Mapping of hydrocarbon-bearing reservoirs using frequency ...

Mapping of hydrocarbon-bearing reservoirs usingfrequency-dependent amplitude vs. oAset (FAVO)

SHUBHAM TIWARI1, DIBAKAR GHOSAL

1,*, RAHUL KUMAR SINGH2 and

SUBBARAO YELISETTI3

1Department of Earth Sciences, Indian Institute of Technology Kanpur, Kanpur 208 016, UP, India.

2Oil and Natural Gas Corporation Limited, GEOPIC, Dehradun, India.

3Texas A and M University-Kingsville, Kingsville, TX, USA.*Corresponding author. e-mail: [email protected]

MS received 3 April 2021; revised 11 August 2021; accepted 27 September 2021

The uncertainty associated with seismic interpretation poses a significant challenge to the hydrocarbonindustry in accurately identifying the potential hydrocarbon zones. Over the years several new techniqueshave emerged to address this problem. Amplitude variation with oAset analysis is one of the prominentmethods to estimate various subsurface properties from pre-stack gathers. Due to the presence of Cuid inreservoir pores, seismic velocity dispersion occurs within the seismic bandwidth, resulting in reCectioncoefBcient as a function of frequency. In this study, a prototype inversion scheme is developed forfrequency-dependent amplitude vs. oAset analysis, which is tested on both the synthetic and Beld data.The synthetic data are generated using a three-layered model with a spherical anomaly. The applicationof this method to synthetic data indicates anomalous high amplitude in P-wave dispersion gradient, andhelps in identifying eAects of spherical inclusion. Further application of this method to Beld data fromNorth Viking Graben, North Sea clearly delineates the hydrocarbon-bearing reservoir identiBed on thewell log data between *1.8 and 1.9 s two-way travel time.

Keywords. Frequency; AVO; inversion; spectral decomposition; North Sea; hydrocarbon.

1. Introduction

Several techniques for the interpretation of seismicdata have emerged over the years, and one suchwidely used technique is amplitude vs. oAset(AVO) analysis (Zoeppritz 1919; Bortfeld 1961;Aki and Richards 1980; Shuey 1985). The AVOtechnique helps to assess changes in seismicreCection amplitude with oAset among receivers ina gather and allows earth scientists to better assesspetrophysical properties (Feng and Bancroft 2006).In conventional AVO analysis, seismic data areinverted to estimate P- and S-wave reCectivityvariations using the least-squares inversion

scheme to provide qualitative estimates of a selec-tion of parameters, which are used to identifyanomalous areas that resulted from a variation inhydrocarbon saturations (Wu et al. 2014).In general, seismic data acquired over an oil, gas

or water-bearing reservoir often preserve the fre-quency-dependent signatures of the reservoirpetrophysical characteristics (Chapman et al.2005). The dispersion of seismic wave at a seismicfrequency range (e.g., 5–80 Hz) depends on theamount of Cuid present in the reservoir pore space.Therefore, an analysis of frequency component ofthe seismic data is an essential task to explore thereservoir properties (Liu et al. 2019). Since seismic

J. Earth Syst. Sci. (2022) 131:43 � Indian Academy of Scienceshttps://doi.org/10.1007/s12040-021-01783-z (0123456789().,-volV)(0123456789().,-volV)

data contain amplitude information associatedwith all frequencies, AVO approximations shouldbe such that it account for all frequencies togetherand use the potential of this Cuid-sensitive rockproperty (Cheng et al. 2012). However, none of theAVO approximations was able to use this Cuid-sensitive property in a comprehensive manner(e.g., Wilson 2010; Liu et al. 2019). In the presentstudy, we developed a new frequency-dependentAVO (FAVO) method based on Liu et al. (2019) toidentify potential hydrocarbon zones. This methodhas been tested using both the synthetic as well asreal data.An important aspect of FAVO scheme is spectral

decomposition, which is a statistical technique andplays an important role translating time informa-tion into frequency domain (Rayner 2001; Ghosaland Juhlin 2018). The technique used in this studyfor spectral decomposition is constrained least-squares spectral analysis (CLSSA) (Puryear et al.2012), which is an improved method compared tothe existing approaches such as continuous wave-let transform and short-time Fourier transform.CLSSA is an iterative regularised spectral inver-sion scheme (Wu et al. 2017; Pant et al. 2019,2020). Regularisation reduces the ambiguity asso-ciated with non-uniqueness in data by limiting themodel to follow applied constraints and thus,reducing an ill-posed problem to a well-posed one(Kirsch 2011).In the present study, initially a test on the

FAVO inversion scheme following Liu et al. (2019)is carried out on the synthetic data for a hydro-carbon-bearing reservoir. Synthetic shot gathersare created by forward modelling using SOFI2Dsoftware (Bohlen et al. 2015) to accurately modelseismic wave Belds in two-dimensional (2D) elasticheterogeneous medium. These shot gathers arethen converted to common depth point (CDP)gathers followed by angle gathers, which is thenspectrally decomposed using CLSSA technique(Puryear et al. 2012; Pant et al. 2019, 2020). Thespectrally decomposed traces are used in FAVOinversion scheme (Liu et al. 2019) to characterisethe Cuid content in the reservoir. Similar steps arecarried out to analyse Beld data from north VikingBeld.

2. Methodology

The workCow behind the FAVO inversion isdescribed in Bgure 1.

2.1 Forward modelling

Forward modelling using 2D Bnite-difference seis-mic wave simulation software (SOFI2D) (Bohlenet al. 2015) is performed to get information abouthow variation of subsurface structures aAects thepropagation of seismic wave Belds in a shot gatherform. Modelling is done using Bnite difference (FD)method because of its ability to accurately modelseismic wave Belds in 2D elastic heterogeneousmedium. FD method described in SOFI2D (Bohlenet al. 2015) utilises a system of Brst-order-coupledelastic equations relating stresses and velocities.This method is based on studies by Virieux (1986)and Levander (1988), who formulated staggered-grid FD scheme, which was Brst proposed byMadariaga (1976).

2.2 Generation of CDP and angle gathers

The generated shot gathers by forward modellingusing SOFI2D software is Brst processed to removecoherent noise present in the data. Subsequently,the data are converted to CDP gathers to enhancethe signal-to-noise ratio. CDP gathers are furtherconverted to angle gathers using Hampson andRussell suite (HRS) software. Angle gathers gen-eration is an essential part of FAVO inversion asthe coefBcients and reCectivity are dependent onthe incident angle (h). Therefore, angle gathers at aparticular angle of incidence are useful in assessing

Forward modelling

CDP gathers

Angle gathers

Spectral decomposition (CLSSA)

AVO inversion

Figure 1. WorkCow behind FAVO inversion.

43 of 9 J. Earth Syst. Sci. (2022) 131:43

the hydrocarbon reservoir. The software requiresvelocity model as an input and eventually uses rayparameter to transform oAset into angle domain.

2.3 Spectral decomposition

To extract the frequency components from theangle gathers, spectral decomposition is a com-pulsory step in FAVO inversion process. Thisstudy uses the CLSSA scheme (Puryear et al. 2012;Wu et al. 2017; Pant et al. 2019, 2020). Regulari-sation stabilises the inverse problem by using priorinformation and thus, reducing an ill-posed prob-lem to a well-posed one (Kirsch 2011). CLSSAmethodology involves constraining the generalFourier series Fm ¼ d (where F is the kernel, m isthe model spectra and d is the data) with a certainmodel and data constraints. This method itera-tively computes the model parameters–frequencyspectra within each window. The parameters usedhere are the centre value of the Hanning window(data parameters) and model spectra (modelparameters), which are similar to the parametersused by Puryear et al. (2012) except that the initialspectra are different from Cat spectra. The con-cerned objective function and the Bnal computa-tional model are given below:

Zðmw; cÞ ¼ kFwmw �W ddk22 þ ckmwk22

m ¼ WmFwTðFw

TFw þ cI Þ�1W dd:

The model spectra update is given by Wm ¼diag abs mð Þð Þ where Wm represents the modelweightage, W d corresponds to the data parameterswhile,Fw,mw and c represent the weighted sinusoidalkernel matrix, the weighted model spectra and theregularisation parameter, respectively.

2.4 FAVO inversion

In the current study we developed a prototypeof FAVO scheme following Liu et al. (2019) inwhich Smith and Gidlow’s equation is modiBedfurther to derive a new improvised FAVO scheme.ReCection coefBcient R according to Smith and

Gidlow (1987) two-term AVO approximation canbe written as:

R hið Þ ¼ A1 hið ÞDV p

V p

þA2 hið ÞDV s

V s

; ð1Þ

where DV p=V p and DV s=V s are P and S wavereCectivity, respectively, and hi is the angle ofincidence. A1 and A2 are deBned as:

A1 hið Þ ¼ 5

8� 1

2

V 2s

V 2p

sin2 hið Þ þ 1

2tan2 hið Þ;

A2 hið Þ ¼ �4V 2

s

V 2p

sin2 hið Þ: ð2Þ

Equation (1) was modiBed as:

R hð Þ ¼ A1 hð ÞDV p

V p

þ B1 hð Þ V 2s

V 2p

DV s

V s

þ 1

8

DV p

V p

� �" #;

ð3Þ

where

A1 hð Þ ¼ 5

8þ 1

2tan2h and B1 hð Þ ¼ �4sin2h: ð4Þ

In real strata R, Vp, Vs and the ratio V 2s=V

2p are

frequency-dependent. Therefore, equation (3) canbe modiBed as:

R h; fð Þ ¼ A1 hð ÞDV p

V p

��f

þ B1 hð Þ V 2s

V 2p

DV s

V s

þ 1

8

DV p

V p

� �" #��f

: ð5Þ

Expanding equation (5) by Taylor series andneglecting second- and higher-order terms off � f 0ð Þ

R h; fð Þ ¼ A1 hð ÞDV p

V p

��f 0

� B1 hð Þ V 2s

V 2p

DV s

V s

þ 1

8

DV p

V p

� �" #��f 0

þ f � f 0ð ÞA1 hð ÞI a1 þ f � f 0ð ÞB1 hð ÞI b1; ð6Þ

where I a1 and I b1 are

I a1 ¼o

of

DV p

V p

� ��f¼f 0

;

I b1 ¼o

of

V 2s

V 2p

DV s

V s

þ 1

8

DV p

V p

� �" #��f¼f 0

: ð7Þ

J. Earth Syst. Sci. (2022) 131:43 of 9 43

The P-wave reCection coefBcient at a referencefrequency can be written as

R h; f 0ð Þ ¼ A1 hð ÞDV p

V p

��f 0

þ B1 hð Þ V 2s

V 2p

DV s

V s

þ 1

8

DV p

V p

� �" #��f 0

: ð8Þ

From equations (5 and 8)

R h; fð Þ � R h; f 0ð Þ ¼ f � f 0ð ÞA1 hð ÞI a1þ f � f 0ð ÞB1 hð ÞI b1: ð9Þ

Let R = R h; fð Þ � R h; f 0ð Þ, then transformingequation (9) into matrix form gives

R ¼ f � f 0ð ÞA1ðhÞ B1ðhÞ

..

. ...

AnðhÞ BnðhÞ

264

375 I a1

I b1

� �: ð10Þ

Let

A ¼ f � f 0ð ÞA1ðhÞ B1ðhÞ

..

. ...

AnðhÞ BnðhÞ

264

375

and

X ¼ I a1I b1

� �:

Then equation (10) transforms to

AX ¼ R: ð11Þ

To solve equation (11), we have used pre-conditioned conjugate gradients (pcg) methodwhich is an iterative inversion method. Inequation (11), A is an n9n matrix and R is acolumn vector of length n. This equation is solvedin Matlab using:

X ¼ pcgðA �AT;AT � RÞ; ð12Þ

where � denotes matrix multiplication, AT is thetranspose of matrix A and pcg denotes pre-condi-tioned conjugate gradient and is an inbuilt functionin Matlab.In equation (10), I a1 and I b1 are the P-wave

dispersion gradient and the mixed dispersiongradient, respectively. The I a1 can be used as aproxy to mark the ‘sweet spots’ of gas reser-voirs and understanding the physical mecha-nism behind the I b1 for a Cuid-Blled reservoir is

unclear. Therefore, only I a1 is used in thisstudy.

3. Results and discussion

3.1 Synthetic test on a three-layered modelwith a Cuid-Blled spherical inclusion

The synthetic model consists of simple three layerswith constant velocities and densities and with aspherical inclusion in the second layer. The modeldimensions include 3 km lateral extent along with600 m vertical extent with a grid spacing of 2 m.Both hydrophone streamer and airgun sources areplaced in the water column at a depth of 10 m tomimic the marine acquisition set up. Details of thesurvey parameters used in modelling are given intable 1. The top layer of the model consists of a 100m thick water column followed by 400 and 100 mthick sedimentary layers in depth. Within thesecond layer there is a spherical inclusion of radius100 m centred at a depth of 250 m, consisting of100 m thick upper gas layer and 100 m thick loweroil layer (Bgure 2).Figure 3 shows the synthetic shot gather gener-

ated by forward modelling using the model shownin Bgure 2. Water–sediment contact and gasreCections are clearly observed on the shot gather(Bgure 3).We generate shot gathers for this model

(Bgure 2) using SOFI2D (Bohlen et al. 2015). WeBrst remove the direct arrivals from the generatedshot gathers, which are then converted into CDPgathers and used as an input to HRS software toconvert into 7� and 11� angle gathers. Thesegathers are then spectrally decomposed at differentfrequencies using constrained least-squares spectralanalysis technique and are used for FAVO inver-sion using equation (12). The reference frequencyduring the inversion is kept as 40 Hz similar to thedominant frequency.

Table 1. Main model parameters used forsynthetic test with spherical inclusion.

Source wavelet Ricker

Type of source Airgun

Source interval 12 m

Number of shots 41

Receiver spacing 12 m

Number of receivers 94

Sampling interval 0.4 ms

Number of samples per trace 2500


3.1.1 Synthetic testing at 7� angle of incidence

Figure 4(a) shows angle gather generated atincidence angle of 7� using the velocity modelshown in Bgure 2 with trace number varying from175 to 260. The eAect of Cuid from sphericalinclusion in the model can be seen from tracenumber ranging from 220 to 240 (Bgure 4a). Sincethe presence of Cuid decreases seismic velocitydrastically, the angle gather is shifted downwardsto *0.4 s two-way travel time (TWT) from itsoriginal position (Bgure 4a). This shift in timemay also result from the conversion of anglegather, as we have carried out the conversionconsidering only vertical variations in velocity inHRS software. To obtain accurate angle gathers,one should incorporate the lateral variation invelocity–depth model. Figure 4(b) shows trace230 taken from angle gather shown in Bgure 4(a).On this single trace, FAVO inversion is per-formed using equation (12) for frequencies 0–70Hz (Bgure 4c). The inversion results clearlyindicate the high-amplitude anomaly at *0.4 sat frequencies ranging from *5 to 20 Hz with apeak amplitude near 10 Hz. The high-amplitude anomaly indicates the presence ofgas, and validates the use of FAVO inversionscheme presented here.

3.2 Field data analysis

The FAVO inversion is applied on the marineAVO data acquired from North Viking Graben,North Sea (Bgures 5 and 6). The regional geology,description of used datasets and results fromFAVO are described in the following sections.

3.2.1 Regional geology

In late Permian to Triassic, the North Viking Gra-ben (Bgure 5) formed by the rifting process. By LateCretaceous, normal basin subsidence and Bllingcontinued. Basin Blls of Cretaceous and Tertiaryoverlay the syn-rift sedimentary deposits of Jurassic(Keys and Foster 1998). Two major reservoirsreported by Keys and Foster (1998) are associatedwith theNorthVikingGraben.Thedeeper reservoir,which is the primary reservoir in the North VikingGraben of Jurassic age, mainly consisted of clasticsediments (Keys and Foster 1998) and associatedwith the Cuvio-marine depositional set up. Mostlyfault-bounded structural traps seal the top of thehydrocarbon-bearing reservoirs, whereas evidenceof base Cretaceous unconformity is also reported insome parts of the graben (Keys and Foster 1998).The second reservoir appears at a shallow depth of*1.6–1.9 s TWT in the seismic stack section(Bgure 7) and consists of Palaeocene deep waterclastics formed in a slope environment.

3.2.2 Datasets

The dataset used in this study is compiled bygeoscientists at Mobil and is available in publicdomain (Keys and Foster 1998). The seismic sourceused in acquisition consists of 24 live airgun arraysfor a total volume of 3650 in3, which was Bred witha shot interval of 25 m from a water depth of 6 m;and a streamer with 120 channels were kept at a 10m water depth for recording. The near oAset and

Vp=1500 m/s (Water)

Vp=1300 m/s (Gas)

Vp=1450 m/s (Oil)Vp=1550 m/s (Sediment)

Vp=1600 m/s (Sediment)

0

0.133

0.391

0.649

TWT (s)

0

100

200

300

400

500

Dep

th (m

)

0 500 1000 1500 2000 2500Distance (m)

600 0.774

Figure 2. Three-layered velocity model along with spherical inclusion used to generate shot gathers. Depth and velocity of eachlayer is shown in the Bgure along with lateral extent of model. The red star and thick red line indicate example locations of a shotand receiver streamer in a marine multichannel seismic acquisition, where seismic energy is propagated through the sphericalinclusion.

Figure 3. Shot gather for the shot marked in Bgure 2. WSC,water sediment contact.


far oAset distances are set as 262 and 3237 m,respectively. The data were recorded for 6 s with asampling interval of 4 ms. As the data wereacquired at a uniform shallow water depth of *350m, long and short period multiples are observed inthe CDP gathers (Bgure 6). These were removed inthe pre-processing stage (Keys and Foster 1998).Figure 6 shows the CDP gathers that were used

to generate angle gathers. Figure 7 shows processedseismic section of the acquired data in which hor-izontal layers are observed in the shallow sectionand dipping reCectors are observed at depth. Theregion enclosed in thick white rectangular box fromCDP 700 to 1050 (Bgure 7) is considered as thezone of investigation intersected by well A at CDP808 (Keys and Foster 1998). P-wave velocity (Vp),S-wave velocity (Vs) and density logs are used inthis study (Bgure 8). Both the velocities and den-sity show sudden drop between *1.8 and 1.9 sTWT (Bgure 8). The CDP gathers are converted toangle gathers using the P-wave velocity in the welllogs using HRS software.

3.2.3 Inversion results

Figures 9(a) and 10(a) show the angle gathers at 7�and 11� angle of incidences in which the blackboxes show the regions of investigation on whichangle gather FAVO inversions are performed. Theshallow reCectors show a high-frequency content inthe 7� incident angle gather than that of at 11�angle of incidence (Bgures 9a and 10a), whereas thedeeper reCectors are boosted up in the 11� incidentangle gather than that of at 7�. Figures 9(b) and10(b) show the FAVO inversion results for theangle gathers at 7� and 11� incident angles,respectively. Inverted P-wave dispersion at 10 Hzfrequency clearly delineates the target zone from

Figure 5. Location of North Viking Graben, North Sea onworld map marked by thick white rectangle.

Figure 6. CDP gathers from North Sea used to generate anglegathers.

(a)(a) (b)(b) (c)(c)

Figure 4. (a)Angle gather at anangle of incidence of 7� showing eAect of spherical inclusion. (b)Tracenumber 230 fromangle gathershown in (a). (c) AVO inversion of trace number 230 showing P-wave dispersion gradient Ia1 clearly highlighting the eAect of Cuid.


*1.8 to 1.9 s at trace numbers ranging from 775 to925 and 750–1000 for the angle gathers at 7� and11� angle of incidences, respectively. For both thecases, the anomalies follow the trend of the dippingreCectors. One stark difference appears in theinverted result is the lateral continuity of theanomaly. The anomaly observed in the 11� inci-dence angle gather appears to be more laterally

continuous (Bgures 9b and 10b). The anomaly atthe trace 825 at 7� incident angle (Bgure 9b) isbroad in its temporal extent and extended from 1.8to 1.9 s TWT, whereas the anomaly observed at11� incident angle is more localised around 1.85 sTWT. The location of the anomaly matches wellwith the well log data, where a sudden drop in theVp, Vs and the density are observed (Bgure 8).

Figure 7. Stacked seismic section of the data acquired from North Viking Graben with the location of well A indicated in Bgure.A thick white rectangular box shows the target region used for analysis.

Figure 8. Variation of P-wave velocity, S-wave velocity and density logs with time from well A. The time window within thedashed lines corresponds to the hydrocarbon reservoir identiBed from FAVO inversion in Bgures 9 and 10. Location of the well isshown in Bgure 7.


The data used in this study collected over astructurally simple and horizontal interfaces inwhich the presence of hydrocarbons are validatedfrom the well log data and AVO studies (Keysand Foster 1998). The usage of such datasets issuitable to establish the proof of the conceptbehind the FAVO analysis and its applicability.The application of this method to data from acomplex tectonic regime with steep dips such asthe Cascadia margin will validate the more robustapplicability of this method. In future, the workcan further be extended by accounting for varia-tion in subsurface properties while performingdispersion analysis of poroelastic gathers. Also,the eDciency of the algorithm can further be

tested by parallelising the code to reduce compu-tational cost. This is beyond the scope of thepresent study.

4. Conclusions

The intention of this work was to provide aninsight into the FAVO technique. This techniquehas emerged over the years to address the inherentambiguity associated with seismic interpretation.It focusses on the velocity dispersion caused by thepresence of Cuid in the subsurface, which leads toreCection coefBcient being frequency-dependent. Inthe current work, the FAVO scheme has been

Figure 9. (a) Angle gather at an angle of incidence 7� from North Viking Graben. A thick black rectangle indicates theapproximate zone used for inversion. (b) P-wave dispersion gradient at 10Hz delineating the target zone.

Figure 10. (a) Angle gather at an angle of incidence 11� from North Viking Graben. A thick black rectangle indicates theapproximate zone used for inversion. (b) P-wave dispersion gradient at 10Hz delineating the target zone.


tested on a synthetic dataset generated using athree-layered model with a spherical inclusion.Analysis shows that the developed algorithm workseDciently to identify Cuid inclusion on syntheti-cally generated data. Furthermore, inversionscheme was tested on Beld data to Bnd P-wavedispersion, which acts as an indicator for thepresence of hydrocarbon. Our results of P-wavedispersion gradient on Beld data at 7� and 11� angleof incidence delineate a potential hydrocarbon zonefrom 1.8 to 1.9 s TWT for a reservoir from NorthViking Graben, North Sea. The modelling resultswere further conBrmed by the velocity and densitylogs from the area. We conclude that the inversionscheme developed in this study can be used as arobust method to delineate potential hydrocarbonreserves, hence, supplementing the ever prevailingdemand for better interpretation and detection ofpotential hydrocarbon zones.

Acknowledgements

This project is funded by the Oil and Natural GasCorporation of India (ONGC). We thank Mobil forthe open access data used in this study, and HRSand Paradigm Echos for providing the academiclicenses for seismic data processing.

Author statement

Shubham Tiwari: Coding, writing, data analysis,and Bgures; Dibakar Ghosal: Conceptualisation,writing, editing, and Bgures; Rahul Singh: Pro-viding datasets, reviewing, and editing; SubbaraoYelisetti: reviewing and editing.

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Corresponding editor: ARKOPROVO BISWAS


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