Application of extended elastic impedance in seismic geomechanics

Javad Sharifi1, Naser Hafezi Moghaddas1, Gholam Reza Lashkaripour1, Abdolrahim Javaherian2,and Marzieh Mirzakhanian3

ABSTRACT

We have evaluated an innovative application of extendedelastic impedance (EEI) to integrate seismic and geomechanicsfor geomechanical interpretation of hydrocarbon reservoirs.EEI analysis is used to extract geomechanical parameters.To verify and assess the capabilities of EEI analysis forextracting geomechanical parameters, we selected a jointed,oil-bearing, shale carbonate reservoir in the southwest of Iran,and we used petrophysical data and core analysis to estimatestatic and dynamic moduli of the reservoir rock. We calculatedthe corresponding EEI curve to different intercept-gradient co-ordinate rotation angles (the chi angle, χ), and we selected theangles of the maximum correlation for the corresponding geo-mechanical parameters. Then, combining the intercept and

gradient, we generated 3D reflectivity patterns of EEI at differ-ent angles. To obtain a cube of geomechanical parameters, weperformed model-based inversion on the EEI reflectivity pat-tern. A comparison between the modeling results and well dataindicated that the geomechanical parameters estimated by ourmethod were well-correlated to the observed data. Accord-ingly, we extracted the geomechanical and rock-physicalparameters from the EEI cube. We further found that EEIanalysis was capable of giving a 3D mechanical earth modelof the reservoir with the appropriate accuracy. Finally, we veri-fied the proposed methodology on a blind well and comparedthe results with those of the simultaneous inversion, indicatingcomparable levels of accuracy. Therefore, application of thismethod in seismic geomechanics can bring about significantprogress in the future.

INTRODUCTION

Rock-mechanical parameters such as the Young’s modulus, com-pressive strength, Poisson’s ratio, and brittleness play essential rolesin wellbore stability, hydraulic fracturing, geomechanical modeling,and other engineering techniques (Fjær et al., 2008; Herwanger andKoutsabeloulis, 2011; Kidambi and Kumar, 2016; Xu et al., 2016).Therefore, to solve a wide spectrum of problems raised in hydrocar-bon exploration and production, it is necessary to develop a geome-chanical multidisciplinary approach including rock physics, rockmechanics, exploration seismology, structural geology, and petro-leum engineering. During the past few decades, the mechanical earthmodel (MEM), which shows the stress conditions in reservoirs andmechanical behavior of rocks, has developed into a vital tool for such

a purpose. One-dimensional MEMs can be built with static and dy-namic relationships based on well-logging data and laboratory tests.However, 3D MEMs represent the models of choice for explorationand development purposes and can be derived from a 1D MEM viaseveral multidisciplinary approaches (Plumb et al., 2000; Zoback,2007; Olson et al., 2009; Kidambi and Kumar, 2016; Xu et al., 2016).In recent years, the integration of well logs with seismic-survey

data for estimating rock-mechanics parameters has been the mostimportant development in geomechanical research, fueling fastprogress toward 3D geomechanical modeling (Herwanger andKoutsabeloulis, 2011; Gray et al., 2012). Elastic waves can provideuseful information on fluid types and lithology. Therefore, directeffects of changes in elastic and mechanical parameters of rocksgive an opportunity for undertaking qualitative and quantitative

Manuscript received by the Editor 10 April 2018; revised manuscript received 24 November 2018; published ahead of production 04 February 2019; pub-lished online 10 April 2019.

1Ferdowsi University of Mashhad, Department of Geology, Faculty of Science, P.O. Box 9177948974, Mashhad, Iran. E-mail: j_sharifi@mail.um.ac.ir;nhafezi@um.ac.ir (corresponding author); lashkaripour@um.ac.ir.

2Formerly University of Tehran, Institute of Geophysics, Tehran, Iran; presently Amirkabir University of Technology, Department of Petroleum, Engineering,Tehran, Iran. E-mail: javaherian@aut.ac.ir.

3University of Tehran, Institute of Geophysics, Tehran, Iran. E-mail: mirzakhanian@ut.ac.ir.© 2019 Society of Exploration Geophysicists. All rights reserved.

R429

GEOPHYSICS, VOL. 84, NO. 3 (MAY-JUNE 2019); P. R429–R446, 25 FIGS., 1 TABLE.10.1190/GEO2018-0242.1

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

seismic reservoir characterization (Whitcombe et al., 2002; Fjæret al., 2008; Lou et al., 2016). This quantification is usually donethrough seismic attributes and seismic inversion methods (poststackand prestack) based on elastic wave-propagation principles. Seismicprestack studies, such as amplitude variation with offset (AVO)analysis and simultaneous inversion, play vital roles in geomechan-ical modeling and seismic interpretation (Russell et al., 2003; Grayet al., 2012). On the other hand, the extended elastic impedance(EEI) seems to have unused potentials for geomechanical modeling.The EEI analysis calculates impedance values beyond the range ofreal incidence angles observed physically in seismic operation,making it an appropriate tool for lithology and fluid-type detection.In EEI analysis, each angle along the EEI spectrum is related to aparticular reservoir parameter through the maximum value of cross-correlation (Connolly, 1999; Whitcombe, 2002; Whitcombe et al.,2002; Zhen-Ming et al., 2008; Ball et al., 2014a;Mirzakhanian et al.,2017; Aleardi, 2018). In various pieces of research, EEI has beendevised to estimate a wide range of elastic and petrophysical proper-ties for exploration and development purposes (Martins, 2003;Hicks and Francis, 2006; Arsalan and Yadav, 2009; Awosemo,2012; Gharaee Shahri, 2013; Yenwongfai et al., 2017; Aleardi,2018). An interesting application of EEI was proposed by Sharmaand Chopra (2015) for obtaining the pseudodensity from seismicdata without long offsets. Focusing on anisotropy, Martins(2006) and Jyosyula et al. (2015) introduce relationships for apply-ing EEI analysis in anisotropic media.Despite its large potential, EEI analysis requires well-log and pre-

stack seismic data with a high signal-to-noise ratio into which theanisotropic behavior of the medium is well-preserved along withaccurate velocity information. A major challenge with the use ofEEI analysis is the difficulty in finding the appropriate range ofchi angle (the intercept-gradient coordinate rotation angle χ) fora particular petrophysical well log. Whitcombe et al. (2002),Zhen-Ming et al. (2008), and Mirzakhanian et al. (2017) reveal thatthe correlation between EEI and water saturation is weak, as indi-cated by a low correlation coefficient. Later on, focusing on relativerock physics, Ball et al. (2014a), Ball et al. (2014b), and Connolly(2017) find that the theoretical values of χ for several elastic proper-ties (e.g., bulk modulus) depend only on k, the squared ratio of theS-wave (VS) to P-wave (VP) velocity, and given the uncertainty as-sociated with determining the velocities, they find such dependencea challenge for EEI analysis when it comes to the elastic properties.This study presents an application of EEI for obtaining the

geomechanical parameters. For this goal, after reviewing the theo-retical background of EEI, a jointed shale carbonate reservoir insouthwestern Iran was selected as a case study. Beginning with siteinvestigations, rock-mechanics and rock-physics tests were con-ducted on core samples. Then, static and dynamic moduli were ob-tained using petrophysical data, core analysis, and interpretationresults. Then, the P-wave velocity, S-wave velocity, and densitylogs, as well as the geomechanical parameters from laboratory tests,were used to build an MEM, based on which EEI curves were de-veloped. Using AVO attributes such as A and B, an EEI reflectivitywas estimated at each angle. Finally, inverting the data, geomechan-ical sections were obtained for each parameter and represented inthe form of a 3D cube. In addition, the geomechanical cubes derivedfrom the EEI-based method were confirmed by a blind well andcompared with those of another inversion technique, namely, simul-taneous inversion.

THEORY

Zoeppritz’s equations are a set of nonlinear relationships that de-scribe the seismic responses at a plane boundary across whichacoustic properties vary with incidence angle (Shuey, 1985; Ursen-bach, 2002; Haase, 2004; Fathalian and Innanen, 2015; Ball et al.,2018). These equations are the basis for different inversion analysisand seismic interpretation techniques (e.g., amplitude versus angleand AVO studies). Using Zoeppritz’s equations, one can calculatethe amplitudes of reflected or transmitted plane waves for all inci-dence angles. To gain more insight into the factors controlling theamplitude variations with angle/offset and simplify the requiredcomputations, linearized approximations to the Zoeppritz equa-tions, have been developed. Of the several approximations of thisequation, here we used the Aki-Richards equation (Aki and Ri-chards, 1980; Shuey, 1985). Representing a linearized form ofthe Zoeppritz’s equations, the Aki-Richards equation can be ex-pressed as

RðθÞ ¼ aΔVP

2VP

þ bΔVS

2VS

þ cΔρ2ρ

; (1)

where a, b, and c are defined as

a ¼ 1þ sin2 θ; b ¼ −8k sin2 θ; c ¼ 1 − 4k sin2 θ

(1a)

with

k ¼�VS

VP

�2

; (1b)

where R is the reflectivity at angle θ, and VP, VS, and ρ are the P-wave velocity, S-wave velocity, and density, respectively. Moreover,ΔVP, ΔVS, and Δρ are the differential values of P-wave velocity,S-wave velocity, and density, respectively. Although quite similar toShuey (1985), Wiggins et al. (1983) derive an equation based onequation 1 as follows:

RðθÞ ¼ Aþ B sin2 θ þ C sin2 θ tan2 θ; (2)

where A, B, and C are referred to as intercept, gradient, and curva-ture, respectively. For incidence angles lower than 30°, equation 2can be approximated as follows:

RðθÞ ¼ Aþ B sin2 θ; (3)

where

A ¼ 1

2

�ΔVP

V̄P

þ Δρρ̄

�(3a)

and

B ¼ ΔVP

2V̄P

− 4

�VS

VP

�2�ΔVS

V̄S

�− 2

�VS

VP

�2�Δρρ̄

�; (3b)

where V̄P, V̄S, and ρ̄ are the average values of P-wave velocity,S-wave velocity, and density, respectively. Connolly (1999) pro-poses the following formula for deriving reflectivity from the

R430 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

acoustic impedance in terms of changes in the impedance as thewave travels from formation n to formation nþ 1:

RðθÞ ¼ EIðθÞnþ1 − EIðθÞnEIðθÞnþ1 þ EIðθÞn

≈1

2

ΔEIEI

≈1

2Δ lnðEIÞ; (4)

where EI is the elastic impedance. Then, Whitcombe (2002) intro-duces reference constants (e.g., V̄P, V̄S, and ρ̄) to come with adimensionless and normalized EI as

EIðθÞ ¼ V̄Pρ̄

��VP

V̄P

�a�VS

V̄S

�b�ρ

ρ̄

�c�; (5)

where a, b, and c are the same as the exponents defined inequation 1.However, the value of RðθÞ exceeds one, which conflicts with

real seismic data if θ is too large. This was addressed by Whitcombeet al. (2002) by replacing sin2 θ by tan χ and scaling the value ofRðθÞ by having it multiplied by cos χ (where χ is the intercept-gra-dient coordinate rotation angle and takes a value between −90° and90°). With these modifications, a new formula was developed toobtain a new parameter called EEI:

EEIðχÞ ¼ V̄Pρ̄

��VP

V̄P

�p�VS

V̄S

�q�ρ

ρ̄

�r�; (6)

where

p ¼ cos χ þ sin χ; q ¼ −8k sin χ; and

r ¼ cos χ − 4k sin χ: (6a)

Equation 6 eliminates the dramatic effect of the incidence angle onEI and limits the value of reflectivity to [1, −1]. With these mod-ifications applied, the EEI equation offers more applicability for es-timating fluid and lithology from real seismic data (Whitcombeet al., 2002). EEI can also be written as a linearized form of Shuey(1985), where sin2ðθÞ is replaced by tan (χ) as follows:

RðθÞ ¼ Aþ B tanðχÞ; (7)

REEIðχÞ ¼ RðθÞ cos χ ¼ A cos χ þ B sin χ: (8)

Because the value of χ changes between −90° and 90°, it gives anextension of EI for any combination of intercept and gradient. It isnoticeable that EEI is equal to the acoustic impedance at χ ¼ 0° andalso to the gradient impedance at χ ¼ 90°. For any desired param-eter (physical or elastic parameters), the optimum angle (empiricalχ) along the EEI spectrum is the one at which crosscorrelation of thetarget parameter with the EEI spectrum is maximal (Whitcombeet al., 2002; Zhen-Ming et al., 2008; Thomas et al., 2013; Mirza-khanian et al., 2017; Yenwongfai et al., 2017). The significance ofthis feasibility study is to perceive if EEI spectrum variations exhibitany sensitivity to geomechanical parameters, such as Young’smodulus, Poisson’s ratio, bulk modulus, compressive strength,and brittleness.Recent works on relative rock physics have highlighted the need

for precise gradient (B) evaluation before an accurate chi projectioncan be achieved. However, the gradient measurement accuracy is

known to be affected by several factors (Ball et al., 2014a; Msoloand Gidlow, 2015; Connolly, 2017). In their rock-physical studies,Ball et al. (2014a) perform a comparison between actual (theoreticalor constant k) and apparent (empirical) values of χ for a particularset of gradient scaling errors. A study on the errors associated withseismic gradient measurement by Connolly (2017) points out thechallenges of evaluating seismic chi projections at particular anglesbecause there are chances that actual values of χ are significantlydifferent from apparent ones, although the consideration of thedesired aspects of geology for a range of χ values can somewhatmitigate such challenges. Later on, he publishes a report on theweighting of different relative rock properties and equivalent χvalues for a set of elastic properties. According to Connolly (2017),the relationships are exact when a constant k value is assumed (e.g.,0.20, 0.25, and 0.30), and the empirical values are well-correlated tothe corresponding theoretical values.

CASE STUDY

As a case study, the proposed method was applied to a hydro-carbon reservoir in southwestern Iran. Located within the so-calledAbadan Plain, the study area is part of the Zagros Mountains.Zagros is a fold-thrust belt of some 250 km width and 1800 kmlength, where the folding process is estimated to begin in the LateCretaceous when the area had been located close to the equator.According to geologic evidence, the Zagros fold-thrust belt is acollisional belt between the Arabian Plate and the Iran Blockand has experienced intensified folding during the Late Mioceneand Pliocene. Recent earthquakes within the region are indicativeof geologic activity of the Zagros thrust fault and have incurred geo-mechanical problems for reservoirs within the region (Rajabi et al.,2010; Mehrabi and Rahimpour-Bonab, 2014).This case study was performed on an Upper Cretaceous forma-

tion in the Zagros area, herein referred to as L2. The L2 formationconsists of intercalations of black fossils shale and marine inter-bedded limestone shale with some amounts of quartz and dolomite.Deposited in between the L1 and L3 formations, the L2 formation ispartitioned by several disconformities. In terms of lithology, the L1formation is made up of marl to marly limestone, and stratigraphi-cally speaking, it is deposited during the Campanian-Maastrichtianperiod. The L3 formation is composed of Coniacian shales, and ithas played an influential role as the cap rock in the regional petro-leum system (Mehrabi and Rahimpour-Bonab, 2014; Asl andAleali, 2016). The study reservoir has already produced oil fromthe Santonian-Campanian Formation. The reservoir extends over adepth range of 2900–3000 m, with the selected formation (L2)being 190 m thick in the study area.

RESULTS

Geomechanical parameters

Geomechanical characterization and modeling of a hydrocarbonreservoir require information on regional stress, mass rock, and in-tact rock. The regional stress consists of overburden stress (σv),minimum horizontal stress (σhmin), and maximum horizontal stress(σHmax). Also known as overburden stress, the vertical stress at anydepth is a function of density and controls the rock-deformationstrength in a stressful medium. The magnitudes of the minimumand maximum horizontal stresses were determined using the

Seismic geomechanics R431

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

so-called poroelastic formula (Zoback, 2007; Kidambi and Kumar,2016) and horizontal-strain modeling. The poroelastic formula de-pends on Young’s modulus, Poisson’s ratio, compressive strength,and regional pore pressure. Borehole shape is an indicator of in situstress setting, and it has an important role in eliminating the orien-tation of the horizontal stress. In this study, to estimate the orien-tation of σHmax, formation microimager logs were used and boreholebreakouts were interpreted. A borehole breakout takes place whenthe circumferential stress at the wellbore exceeds the strength ofintact rock, causing stress-induced elongations parallel to the maxi-mum horizontal stress (Gough and Bell, 1982; Fjær et al., 2008;Rajabi et al., 2010; Kidambi and Kumar, 2016). The behaviors ex-hibited by rocks and soils are dominantly controlled by theirstrength (i.e., the maximum principal stress at which a sample ofthe rock or soil loses its ability to tolerate applied stress). In general,rock strength can be measured from in situ tests under static or dy-namic conditions, either directly in the laboratory or indirectly byapplying empirical equations. The dynamic moduli of rock are cal-culated from the rock properties (e.g., rock density) and wave-velocity measurements on well logs, whereas the static moduli(e.g., uniaxial compressive strength [UCS], Young’s modulus, bulkmodulus, and Poisson’s ratio) are experimentally calculated basedupon in-lab deformation tests (Mockovčiaková and Pandula, 2003;Zoback, 2007; Mavko et al., 2009; Martınez et al., 2012). In fielddevelopment and geomechanical studies, the static moduli are nor-mally closer to the real values, compared to the dynamic ones. How-ever, the static modulus can only be measured at limited pointswithin a given reservoir horizon or interval, making it incapableof representing the full range of rock properties along the entire wellpath (Fjær et al., 2008; Sharifi et al., 2017a). Therefore, the dynamicmoduli obtained from well logs or seismic surveys are preferred insuch studies because those can provide a wider range of rock prop-erties across the field (Eissa and Kazi, 1988).In this research, to make 1D MEM and verify the results, rock-

physical and rock-mechanical tests were performed on selected coresamples. For this purpose, 13 core plugs taken from L2 formationswithin a depth interval of 60 m along a water-bearing well (no B-01)were selected. First, the core samples were cut, using a diamondsaw, into plugs of 100–120 mm in length and 50 mm in diameter.Then, the plugs were dried in a vacuum oven at 80°C for 24 h. Then,the samples were placed in desiccator in which rock-physics androck-mechanics tests were performed. The samples used in thisstudy consisted of calcite, variable amounts of shale (mainly illite),and minor amounts of kaolinite, dolomite, and quartz. Scanningelectron microscopic microphotographs showed that the interpar-ticle porosity was the dominant pore type in the samples. In addi-tion, based on the results of X-ray diffraction analyses, the selectedsamples were found to contain calcite with some amounts of clay(mainly kaolinite and illite) bound together with a calcite cement.Thin-section studies showed that, even though digenetic processeshave been active during the deposition stage, those imposed no sig-nificant effect on the reservoir quality. Moreover, the core plugswere examined for induced discontinuity and microcracks usingcomputed tomography (CT) scan imaging. According to the CT-scan images, no crack and/or discontinuity was observed insidethe samples; hence, the anisotropy effect was neglected (Sharifiet al., 2017a, 2017b).For the sake of static moduli, the samples were subjected to

multistage triaxial compression tests according to Kim and Ko

(1979), Khosravi et al. (2012), and Hashiba and Fukui (2014).The tests were performed at 80°C and under reservoir stress andfluid conditions (brine-bearing well no. B-01 containing NaCl at220,000 ppm). For this purpose, each specimen was placed in atriaxial loading cell designed by CSIRO and subjected to uniformhydrostatic loading at 0.5 MPa∕min until the desired confiningpressure (σ1 ≠ σ2 ¼ σ3) was reached. Then, increasing the axialload at a constant and continuous strain rate within the elastic regionof the rock, the axial and lateral deformations were monitored asfunctions of the applied load. Axial loading and unloading cycleswere applied at different confining pressures to make measurementsof elastic properties under different potential stress paths.Dynamic modulus was calculated using rock-physics laboratory

tests and well-log frequencies (f ∼ 10–20 kHz). In the laboratory,the conventional pulse transmission technique was used to deter-mine VP and VS on core samples at ultrasonic frequencies(f ∼ 500–1000 kHz). The samples were further subjected towave-velocity measurements at different effective confining pres-sures within the range of 5–60 MPa. This was followed by meas-uring variations of VP and VS versus the effective confiningpressure on dry and saturated samples. The final outputs of therock-physics tests were VP, VS, and density for dry and saturatedconditions.Covered by seismic data, the study area hosted six wells whose

data were used for obtaining in situ dynamic properties. The welllogs used in this research included density, porosity, caliper, P- andS-wave velocities, resistivity, and gamma ray. Petrophysical inter-pretations were also available for the well. To keep the data consis-tent in terms of reference, well-log measurements were representedin meters from the Kelly bushing. Natural gamma-ray and resistivitylogs were used to separate mudstone and shale intervals from otherlithologic units. Shale volume calculations were made by Lario-nov’s (1969) formula. The formation porosity was calculated fromneutron porosity and bulk density logs using a fluid density of1.19 g∕cm3 (brine-saturated rock) and a matrix density of2.69 g∕cm3 (Serra, 1984, 1986). Quality controls (QCs) were con-ducted by rock-physical modeling for all available well logs. In thecourse of the QC process, low-quality logs, wash-outs, and errone-ous intervals (where the caliper log detected breakouts) within thetargeted horizons (the L2 formation) were identified and corrected(Mavko et al., 2009; Xu and Payne, 2009).Consequently, based on the results of the rock-physics tests and

well-log data, the dynamic values of the rock parameters (i.e., Pois-son’s ratio ν, shear modulus μ, bulk modulus K, Young’s modulusE, and closure stress ratio [CSR]) were calculated from the follow-ing equations:

v ¼ V2P − 2V2

S

2ðV2P − V2

SÞ; (9)

μ ¼ ρV2S; (10)

K ¼ μ2ð1þ vÞ3ð1 − 2vÞ ; (11)

E ¼ 3Kð1 − 2vÞ; (12)

R432 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

and

CSR ¼ v1 − v

: (13)

When the applied stress onto a rock exceeds a certain limit, the rockstarts to rupture promptly, releasing some elastic energy; this phe-nomenon is known as brittleness. In other words, brittleness mea-sures the rate of strain prior to rupture, which is defined as the

brittleness index (BI). BI can be either deter-mined via in-lab tests (which is a time- andcost-intensive task but gives highly precise re-sults) or estimated from well-log data usingmathematical formulas (Gray et al., 2012; Louet al., 2016). In this research, it was estimatedfrom laboratory data as a function of Young’smodulus and Poisson’s ratio, as follows:

BI ¼ 50%

�

Emin − EEmin − Emax

þ vmin − vvmin − vmax

�; (14)

where Emax and Emin are the maximum and mini-mum values of Young’s modulus, respectively.Details of the calculation and interpretation of

static and dynamic moduli were thoroughly an-alyzed and investigated by Sharifi et al. (2017a,2017b) whose results are used herein. The resultsof geomechanical tests confirmed that static anddynamic moduli exhibit similar behaviors and

Figure 1. Results of rock-mechanical and rock-physical laboratory tests on core sam-ples (in dry and saturated conditions) along with the results of well-log data, indicatinghow the static and dynamic (a) Young’s moduli and (b) bulk modulus are correlated toone another. The obtained correlation coefficients show that the laboratory tests, as com-pared with static measurements, tend to produce higher correlation coefficients. Thelower correlation coefficient of well-log data can be attributed to environmental effectson the well-log data (Sharifi et al., 2017a, 2017b).

Figure 2. EEI analysis for χ values ranging from −90° to 90° atwells (a) B-01 and (b) A-03. It is noticeable that EEI is equal tothe acoustic impedance when χ is zero. The color scaling indicatesEEI in m∕s:g∕cm3.

Figure 3. The maximum crosscorrelation of EEI to geomechanicalparameters for intact rock at wells (a) B-01 and (b) A-03.

Seismic geomechanics R433

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

can be linked to one another through a simple linear or nonlinearrelationship. Accordingly, Figure 1a demonstrates the correlationrelating static and dynamic Young’s moduli of the core plugs (insaturated and dry conditions), as obtained from well logs. Figure 1bshows the correlation between static and dynamic bulk moduli ofthe core samples in saturated and dry condition, as obtained fromwell logs. The three curves seen on these figures refer to the regres-sion results based on well-log data, data from the tests on saturatedcore samples, and that from the tests on dry core samples. Once thetests were carried out, a 1D MEM was built for each well for thesake of dynamic-to-static conversion, with the results of the staticmeasurements used to validate the EEI analysis results.

EEI analysis

The main focus of this paper is on EEI analysis for making thegeomechanical template and MEM using seismic data. The EEIcurve is sensitive to numerous elastic and petrophysical parametersat different values of χ. Therefore, in this section, the optimum valueof χ for each parameter was obtained according to the maximumvalue of crosscorrelation of the desired parameter to the EEI spec-trum logs at different values of χ (Whitcombe et al., 2002; Zhen-Ming et al., 2008; Thomas et al., 2013; Mirzakhanian et al., 2017).Using equation 6, the petrophysical logs (VP, VS, and density) were

Figure 4. The maximum crosscorrelation of EEI to geomechanicalparameters for rock mass and regional stress at wells (a) B-01 and(b) A-03.

Figure 5. The maximum crosscorrelation of EEI to geomechanicalparameters for the (a) bulk modulus and (b) brittleness in all wells.The results show that the corresponding values of χ to differentgeomechanical parameters show the same trend and value in eachwell.

Table 1. Calculated values of χ and correlation coefficientsfor each geomechanical parameter.

Type Target logCorrelationcoefficient

Empiricalχ (°)

Intact rock UCS 0.84 þ38

Young’s modulus 1.00 −42Density × Young’s

modulus1.00 −31

Bulk modulus 0.98 þ12

Shear modulus 0.99 −52Poisson’s ratio 0.93 þ33

Rockmass

Pore pressure 0.76 −57Overburden stress 0.71 −82

Minimum horizontal stress 0.66 þ42

Maximum horizontal stress 0.68 þ41

Brittleness 0.99 −55CSR 0.99 þ40

R434 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

used to build the EEI spectra. Figure 2 shows the correspondingspectra for 181 logs versus depth, with those at well B-01 and wellA-03 being indicated in Figure 2a and 2b, respectively. Continuingwith the research, variations of EEI with χ were plotted and cross-correlated to each geomechanical parameter. In this study, 12 differ-ent geomechanical parameters were crosscorrelated to EEI at fivewells. Figure 3a shows the results of the crosscorrelation of EEIto the geomechanical parameters of the intact rock in well B-01,and Figure 3b shows similar results for well A-03. In the sameway, Figure 4a and 4b shows the crosscorrelation of the rock massand regional stress in wells B-01 and A-03, respectively. Figure 5aand 5b compares the crosscorrelations of the geomechanical param-eters among different wells in terms of the bulk modulus and brit-tleness, respectively. Table 1 shows the obtained value of χ(empirical χ) and the correlation coefficients for each geomechan-

ical parameter from all of the wells by averaging. Using Table 1, onecan obtain a value for each parameter at each angle from the seismicsection. It should be emphasized that static and dynamic valuesexhibit the same trend and behavior, indicating that the results ofthe EEI analysis (correlation coefficients and χ) are insensitive tothe choice of static or dynamic values. According to Table 1, thehighest correlation was obtained for the Young’s modulus, whereasthe in situ stresses (σhmin and σHmax) gave the lowest correlationvalues.

EEI inversion

As a final step, using the presented static-dynamic relationships,well logs, and seismic data, a 3D MEM was estimated from the EEIinversion results. The seismic data included prestack-migrated

Figure 6. EEI section estimated from EEI analysisat well A-02 after performing a model-based in-version on the related EEI reflectivity series to cal-culate the Young’s modulus. The colored datashow EEI (in m∕s:g∕cm3) at a χ value of −42°.The EEI inversion results are in good agreementwith the measured EEI from well logs at well lo-cations, verifying the EEI inversion. The blackcurve refers to EEI at −42° at a well location.

Figure 7. EEI section of CSR estimated from EEIanalysis at well B-01 after performing a model-based inversion on the related EEI reflectivityseries. The color data refer to EEI (inm∕s:g∕cm3) at a χ value of 40°. The EEI inversionresults appropriately match the EEI data from welllogs at well locations, verifying the EEI inversion.The black curve is the EEI at 40° at a well location.

Figure 8. EEI section of brittleness estimatedfrom EEI analysis at well A-01 after performinga model-based inversion on the related EEI reflec-tivity series. The color data show EEI (inm∕s:g∕cm3) at a χ value of −55°. The EEI inver-sion results well match the EEI data from well logsat well locations, verifying the EEI inversion. Theblack curve shows EEI at −55° at a well location.

Seismic geomechanics R435

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

common-midpoint gathers processed using Kirchhoff prestack timemigration (inline and crossline spacing of 25 m, sampling rateof 4 ms, and fold coverage of 78). Angle stacks were providedat incidence angles ranging from 5° for near-angle stacks to 35°for far-offset angles. The survey covered an area of approximately371 km2. Well logs were available at six wells. Check-shot datawere used for time-to-depth conversion.Corresponding well logs to each location were selected for EEI

spectrum generation within the angle range of −90° to þ90°. TheEEI logs were crosscorrelated to objective logs to find the optimumvalue of χ at which the value of crosscorrelation for the target logwas maximized. Then, two sections, namely, sections A and B,were extracted through AVO analysis and used for calculatingthe EEI reflectivity series (Hampson et al., 2001; Russell et al.,2003). Next, the reflectivity section at the target value of χ was cal-culated. Below is an example of the calculations performed for theYoung’s modulus with maximum crosscorrelation with EEI spec-trum at a χ of −42°:

REEIð−42°Þ ¼ A cosð−42°Þ þ B sinð−42°Þ: (15)

In the next step, a filtered version of the initial EEI model, hereinreferred to as low-frequency model (LFM), was created. For doingthis, the data from five wells (wells A-01 to A-04 and B-01) were

considered as inputs to the model. Inverse distance power methodwas used to interpolate different parameters and build the LFM forthe frequency range of 0–10 Hz (Oldenburg et al., 1983; Hampsonet al., 2001; Pendrel, 2015; Ray and Chopra, 2016) at an objectivevalue of χ. Then, a statistical wavelet was extracted from the EEIreflectivity series for the considered value of χ. Subsequently, EEIwas extracted by applying a model-based inversion (Russell et al.,2003) on the related EEI reflectivity series. Finally, the results werescaled via static-dynamic conversion to obtain absolute values ofthe geomechanical parameters. A combination of multivariate re-gression with a neural network was used to scale the EEI to thegeomechanical parameters (Hampson et al., 2001; Banchs andMichelena, 2002; Herrera et al., 2006; Khoshdel and Riahi, 2011).Alternately, one could apply colored inversion, wherein the relativescaling is performed instead of building LFM, estimating wavelet,and then running a model-based inversion. Figures 6, 7, and 8 showthe results of EEI inversion at well location for Young’s modulus,bound Poisson’s ratio or CSR, and brittleness, respectively. Scaled3D EEI models of static Young’s modulus, CSR, and brittleness areshown in Figures 9, 10, and 11, respectively, based on the static-dynamic relationships. Horizontal slices (maps) of the geomechan-ical parameters were extracted using root-mean-square values fromthe related volumes within windows, which were 10–15 ms belowthe top of the L2 formation.

Figure 9. The static Young’s modulus (in GPa) es-timated from the EEI analysis at well A-02 afterperforming a model-based inversion (on the re-lated EEI reflectivity) and scaling. The black curveis the static Young’s modulus at a well location.The obtained Young’s modulus values rangedfrom 1 GPa for jointed shale carbonate to25 GPa for dense-stiff carbonate. The horizon slicerepresents the time interval from 1870 to 1880 ms(L2 formation).

R436 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

Blind-well analysis

To confirm the capability of the proposed approach and obtain op-timal inversion results, QCwas performed by conducting a blind-welltest. An acceptable inversion method is supposed to yield a goodmatch between the elastic properties measured from the wells andthose from seismic inversion at the blind well. In this regard, a devel-opment well outside the study area was selected as a blind well (wellA-10). The blind well was not considered in the process of buildingthe LFM and related analysis. Next, using the respective formula andstatic-dynamic conversion relationships, the static Young’s moduluswas calculated from the blind well data. Then, using the obtainedvalues of the Young’s modulus from the EEI inversion, the curveof the Young’s modulus for the blind well was developed (Figure 12).Graphically, the results show that the inverted EEI values followedthe actual values of the Young’s modulus at the blind well location(well A-10). A distribution map of the Young’s modulus is presentedin Figure 12. In the same way, the brittleness parameter was alsoverified within the related section at well A-10, which was hereinconsidered as a blind well (Figure 13).

Simultaneous inversion

To confirm the results using another inversion method, simulta-neous inversion was performed on the selected seismic section, and

the results for well A-02 were investigated. The simultaneous inver-sion implemented herein is based on the work by Hampson et al.(2005). All parameters, including seismic data, well log, and hori-zons were the same as those applied to the EEI inversion. Then, aninversion algorithm was applied to obtain a set of seismic sections,such as the P-impedance, S-impedance, and density sections. Next,with the aim of obtaining an elasticity formula, a 3D section of theYoung’s modulus was calculated using VP, VS, and density data, asshown in Figure 14, which presents the scaled section. Figure 14further shows the horizon slice within the time interval of 1870–1880 ms.

DISCUSSION

Interpretation of EEI analysis

The results of the EEI analysis show that as far as geomechanicalparameters are concerned, similar values of crosscorrelation of χwere obtained at the different wells. Even though the obtained val-ues of χ and correlation values at selected wells were slightly differ-ent (approximately �3°), the differences were small enough tojustify neglecting them. The values of χ obtained in this researchwere in agreement with those in previously published papers (Whit-combe et al., 2002; Zhen-Ming et al., 2008; Gharaee Shahri, 2013;

Figure 10. Section and horizon slice (L2 forma-tion) of the CSR estimated from EEI analysis atwell B-01 after performing a model-based inver-sion (on the related EEI reflectivity) and scaling.The black curve is the CSR at a well location. Thehorizon slice represents the time interval from1870 to 1880 ms.

Seismic geomechanics R437

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

Connolly, 2017; Mirzakhanian et al., 2017; Yenwongfai et al.,2017). The small differences could be resulting from the depend-ency of the geomechanical parameters on the k factor (Ball et al.,2014a; Connolly, 2017). Nevertheless, the high degree of correla-tion indicated large potentials of the proposed method when appliedto data of good quality.Following the EEI analysis, the estimated values of the geome-

chanical parameters using the EEI-based method were verifiedagainst the results of rock-physics and rock-mechanics tests throughcrossplots. Figure 15 compares the static Young’s modulus and theequivalent EEI curves at well A-02. Figure 15 shows that EEI ex-hibits a good match with the static Young’s modulus at −42°. Inaddition, results of the Young’s modulus from core data confirmedthe EEI results. The considerable level of scattering in the labora-tory test data (such as those obtained from rock-physics and rock-mechanical tests, especially in saturated samples) stems from twodifferent facts. First, the core samples were not homogeneous on amicroscopic scale; rather, they hosted microcracks that influencedthe wave velocity, especially at high frequencies. Second, in thelaboratory, wave velocity measurements on the core plugs wereperformed at ultrasonic frequencies (typically approximately500–1000 kHz), whereas sonic velocities (i.e., those extracted fromsonic-log data) were measured at much lower frequencies (inter-mediate frequencies, as compared with seismic measurements).

Moreover, such measurements were made along the wellbore axis,which are frequently not perpendicular to the bedding orientation,causing anisotropic effects (Han and Batzle, 2004; Delle Piane et al.,2014; Pimienta et al., 2015; Nooraiepour et al., 2017).In the same way, Figures 16 and 17 compare the elastic param-

eters and the equivalent EEI curves at certain values of χ for CSRand brittleness at wells B-01 and A-01, respectively. According tothe results, the considered geomechanical parameters were compa-rable with the related EEI curves, and core data further confirmedthe EEI results. Moreover, the EEI analysis results were crosscorre-lated to geomechanical logs at the well locations (Figures 18, 19,and 20). The results showed that the estimated parameters from theEEI analysis matched the well-log data at the well location prettywell considering zero-angle elastic impedance. Consequently, theo-retically speaking, the EEI method can estimate geomechanicalparameters with appropriate accuracy.

Interpretation of the EEI inversion

The previous section showed that, when performed at an appro-priate value of χ, EEI analysis can represent a particular geomechan-ical parameter. Accordingly, EEI inversion was performed on aseismic section at different values of χ, followed by scaling andacquiring a seismic section for each geomechanical parameter.

Figure 11. Section and horizon slice (L2 forma-tion) of the brittleness estimated from EEI analysisat well A-01 after performing a model-basedinversion on the related EEI reflectivity series fol-lowed by scaling. The black curve is the brittlenessat a well location. The horizon slice represents thetime interval from 1870 to 1880 ms.

R438 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

Subsequently, the acquired cubes were analyzed to evaluate the ac-curacy of the EEI inversion for each parameter. Figure 21 shows acrossplot of the static Young’s modulus versus the inverted Young’smodulus at selected wells. Figure 22 presents the crosscorrelation ofCSR data extracted from the EEI inversion versus that from welldata at well B-01. The inverted brittleness values at well A-01are crossplotted versus the measured brittleness values in Figure 23.Accordingly, the proposed EEI method seems to be capable of pre-senting good estimations of the considered geomechanical param-eters from a seismic section. However, it should be noted that animportant issue to address is the relationship between geomechan-ical parameters and well-log data at particular angles (EEI analysis).The poor correlation between the EEI-inverted and real data (i.e.,

the inconsistency observed on the crossplots presented in Fig-ures 21–23) is sourced from the uncertainties inherent in the realdata because of the respective measurement methods (e.g., seismicsurvey and well logging) and those associated with the modelingapproach (i.e., different algorithms and constraints) (Thore, 2015).However, depending on the choice of the inversion algorithm, someof those parameters may render irrelevant (e.g., inversion-relatedparameters — for instance, the colored inversion does not requireany of the mentioned parameters). Interpretation of the associatederror with EEI-based inversion is beyond the scope of this paper.There are chances that combinations of other inversion methods

with EEI can contribute to appropriate estimation of geomechanicalparameters at such values of χ. Therefore, the EEI method cannotact beyond the inversion error, and the uncertainty encountered withseismic data and modeling impose limitations on the EEI approach.Regarding the seismic data, one can incorporate the associated un-certainty into the inversion scheme. However, regarding the asso-ciated uncertainty with modeling, it is recommended to performblind-well analysis or run multiple inversions (e.g., simultaneousinversion method).

Interpretation of blind-well analysis results

Young’s modulus logs were extracted from the related volumes atthe blind-well location for QC. Figure 24a and 24b shows crossplotsof the inverted Young’s modulus and brittleness, respectively, ver-sus measured values along well A-10 within the L2 formation. Ingeneral, the predicted Young’s modulus was seen to be highlycorrelated to the well measurements, emphasizing the reliabilityof the proposed EEI inversion for predicting geomechanicalparameters.A more thorough review of the obtained correlation coefficients

showed that the extracted log from the inversion exhibited furtherscattering than the measured well logs. Results of the blind-welltests showed similar behavior to other wells across the study area,

Figure 12. Blind well analysis: the section ofstatic Young’s modulus (in GPa) estimated fromthe EEI analysis using the data along wells B-01 and A-01 to A-04 after performing a model-based inversion and scaling. The black curve isthe static Young’s modulus at well A-10. The hori-zon slice represents the depth interval from 1900to 1910 ms.

Seismic geomechanics R439

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

confirming the generalizability of the proposed method and the welllocation independence of the incurred error. Nevertheless, the lowercorrelation coefficients obtained in the blind-well test, as comparedwith other wells, were attributed to the factors affecting the pro-posed EEI-based method, such as the variation of χ across the se-lected reservoir.

Interpretation of the simultaneous inversion

The results obtained from the EEI-based inversion were com-pared to those of the simultaneous inversion at well A-02. A cross-plot of the results of the simultaneous inversion versus the measuredstatic Young’s modulus showed a strong correlation coefficient atthe well location (Figure 25). This crossplot was further comparedwith the static Young’s modulus obtained from the EEI-based in-version (Figure 21, well A-02) at χ value of −42°. The results of thecomparison indicate that the proposed EEI-based method can esti-mate the geomechanical parameters with an appropriate accuracy,i.e., comparable with that of the simultaneous inversion method.A typical approach toward lowering the uncertainty in seismic

exploration is to adopt different analyses before concluding a finalmodel. In this respect, the simultaneous inversion presumably con-tributes to lower uncertainty of the final geomechanical model, but

one should take into consideration two basic requirements for si-multaneous inversion of reservoir attributes: long-offset seismicdata and S-wave velocity in LFM and modeling, both of whichare usually not readily available. In addition, the accuracy withwhich rock mechanical parameters can be extracted from suchlong-offset data depends on the quality of the seismic data, makingthe extracted parameters highly unreliable in some cases. Sharmaand Chopra (2015) discuss a novel methodology for estimating rockdensity using EEI with no need for long-offset seismic data. Theyfurther compare the proposed approach with simultaneous imped-ance inversion, ending up confirming that the proposed methodgives promising results. Besides, the EEI-based method can be usedto synthesize pseudologs (e.g., S-wave velocity) of geomechanicalparameters in offshore data at an arbitrary well location (Neves et al.,2004; Awosemo, 2012; Sharma and Chopra, 2015; Hughes andGrant, 2017; Aleardi, 2018). The important point to note is thatEEI reflectivity sections at arbitrary values of χ can be used directlyas a seismic-geomechanical attribute with no need for inversion,provided that the cube can be scaled to absolute values. Once thisscaling is addressed, EEI analysis will be even more applicable thanother inversion methods because it is free of the common errors inthe other inversion methods, such as those associated with waveletextraction and LFM.

Figure 13. Results of the analysis on the secondblind well: the brittleness section estimated fromthe EEI analysis by model-based inversion andscaling at wells B-01 and A-01 to A-04. The blackcurve is the brittleness at well A-10. The horizonslice represents the depth interval from 1920 to1930 ms.

R440 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

Figure 14. The section obtained from simultane-ous inversion on prestack data at well A-02 in theL2 formation. The black curve is the staticYoung’s modulus at a well location. The horizonslice shows the time interval from 1870 to1880 ms.

Figure 15. Comparisons between the elasticparameters and the equivalent EEI curves at wellA-02. The static Young’s modulus is shown aswell. The EEI (χ ¼ −42°) is calculated from theEEI analysis, whereas EEI (χ ¼ 0°) denotes theacoustic impedance at a well location. Herein,the Young’s modulus is the static value from lab-oratory tests (rock-physical and rock-mechanicaltests) and well logs. The solid black circles are val-ues of the Young’s modulus obtained from labo-ratory tests.

Figure 16. Comparisons between the CSR param-eters and equivalent EEI curves at well B-01. TheEEI (χ ¼ 40°) is calculated from EEI analysis,whereas EEI (χ ¼ 0°) is the acoustic impedanceat a well location, with CSR being a parametermodeled from well tests, laboratory tests (rock-physical and rock-mechanical tests), and welllogs. To confirm the results, in situ CSR dataare shown as solid black circles.

Seismic geomechanics R441

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

Figure 17. A comparison between the elasticparameters and equivalent EEI curves at well A-01. Brittleness log is further demonstrated. TheEEI (χ ¼ −55°) is calculated from EEI analysis,whereas EEI (χ ¼ 0°) is the acoustic impedanceat a well location. Also, brittleness is a staticparameter modeled from laboratory tests (rock-physical and rock-mechanical tests) and well logs.Marked as solid black circles, the brittleness val-ues obtained from laboratory tests confirm themodeling accuracy.

Figure 18. Crosscorrelation of the EEI versus thestatic Young’s modulus log for well A-02 (a) atzero χ and (b) at the maximum correlation angle(here, χ is −42°).

Figure 19. Crosscorrelation of the EEI versus theCSR for well B-01 (a) at zero χ and (b) at themaximum correlation angle (here, χ is 40°).

Figure 20. Crosscorrelation of EEI versus brittle-ness for well A-01 (a) at zero χ and (b) at the maxi-mum correlation angle (here χ is −55°).

R442 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

Generalizability and limitations

In practice, the presence of anisotropy, seismic noise, velocityerrors, and similar phenomena ends up with a situation in whichthe proposed methodology in this paper may fail to give comparableresults in other reservoirs or with other data sets. So, prior to under-taking an EEI seismic-geomechanical inversion, one needs to cal-culate and verify the correlation values at each well along with localreservoir interval. In this section, a discussion is provided on thegeneralizability and limitations of the proposed approach on the ba-sis of theoretical backgrounds and data uncertainty. A limitation ofthe proposed methodology was related to the theoretical back-ground of the EEI method. Recent developments in relativerock-physics provide ways to obtain theoretical, rather than empiri-cal, optimum values of χ and explain such high maximum cross-correlations of EEI with elastic parameters. Based on theformalism provided by relative rock physics, theoretical valuesof χ depend only on the value of the factor k: the background ratioðVS∕VPÞ2. Ball et al. (2014a) and Connolly (2017) prove that theempirical χ values are in good agreement with the theoretical χ val-ues. The sole dependency of χ to the k factor is the most significantlimitation of this method, thereby affecting its generalizability whenapplied for the parameters that are independent of k. Looking for a

workaround, provided the gradient errors are adequately stable, onecan test different χ values on the seismic data to find the optimal onein terms of the enhancement achieved in the geologic aspects ofinterest. Anyway, the workaround will end up with unreliable re-sults if a complex velocity field is encountered (Connolly, 2017).Interpretation of EEI analysis showed that the geomechanical

parameters obtained from the EEI analysis matched pretty well withwell-log data at well locations with correlation coefficients exceed-ing 90%. This was while correlation coefficients below 80% wereobtained for seismic data. The good generalizability of this methodwas successfully indicated by the blind-well test results, whichhighlighted the independency of this method to the well position.Based on the results, one could infer that a major portion of theprediction error came from the inversion method, which is knownto be dependent on LFM, wavelet estimation, and inversion algo-rithm (sources of error). As mentioned before, the uncertainties as-sociated with the used seismic data and modeling procedure are thespecial limitations of the model-based EEI inversion method; how-ever, the uncertainty associated with the original data quality refersto a limitation suffered by virtually all inversion methods. Relativeinversion methods, such as colored inversion, provide alternativesolutions to address this limitation.

Figure 21. Crosscorrelation of static Young’smodulus extracted from the EEI inversion versuswell data for all wells with a sampling interval of4 ms.

Seismic geomechanics R443

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

In the present research, azimuthal seismic data were not avail-able. However, the generalizability of this technique to anisotropicmedia can be inferred from the works by Martins (2006) and Jyo-syula et al. (2015) who introduce the concept of anisotropic EEI andshow its capabilities in anisotropic reservoirs and propose the aniso-tropic extended elastic impedance (AEEI). In the meantime, particu-lar considerations shall be taken before applying AEEI to azimuthal

seismic data. From a theoretical point of view, the value of χ mayvary with the azimuth. Accordingly, one should begin with an EEIanalysis to obtain the optimum value of χ (for each geomechanicalparameter) at each azimuth before the EEI inversion can be per-formed azimuthally at the χ (s) of interest. For AEEI researchworks, it is recommended to obtain azimuth-dependent static anddynamic relationships.

CONCLUSION

EEI analysis can be used as a tool to decrease the risk of geo-mechanical interpretation and obtain physical and mechanicalparameters of reservoir rocks. The feasibility study performed inthis research showed that EEI can contribute to the developmentof MEM and reservoir geomechanics interpretation. In addition,presenting a new approach to a seismic-geomechanical hybridmethod, this study can lead to significant progress in seismic geo-mechanics in the future. The results of this research showed that EEIanalysis can enhance the geomechanical interpretability of hydro-carbon reservoirs. The comparison between measured parametersand EEI inversion data confirmed that, when incorporated intoEEI analysis, prestack seismic data can be used to directly estimaterock-physical and rock-geomechanical parameters across the entirebody of a reservoir. The results revealed that EEI values at differentvalues of χ (the intercept-gradient coordinate rotation angle) arerepresentative of different geomechanical parameters. Results ofthe blind-well analysis showed that elastic properties obtained from

Figure 22. Crosscorrelation of CSR extracted from the EEI inver-sion versus the CSR from well data at well B-01 with a samplinginterval of 4 ms.

Figure 23. Crosscorrelation of measured brittleness versus the oneextracted from the EEI inversion at well A-01 with a sampling in-terval of 4 ms.

Figure 24. Crosscorrelation of the (a) staticYoung’s modulus and (b) brittleness obtainedfrom the EEI inversion versus the measured valuesat the blind well (A-10) with a sampling interval of4 ms, constrained to L2 formation.

Figure 25. Crosscorrelation of static Young’s modulus obtainedfrom simultaneous inversion versus measured values at well A-02 with a sampling interval of 4 ms.

R444 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

EEI inversion are consistent with the measured data at well loca-tions, with the proposed method further compared with other inver-sion methods. EEI can also provide valuable information forobtaining geomechanical parameters from seismic interpretationand making pseudologs of geomechanical parameters. The mainsuperiority of this method over the conventional seismic inversionmethod is its applicability as a relative inversion method for fieldslacking any S-wave velocity log to perform prestack inversion andalso for deep offshore fields with no drilled well. Also, the chi-anglereflectivity series obtained from this method can serve as a seismic-geomechanical attribute that can be used similar to any other seis-mic attribute. Modeling-associated uncertainties and deviation ofthe empirical value of χ from the theoretic value of χ are limitationsof this method. Accordingly, before one can go through the calcu-lation of the optimum value of χ for each geomechanical parameterwhen applying EEI to a particular reservoir, it is necessary to under-take a feasibility step. This step must be reviewed for different lith-ologies and calibrated for the specific reservoir of interest. It is alsorecommended to use other seismic analyses along with EEI analysisfor geomechanical interpretation of a reservoir, so as to attain moreaccurate results.

ACKNOWLEDGMENTS

The authors are thankful to the staff of the University of Olso andN. H. Mondol for their invaluable technical support and guidance.We would also like to appreciate the GEOPHYSICS’ editors and re-viewers for their great contributions into and comments on thispaper.

DATA AND MATERIALS AVAILABILITY

Data associated with this research are confidential and cannot bereleased.

REFERENCES

Aki, K., and P. Richards, 1980, Quantitative seismology: Theory andmethods: W. H. Freeman and Co.

Aleardi, M., 2018, Estimating petrophysical reservoir properties through ex-tended elastic impedance inversion: Applications to off-shore and on-shore reflection seismic data: Journal of Geophysics and Engineering,15, 2079–2090, doi: 10.1088/1742-2140/aac54b.

Arsalan, S. I., and A. Yadav, 2009, Application of extended elastic imped-ance: A case study from Krishna-Godavari Basin, India: The LeadingEdge, 28, no. 10, 1204–1209, doi: 10.1190/1.3249775.

Asl, S., and M. Aleali, 2016, Microfacies patterns and depositional environ-ments of the Sarvak Formation in the Abadan plain, Southwest of Zagros,Iran: Open Journal of Geology, 6, 201–209, doi: 10.4236/ojg.2016.63018.

Awosemo, O. O., 2012, Evaluation of elastic impedance attributes in off-shore High Island, Gulf of Mexico: M.S. thesis, University of Houston.

Ball, V., J. P. Blangy, C. Schiott, and A. Chaveste, 2014a, Relative rockphysics: The Leading Edge, 33, 276–286, 276–278, 280–282, 284–286, doi: 10.1190/tle33030276.1.

Ball, V., L. Tenorio, J. P. Blangy, M. Thomas, and C. Schiott, 2014b, Un-certainty quantification of two-term relative elastic inversion: 76th AnnualInternational Conference and Exhibition, EAGE, Extended Abstracts,RM09, doi: 10.3997/2214-4609.20147465.

Ball, V., L. Tenorio, C. Schiøtt, M. Thomas, and J. P. Blangy, 2018, Three-term amplitude-variation-with-offset projections: Geophysics, 83, no. 5,N51–N65, doi: 10.1190/geo2017-0763.1.

Banchs, R. E., and R. J. Michelena, 2002, From 3D seismic attributes topseudo-well-log volumes using neural networks: Practical Considera-tions, 21, 996–1001.

Connolly, P., 1999, Elastic impedance: The Leading Edge, 18, 438–452, doi:10.1190/1.1438307.

Connolly, P., 2017, Chi: 79th Annual International Conference and Exhibi-tion, EAGE, Extended Abstracts, Tu A3 03.

Delle Piane, C., J. Sarout, C. Madonna, E. H. Saenger, D. N. Dewhurst, andM. Raven, 2014, Frequency-dependent seismic attenuation in shales:Experimental results and theoretical analysis: Geophysical JournalInternational, 198, 504–515, doi: 10.1093/gji/ggu148.

Eissa, E. A., and A. Kazi, 1988, Relation between static and dynamicYoung’s moduli of rocks: International Journal of Rock Mechanicsand Mining Sciences and Geomechanics Abstracts, 25, 479–482, doi:10.1016/0148-9062(88)90987-4.

Fathalian, A., and K. Innanen, 2015, AVO modelling of linearized Zoeppritzapproximations: CREWES Research 27.

Fjær, E., R. M. Holt, P. Horsrud, A. M. Raaen, and R. Risnes, 2008, Petro-leum related rock mechanics, 2nd ed.: Elsevier.

Gharaee Shahri, S. A., 2013, Application of extended elastic impedance(EEI) to improve reservoir characterization: M.S. thesis, Norwegian Uni-versity of Science and Technology.

Gough, D. I., and J. S. Bell, 1982, Stress orientations from borehole wallfractures with examples from Colorado, east Texas, and northern Canada:Canadian Journal of Earth Sciences, 19, no. 7, 1358–1370, doi: 10.1139/e82-118.

Gray, D., P. Anderson, J. Logel, F. Delbecq, D. Schmidt, and R. Schmid,2012, Estimation of stress and geomechanical properties using 3D seismicdata: First Break, 30, 59–68, doi: 10.3997/1365-2397.2011042.

Haase, A. B., 2004, Modelling of linearized Zoeppritz approximations:CREWES Research Report 16.

Hampson, D. P., B. H. Russell, and B. Bankhead, 2005, Simultaneous in-version of prestack seismic data: 75th Annual International Meeting,SEG, Expanded Abstracts, 1633–1636, doi: 10.1190/1.2148008.

Hampson, D. P., J. Schuelke, and J. A. Quirein, 2001, Use of multi-attributetransforms to predict log properties from seismic data: Geophysics, 66,220–236, doi: 10.1190/1.1444899.

Han, D., and M. L. Batzle, 2004, Gassmann’s equation and fluid-saturationeffects on seismic velocities: Geophysics, 69, 398–405, doi: 10.1190/1.1707059.

Hashiba, K., and K. Fukui, 2014, New multi-stage triaxial compression testto investigate the loading-rate dependence of rock strength: GeotechnicalTesting Journal, 37, 1087–1091, doi: 10.1520/GTJ20140061.

Herrera, V. M., B. Russell, and A. Flores, 2006, Neural networks in reservoircharacterization: The Leading Edge, 25, 402–411, doi: 10.1190/1.2193208.

Herwanger, J., and N. Koutsabeloulis, 2011, Seismic geomechanics: How tobuild and calibrate geomechanical models using 3D and 4D seismic data:EAGE Publications.

Hicks, G. J., and A. Francis, 2006, Extended elastic impedance and its re-lation to AVO crossplotting and Vp/Vs: Presented at the 68th EAGEConference and Exhibition incorporating SPE EUROPEC, EAGE, Ex-panded Abstracts, P056, doi: 10.3997/2214-4609.201402386.

Hughes, M., and S. Grant, 2017, The use of large numbers of pseudo wellsfor seismic inversion: Presented at the 4th International Workshop onRock Physics.

Jyosyula, S., F. Ruiz, and C. Cobos, 2015, Anisotropic extended elasticimpedance for fractured reservoirs: 77th Annual International Conferenceand Exhibition, EAGE, Extended Abstracts, We N105 12.

Khoshdel, H., and M. A. Riahi, 2011, Multi attribute transform and neuralnetwork in porosity estimation of an offshore oil field — A case study:Journal of Petroleum Science and Engineering, 78, 740–747, doi: 10.1016/j.petrol.2011.08.016.

Khosravi, A., N. Alsherif, C. Lynch, and J. McCartney, 2012, Multistagetriaxial testing to estimate effective stress relationships for unsaturatedcompacted soils: Geotechnical Testing Journal, 35, 128–134.

Kidambi, T., and G. S. Kumar, 2016, Mechanical earth modeling for a ver-tical well drilled in a naturally fractured tight carbonate gas reservoir in thePersian Gulf: Journal of Petroleum Science and Engineering, 141, 38–51,doi: 10.1016/j.petrol.2016.01.003.

Kim, M., and H. Ko, 1979, Multistage triaxial testing of rocks: GeotechnicalTesting Journal, 2, 98–105, doi: 10.1520/GTJ10435J.

Larionov, V. V., 1969, Borehole radiometry: Nedra, Moscow: Presented atthe SPWLA Annual Logging Symposium Transactions, Paper, 10, 26.

Lou, N., T. Zhao, and Y. Zhang, 2016, Calculation method about brittlenessindex in Qijia Oil field tight sandstone reservoir Daqing China: IOSRJournal of Engineering (IOSRJEN), 6, 14–19.

Martınez, J., D. Benavente, and M. A. Garcıa-del-Cura, 2012, Comparisonof the static and dynamic elastic modulus in carbonate rocks: Bulletin ofEngineering Geology and the Environment, 71, 263–268, doi: 10.1007/s10064-011-0399-y.

Martins, J. L., 2003, A second-order approach for P-wave elastic impedancetechnology: Studia Geophysica et Geodaetica, 47, 545–564, doi: 10.1023/A:1024759517596.

Martins, J. L., 2006, Elastic impedance in weakly anisotropic media: Geo-physics, 71, no. 3, D73–D83, doi: 10.1190/1.2195448.

Mavko, G., T. Mukerji, and J. Dvorkin, 2009, The rock physics hand-book: Tools for seismic analysis of porous media: Cambridge UniversityPress.

Seismic geomechanics R445

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

Mehrabi, H., and H. Rahimpour-Bonab, 2014, Paleoclimate and tectoniccontrols on the depositional and diagenetic history of the Cenomanian-early Turonian carbonate reservoirs, Dezful Embayment, SW Iran: Facies,60, 147–167, doi: 10.1007/s10347-013-0374-0.

Mirzakhanian, M., J. Sharifi, M. R. Sokooti, and N. H. Mondol,2017, Sensitivity analysis of multi-angle extended elastic impedance(MEEI) to fluid content: A carbonate reservoir case study from an IranianOil field: Presented at the 3rd Seminar Petroleum GeophysicalExploration.

Mockovčiaková, A., and B. Pandula, 2003, Study of the relation between thestatic and dynamic moduli of rocks: Metabk, 42, 37–39.

Msolo, A., and M. Gidlow, 2015, Relative rock physics templates in theelastic impedance domain: 85th Annual International Meeting, SEG, Ex-panded Abstracts, 575–579, doi: 10.1190/segam2015-5864583.1.

Neves, F. A., H. M. Mustafa, and P. M. Rutty, 2004, Pseudo-gamma rayvolume from extended elastic impedance inversion for gas exploration:The Leading Edge, 23, 536–540, doi: 10.1190/1.1766237.

Nooraiepour, M., N. H. Mondol, H. Hellevang, and K. Bjørlykke, 2017,Experimental mechanical compaction of reconstituted shale and mud-stone aggregates: Investigation of petrophysical and acoustic propertiesof SW Barents Sea cap rock sequences: Marine and Petroleum Geology,80, 265–292, doi: 10.1016/j.marpetgeo.2016.12.003.

Oldenburg, D. W., T. Scheuer, and S. Levy, 1983, Recovery of the acousticimpedance from reflection seismograms: Geophysics, 48, 1318–1337,doi: 10.1190/1.1441413.

Olson, J. E., S. E. Laubach, and R. H. Lander, 2009, Natural fracture char-acterization in tight gas sandstones: Integrating mechanics and diagenesis:AAPG Bulletin, 93, 1535–1549, doi: 10.1306/08110909100.

Pendrel, J., 2015, Low frequency models for seismic inversions: Strategiesfor success: 85th Annual International Meeting, SEG, Expanded Ab-stracts, 2703–2707, doi: 10.1190/segam2015-5843272.1.

Pimienta, L., J. Fortin, and Y. Guéguen, 2015, Bulk modulus dispersion andattenuation in sandstones: Geophysics, 80, no. 2, D111–D127, doi: 10.1190/geo2014-0335.1.

Plumb, R., S. Edwards, G. Pidcock, D. Lee, and B. Stacey, 2000, Themechanical earth model concept and its application to high-risk well con-struction projects: Presented at the ADC/SPE Drilling Conference.

Rajabi, M., S. Sherkati, B. Bohloli, and M. Tingay, 2010, Subsurfacefracture analysis and determination of in-situ stress direction usingFMI logs: An example from the Santonian carbonates (Ilam Formation)in the Abadan Plain, Iran: Tectonophysics, 492, 192–200, doi: 10.1016/j.tecto.2010.06.014.

Ray, A. K., and S. Chopra, 2016, Building more robust low-frequency mod-els for seismic impedance inversion: First Break, 34, 47–52.

Russell, B. H., K. Hedlin, F. J. Hilterman, and L. R. Lines, 2003, Fluid-prop-erty discrimination with AVO: A Biot-Gassmann perspective: Geophys-ics, 68, 29–39, doi: 10.1190/1.1543192.

Serra, O., 1984, Fundamentals of well-log interpretation: The acquisition oflogging data: Elsevier, Developments in Petroleum Science 15A.

Serra, O., 1986, Fundamentals of well-log interpretation: The interpretationof logging data: Elsevier, Developments in Petroleum Science 15B.

Sharifi, J., M. Mirzakhanian, A. Javaherian, M. R. Saberi, and N. HafeziMoqadas, 2017a, An investigation on the relationship between staticand dynamic bulk modulus on an Iranian Oilfield: 79th AnnualInternational Conference and Exhibition, EAGE, Extended Abstracts,Th SP1 08.

Sharifi, J., M. Mirzakhanian, N. H. Mondol, and M. R. Saberi, 2017b,Proposed relationships between dynamic and static Young modulus ofa weak carbonate reservoir using laboratory tests: Presented at the 4thInternational Workshop on Rock Physics.

Sharma, R. K., and S. Chopra, 2015, Estimation of density from seismicdata without long offsets — A novel approach: 85th Annual Interna-tional Meeting, SEG, Expanded Abstracts, 2708–2712, doi: 10.1190/segam2015-5851566.1.

Shuey, R. T., 1985, A simplification of the Zoeppritz equations: Geophysics,50, 609–614, doi: 10.1190/1.1441936.

Thomas, M., V. Ball, J. P. Blangy, and A. Davids, 2013, Quantitative analy-sis aspects of the EEI correlation method: 83rd Annual InternationalMeeting, SEG, Expanded Abstracts, 2321–2325, doi: 10.1190/segam2013-0224.1.

Thore, P., 2015, Uncertainty in seismic inversion: What really matters?: TheLeading Edge, 34, 1000–1004, doi: 10.1190/tle34091000.1.

Ursenbach, C. P., 2002, Optimal Zoeppritz approximations: CREWES Re-search Report 14.

Whitcombe, D. N., 2002, Elastic impedance normalization: Geophysics, 67,60–62, doi: 10.1190/1.1451331.

Whitcombe, D. N., P. A. Connolly, R. L. Reagan, and T. C. Redshaw, 2002,Extended elastic impedance for fluid and lithology prediction: Geophys-ics, 67, 63–67, doi: 10.1190/1.1451337.

Wiggins, R., G. S. Kenny, and C. D. McClure, 1983, A method for deter-mining and displaying the shear-velocity reflectivities of a geologic for-mation: European Patent Application 0113944.

Xu, H., W. Zhou, R. Xie, L. Da, C. Xiao, Y. Shan, and H. Zhang, 2016,Characterization of rock mechanical properties using lab tests and numeri-cal interpretation model of well logs: Mathematical Problems in Engineer-ing, 2016, Article ID 5967159, 1–13.

Xu, S., and M. A. Payne, 2009, Modeling elastic properties in carbonaterocks: The Leading Edge, 28, 66–74, doi: 10.1190/1.3064148.

Yenwongfai, H. D., N. H. Mondol, J. I. Faleide, and I. Lecomte, 2017,Prestack simultaneous inversion to predict lithology and pore fluidin the Realgrunnen Subgroup of the Goliat Field, southwesternBarents Sea: Interpretation, 5, no. 2, SE75–SE96, doi: 10.1190/INT-2016-0109.1.

Zhen-Ming, P., L. Ya-Lin, W. Sheng-Hong, H. Zhen-Hua, and Z. Yong-Jun,2008, Discriminating gas and water using multi-angle extended elasticimpedance inversion in carbonate reservoirs: Chinese Journal of Geo-physics, 51, 639–644, doi: 10.1002/cjg2.v51.3.

Zoback, M., 2007, Reservoir geomechanics: Cambridge University Press.

R446 Sharifi et al.

Dow

nloa

ded

04/2

1/19

to 9

1.98

.194

.134

. Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/