. We think that it is possible to detect the upper surface of SMS using vertical dipoles. When integrating horizontal dipoles and vertical dipoles, it is possible to obtain high resolved inversion result. Our next plan is to simulate forward calculation with low frequency in frequency domain.

ACKNOWLEDGMENTS We are greatly thankful to financial support of SMS exploration project by Ministry of Education, Culture, Sports, Science and Technology in Japan. We are also grateful for the financial support from the Japan Society for the Promotion of Science (JSPS).

side of anomaly. In case of FIgure 4(b), the horizontal flow of an electric current is dominant around the anomaly. The lower surface of the anomaly is resolved correctly because the electric current doesn’t go thought the anomaly below the lower surface of anomaly. The vertical position of anomaly isn’t resolved accurately because of horizontal flow of electric current around the anomaly. The effect of integration of different orientation of dipoles From the above results, we integrated the results of the different directed dipoles. To unify these results, we changed the gradient muting range. The top surface of the gradient muting is set considering the results of Figure 4(a). We set the effective gradient range from z=138 to z=170. Employing the gradient muting, we used the horizontally directed transmitter and receivers. In this case, the starting model was also set to a 0.45 S/m half-space. The result is shown in Figure 4(c). Figure 5 also shows that the inversion results of conductivity with regard to vertical position in the grid of y=128. In these figures, the upper surface of anomaly is almost resolved than the result of Figure 4(a) and that the lower surface of anomaly is detected than the result of Figure 4(b).

CONCLUSIONS The full waveform CSEM inversion is developed and implemented for a synthetic SMS model. We also implemented GPU computing to obtain significant speedup of the calculation time. In this research, we compared the effect of the direction of dipoles, and discussed the resolution of conductive anomaly. From the results, we find that the resolution depends on the orientations of transmitter and receivers. When the horizontal dipoles are employed, the obtained inversion result has a resolution to thickness of SMS. When the vertical dipoles are employed, the obtained inversion result has much resolution to upper surface of SMS. We integrated the inversion results of

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http://dx.doi.org/10.1190/segam2012-1244.1 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2012 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES

Black, N., G. A. Wilson, A. V. Gribenko, and M. S. Zhdanov, 2011, 3D inversion of time-lapse CSEM data for reservoir surveillance: 80th Annual International Meeting, SEG, Expanded Abstracts, 716720. Constable, S., 2010, Ten years of marine CSEM for hydrocarbon exploration: Geophysics, 75, no. 5, 75A67-75A81. Constable, S., and L. J. Srnka, 2007, An introduction to marine controlled source electromagnetic methods for hydrocarbon exploration: Geophysics, 72, no. 2, WA3-WA12. Ernst, J. R., H. Maurer, A. G. Green, K. Holliger, 2007a, Full-waveform inversion of crosshole radar data based on 2-D finite-difference time-domain solutions of Maxwell’s equations: IEEE Transactions on geoscience and remote sensing, 45, 2807-2828. Ernst, J. R., A. G. Green, H. Maurer, K. Holliger, 2007b, Application of a new 2D time-domain fullwaveform inversion scheme to crosshole radar data: Geophysics, 72, no. 5, 153-164. Imamura, N., T. Goto, J. Takekawa, H. Mikada, 2011, Application of marine controlled-source electromagnetic sounding to submarine massive sulphides explorations: 81st Annual International Meeting, SEG, Expanded Abstracts, 730-734. Kowalczyk, P., 2008, Geophysical prelude to first exploitation of submarine massive sulphides: First Break, 26, 99-106. Maaø, F. A., 2007, Fast finite-difference time-domain modeling of marine-subsurface electromagnetic problems: Geophysics, 72, no. 2, A19-A23. Nagaoka T. and S. Watanabe, 2011, GPU-Based 3D-FDTD computation for electromagnetic field dosimetry: Proceedings of IEEE Africon. Nakayama, K., T. Shingyouji, M. Mottori, M. Yasui, Y. Kobayashi, A. Yamazaki, and A. Saito, 2011, Marine time-domain electromagnetic technologies for the ocean bottom mineral resources: Proceedings of the 10th SEGJ International Symposium, 433-436. Owens, J. D., M. Housto, D. Luebke, S. Green, J. E. Stone and J. C. Phillips, 2008, GPU computing: Proceedings of the IEEE, 96, 879-899. Støren, T., J. J. Zach, and F. Maaø, 2008, Gradient calculations for 3D inversion of CSEM data using a fast finite-difference time-domain modeling code: Annual International Conference and Exhibition, EAGE, Extended Abstracts. Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, 1259-1266. Wang, T., M. Oristaglio, A. Tripp and G. Hohmann, 1994, Inversion of diffusive transient electromagnetic data by a conjugate gradient method: Radio Science, 29, 1143-1156.

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Zach, J. J., F. Roth, and H. Yuan, 2008, Data preprocessing and starting model preparation for 3D inversion of marine CSEM surveys: Annual International Conference and Exhibition, EAGE , Extended Abstracts.

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