Introduction

Exploration for oil and gas has been an ongoing work in the Niger Delta Basin. Various tools have been used by past researchers to study its sedimentology, stratigraphy and economic prospects (Short and Stauble 1967; Weber and Daukoru 1975; Azeez 1976). However, the biggest breakthrough in petroleum and natural gas exploration came through the use of seismic method (Gadallah and Fisher 2009). Seismic method has been effective in identifying subsurface geological conditions favorable to the accumulation of hydrocarbon. However, seismic data have limited frequency content that might not be able to resolve thin layers, inconsistent low frequency for reservoir properties prediction coupled with low vertical resolution. Accurate delineation and assessment of quality of hydrocarbon reservoirs is vital for development planning to reduce risks in selecting new drilling locations (Simm and Bacon 2014; Adeoti et al. 2018). This would require the integration of seismic and well data for enhanced vertical and lateral resolution for quantitative interpretation. Seismic inversion is a sophisticated tool used by the oil and gas companies to integrate 3D seismic data with petrophysical measurements from wells to improve spatial resolution, reduce risk in exploration and enhance development plan (Neves et al. 2004; Avseth et al. 2005; Alfaro et al. 2007; Suslick et al. 2009; Adeoti et al. 2017). Since reflected seismic wave amplitudes are functions of acoustic/elastic impedance, it becomes necessary to analysis seismic data stacked at various offset and angle of incidence ranges to exploit AVO (amplitude variation with offset)/AVA (amplitude variation with angle) information in the data. Simultaneous inversion is capable of converting several angle stacks to elastic parameters which are capable of discriminating lithology and pore fluids within the reservoirs (Lavergne and Willm 1977; Lindseth 1979; Torres and Sen 2004; Hampson et al. 2006; Prskalo 2007; Jason 2013) while the elastic inversion converts specified angle stack to provide additional measurement which will improve the identification of hydrocarbon bearing reservoirs (Aki and Richards 1980; Connolly 1999 and Yilmaz 2002; Veeken and Da Silva 2004). There are several inversion techniques that could be adopted to invert seismic data to qualitative estimates of elastic parameters, but all require some prior information to constrain the inversion (Aki and Richards 1980; Sheriff 1992; Connolly 1999; Yilmaz 2002; Veeken and Da Silva 2004; Chopra and Marfurt 2005; Filippova et al. 2011; Adekanle and Enikanselu 2013). The inability of the traditional seismic data to properly delineate hydrocarbon reservoirs from subtle seismic features in ‘Sandfish’ field located offshore, Niger Delta informed the use of simultaneous and elastic impedance inversion to estimate elastic volumes and derived reservoir properties away from well locations. This would assist in delineating the hydrocarbon prospect and optimizing development plans in the study area.

Geology of the study area

The study area ‘Sandfish’ field falls within Niger Delta and covers about 614.4 km2 (Fig. 1). The Niger Delta province in the Gulf of Guinea basin is a major focus for exploration in West Africa. It is located at the southeastern end of Nigeria, bordering the Atlantic Ocean and extends from about latitudes 4o 00’ to 6o 00’ N and longitudes 3o 00’ to 9o 00’ E (Nwachukwu and Chukwura 1986). The Niger Delta region (Fig. 2) is known for its proficiency in hydrocarbon production among the sedimentary basins in Nigeria. The three major stratigraphic units recognized in the Niger Delta oil and natural gas province are the Akata, Agbada and Benin Formations (Short and Stauble, 1967). It has one petroleum system known as Tertiary Niger Delta (Akata-Agbada) and covers about 300 000 km2 (Evamy et al. 1978; Stacher 1995; Kulke 1995; Ekweozor and Daukoru 1984). The Delta began developing in the Eocene with accumulated sediments of over 10-km thickness (Kaplan et al. 1994). The primary source rock was identified as the upper Akata formation, the marine shale facies of the delta, with possible contribution from interbedded marine shale of the lowermost Agbada formation (Fig. 2). Oil is produced from sandstone facies within the Agbada formation; however, Turbidite sand in the upper Akata formation is a potential target in deep water offshore and possibly beneath currently producing intervals onshore (Short and Stauble 1967; Doust and Omatsola 1990; Tuttle et al. 1999).

Fig. 1
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Map of Niger Delta showing ‘Sandfish’ field (reproduced from Adeoti et al. 2017)

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Fig. 2
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Stratigraphic column showing different formations of Niger Delta (Corredor et al. 2005)

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Theoretical concept

Inversion of seismic data for elastic parameters involves two main stages: (1) estimate the reflectivity as a function of incidence angle for each point at the subsurface, and (2) inverting the reflectivity to estimate the corresponding elastic parameters in accordance to some mathematical models. The Aki-Richard (1980) approximate equation of Zoeppritz formula expressed in Eq. (1) was used in this study. This was used because it allows the estimation of three parameters (ZP, ZS and ρ) from which these elastic parameters other reservoir properties were derived. The reflection coefficient (Rpp) was obtained from the linear combination of the three elastic parameters P-wave velocity, S-wave velocity and density. The approximation of the Zoeppritz’s equation is only valid for small angles, and it assumes a horizontal layered earth model (Aki and Richards 2002).

$$R_{{{\text{pp}}}} \left( \theta \right) \approx A + B \sin^{2} \theta + C\sin^{2} \theta \tan^{2} \theta$$
(1)

, where Rpp (θ) = reflection coefficient at a given angle; θ = average of the incidence and transmission angles at a plane reflecting interface; A = Intercept; it’s the normal incidence reflection coefficient; B = AVO Gradient; it describes the variation at intermediate offsets.

Methodology

Data gathering

The data set used in this study was obtained from Chevron Nigeria Limited with permission from the Department of Petroleum Resources (DPR). This includes 3D seismic data of five angles stacks ranging from (6 to 42°) with four wells (Sfn-01, Sfn-02 and Sfn-05). The seismic data with bandwidth frequency range of (6–55) Hz, sampled at 4 ms and covering in lines (10, 242–11, 061) and cross lines (101, 739–131, 747) with bin spacing of 25 m by 1 m, respectively, as presented in Fig. 3. Three wells (Sfn-01, Sfn-02, Sfn-05) with the logs (P-sonic, S-sonic, density, porosity, gamma ray, resistivity and water saturation and check-shots) were used in this study. The check-shots from wells (Sfn-01, Sfn-02, Sfn-05) were used to establish the time-depth relation. Sfn-04 was used to validate inverted volume away from well control as a blind test. The interpreted horizons (E01, K01, N01 and P01) of the range 1500–2450 ms guided the inversion. The flow chart of the various steps adopted in this study is shown in Fig. 4.

Fig. 3
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Base map of ‘Sandfish’ field showing seismic coverage and position of wells

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Fig. 4
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Flow chart of the various steps adopted in this study

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Well log and AVA analysis

The petrophysical logs (P-sonic, S-sonic, gamma ray, resistivity, water saturation, density and neutron porosity) were used to identify the reservoirs. The P-sonic, S-sonic and density logs were used to generate ZP and ZS logs while the combination of gamma ray, resistivity and water saturation logs were used for qualitative interpretation which involved the picking of sand tops at the target reservoirs. The check-shots were used to generate synthetic seismograms used for the seismic to well tie. The plot of amplitude variation with angle of incidence at the (N01) reservoir was carried out to reveal the AVO/AVA class of the hydrocarbon bearing sand according to Rutherford and Williams (1989) and Castagna and Swan (1997).

Simultaneous inversion

Simultaneous inversion was carried out to invert the seismic data into elastic properties descriptive of target reservoirs (Berge et al. 2002; Pendrel et al. 2000; Jason 2013). During the inversion, five angle stacks were simultaneously inverted to ZP, ZS and ρ from which other reservoir properties were derived for quantitative interpretation according to Bacon et al. (2003); Contreras et al. (2006) and Adeoti et al. (2017). The angle stacks (6–12°, 12–18°, 18–26°, 26–32° and 32–42°) were tied to the wells (Sfn-01, Sfn-02, Sfn-05) to ensure good correlation of events and for accurate extraction of wavelets from each of the angle stacks. The wavelets extracted from each of the angle stacks were used in the inversion. The low (0–2 Hz) frequency models built from the interpolation of filtered P-sonic, S-sonic and density logs were used to broaden the seismic frequency spectrum and to constrain the inversion. The sparse-spike inversion of Jason’s Rock-Trace was used to iterate trial inversions until the model sufficiently matched the seismic data. The product of the simultaneous inversion (ZP, ZS and ρ) were used to derive Lambda-rho \((\lambda \rho )\) volume as stated in Eq. (2) for lithology and fluid discrimination in ‘Sandfish’ field (Bacon et al. 2003; Contreras et al. 2006). Other reservoir properties such as mu-rho (µρ), Poisson’s-ratio (σ) were determined in Adeoti et al. (2017).

$${\text{Lambda}} - {\text{rho}},\;Z_{P}^{2} - 2Z_{S}^{2} = \lambda \rho$$
(2)

The quality of the inverted volumes was checked by plotting the well ZP versus the inverted ZP from simultaneous inversion. This was further validated by the display of the inverted ZP from simultaneous inversion (band-limited) with inserted gamma ray log from wells (Sfn-04 and Sfn -05).

Elastic inversion (EI)

EI provides a new approach to calibrate and invert incidence angle seismic data in a fashion analogous to zero-offset data (Karbalaali et al. 2013). The near (6–12°) and far-far (32–42°) angle stacks were inverted to generate elastic volumes which revealed the variation of impedance with angle of incidence. Near and Far-far stacks were tied to wells (Sfn-01, Sfn-02 and Sfn-05) for accurate wavelets extraction. The low frequency models, extracted wavelets and the four interpreted horizons (E01, K01, N01 and P01) were used in the inversion (Aki and Richards 1980; Connolly 1999; Yilmaz 2002; Nguyen and Larry 2008). The inverted elastic volumes generated were compared with the inverted ZP obtained from simultaneous inversion (Adeoti et al. 2017). This was carried out to determine the effectiveness of near and far-far elastic impedance volume in delineating hydrocarbon reservoirs in ‘Sandfish.’ The quality of the elastic inversion was checked by plotting ZP from simultaneous inversion with EI 37.2. Fig. 5.

Fig. 5
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Comparison of N-01 and P-01 reservoirs from Sfn-05 with seismic amplitudes variation at the intervals of interest (Adeoti et al. 2017)

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Results and discussions

Identification of reservoirs and AVA analysis

The three reservoirs delineated are (K-01, N-01, and P-01) at the 2179 m, 2484 m and 3048 m, respectively, with net to gross thickness of about 30 m. The plot of amplitude variation with angle of incidence (Fig. 6) at the N-01 reservoir reflected typical class III AVO/AVA hydrocarbon bearing sand. The sands (K-01, and N-01 and P-01) were described as low impedance sands (Adeoti et al. 2017).

Fig. 6
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Plot of amplitude reflection coefficient at N-01 reservoir versus angle of incidence (Rutherford and Williams 1989) demonstrated by Adeoti et al. (2017)

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Inversion quality check

The cross-plot of inverted ZP from simultaneous inversion and well ZP (Fig. 7) gave correlation coefficient of 86% indicative of high quality inverted volume which will reduce exploration risk. The delineated reservoirs (Fig. 8) showed good match with the sand tops away from the well control validated by a blind well test.

Fig. 7
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Cross-plot of inverted ZP from simultaneous inversion and well ZP (Adeoti et al. 2017)

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Fig. 8
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Inverted ZP from Simultaneous inversion with inserted gamma ray log from Sfn-04 and Sfn-05 (Adeoti et al. 2017)

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Derived Reservoir (Lambda-rho) Volume from Simultaneous Inversion

Figure 9 is the Lambda-rho volume derived from the combination ZP and Zs of simultaneous inversion. It shows high resistivity response from the overlain resistivity log coinciding with low lambda-rho (yellow to red). The low lambda-rho indicates presence of hydrocarbon in the delineated sand. This shows that Lambda-rho is a good litho-fluid discriminator in area of investigation.

Fig. 9
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Lambda-rho with overlain resistivity log (Adeoti et al. 2017)

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Elastic impedance volume

Figure 10 is the EI 9.2 (full-bandwidth) which shows the gradual increase in impedance with depth, low impedance (yellow to red) indicates hydrocarbon bearing sands (K01 and N01) having good match with the low gamma ray response. The EI 9.2 (band-limited) is displayed in Fig. 11, the high impedance (blue) indicates background shale while the low impedance (yellow to red) depicts hydrocarbon bearing sands which has good match with the identified sands from the gamma ray curve. Figure 12 is the EI 37.2 (full-bandwidth) which gradually increases with depth, the low impedance (yellow to red) indicates hydrocarbon bearing sands (K01 and N01) with high match with the low gamma ray response. The EI 37.2 (band-limited) displayed in Fig. 13 shows high impedance (blue) as background shale while the low impedance (yellow to red) indicates hydrocarbon bearing sands which have high match with the sands from the gamma ray curve. The reservoirs are more evident on the EI 37.2 than on EI 9.2 because far-far angle stack is more sensitive to changes in fluid saturation (Connolly 1999). Figure 14.

Fig. 10
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Inverted EI 9.2 (full-bandwidth) with inserted gamma ray log

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Fig. 11
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EI 9.2 (band-limited) with inserted gamma ray log

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Fig. 12
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EI 37.2 (full-bandwidth) with inserted gamma ray log

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Fig. 13
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EI 37.2 (band-limited) with inserted gamma ray log

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Fig. 14
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Plot of inverted ZP from simultaneous inversion and inverted far-far elastic volume

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Comparison of simultaneous with elastic impedance volume

The plot of inverted ZP from simultaneous inversion and inverted far-far elastic volume (Fig. 15) reflected 82% correlation coefficient indicating that this could be adopted in other fields with limited data but with similar geological setting.

Fig. 15
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Comparison of EI 9.2, inverted ZP and EI 37.2

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Figures (15 and 16) show the correlation of inverted ZP from the simultaneous inversion from Adeoti et al. (2017) with the near and far-far elastic volumes (Full bandwidth and band-limited band). The elastic volumes showed good correlation at 1850 ms and 2050 ms which represent sands K01 and N01. The reservoirs are of low impedance (4880 to 6710) g.m/cc.s) sands with corresponding low gamma response.

Fig. 16
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Comparison of EI 9.2, inverted ZP and EI 37.2

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Uncertainty and limitations

The approximation of the Zoeppritz’s equation adopted in this research is only valid for small angles, and it assumes a horizontal layered earth model (Aki and Richards 2002). The Zoeppritz’s equations are no longer sufficient if we are to include anisotropy in our model.

Conclusion

Gamma ray response below the 70-API point is classified as sand while response greater than 70-API is classified as shale. High resistivity response with neutron-density overlay and low water saturation response were used in the picking of sand tops of identified reservoirs (K01, N01 and P01) at 2179 m, 2484 m and 3048 m, respectively. The AVO/AVA analysis which has proven effective in discriminating fluids in reservoirs agreed with the plot of amplitude reflection variation at N-01 reservoir versus angle of incidence according to Rutherford and Williams (1989). The plot reflected class III AVO/AVA hydrocarbon bearing sand as demonstrated by Adeoti et al. (2017). The cross-plot of inverted ZP from simultaneous inversion and well ZP gave correlation coefficient of 86% indicative of high quality inverted volume which will reduce exploration risk in the study area. The cross-plot of inverted ZP from simultaneous inversion and EI 37.2 gave correlation coefficient of 82% which shows that the technique could be adopted in region with limited data but with similar geological setting. Hence, the study has shown the efficacy of seismic inversion to delineate hydrocarbon bearing sands in ‘Sandfish’ Field, Niger Delta. The generated elastic volumes will reduce risk, enhance hydrocarbon discovery and optimize development plans in the study area.