Seafloor bathymetry in deep and shallow water marine CSEM responses of Nigerian Niger Delta oil field: Effects and corrections

Journal of Applied Geophysics 123 (2015) 194–210

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Seafloor bathymetry in deep and shallow water marine CSEM responses of Nigerian Niger Delta oil field: Effects and corrections Adetayo Femi Folorunso a,b, Yuguo Li a,⁎ a b

Key Lab of Submarine Geosciences and Prospecting Techniques of Ministry of Education, Ocean University of China, 238 Songling Road, Qingdao 266100, China Department of Geosciences, University of Lagos, Lagos, Nigeria

a r t i c l e

i n f o

Article history: Received 30 December 2014 Received in revised form 12 October 2015 Accepted 19 October 2015 Available online 19 October 2015 Keywords: Deep water Shallow water Reservoirs mCSEM response Tx–Rx offsets Topographic undulations Bathymetry correction

a b s t r a c t Topography distortions in bathymetrically acquired marine Controlled-Source Electromagnetic (mCSEM) responses are capable of misleading interpretation to the presence or absence of the target if not corrected for. For this reason, the effects and correction of bathymetry distortions on the deep and shallow seafloor mCSEM responses of the Niger Delta Oil province were examined in this paper. Marine CSEM response of the Niger Delta geological structure was modelled by using a 2.5D adaptive finite element forward modelling code. In both the deep water and shallow water cases, the bathymetry distortions in the electric field amplitude and phase were found to get smaller with increasing Tx–Rx offsets and contain short-wavelength components in the amplitude curves which persist at all Tx–Rx offsets. In the deep water, topographic effects on the reservoir signatures are not significant, but as water depth reduces, bathymetric distortions become more significant as a result of the airwave effects, masking the target signatures. The correction technique produces a good agreement between the flat-seafloor reservoir model and its equivalent bathymetric model in deep water at 0.25 Hz, while in shallow water, the corrected response only shows good agreement at shorter offsets but becomes complicated at longer offsets due to airwave effects. Transmission frequency was extended above and below 0.25 Hz in the frequency spectrum and the correction method applied. The bathymetry correction at higher frequency (1.75 Hz) is not effective in removing the topographic effects in either deep or shallow water. At 0.05 Hz for both seafloor scenarios, we obtained the best corrected amplitude profiles, removing completely the distortions from both topographic undulation and airwave effects in the shallow water model. Overall, the work shows that the correction technique is effective in reducing bathymetric effects in deep water at medium frequency and in both deep and shallow waters at a low frequency of 0.05 Hz. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In recent years, there has been an upsurge in mCSEM surveys by the offshore hydrocarbon industries around the world following the academic development and industrial adoption, promotion and commercialization of the technology as a valuable tool for characterizing offshore petroleum reservoirs (Key, 2012). Today, the technology has metamorphosed from obscure post-seismic survey to survey done concurrently with seismic using the same lateral coverage as marine seismic methods. Application of the method is no longer limited to offshore hydrocarbon exploration as it has been applied in reservoir appraisal, reservoir monitoring, mapping water–oil contacts, estimation of hydrocarbon volumes, mapping gas hydrates and sequestration of carbon dioxide (Ellingsrud et al., 2002; Weitemeyer et al., 2006; Lien and Mannseth, 2008; Liang et al., 2012). ⁎ Corresponding author. Tel.: +8653266782862. E-mail address: [email protected] (Y. Li).

http://dx.doi.org/10.1016/j.jappgeo.2015.10.014 0926-9851/© 2015 Elsevier B.V. All rights reserved.

The initial development of the method favored deep water survey because the technology emerged from a study of the electric conductivity structure of the deep ocean lithosphere (Cox, 1981). Since its use in offshore hydrocarbon exploration, a number of challenges have emerged which include, but are not limited to, variations in seafloor topography (bathymetry) and exploring in shallow water environments. In most cases, mCSEM survey usually assumes flat seafloor topography but in reality flat topography beneath the ocean is almost impossible owing to a number of geological phenomena that produce undulations in ocean floor, the most important one being variation in topography in the survey area. The topographic undulation affects mCSEM data because there is conductivity contrast between seawater and the subseafloor sediment. The resulting bathymetry effects, if not corrected for, may lead to misinterpretation of correct place and depth of target below the mudline. The second challenge – airwave – arises from signal contribution from electromagnetic coupling between the highly resistive atmosphere (air) and the underlying geology, which can mask the target from detection. The airwave is less attenuated in shallow water

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than deep water columns because shallow water provides less conductive material to diffuse through compared to the deep water. In the Niger Delta oil region, hydrocarbon exploration started from onshore and shallow water environment, and only recently exploration began in the deep water area. Today, active exploration works are still ongoing in both shallow and deep water areas. To constrain the magnitude of bathymetry in the Niger Delta area, we used a seismic line across the offshore Niger Delta in our model as indicated in Fig. 1. The seismic line extends from shallow water (b 300 m) to water depth of greater than 4 km (see Fig. 2). In our previous work (Folorunso et al., 2015), we pointed out that Nigeria Niger Delta hydrocarbon province extends to water depth of more than 5000 m. The geology of the province is a little complex, made up of three lithological units: Akata (mainly sand), Agbada (sand intercalated with shale) and continental sands of the Benin Formations (Obaje, 2009) (Fig. 3A). The reservoirs we modelled are embedded in Agbada Formation structurally controlled by growth faults and rollover anticlines structures, shown in Fig. 3B, to form three layers of resistive hydrocarbon reservoirs. For detailed geology of the province engaged in our modelling, the readers are advised to read Doust and Omatsola (1990), Obaje (2009) and Folorunso et al. (2015). In this paper, we present a correction method to bathymetrically distorted mCSEM responses in both deep and shallow water environments of an electric conductivity model from the Niger Delta oil field of known geology. The method is an extension of Fox et al. (1980) DC resistivity topographic data correction where topographic effects are removed by normalizing the observed data with the topography model

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response and then multiplying it by the theoretical response of a halfspace (background response in our model). This was later adopted in magnetotelluric method (Chouteau and Bouchard, 1988). A number of both finite difference (FD) and finite element (FE) codes have been written to demonstrate the importance of collecting detailed and accurate topographic information for mCSEM surveys for better imaging of the reservoir (MacGregor et al., 2001; Um, 2005; Li and Key, 2007). We choose to use the FE code of Li and Key (2007) because the FE approximation permits precise representation of bathymetry with the use of a grid that can conform to any arbitrary surface (Li and Constable, 2007). 2. The correction method We modeled the geologic structure of Niger Delta with and without bathymetry and simulated inline horizontal E-field responses for the deep water models with and without the reservoir using the 2.5D finite element (FE) forward modelling code for marine CSEM methods (Li and Key, 2007). Adaptive finite element methods have been known as powerful tools for numerical modelling of complex problems. It adaptively refines the finite-element mesh using a posteriori error estimator to produce EM responses to as high degree of accuracy as the user desires, which was in this case, 1% error tolerance applied for all refinements though it resulted in increased computation time. The code uses a fully unstructured triangular element grid in order to accommodate both large and small scale heterogeneities in structures. Owing to the complexity of Niger Delta models presented here and the design of

Fig. 1. The geological map of Nigeria showing the location of Niger Delta Oil province and the location of the seismic line in the deep offshore. Insert is map of Africa showing Nigeria location (modified from Corredor et al., 2005; Connors et al., 2009).

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Fig. 2. Typical bathymetry variations in the Niger Delta region obtained from a seismic profile. (b) is an enlargements of parts of (a). Variation in topography is as high as 1000 m and more. The seismic line extends from the shelf to basin floor. (Redrawn from Connors et al., 2009).

this work, the code was modified to enhance calculations with multifrequencies, multiple transmitters and array of receivers in excess of two digits (receivers above 99). The FE code uses the secondary-field formulation to avoid problems related with rapidly varying fields around the source. Readers can find details in Li and Key (2007). The model includes the air (high resistivity around 1.e12 Ωm) in addition to other configurations shown in Fig. 4. Responses from ‘flat’ seafloor model (model without bathymetry) will be used to normalize the bathymetry model responses. To correct for the bathymetry distortion, Sasaki (2011) stated that the ratio of the bathymetrically distorted subsurface response to the bathymetric model response and the ratio of the undistorted (flat seafloor/corrected) subsurface response to the theoretical response of a background (without bathymetry) model are equal. This in our model could be expressed mathematically for a

given source–receiver combination as: ED =EB ¼ EC =E F

ð1Þ

where ED and EC represent the distorted and undistorted/corrected (free of bathymetry effect) E-fields, while EB and EF are the calculated responses for the bathymetric background model and flat seafloor model without the reservoir respectively. From Eq. (1), the corrected CSEM response (ΕC) can be derived thus: EC ¼ ðED =EB ÞE F :

ð2Þ

If the ratio EF:EB is taken as a constant κ, it follows that the level of correction in mCSEM response represented by EC is directly

Fig. 3. The Niger Delta (A) regional stratigraphy showing the major lithofacies units and associated resistivity values obtained from well logs. (B) Niger Delta petroleum reservoir structures and associated traps used in our models. (modified from Doust and Omatsola, 1990; Corredor et al., 2005; Folorunso et al., 2015; Stacher, 1995).

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Fig. 4. Niger Delta seismic-derived bathymetric model showing bathymetry seafloor with the ridges and valleys used in the computation of mCSEM response with 2.5D FE forward modelling code. Three hydrocarbon layers were involved. ‘r’ is the water depth which is equal to 2500 and 700 m for the deep and shallow water models respectively. The HED is towed 50 m above the seafloor.

proportional to the distortion (ED) caused by bathymetric effect in the CSEM response and indirectly related to the bathymetric background model. The constant κ is thus the complex correction coefficient given by Chouteau and Bouchard (1988) as: κ ¼ E F =EB

ð3Þ

and the corrected CSEM response becomes: EC ¼ κED :

ð4Þ

This removes the effect of rough topography in the data and consequently improves the Magnitude Variation with Offset (MVO) profiles of the corrected response as shown in Fig. 5. From Fig. 5, one can see that the distortion effects of topography on the bathymetry model response (marked BG-TOPO and OIL-TOPO in Fig. 5) is clearly seen in the MVO characterized by ‘short-wavelength’ anomalies persisting at all Tx–Rx offsets, more in the amplitude than in the phase. The shortwavelength features disappear after the correction (marked as “OILCORR” in Fig. 5) and the MVO's of corrected responses are almost the same with those of the flat seafloor model with reservoir marked as ‘OIL-Flat’ after the effect of bathymetry has been removed. 2.1. Deep water bathymetry case We consider here rough seafloor topography similar to a submarine ridge in which the highest and lowest topography are considered as ‘ridge’ and ‘valley’, respectively. For this scenario, both the deep and

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shallow water cases are considered and the joint effects of both the airwave and bathymetry for the shallow water case are also considered. The deepest water depth range, r, to the valley is 2500 m; while the highest peak of the ridge to the lowest base of the valley is 500 m for the deep model. Hence, for a flat seafloor of 2500 m depth, the water depth at the peak of the ridge for the equivalent bathymetric model is 2000 m as shown in Fig. 4. The sediment region enclosed within the 500 m bathymetry range becomes the zone of anomalous resistivity, or what Newman and Alumbaugh (1995) described as ‘equivalent source’. For the deep water case, the water has a resistivity of 0.3 Ωm with depth varying from 2000 to 2500 m for the ‘hills’ and ‘valleys’, respectively. The structure below the seafloor consists of three 100 Ωm hydrocarbon reservoir layers embedded in a stack of structurally controlled growth fault, antithetic fault and rollover structures. The background is made of thick overburden sediment of the Benin Formation (1 Ωm), sediment of the Agbada Formation (host rock 2 Ωm) intercalated with shale (5 Ωm) and shale of Akata Formation representing the source rock (10 Ωm). The models geometries used the same modelling domain of 50-km width and 50-km height, whereas the reservoir lateral extent varies from 9330 to 11,500 m with uneven thickness of 50 to 200 m in an oval shape typical of the Niger Delta reservoir structures. Maximum grid refinement of 20 was used in the modelling while adaptive refinement iteration was set at 5% computed at wavenumbers kx = 0.000032, 0.00010 and 0.031623 m−1. A horizontal electric dipole (HED) transmitter Tx is assumed to be towed at a height of 50 m along a line passing directly above a linear array of 101 receivers positioned on the seafloor along the y-axis from y = 0 to y = 20 km, at 200 m spacing. The background model is set similar to the reservoir model without the oil layer. Flat seafloor (background and reservoir) models were also created, with the same parameters, to see clearly the effect of bathymetry on the mCSEM data and to verify the suitability of the correction method. Fig. 6 shows the responses for the transmitter–receiver (Tx–Rx) geometries where the source (Tx) is located on the left side of the receiver (Rx) for both flat and bathymetric models with and without the resistive reservoirs. The amplitude and phase responses are plotted against Tx–Rx midpoint at selected transmitter–receiver (Tx–Rx) offsets (1 to 10 km) to show clearly the slightest anomalies in wavelength in the profiles. A close look at Fig. 6A–D, indicates that the background and reservoir profiles of the flat models are lacking in the short-wavelength features that characterized the profiles of bathymetry models (background and reservoir — Fig. 6E–H) at all Tx–Rx offsets, though more gentle in the phase at larger offsets. Also, the bathymetry distortions in the electric field amplitude and phase of the bathymetry models appear to get smaller with increasing Tx–Rx offsets and the shortwavelength components in the amplitude curves are consistent at all Tx–Rx offsets. Despite these wavelength variations in the amplitude and phase responses there is no significant difference between the amplitudes of models without and with topography depicted in Fig. 6C and

Fig. 5. The Magnitude Versus Offset (MVO) of corrected E-field responses: amplitude (A) phase (B) for the models shown in Fig. 4. Note the effect of topographic distortion in the bathymetry seafloor models and its consequent disappearance in the corrected response in both the amplitude and phase. ‘BG_TOPO’ and OIL-TOPO are background and reservoir responses for the bathymetry models; ‘BG-Flat’ and ‘OIL-Flat’ are background and reservoir responses for the flat-seafloor models, while ‘OIL-CORR’ is the corrected response based on Eq. (4).

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Fig. 6. Horizontal E-field responses at Tx–Rx offsets (1 to 10 km), plotted as Tx–Rx versus mid-point for the flat and bathymetric seafloor topography models with and without the resistive reservoirs in the deepwater (r = 2500 m in Fig. 4). Amplitude (A) and phase (B) for the background of flat seafloor topography model; amplitude (C) and phase (D) for the flat seafloor topography model with the reservoirs; amplitude (E) and phase (F) for the background of bathymetry model; amplitude (G) and phase (H) for the bathymetry model with the reservoirs. The background resistivities for all layers are shown in Fig. 4. The source frequency is 0.25 Hz.

D and G and H. So, the effect of seafloor topography on the reservoir signature is not significant in deepwater at 0.25 Hz. The distortion observed in phase shift can be attributed to the presence of the

reservoirs since this is absent in the background models without and with the bathymetry (Fig. 6A and B and E and F respectively). Normalizing the electric field response of the bathymetry model with reservoir by the response of the model without the reservoir

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Fig. 7. Normalized amplitude (A) and phase difference (B) for the E-field responses of flat seafloor model with the reservoirs; and Normalized amplitude (C) and phase difference (D) for the E-field responses of the bathymetry model with the reservoirs shown in Fig. 6C, D, G and H respectively. Note that this normalization does not completely remove short wavelength variation in the amplitudes.

appears not to remove the short-wavelength amplitude in both the amplitude and phase response. Whereas, such a normalization in flat model clearly shows anomaly which is consistent with the presence of resistive hydrocarbon (Fanavoll et al., 2010; Folorunso et al., 2015). Despite the presence of the short wavelength features, the target signatures of the reservoirs are obviously observed, as the magnitudes of normalized anomalies (Fig. 7C and D) compared to those of the flatsea model (Fig. 7A and B) appear to be consistent. Sasaki (2011) noted that such normalization differs, depending on the background resistivity in the bathymetric model. This explains the nature of curves derived in our model when compared to Fig. 6a and b of Sasaki (2011) bathymetry model. It is also noted that the two peaks of signatures (more distinct in the amplitude than in the phase) correspond well to the centers of the multiple reservoirs. This is further corroborated in the single resistive layer model presented later in this paper. The first peak represents response from the two vertically placed reservoirs to the left and the second standing for the single reservoir layer to the right of Fig. 4.

2.2. Shallow water bathymetry case Shallow water bathymetry model considered here is similar to the deep water model except for depth to the seafloor. The highest peak of the ridge (seafloor-sediment contact) to the lowest point at the valley is also 500-m, the same as in the deep water case earlier described. Depth to the shallowest part of the sea is 200-m, making the ‘r’ a total of 700-m. Thus, a flat-equivalent of the model has a seafloor of 700-m (See Fig. 4). The model transmission geometries, height of HED, reservoir extent and number of receivers are the same as the deepwater model. Also, the background model is similar to the reservoir model without the oil layer and the flat seafloor (background and reservoir) models were also created for the same purpose, as in the deep water case.

The responses of the shallow water models are plotted as Tx–Rx midpoint versus offset and depicted in Fig. 8, for the flat and bathymetric seafloor models with and without the oil layers to clearly show the effect of topography. Bathymetry effects on the shallow water model could be understood well by studying and comparing amplitude and phase plots from flat and bathymetry seafloor models. For example, at short offset of 1 km, EM signals are not deep enough to interact with the target oil layer as evident in the model responses in Fig. 8A–D, especially the amplitudes. Considering the bathymetry responses in Fig. 8E– H, the sinusoidal-like curves at offset 1 km (more in the phase than in the amplitude) of both background and reservoir models attest to the effect of topography distortions on the bathymetry model, rather than the presence of the reservoir. It then follows that the bathymetry distortion becomes more significant as the water becomes shallower (consider plots from the two bathymetry background models in Figs. 6F and 8F). This distortion is much higher at longer offsets (see offsets 8–10 in Fig. 8F and H) in such that it becomes practically difficult to identify the target response without incorporating the seafloor topography in the mCSEM model and correcting for its effects. Sasaki (2011) observed that because bathymetry undulation is greater relative to the thickness of the water in shallow water, bulk resistivity variations associated with seafloor topography are more significant in the shallow water for a given Tx–Rx offset. This makes the bathymetric distortions due to the induced currents greater in shallow water. The larger distortions at long offsets are believed to be complicated by the airwave responses which are prominent in the phase (Fig. 8F and G). But note that the distortions at longer offsets are greater in the background phase response than in the reservoir phase response. The response pattern of the flat and bathymetry background models at all offsets is not similar; whereas there seems to be, at least, a similarity in the response pattern between the flat and bathymetry reservoir models. This possibly indicates that the response pattern here is controlled by both the Tx–Rx geometries relative to the sea surface and

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Fig. 8. Horizontal E-field responses at Tx–Rx offsets (1 to 10 km), plotted as Tx–Rx versus mid-point for the shallow water flat and bathymetric topography models with and without the resistive reservoirs (r = 700 m in Fig. 4). Amplitude (A) and phase (B) for the flat topography model without the reservoirs; amplitude (C) and phase (D) for the flat topography model with the reservoirs; amplitude (E) and phase (F) for the bathymetry model without the reservoirs; amplitude (G) and phase (H) for the bathymetry model with the reservoirs. The background resistivities for all layers are shown in Fig. 4. The source frequency is 0.25 Hz.

by the resistivity variations associated with the seafloor topographic changes. This is supported by Li and Constable's (2007) observation that transmission frequency, seabed conductivity, seawater depth, transmitter–receiver geometry, and roughness of the seafloor topography affect the bathymetry response in mCSEM technology.

The normalized responses are depicted in Fig. 9. The presence of the target reservoir represented by enhanced values of normalized amplitude ratio (Folorunso et al., 2015), can be seen in the figure, with almost the same percentage of anomaly, at longer offsets, when compared to the deep-water case. In the shallow water case, bathymetry and flat

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Fig. 9. Normalized amplitude (A) and phase difference (B) for the electric field responses of flat model with the reservoirs; and Normalized amplitude (C) and phase difference (D) for the electric field responses of the bathymetry model with the reservoirs shown in Fig. 8C, D, G and H respectively. Note that this normalization does not remove short wavelength variation in the amplitudes.

models with the reservoirs do not follow the same pattern as well as the amount and quality of the anomaly obtained, especially at longer offset above 6 km. This is complicated by the effect of airwave on the

bathymetry reservoir model because bathymetry undulation is greater here (200-m seawater depth) than in the flat model which has seawater depth of 700 m. To verify this, we normalized the shallow water mCSEM

Fig. 10. Normalized amplitude (A) and phase difference (B) for the electric field responses of flat model with the reservoirs for 200 m water depth; and Normalized amplitude (C) and phase difference (D) for the electric field responses of the bathymetry model with the reservoirs, normalized with flat seafloor model of 200 m sea depth, shown in Fig. 8C, D, G and H respectively.

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Fig. 11. Corrected Amplitude (A) and phase (B) responses for the deepwater reservoir model, shown in Fig. 6G and H respectively, corrected for bathymetric effects using Eq. (4) (black broken lines), and the corresponding responses of the flat-seafloor reservoir model (coloured solid lines), shown in Fig. 6C and D. Note that both the flat-seafloor and the deepest portion of the bathymetry models have water layer of 2500 m.

bathymetry response with flat seafloor model of 200-m water depth and the results are displayed in Fig. 10. Both the amplitudes and phases of the flat and bathymetry reservoir models show a similar normalized response pattern, possibly because airwave effects in both model responses are the same in magnitudes. Thus, the airwave has significantly increased the amplitude responses at shallow water depth of 200 m more than at 700 m water depth, seeing more at long offsets. 3. The corrected results We applied the topography correction method described previously to the bathymetry model with reservoirs shown in Fig. 6G and H and compared the result to the flat seafloor model with reservoirs in Fig. 6C and D, in deepwater. The result depicted in Fig. 11 shows a good

match of the corrected response (black broken lines) with the flatseafloor reservoir model response (coloured solid lines) especially the amplitude, at all Tx–Rx offsets, which indicates that the correction technique is effective in reducing bathymetry effects in the Niger Delta model. Note that there are some discrepancies particularly in the phase plots thought to be due to the differences in the Tx–Rx geometry between the bathymetric and flat-seafloor models relative to the target. The wider discrepancies towards the end of each selected offset, in the amplitude profiles, correspond to where the midpoint of Tx and Rx is located over the intersection of the two vertically displayed oil layer to the left, on one side, and the top single layer to the right, on the other side. It was marked out at different depths as the EM signals go deeper beneath the seafloor. The discrepancies disappear in single layer model as will be seen later in Section 3.2. Except for these, the discrepancies in the

Fig. 12. Corrected Amplitude (A) and phase (B) responses for the shallow water reservoir model, shown in Fig. 8G and H respectively, corrected for bathymetric effects using Eq. (4) (black broken lines), and the corresponding responses of the flat-seafloor reservoir model (coloured solid lines), shown in Fig. 8C and D. (C) and (D) are amplitude and phase extracts from (A) and (B) respectively. Note that both the flat-seafloor model and the deepest portion of the bathymetry model have water layer of 700 m.

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Fig. 13. Horizontal E-field responses at Tx–Rx offsets (1 to 10 km), plotted as Tx–Rx versus mid-point for the bathymetric models with and without the resistive reservoirs (r = 2500 m in Fig. 4). Amplitude (A) and phase (B) for the background models; amplitude (C) and phase (D) for the model with the reservoirs at 1.75 Hz; amplitude (E) and phase (F) for the background models; amplitude (G) and phase (H) for the model with the reservoirs at 0.05 Hz. Note that amplitudes at larger offsets in the 1.75 Hz frequency plots, fall below the fundamental instrumental noise of 1e−15 V/Am2 and are excluded in the amplitude and phase profiles.

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Fig. 14. Corrected Amplitude (A) and phase (B) responses for the deepwater reservoir topographic model at 1.75 Hz, Amplitude (C) and phase (D) responses for the deepwater reservoir topographic model at 0.05 Hz. Corrected responses are in black broken lines and the flat-seafloor reservoir model responses in coloured solid lines. (E) and (F) are amplitude and phase extracts from (C) and (D) respectively. Note that both the flat-seafloor and the deepest portion of the bathymetry models have water layer of 2500 m.

amplitude are generally negligible, taking into account the variations in the background resistivities of the constituent layers. For the shallow-water bathymetry model, we first corrected for the model displayed in Fig. 8G and H and compared the result to the shallow-seafloor flat model with reservoirs in Fig. 8C and D. Fig. 12 depicts the result showing a good match at shorter offsets (offsets of 1 to 5 km) in the amplitude curves. At longer offsets (offsets of 6 to 10 km), airwave effect is high and thus complicates the distortions in the bathymetry model response as evident in Fig. 12C and D. The difference in the phase profiles is very significant as it departs widely from the equivalent flat-seafloor reservoir model. The difference is thought to be due to the difference in the airwave responses in the two models, knowing fully that the bathymetry model response is more affected by airwave than the flat-seafloor model response, being at depth shallower than the flat-seafloor model. We further use the 200-m shallow flatseafloor model response to normalize the shallow water bathymetry model response to see if we could get a better result. The result for both amplitude and phase profiles (not shown) deviate further from

the flat-seafloor model response, possibly due to the differences in water depth between the deepest portions of the bathymetry and the flat-seafloor models. The target and bathymetry responses are coupled through the airwave effect in shallow water making the correction method appear not applicable at longer offsets beyond which the airwave signature becomes significant. 3.1. mCSEM (Tx–Rx) offsets variation with frequencies In this section, we intend to show how the choice of frequency can enhance the effectiveness of the correction method. For this, we choose a higher frequency above (1.75 Hz) and below (0.05 Hz) the 0.25 Hz frequency considered previously in this study. We first consider the horizontal E-field responses at Tx–Rx offsets (1 to 10 km), plotted as Tx– Rx versus mid-point for the deep water bathymetry models with and without the resistive reservoirs depicted in Fig. 13. The result shows that at higher frequency (1.75 Hz), amplitudes of larger offsets fall below the typical instrument noise floor of 1e − 15 V/Am2, and are

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Fig. 15. Horizontal E-field responses at Tx−Rx offsets (1 to 10 km), plotted as Tx–Rx versus mid-point for the bathymetric topography models with and without the resistive reservoirs for shallow water. Amplitude (A) and phase (B) for the model without the reservoirs; amplitude (C) and phase (D) for the model with the reservoirs at 1.75 Hz; amplitude (E) and phase (F) for the model without the reservoirs; amplitude (G) and phase (H) for the model with the reservoirs at 0.05 Hz.

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Fig. 16. Corrected Amplitude (A) and phase (B) responses for the shallow water topographic reservoir model at 1.75 Hz, Amplitude (C) and phase (D) responses for the shallow water topographic reservoirs model at 0.05 Hz. Corrected responses are in black broken lines and the flat-seafloor reservoir model responses in coloured solid lines. Note that both the flat-seafloor and the deepest portion of the bathymetry models have water layer of 700 m.

thus excluded in the plot shown in Fig. 13A–D. Though the bathymetric effects in the electric field amplitude and phase get smaller with increasing Tx–Rx offsets and short-wavelength components in the amplitude plots also persist at all Tx–Rx offsets just as at 0.25 Hz, the magnitudes of anomalous responses at the higher frequency is much larger. It is capable of masking the target signature. At lower frequency of 0.05 Hz, the magnitudes of the short-wavelength components in the amplitude are smaller. It appears that bathymetry distortion, evident in the short-wavelength features, in deepwater mCSEM worsened with increasing transmission frequencies. The same correction technique was applied to mCSEM response from the two frequencies and the results are displayed in Fig. 14. Again, at the higher frequency of 1.75 Hz, the correction method does not produce a good match, partly due to the fact that the target signature is deeper than what high frequency could map. At the lower frequency of 0.05 Hz, the corrected results compare favorably with the flat-seafloor model response, perhaps, better than models at the 0.25 Hz frequency earlier reported especially in the amplitude profiles. It also means that the correction method is better at lower frequency for the deeper seafloor model than at higher frequency, though it created high spatial frequency oscillations in the phase profiles, which could be a numerical artifact and may be absent in real data especially if caused by the finite element model. At shallow water with the two frequencies, Fig. 15 shows the inline E-field responses plotted for selected Tx–Rx offsets (1 to 10 km), for the deep water bathymetry models with and without the resistive reservoirs. The large magnitude of distortions observed at 1.75 Hz is thought to be contributions from both topographic and airwave effects. The distortions hold the potential to mask the target signatures, in such that it might be impossible to infer the reservoir responses from Fig. 15C and D without modelling the bathymetric responses and without effective correction technique to mitigate the masking effects. Also, the

distortions become weaker as the frequency of transmission decreases as depicted in Fig. 15E–H. The bathymetric correction technique at 1.75 Hz frequency was completely not in good agreement with the flat-seafloor model (shown in Fig. 16A and B). The present knowledge of mCSEM technology favours high frequency for shallow water mCSEM exploration (Constable, 2010; Folorunso et al., 2015). But we must add that in most cases where this deduction was made, a single resistive hydrocarbon layer was involved, contrary to three layers in our model. Folorunso and Li (2014) has previously observed that E-field measured when transmitted EM waves interacted with two resistive layers is higher in magnitude than measured electric signal from the individual layer. From our shallow water bathymetry model of Niger Delta oil region, the high frequency appears not the best, at least, for the correction of bathymetry and airwave effects. Frequency of 0.05 Hz produces a good correction match in both amplitude and phase profiles, removing completely distortions from both topography and airwave effects. This happens to be the best fit obtained in all the models hereby examined as shown in Fig. 16. Fig. 17 shows the corrected plots for all the frequencies as short (2km), intermediate (5-km), and long (8-km) offsets. For the deepwater model, the correction technique has good agreement with the flatseafloor model at all offsets at the frequencies of 0.25 and 0.05 Hz but agreement is generally poor at 1.75 Hz as shown in Fig. 17 (first column). At shallow water, the correction method only show good agreement at 0.05 Hz frequency at all offsets. Correction at frequency of 0.25 Hz is good at short and intermediate offsets (Fig. 17, second column), while correction at higher frequency of 1.75 Hz is generally poor. The good agreement in the correction at low frequency (0.05 Hz) over higher frequencies, in the shallow water model, as the EM signals propagate from the source to the receivers interacting with the three oil layers arouse interest, because high frequency is usually employed

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Fig. 17. Corrected Amplitude responses (black broken lines), and the corresponding responses of the flat-seafloor reservoir model (coloured solid lines) at 2-km (A) 5-km (B) and 8-km (C) offsets for the deepwater models (first column); and 2-km (D) 5-km (E) and 8-km (F) offsets for the shallow seafloor models (second column), at the frequencies of 1.75, 0.25 and 0.05 Hz.

in shallow water mCSEM exploration. The signals, variably attenuated by the highly conductive heterogeneous background layers, are improved by the resistive oil layers, enhancing the responses measured by receivers on the seafloor. The fact that correction at this frequency is effective is undisputable even from the phase profiles in Fig. 16D. Mittet (2008) once noted that the CSEM phase might be more diagnostic of the reservoir response than amplitude in the shallow water. From all indications, correction at the low frequency of 0.05 Hz frequency for shallow water is far better than at higher frequencies. This modelling shows that the correction technique is effective in reducing bathymetric effects in shallow water by transmitting at low frequency of 0.05 Hz as reflected in both the amplitude and phase profiles. 3.2. mCSEM (Tx–Rx) offsets variation in single target

Fig. 18. Niger Delta single oil-layer bathymetry seafloor model. All parameters are the same with the multiple oil-layers model shown in Fig. 4.

In order to compare the mCSem offsets variation in single resistive target with the multiple-target model presented here, two reservoir layers were removed form the model in Fig. 4 and the remaining single

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Fig. 19. Single oil-layer horizontal E-field responses plotted as Tx–Rx versus mid-point for the flat and bathymetric seafloor models with the resistive reservoir in deep water; Amplitude (A) and Phase (B) for the flat seafloor model; Amplitude (C) and Phase (B) for the bathymetry model.

reservoir-layer model is shown in Fig. 18. Both flat seafloor and bathymetry models, with and without the reservoir, were created for the single oil-layer models in order to compare with the multiple oil-layers model described above. The responses for the transmitter–receiver geometries where the source (Tx) is located on the left side of the receiver (Rx) for both flat and bathymetric models with the resistive reservoir were also obtained as depicted in Fig. 19. Qualitative inspection of Fig. 19 shows that the amplitude decay slows when the resistive oil layer was encountered which leads to increase in the amplitude measured by receivers on the seafloor. In the phase profile, the resistive layer causes depressions corresponding to the position of the reservoir layer (Fig. 19B and D). This phenomenon is largely absent in the flat and bathymetry background models. Effects of the bathymetry, like in the models earlier explained, are marked off with the presence of short wavelength variations noticed in the amplitude and phase responses. The same goes for the shallow model (not shown). Normalized electric field responses of the bathymetry models with reservoir by the responses of the models without the reservoir for the single resistive layer models (deep water) are displayed in Fig. 20. From both amplitude and phase plots, one can notice a shift in the

peak of each plot corresponding to the position of the oil layer in the model. For examples, the normalized electric field peaks at the left side of the profile corresponding to the position of the single resistive oil layer in Fig. 20, compare to two peaks of the model earlier displayed in Fig. 7. This further shows that the peaks in the normalized electric field profile are signature from the resistive hydrocarbon layer as earlier asserted. The same scenario plays out at 0.05 Hz frequency and in the shallow water models (also not shown to avoid tautology). Fig. 21 depicts the result of applying the same correction technique to the single oil-layer in deep and shallow water models at the frequency of 0.25 Hz. Though the corrected amplitude and phase responses of the single-target and multiple-targets models are not the same qualitatively, but a careful inspection of the responses juxtaposed with the positions of the resistive layers in both single-target and multiple-targets models reveals similarity in the corrected responses of both models, at the same frequency. At deep water, amplitude of the corrected responses appear more fitted to the flat seafloor for the single oil-layer than for the multiple oil-layers model because of the absence of the other overlying resistive oil-layer. The corrected phase profile is not in good agreement at offsets above 4 km (Fig. 21B), but still fairly better than its multiple-targets equivalent. For the shallow seafloor model,

Fig. 20. Single oil-layer normalized electric fields in deep water; Normalized amplitude (A), and Phase (B) (flat seafloor), Normalized Amplitude (C) and Phase (D) (bathymetry model).

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Fig. 21. Corrected responses for the deep and shallow seafloor models at 0.25 Hz; Amplitude (A) and phase (B) for the deepwater reservoir model, Amplitude (C) and phase (D) for the shallow water reservoir model, corrected for bathymetric effects (black broken lines), and the corresponding responses of the flat-seafloor reservoir model (coloured solid lines).

the corrected responses at 0.25 Hz do not agree with the flat seafloor model response especially at larger offset, as observed in the multiple oil-layers model, but agreement is generally good at shorter offsets in both scenarios (Fig. 21C–D). It should be noted that the wider discrepancies marked where the midpoint of Tx and Rx is located over the three layers, as mentioned in the amplitude response of the earlier model, disappears in the single oil-layer model.

At 0.05 Hz frequency, corrected amplitude responses for the deep seafloor model show a good agreement with the equivalent flat seafloor model, similar to the corrected responses from the multiple oil-layers model as shown in Fig. 22A. but the phase response differs completely, which to some extent, shows differences in mCSEM interaction with multiple resistive layers compare to single resistive layer. Also, the high frequency wiggles persist in the phase traces at this frequency.

Fig. 22. Corrected responses for the deep and shallow seafloor models at 0.05 Hz; Amplitude (A) and phase (B) for the deepwater reservoir model, Amplitude (C) and phase (D) for the shallow water reservoir model, corrected for bathymetric effects (black broken lines), and the corresponding responses of the flat-seafloor reservoir model (coloured solid lines).

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The corrected phase responses deviated widely from the counterparts' flat seafloor model responses, when compared with the similar responses from multiple-reservoirs model. At shallow seafloor, the agreement between corrected and flat seafloor amplitude responses is good much like in the multiple-targets model, at all offsets (Fig. 22C– D). The phase responses also differs, showing marginal agreement between the two responses at shorter offsets, but widely digressed at longer offset, which was a different scenario observed in the phase responses at deep water model. Correction at the frequency of 0.05 Hz is quite effective in shallow water than in the deep water models, meaning that as water depth reduces mCSEM exploration in the Niger Delta favours low frequency. This is applicable to multiple and single reservoir target as the differences in the corrected responses are not significantly wide.

Acknowledgements A.F. Folorunso acknowledges the support of the Chinese Government Scholarship and the Nigeria Tertiary Education Tax Fund (TETFUND) for the fellowships offered. All authors appreciate the Key Lab of Submarine Geosciences and Prospecting Techniques of Ministry of Education, Ocean University of China for providing suitable academic environment for the research. Contributions from Li Ying are highly appreciated. Phase shift short code of David Myer (SCRIPPS) to provide difference in two phases was greatly appreciated. We are grateful for the constructive comments provided by the editor and other anonymous reviewers whose comments and suggestions have greatly improved this work. References

4. Conclusion Bathymetry effects on the deep and shallow seafloor of Nigeria Niger Delta Oil province were examined in this paper. Three oil layers were encountered by the propagating EM signals in our model but single reservoir-layer models were created in both water cases for comparison. Topographic distortions in the mCSEM responses of bathymetrically acquired data are capable of misleading interpretation to the presence or absence of the target if not corrected for. In fact, at certain higher frequency and shallow water, we found that the target signature can be masked completely by the distortions from bathymetry undulations if not corrected for. The effect of seafloor topography on reservoir signature is smaller in deepwater but the bathymetric distortion becomes bigger as the water becomes shallower and offsets becomes longer, masking the target signatures. The higher distortions at long offsets are complicated by the airwave responses. First, normalization of the bathymetry reservoir model with bathymetry background model was done for both deep and shallow water cases at 0.25 Hz frequency. The target responses remain visible represented by two peaks of signatures in the amplitude and phase profiles corresponding to the centers of the three reservoirs, only for the deep water. For single oil-layer model, the peak in the amplitude and phase is located directly above the reservoir. For the shallow water, the target signatures in the normalized profiles are still seen but maintain no similarity in pattern with the flatseafloor reservoir model as observed in the deepwater case. We applied the correction method first to the deep seafloor model, at 0.25 Hz, and found that the agreement between the flat-seafloor reservoir model and its counterpart bathymetric model corrected for topographic effects is generally good. For shallow water at the same frequency, corrected bathymetry plots only show a good match at shorter offsets but complicated at longer offsets due to airwave effects. Further corrections were made at two frequencies of 1.75 and 0.05 Hz for both water depths. High frequency (1.75 Hz) does not produce a good match when corrected for topographic effects at both deep and shallow water. At deeper water, the target signatures were not mapped as the amplitude falls below the instrumental noise while at shallow water; the airwave was intense, rendering the correction method invalid. At the low frequency (0.05 Hz) for both water scenario, the best correction match in both amplitude and phase profiles was obtained, removing completely distortions from both topographic and airwave effects, whereas, bathymetric correction technique at 1.75 Hz frequency was completely out of order. The correction for single resistive target was equally good and portends similarity with the multiple-reservoirs model in amplitude but the phase differ greatly. Corrected phase profiles still suggest differences in the EM signals' interaction with multiple oil-layers and single oil-layer as it propagate from the source to the seafloor receivers, if qualitatively considered.

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