Inspiration for Seismic Diffraction Modelling, Separation, and Velocity

applied sciences

Article Inspiration for Seismic Diﬀraction Modelling, Separation, and Velocity in Depth Imaging

Yasir Bashir 1,2,* , Nordiana Mohd Muztaza 1, Seyed Yaser Moussavi Alashloo 3 , Syed Haroon Ali 4 and Deva Prasad Ghosh 2

1 School of Physics, Universiti Sains Malaysia, USM, Penang 11800, Malaysia; [email protected] 2 Centre for Seismic Imaging (CSI), Department of Geosciences, Universiti Teknologi PETRONAS, Seri Iskandar 32610, Malaysia; [email protected] 3 Institute of Geophysics, Polish Academy of Sciences, 01-452 Warsaw, Poland; [email protected] 4 Department of Earth Sciences, University of Sargodha, Sargodha 40100, Pakistan; [email protected] * Correspondence: [email protected] or [email protected]; Tel.: +60-16-2504514

Received: 7 April 2020; Accepted: 8 May 2020; Published: 26 June 2020

Abstract: Fractured imaging is an important target for oil and gas exploration, as these images are heterogeneous and have contain low-impedance contrast, which indicate the complexity in a geological structure. These small-scale discontinuities, such as fractures and faults, present themselves in seismic data in the form of diffracted waves. Generally, seismic data contain both reflected and diffracted events because of the physical phenomena in the subsurface and due to the recording system. Seismic diffractions are produced once the acoustic impedance contrast appears, including faults, fractures, channels, rough edges of structures, and karst sections. In this study, a double square root (DSR) equation is used for modeling of the diffraction hyperbola with different velocities and depths of point diffraction to elaborate the diffraction hyperbolic pattern. Further, we study the diffraction separation methods and the effects of the velocity analysis methods (semblance vs. hybrid travel time) for velocity model building for imaging. As a proof of concept, we apply our research work on a steep dipping fault model, which demonstrates the possibility of separating seismic diffractions using dip frequency filtering (DFF) in the frequency–wavenumber (F-K) domain. The imaging is performed using two different velocity models, namely the semblance and hybrid travel time (HTT) analysis methods. The HTT method provides the optimum results for imaging of complex structures and imaging below shadow zones.

Keywords: diﬀraction modelling; double square root equation; travel time; dip frequency ﬁltering; migration

1. Introduction Seismic diffraction events are produced because of small-scale elements in the subsurface, such as faults, fractures, channels, and rough edges of salt bodies; or because of small changes in the seismic reflectivity, such as those produced by fluid occurrence or fluid movement in the period of production. These diffracted waves contain the most important information for subsurface discontinuities [1]. The diffraction theory sometimes makes it impossible to understand the qualitative properties of diffraction phenomena [2]. Further, these diffraction data are also used for travel time approximation for anisotropic imaging [3]. The separation of diffraction is widely used [4–7] for enhancement of seismic imaging, such as fault, fracture, complex variable velocity structure, and karstification imaging [8]. Further, the diffraction response for a nonzero separation of the source and receiver was presented by Berryhill in 1977 [9], in which theoretical support was obtained for applying the zero-separation theory to stack the seismic data. Amplitude preservation of seismic waves was achieved by Hilterman in

Appl. Sci. 2020, 10, 4391; doi:10.3390/app10124391 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 15 Appl. Sci. 2020, 10, 4391 2 of 15 waves was achieved by Hilterman in 1975 [10] by using the front sweep velocity approach, in which a graphical method evolves. The last decade was devoted to theoretical work and many methods 1975 [10] by using the front sweep velocity approach, in which a graphical method evolves. The last were introduced, however the lack of implementation in the real world was limited due to computing decade was devoted to theoretical work and many methods were introduced, however the lack of power and facilities. In this decade, the computation increased drastically and the technology implementation in the real world was limited due to computing power and facilities. In this decade, development increased compared to the last decade. Diffraction enhancement in prestack seismic the computation increased drastically and the technology development increased compared to the data was introduced by Bansal in 2005 [11]. He introduced the most effective techniques, which last decade. Diffraction enhancement in prestack seismic data was introduced by Bansal in 2005 [11]. involve the decomposition of seismic gather data into eigensections and flows based on radon He introduced the most effective techniques, which involve the decomposition of seismic gather transformations. Diffraction imaging using the multifocusing method was used in 2009 by Berkovitch data into eigensections and flows based on radon transformations. Diffraction imaging using the [12], in which the diffraction focusing stack (DMFS) was used to separate the diffraction energy in a multifocusing method was used in 2009 by Berkovitch [12], in which the diffraction focusing stack stack section and defocus the reflection energy over a large area. Diffraction separation has been (DMFS) was used to separate the diffraction energy in a stack section and defocus the reflection energy widely used by Fomel since 2002 [13] using the Claerbout principle [14], and has contributed to the over a large area. Diffraction separation has been widely used by Fomel since 2002 [13] using the field of seismic diffraction imaging. Claerbout principle [14], and has contributed to the field of seismic diffraction imaging. Diffraction hyperbolic patterns occur frequently in seismic sections, and their existence is Diffraction hyperbolic patterns occur frequently in seismic sections, and their existence is usually usually taken as evidence of abrupt discontinuities in the subsurface reflector geometry [10]. taken as evidence of abrupt discontinuities in the subsurface reflector geometry [10]. Geophysicists Geophysicists understand ray path geometry; for every “point” diffractor, the edge of the reflector understand ray path geometry; for every “point” diffractor, the edge of the reflector and fault give and fault give rise to a hyperbolic pattern in a zero-offset section [9]. In an inclined case, a series of rise to a hyperbolic pattern in a zero-offset section [9]. In an inclined case, a series of diffractions are diffractions are originated along the fault surface so that the apex of each curve is on the fault plane. originated along the fault surface so that the apex of each curve is on the fault plane. A conventional processing workflow suppresses the diffractions and enhances the reflections. A conventional processing workflow suppresses the diffractions and enhances the reflections. Diffracted and reflected seismic waves are fundamentally different physical phenomena [15]. As Diffracted and reflected seismic waves are fundamentally different physical phenomena [15]. As shown shown in Figure 1, the source and receiver are on the surface. Once they are active, the reflections are in Figure1, the source and receiver are on the surface. Once they are active, the reflections are recorded recorded on a continuous reflector and a diffraction hyperbola is produced at the edges. This is on a continuous reflector and a diffraction hyperbola is produced at the edges. This is because of because of the lateral acoustic impendence contrast. Further diffraction hyperbolas have positive to the lateral acoustic impendence contrast. Further diffraction hyperbolas have positive to negative negative amplitudes, which generally decrease with time. The common practice during processing is amplitudes, which generally decrease with time. The common practice during processing is that that reflected waves are tuned and diffracted waves are suppressed by being considered as noise, but reflected waves are tuned and diffracted waves are suppressed by being considered as noise, but these these diffracted events carry the most important information about the subsurface. diffracted events carry the most important information about the subsurface.

FigureFigure 1. 1. GraphicalGraphical representation representation of the didiffractionﬀraction phenomenon phenomenon with with the the geometry geometry of of the the source source and

andreceiver receiver functions functions produced produce atd the at edgesthe edge of thes of reﬂectors the reflectors (D1 and (D1 D2). and AD2). phase A phase change change of 180 of◦ is 180° shown is shownon either on either side of side the of curves the curves [16]. .[16]

TheThe separati separationon of of seismic seismic diffraction diffraction is is not not an an innovative innovative idea. idea. A A previous previous study study [17] [17 ]used used diffractiondiffraction to to estimate estimate the the velocity velocity from from forward forward mode modelingling and andthe local the localslant stack. slant stack.Another Another study [18]study used [18 a] common used a common diffraction diff poinractiont section point for section imaging for imagingof diffraction of di ffenergyraction and energy detecti andon detection of local heterogeneitiesof local heterogeneities,, while another while study another [19] study simulate [19]d simulated diffraction di responsesffraction responsesto enhanc toe the enhance velocity the analysis.velocity analysis. InIn this this paper, paper, we we have have developed developed a aunique unique approach approach by by integrating integrating the the previous previous solution solutionss used used forfor m multipleultiple eliminations. eliminations. This This method method can can separate separate diffraction diffraction energy energy and and suppress suppress the the reflection reflection amplitudeamplitude,, which is is necessary necessary for for Amplitude Amplitud versuse versus offset offset (AVO) (AVO) analysis analysis [20]. For [20] imaging. For imagingpurposes, purposes,a simple anda simple fast methodand fast is method used, which is used, follows which the follows one-way the waveone-way equation wave equation migration, migration as explained, as Appl. Sci. 2020, 10, 4391 3 of 15

Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 15 below. We started with the zero-offset or processed stacked seismic data as the input and applied the Fourierexplained transform below. to We convert started our with data the fromzero- theoffset time or processed domain to stacked the frequency seismic data domain. as the input and applied the Fourier transform to convert our data from the time domain to the frequency domain. 2. Materials and Methods 2. Materials and Methods 2.1. Diffraction Modelling 2.1.The Dif principlefraction Modelling of the di ffraction theory is mainly based on the subsurface behaving similarly to acousticThe media. principle This of means the diffraction that shear theory waves is aremainly not consideredbased on the for subsurface diffraction behaving studies; similarly only primary to wavesacoustic cause media. the production This means of that diff shearraction waves with are low not reflectivity considered andfor diffraction constant velocity.studies; only The primary scalar wave equationwaves iscause used the to production satisfy the of wave diffracti equation.on with The low reflectorreflectivity is and an ensemble constant velocity. of individual The scalar elements wave and theequation response is is used the sumto satisfy or integration the wave equation. of each element.The reflector The is zero-o an ensembleffset solution of individual is available elements and and further planningthe response to extended is the forsum the or nonzero-o integrationff set. of each element. The zero-offset solution is available and further planning to extended for the nonzero-offset. When the source and receiver are separated, the envelope of arrival times (diffraction curve) has a When the source and receiver are separated, the envelope of arrival times (diffraction curve) has different shape due to the increased travel times. This can be explained by the “double square root a different shape due to the increased travel times. This can be explained by the “double square root equation (DSR)” for travel time, which is: equation (DSR)” for travel time, which is: s 푥 s 푥 푇푚 2 퐿L− x 2 푇푚 2 퐿L + x 2 √ Tm 2 222 √Tm 2 22 2 (1) T푇퐿 = ( ))++ [ [ − ] ] ++ ( ( )) ++ [ ]] (1) L 22 푉V 22 푉V where Tm is the time, V is the velocity, and x is the separation between the normal incident (single where Tm is the time, V is the velocity, and x is the separation between the normal incident (single square root equation) and the separated shot receiver (double square root equation). The curve is square root equation) and the separated shot receiver (double square root equation). The curve is greatest at the observation location over the point source. At location L, the velocity becomes smooth L greatestand Equation at the observation (1) simplifies location into: over the point source. At location , the velocity becomes smooth and Equation (1) simplifies into: r 퐿22 √ 2 L T푇L퐿 == Tm푇푚 + (2) (2) 푉V22 TheTh abovee above is is the the usual expression expression used used for for reflection reflection times times from afrom horizontal a horizontal reflector. reflector.This Thisobservation observation forms forms the the basis basis of the of velocity the velocity determination determination method. method. UsingUsing Equation Equation (2) (2) in in MATLAB, MATLAB, wewe observedobserved the the behavior behavior ofof diffraction diffraction hyperbola hyperbola by taking by taking differentdifferent background background velocity velocity values, values, such such asas 2000,2000, 3500, and and 5000 5000 m/sec m/sec,, as as shown shown in Figure in Figure 2. 2.

FigureFigure 2. Di2. ﬀDiffractionraction hyperboloids hyperboloids withwith constant velocity velocity at at:: (a) ( a2000) 2000 m/s mec,/sec, (b) (3500b) 3500 m/sec, m/ sec,and and(c) (c) 50005000 m/sec. m/sec. The The curvature curvature of of the the hyperboloids hyperboloids is spread spread out out with with an an increase increase of velocity. of velocity. Appl. Sci. 2020, 10, 4391 4 of 15

Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 15 We model the 3D diffraction curves on a point diffractor of different velocities. Figure2 explains We model the 3D diffraction curves on a point diffractor of different velocities. Figure 2 explains the hyperbolic pattern of diffraction concerning offset and depth; as the depth increases, the curvature the hyperbolic pattern of diffraction concerning offset and depth; as the depth increases, the of the hyperbola is smothered. The effect of velocity can be found by comparing Figure2a–c. The scale curvature of the hyperbola is smothered. The effect of velocity can be found by comparing Figure 2a– of all parts of the hyperbolas is the same on the X-axis (offset) and Y-axis (depth), but there is a change c. The scale of all parts of the hyperbolas is the same on the X-axis (offset) and Y-axis (depth), but of the velocity in the point diffractor. Velocity directly affects the diffraction hyperbolic curvature, such there is a change of the velocity in the point diffractor. Velocity directly affects the diffraction ashyperbolic in a high-velocity curvature, area. such Theas in di aff highraction-velocity pattern area is.more The diffraction complex and pattern more is dimorefficult complex to interoperate and duringmore difficult processing. to interoperate Separation during of diff processing.raction events, Separation which areof diffraction complex inevents, deeper which regions, are complex will be more diinffi deepercult because regions, of will their be similaritymore difficult with because reflection of their data. similarity with reflection data. Further,Further, we extend ou ourr algorithm algorithm from from constant constant velocity velocity to tovariable variable velocity. velocity. Increasing Increasing and and decreasingdecreasing velocityvelocity didiffractionffraction behavior can can be be observed in in Figure Figure 33a,ba,b,, respectively. The shape of the ditheffraction diffraction curve curve at 1000 at 1000 m/ secm/sec velocity velocity changes changes as as the the depth depth changes. changes. ThisThis analysisanalysis indicates indicates that that the ditheffraction diffraction curve curve is not is not only only dependent dependent on on velocity velocity but but also also on on depth. depth.

FigureFigure 3. 3. DiffractionDiffraction hyperboloids: hyperboloids: (a) increasing (a) increasing velocity velocity with depth with and depth (b) anddecreasing (b) decreasing velocity with velocity withdepth. depth. 2.2. Dip Frequency Filtering 2.2. Dip Frequency Filtering FilteringFiltering is a a well well-known-known method method used used toto separate separate seismic seismic events events that that are areavailable available in the in seismic the seismic data,data, using the suitable suitable apparent apparent velocity velocity as as the the selection selection criterion. criterion. The The gradient gradient of apparent of apparent velocity, velocity, VVappapp == dx/dt,dx/dt, will will give give the the arrivals arrivals for for the the seismic seismic data data section. section. TheThe one-dimensionalone-dimensional Fourier Fourier transform transform F(Fu)( uof) ofa single a single variable, variable, namely namely a continuous a continuous function function ff(x),), is defined defined by by the the following following equation equation [21] [21: ]: ∞Z 퐹(푢) = ∫ 푓(∞푥) exp (−푗2휋푢푥)푑푥 F(u) = f (x) exp ( j2πux)dx (3) (3) −∞ − −∞ where = √−1. Conversely, given F(u), we can obtain f(x) by employing the inverse Fourier transform, where = √ 1. Conversely, given F(u), we can obtain f (x) by employing the inverse Fourier transform, as given below− : as given below: Z∞ 푓(푥) = ∫ 퐹∞(푢) exp (푗2휋푢푥) (4) f (x) =−∞ F(u) exp (j2πux) (4) These two equations contain the pair of Fourier−∞ transforms and were used to convert our data These two equations contain the pair of Fourier transforms and were used to convert our data from the time domain to the frequency domain. They were easily extended to the two variables u and from the time domain to the frequency domain. They were easily extended to the two variables u v. and v. For the illumination of the coherent wavefront of the constant amplitude, the distribution of the For the illumination of the coherent wavefront of the constant amplitude, the distribution of the amplitude in the spatial frequency spectrum b(x, y) and the object plane B(u, v) can be defined by amplitudeusing the inverse in the spatialFourier frequency transform spectrum[22]: b(x, y) and the object plane B(u, v) can be defined by using the inverse Fourier transform∞ [22]:∞ 푏(푥, 푦) = ∫ . Z∫ 퐵(Z푢, 푣) exp (−푖2휋(푢푥 + 푣푦)) 푑푢 푑푣 (5) ∞ ∞ b(x, y)− =∞ −∞ . B(u, v) exp ( i2π(ux + vy)) du dv (5) − ⇌ Alternatively, it can be explained−∞ −∞using a simplified notation, where shows the pair of Fourier transforms. Appl. Sci. 2020, 10, 4391 5 of 15

Alternatively, it can be explained using a simpliﬁed notation, where shows the pair of Fourier transforms. b(x, y) B(u, v) (6)

A spatial frequency spectrum is deﬁned as the description of the image forming process.

B0(u0v0) b(x, y). a(x, y) (7)

= B0(u0, v0) ∗ A (u0v0) (8) where A (u0v0) a(x, y) is called the spread function, the * symbol shows the convolution, and (u0, v0) are the coordinates of the spectrum window for magnification of the filter amplitude. Filtering is applied to the frequency–wavenumber (F-K) spectrum to separate the diffracted events from the reflection data by defining a filter, in which slopes monotonically increase and amplitudes of the data correspond to the slopes of dipping events, for example in an inclined structure:

dt 1 Slope = = (9) dx Vapp

2.3. Diffraction Separation The underlying hypothesis works for modeling and separating the diffracted events from the reflection seismogram. In zero-offset or stack data, the reflection events have a higher and strong amplitude. Removing those events exposes other comprehensible information, often in the form of seismic diffraction. We applied the Fourier transform and converted our data from the time domain to the frequency domain. The F-K spectrum is the sketch of the amplitude distribution with the wave number. Through minimizing the forecast for outstanding work, many iterative tasks were performed whilst developing the local slope filter to remove the specular reflection from the seismic data. An equivalent impression with an application based on the prediction error filters was investigated by Claerbout (1994). Even though separation of reflection and diffraction energy is never precise, our procedure satisfies the practical purpose of improving the wave response of small subsurface discontinuity, such as for faults, fractures, Karst sections, and unconformities. The obtained research results show that the goals of filtering and separating the diffraction from full-wave seismic data were achieved.

2.4. Imaging Diffraction The various imaging algorithms used for the wave equation revealed similar structural imaging; however, the same processing capabilities and faster implementation were considered using these techniques. Here, we used a constant velocity earth model, while for imaging purposes the Stolt migration method was used. Corresponding to other migration methods, this migration method can be retreated and made into a modeling program. One of the drawbacks or limitations in the principle is that the Stolt migration is imitated in the depth variation of the velocity for better imaging. The simplest sketch of the Stolt migration method can be defined by the following equations after applying the idea that the migrated image at the location of (x, z) is the exploding reflector wave at time t = 0: r 2 w 2 kz = k (10) ∓ v2 − x     v k  v q  z  2 2 P(kx, kz, t = 0) =  q P kx, 0, ω = ky + kz (11) 2 2 2  2  kx + kz  Appl. Sci. 2020, 10, 4391 6 of 15

Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 15 where P (kx, z = 0, ω) is the zero-offset section and P (kx, kz, t = 0) is the migrated section in the frequency–wavenumberIn the southeast Asian domain. basins, there are several geophysical challenges [23]. Some of them are listed below: 2.5. Regional Geology  Imaging thin sands, which is often beyond seismic resolution;  In theImaging southeast below Asiangas clouds basins,; there are several geophysical challenges [23]. Some of them are listed below:Karst imaging in carbonate fields;  Fractured basement imaging and its internal architecture;  ImagingUnderstanding thin sands, the which wave propagation is often beyond of ineffective seismic resolution;media and related anisotropy; •  ImagingVelocity below analysis gas and clouds; anisotropy; •  KarstMultiple imaging eliminations in carbonate; fields; •  FracturedDiffraction basement imaging imaging for small and-scale its events internal. architecture; • UnderstandingThe focus of this the research wave propagation is to image the of fractures ineffective that media are the and main related challenges anisotropy; faced in the field, • includingVelocity fractured analysis basement and anisotropy;s, fracture distribution, connectivity, and lateral variation, which cause • poor seismic imaging. Multiple eliminations; • A regional map of the Malaysian basin is shown in Figure 4a—on the left side is the Malay Basin, Diffraction imaging for small-scale events. • the right side shows the Sabah Basin, and the below-right side shows the Sarawak Basin. TheAs focus mentioned, of this research our objectives is to image are to the foc fracturesus on fractures, that are so the in main this study challenges the Malay faced B inasin the is field, includingconsidered. fractured A regional basements, cross- fracturesection of distribution, the Malay connectivity, Basin is shown and in lateral Figure variation, 4b,c. As whichalready cause mentioned, the difference between a good well and a dry well is whether it encounters main fracture poor seismic imaging. corridors, which must be known before drilling. However, the identification of fractures is impossible A regional map of the Malaysian basin is shown in Figure4a—on the left side is the Malay Basin, without imaging the fractured basement, and these complex structures cannot be identified by theconventional right side shows imaging the alone. Sabah Basin, and the below-right side shows the Sarawak Basin.

Figure 4. (a) Geographical map of the Malay Basin. Shown are the provinces of Peninsular in the Malay Figure 4. (a) Geographical map of the Malay Basin. Shown are the provinces of Peninsular in the Basin,Malay Sarawak, Basin, Sarawak, and Sabah and Basin Sabah [24 Basin]. The [24] Malay. The BasinMalay subsurfaceBasin subsurface structure struc shownture shown with with a regional a cross-section view. (b) South-west to north-south section. The fractured basement can be seen at a depth of 2–5 km and varies with lateral extension. (c) North-west to south-east section [5]. Appl. Sci. 2020, 10, 4391 7 of 15

As mentioned, our objectives are to focus on fractures, so in this study the Malay Basin is considered. A regional cross-section of the Malay Basin is shown in Figure4b,c. As already mentioned, the difference between a good well and a dry well is whether it encounters main fracture corridors, which must be known before drilling. However, the identification of fractures is impossible without imaging the fractured basement, and these complex structures cannot be identified by conventional imaging alone.

3. Results and Discussion

3.1. Detection of Faults and Fractures In general geology, a fracture is any kind of separation or break in a rock formation. Examples are joints or faults in which the formation is divided into two or more pieces [25]. In geology, fracture is a broad term that includes faults, fractures, and discontinuities. These fractures can provide access for fluids, such as water or hydrocarbons, to move into the rocks [26]. Therefore, the model shown in Figure5a is the fractured basement model from the Malay Basin. The number of faults and fractures present in the igneous basement are a challenge for seismic imaging. This field produces oil from the fractured basement. For simplicity in testing the diffraction imaging algorithm and concept, weAppl. extracted Sci. 2020, 10 a, partx FOR of PEER the REVIEW fractured model, which is shown in Figure5b. 8 of 15

FigureFigure 5.5. ((aa)) MalayMalay BasinBasin ﬁeld, field, which which contains contains extensive extensive faults faults and and fractures fractures in in the the igneous igneous basement basement [28 ]. ([28b) Input]. (b) Input initial initial velocity velocity model model for seismic for seismic analysis analysis [8]. [8].

A finite difference modeling technique is performed to generate the gather data using a zero-offset configuration. Figure6a shows the zero-o ffset section; diffractions are produced at the edges of the reflector and a series of diffraction curves appear on the fault plane. The amplitude of the hyperbola decreases with increasing depth because of the attenuation factor. Furthermore, the curvature of the hyperbola is higher in the shallow section than in the deeper section. A 3D projection of the hyperbolic curves is shown in Figures2 and3, which describe the fundamentals of the di ffraction with respect to velocity and depth. The frequency–wavenumber (F-K) analysis is a standard array technique that simultaneously calculates the power distributed among different speeds and directions of approach [27]. Figure6b shows the results in the F-K domain for the zero-offset data. Here, we can see that the amplitude from the reflection occurs at a speed of zero cycles per second. Further, the diffraction amplitude is shown away from zero with the lower amplitude. The filter, which is designed based on the dip of the frequency cut-off, removes the reflection and preserves the diffraction only by looking into the spectrum. This filter was design based on trial and error analysis. Finally, the output of the filter is shown in Figure6c. Figure6d shows the di ffraction section, which is achieved by DFF. The reflection is removed and diffraction is enhanced. A series of diffractions appears on the fault plane. Diffraction stacking can help in fault interpretation.

Figure 6. (a) Seismic response of the input velocity model; a series of diffractions are generated at the fault location. (b) The frequency–wavenumber (F-K) spectrum, which shows the amplitude distribution with wave cycles per kilometer. (c) F-K spectrum after application of the designed filter; only the diffraction amplitude is displayed, while the reflection amplitude has been removed. (d) After separation using the DFF filtering algorithm, diffractions are preserved and reflections are successfully suppressed. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 15

Figure 5. (a) Malay Basin field, which contains extensive faults and fractures in the igneous basement Appl. Sci. 2020, 10, 4391 8 of 15 [28]. (b) Input initial velocity model for seismic analysis [8].

Figure 6. (a) Seismic response of the input velocity model; a series of diffractions are generated Figure 6. (a) Seismic response of the input velocity model; a series of diffractions are generated at the at the fault location. (b) The frequency–wavenumber (F-K) spectrum, which shows the amplitude fault locationdistribution. (b) withThe wave frequency cycles per–wavenumber kilometer. (c ) F-K(F-K spectrum) spectrum, after application which shows of the designed the amplitude distributionfilter; with only wave the di ffcycleractions per amplitude kilometer is displayed,. (c) F-K while spectrum the reflection after application amplitude has of been the removed.designed filter; only the (diffractiond) After separation amplitude using theis displayed DFF filtering, while algorithm, the direflectionffractions are amplitude preserved andhas reflectionsbeen removed are . (d) After separationsuccessfully using suppressed. the DFF filtering algorithm, diffractions are preserved and reflections are successfullyDiff ractionsuppressed stacking. or imaging can add information to an interpreter for fault and fracture identification. The Stolt migration is applied to the diffraction and reflection data, which are shown in Figure7a,b. The di ffractions are imaged properly and the point diffractions show the locations of the faults and a probable discontinuous surface. Figure7b shows the migrated synthetic seismic data without diffraction separation; not all of the components of the faults are illuminated, as desired. Furthermore, separating the diffractions would help us to interpret the faults, as the apex of each diffraction shows the continuity of the fault plane. Figure7c is the amplitude spectrum of the migrated data in the time–distance (t-x) domain, which shows the amplitude distribution with the trace number. At the fault location, the amplitude is very low or near to zero because most of the migration algorithms kill the diffractions that are considered as noise. In this context, diffraction separation is needed to improve the imaging results. Appl. Sci. 2020, 10, 4391 9 of 15 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15 Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 15

Figure 7. ((aa)) Migrated Migrated seismic seismic section, section, The The point point diffractor diffractor shows the location of the discontinuity and Figure 7. (a) Migrated seismic section, The point diffractor shows the location of the discontinuity and the fault indicator. indicator. (b (b) )Full Full-wave-wave seismic seismic migrated migrated section; section; all all components components of the of the fault fault are aremissing missing.. (c) the fault indicator. (b) Full-wave seismic migrated section; all components of the fault are missing. (c) (Amplitudec) Amplitude spectrum spectrum (frequency (frequency bandwidth) bandwidth) of ofthe the migrated migrated data data,, show showinging that that the the didiffractionffraction Amplitude spectrum (frequency bandwidth) of the migrated data, showing that the diffraction amplitude is biased. amplitude is biased. 3.2. Generalized Workflow 3.2. Generalized Workflow 3.2. GeneralizeThis workd presentsWorkflow a simple and robust approach based on a frequency domain algorithm This work presents a simple and robust approach based on a frequency domain algorithm along alongThis with work a user-friendly presents a simple interface. and robust Usually, approach in a stack based data, on the a frequency reflection domain events havealgorithm higher along and with a user-friendly interface. Usually, in a stack data, the reflection events have higher and stronger withstronger a user amplitudes.-friendly interface Removing. Usually, those in events a stack exposes data, the other reflection comprehensible events have information, higher and stronger often in amplitudes. Removing those events exposes other comprehensible information, often in the form of amplitudes.the form of Removing seismic di thoseffraction. events After exposes using other a Fourier comprehensible transform information, to convert often our datain the from form the of seismic diffraction. After using a Fourier transform to convert our data from the time domain into seismictime domain diffraction. into theAfter frequency using a Fourier domain, transform the F-K (frequency–wavenumber)to convert our data from the spectrum time domain shows into the the frequency domain, the F-K (frequency–wavenumber) spectrum shows the amplitude distribution theamplitude frequency distribution domain, the with F-K the (frequency wavenumber.–wavenumber) Through spectrum minimizing shows the the forecast amplitude for outstandingdistribution with the wavenumber. Through minimizing the forecast for outstanding work, many iteration tasks work,with the many wavenumber. iteration tasks Through were m performedinimizing the whilst forecast developing for outstanding the local work, slope many filter foriteration separation tasks were performed whilst developing the local slope filter for separation of specular reflection from the wereof specular performed reflection whilst from developing the full-wave the loca seismicl slope behavior, filter for separation which is based of specular on equivalent reflection impression from the full-wave seismic behavior, which is based on equivalent impression and prediction error filters fulland-wave prediction seismic error behavior, filters [which5,29]. The is based separation on equivalent of reflection impression and di ff andraction prediction energy error is accurate, filters [5,29]. The separation of reflection and diffraction energy is accurate, as this method accommodates [5,as29 this]. The method separation accommodates of reflection wave and responses diffraction from energy small is subsurface accurate, as discontinuities, this method accommodates such as faults, wave responses from small subsurface discontinuities, such as faults, fractures, karst sections, and wavefractures, responses karst sections, from small and subsurface unconformities, discontinuities which appear, such as as di fffaults,raction fractures, in the data. karst The section uniquenesss, and unconformities, which appear as diffraction in the data. The uniqueness of our methodology is the unconformitiesof our methodology, which is appear the integration as diffraction of essential in the approachesdata. The uniqueness for diffraction of our modeling, methodology separation, is the integration of essential approaches for diffraction modeling, separation, and imaging. A generalized integratand imaging.ion of Aessential generalized approaches workflow for diffraction and steps takenmodeling, to perform separation, diffraction and imaging. separation A generalized for data are workflow and steps taken to perform diffraction separation for data are given below. workflowgiven below. and steps taken to perform diffraction separation for data are given below.  Generate a velocity model, i.e., the fractured or Marmousi model;  GenerateGenerate a a velocit velocityy model, model, i.e. i.e.,, the the fractured fractured or or Marmousi model model;;  Use finite difference wave propagation to record the seismic behavior in the provided geological  Use finite difference wave propagation to record the seismic behavior in the provided geological modelUse finite; difference wave propagation to record the seismic behavior in the provided model;  Ingeological the case model;of raw data from the field, initial processing is needed to improve the data quality  In the case of raw data from the field, initial processing is needed to improve the data quality (includingIn the case sorting, of raw dataCDP fromordering, the field, NMO initial correction, processing and stacking, is needed if tothe improve data are theprestack data qualityed); (including sorting, CDP ordering, NMO correction, and stacking, if the data are prestacked);  Apply(including a Fourier sorting, transform CDP ordering, to observe NMO the correction, spectrum andof amplitude stacking, ifdis thetribution data are in prestacked); the frequency  Apply a Fourier transform to observe the spectrum of amplitude distribution in the frequency wavenumberApply a Fourier; transform to observe the spectrum of amplitude distribution in the wavenumber;  Designfrequency the wavenumber;filter based on the dip component of the data in the dt/dx plane;  Design the filter based on the dip component of the data in the dt/dx plane;  ConvolutDesign thee the filter proposed based on dip the frequency dip component filter (DFF) of the with data seismic in the dt data/dx plane;to separate the diffraction  Convolute the proposed dip frequency filter (DFF) with seismic data to separate the diffraction fromConvolute reflection the; proposed dip frequency filter (DFF) with seismic data to separate the diffraction from reflection;  Applyfrom reflection; an inverse Fourier transform to convert the frequency–wavenumber data into the time–  Apply an inverse Fourier transform to convert the frequency–wavenumber data into the time– distanceApply an domain. inverse Fourier transform to convert the frequency–wavenumber data into the distance domain. time–distance domain. 3.3. Marmousi Model 3.3. Marmousi Model Appl. Sci. 2020, 10, 4391 10 of 15

Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 15 3.3. Marmousi Model Appl.The Sci. 20Marmousi20, 10, x FOR model PEER REVIEW was generated at the Institute Francais du Petrole (IFP) and is used10 of to 15 test imagingThe tools Marmousi to improve model and was enhance generated imaging at the- Instituterelated algorit Francaishms. du The Petrole original (IFP) Marmousi and is used data to testset The Marmousi model was generated at the Institute Francais du Petrole (IFP) and is used to test isimaging generated tools using to improve a 2-D acoustic and enhance finite imaging-relateddifference modeling algorithms. program The [8] original. Marmousi data set is imaging tools to improve and enhance imaging-related algorithms. The original Marmousi data set generatedThe seismic using aimaging 2-D acoustic target finite zone di isff erencea reservoir modeling located program at a depth [8]. of about 2500 m. The model is generated using a 2-D acoustic finite difference modeling program [8]. containsThe many seismic reflectors, imaging steep target dips, zone and is a strong reservoir velocity located variations at a depth in ofboth about the 2500lateral m. and The vertical model The seismic imaging target zone is a reservoir located at a depth of about 2500 m. The model contains many reflectors, steep dips, and strong velocity variations in both the lateral and vertical directioncontainss many(with areflectors, minimum steep velocity dips, ofand 1500 strong m/s velocityand a maximum variations velocity in both ofthe 5500 lateral m/s). and vertical directionsdirectionFigures (with (with8a shows aa minimumminimum the Marmousi velocity of ofmodel 1500 1500 m/sin m /thes and and ( xa- azmaximum) maximum domain, velocity which velocity ofcontains of5500 5500 m/s). a m huge/ s). number of faultsFigure Figureand folds,8 a8a shows shows representing thethe MarmousiMarmousi a challenging model in indistribution the the ( (x-xz-)z )domain, domain, of velocity which which anomalies contains contains a and huge a hugediscontin number numberuities. of of Thefaultsfaults configuration and and folds,folds, representingrepresenting of the survey a a challenging challenging was set up distribution distribution as an end -ofon ofvelocity shooting velocity anomalies anomalies geometry, and and and discontin discontinuities. the datauities. were recordedTheThe configuration configuration in the shot of ofdomain, the the survey survey as wasshown was set set upin Figure upas an as end-on an8b. endExtensive shooting-on shooting processing geometry, geometry, for and improving the and data the were data the signal recordedwere to noiseinrecorded the shot ratio in domain, andthe shot suppressing as domain, shown as in shown dispersionFigure 8inb. Figure Extensive artifacts 8b. Extensive processing is applied processing for to improving the for raw improving the data signal forthe to signal diffractionnoise to ratio enhancement.andnoise suppressing ratio andA dispersionclose suppressing-up of artifacts data dispersion for is the applied three artifacts to shots the rawis is apshown dataplied for in to di Figureff theraction raw 9 enhancement.before data forand diffractionafter A close-upnormal moveoutofenhancement. data for (NMO) the threeA correction,close shots-up of is which showndata for shows in the Figure three a flatness9 shotsbefore of is and moveoutshown after in normal inFigure the gather 9 moveout beforeed data.and (NMO) after correction,normal whichmoveout shows (NMO) a flatness correction, of moveout which shows in the a gathered flatness of data. moveout in the gathered data.

Figure 8. (a) Marmousi velocity model with a velocity range from 1650 to 4600 m/sec. Three major FigureFigure 8.8. ((aa)) MarmousiMarmousi v velocityelocity m modelodel with with a avelocity velocity range range from from 1650 1650 to to4600 4600 m/sec. m/sec. Three Three major major faults containing unconformity and overburden cause complexity in the velocity model for anticline faultsfaults containing containing unconformity and and overburden overburden cause cause complexity complexity in inthe the velocity velocity model model for foranticline anticline structurestructures.structures.s. ( (b(bb)) )Synthetic SyntheticSynthetic ss shothothot gather gather data data areare are generated generated generated using using using finite finite ﬁnite difference difference diﬀerence modeling. modeling.

Figure 9. Seismic gather data (a) before the NMO correction and (b) after the NMO correction. Events FigFigureure 9. 9. SeismicSeismic gather gather data data ( (aa)) before before the the NMO NMO correction correction and and ( (bb)) after after the the NMO NMO correction. correction. Events Events are slightly straight at the true reflection points. areare slightly slightly straight straight at at the the true true reflection reflection points. 3.4.3.4. Importance Importance ofof VelocityVelocity for Seismic Depth Depth Imaging Imaging 3.4. Importance of Velocity for Seismic Depth Imaging VelocityVelocity plays plays a a key key role role in in various various aspects aspects of seismicof seismic methods, methods, especially especially in migration,in migration, as aas correct a Velocity plays a key role in various aspects of seismic methods, especially in migration, as a velocitycorrect velocity is needed is needed for proper for proper stacking stacking of the of di theffracted diffracted energy energy from from the flanksthe flanks of the of the hyperbola hyperbola to the correct velocity is needed for proper stacking of the diffracted energy from the flanks of the hyperbola apex,to the as apex well, as forwell the as reflection.for the reflect A velocityion. A velocity field is field essential is essential for field for development field development planes, planes including, toincluding the apex but, as notwell limited as for to: the reflection. A velocity field is essential for field development planes, but not limited to: including but not limited to: a) Gain derivation of wavefield divergence and attenuation; a) Gain derivation of wavefield divergence and attenuation; Appl. Sci. 2020, 10, 4391 11 of 15

(a)Appl. Sci.Gain 2020 derivation, 10, x FOR PEER of wavefield REVIEW divergence and attenuation; 11 of 15 (b) Multiple eliminations, wavefield continuation, or Radon demultiple processes; b) Multiple eliminations, wavefield continuation, or Radon demultiple processes; (c) Seismic imaging for structures and reservoirs; c) Seismic imaging for structures and reservoirs; (d) Lithology prediction through Vp/Vs (Velocity of P-wave and S-wave) and elastic inversion; d) Lithology prediction through Vp/Vs (Velocity of P-wave and S-wave) and elastic inversion; (e) Pressure prediction; e) Pressure prediction; (f)f) Porosity prediction from acousticacoustic impedanceimpedance (AI);(AI); (g)g) TimeTime-epth-epth (T-X)(T-X) conversion;conversion; (h)h) Volumetric calculation;calculation; (i)i) Net sand map plots.plots. VelocityVelocity estimation estimation is a is key a processing key processing parameter. parameter. The sensitivity The sensitivity and accuracy and can accuracy be significantly can be improvedsignificantly with improved the use with of athe long use spread of a long survey spread design survey and design by consumingand by consuming higher-order higher terms.-order Anterms anisotropic. An anisotropic model maymodel be may required be required in certain in geologiccertain geologic situations. situations. ToTo enhanceenhance thethe processingprocessing andand imagingimaging accuracy,accuracy, aa velocityvelocity analysisanalysis waswas performedperformed usingusing twotwo didifferentfferent methods:methods: (1)1) Semblance analysis;analysis; (2)2) Hybrid travel time.time. SemblanceSemblance analysisanalysis isis thethe conventionalconventional way ofof calculatingcalculating velocity during the NMO correction. ItIt allowsallows forfor thethe refinementrefinement ofof seismicseismic data.data. ThisThis isis donedone byby developingdeveloping aa velocityvelocity spectrumspectrum displaydisplay toto determinedetermine thethe velocityvelocity throughthrough didifferentfferent layerslayers atat depth.depth. TheThe velocityvelocity datadata areare usedused toto correctcorrect thethe curvescurves ofof thethe hyperbolashyperbolas andand createcreate aa flatflat line,line, wherewhere allall pointspoints areare at at an an equal equal depth. depth. TheThe hybridhybrid traveltravel timetime methodmethod isis describeddescribed inin Figure 1010,, which shows the raytracing phenomena inin aa complexcomplex andand heterogeneousheterogeneous mediummedium withwith 100100 rays.rays. ParaxialParaxial opticsoptics cancan bebe defineddefined asas ray-tracingray-tracing accomplishedaccomplishedwithin withinthe the limitslimitsof of veryvery smallsmall rayray anglesangles andand heights.heights. ThisThis allowsallows usus toto makemake aa number ofof simplifiedsimplified assumptionsassumptions thatthat makemake thethe raytracingraytracing arithmeticarithmetic considerablyconsiderably easier.easier.

FigureFigure 10.10. TrajectoriesTrajectories of of 100 100 rays rays emitted emitted by by a source a source point point in a in heterogeneous a heterogeneous medium. medium. Shadow Shadow zone andzone multipathing and multipathing eﬀects effect can bes can seen be [ 30seen]. [30].

TheThe eikonaleikonal di differentialfferential equation equation is used is used for the for elementary the elementary mathematical mathematical models, modelswhich describe, which thedescribe travel the time trave (eikonal)l time (eikonal) propagation propagation in a velocity in a velocity model. model. The The benefits benefits of of this this method method inin comparisoncomparison with ray ray tracing tracing techniques techniques are are the the capability capability to to work work in incons consistentistent model model grids, grids, the thewide wide-ranging-ranging coverage coverage of ofthe the receiver receiver space, space, and and the the reasonable reasonable numerical numerical robustness. A commoncommon implementationimplementation ofof thethe finite-difinite-differencefference eikonaleikonal equationequation isis calculatingcalculating thethe first-arrivalfirst-arrival traveltravel timestimes thoughthough frequency-dependentfrequency-dependent enrichment.enrichment. TheThe eikonaleikonal equation,equation, describingdescribing thethe traveltravel timetime propagationpropagation inin anan isotropicisotropic medium,medium, hashas thethe followingfollowing form:form: ( τ)2 = n2(x, y, z) (12) (∇∇휏)2 = 푛2(푥, 푦, 푧) (12) where 휏(푥, 푦, 푧) is the travel time from the source to the receiver point with coordinates (x,y,z) and n is the slowness at that point (the velocity v equal to 1/n) [31]. Appl. Sci. 2020, 10, x FOR PEER REVIEW 12 of 15

This method calculates each travel time table using paraxial raytracing, then in the shadow zone (Figure 10) the travel times are computed by solving the eikonal equation.

3.5. Diffraction Separation and Imaging using Correct Velocity Model After careful consideration of the velocity analysis and stacking process (Figure 11a), the data are ready for DFF as an input. Figure 11b shows the separated diffraction with an enhanced amplitude, which allows the hyperbola to be observed more accurately. For quality control (QC) purposes, full-wave and diffraction difference sections are generated to ensure the accuracy of the algorithm, as shown in Figure 11c. We considered two methods to compare the results of imaging using different velocity modeling techniques. Figure 12a shows the image section using semblance velocity analysis, which was used because of uncertainties in picking the velocity, as this is an interactive process and the chance of error is greater. In this analysis, the three major faults are not imaged and interpretation is difficult. Further, the aim of migration was to delineate the reservoir below 2.5 km, which was not resolved because of velocity error. The second method used for migration is the hybrid travel time method, which incorporates both the eikonal solver and the paraxial raytracing algorithm to calculate the velocity. It also handles the shadow zone and multipathing effects in the data. Figure 12b is a migrated seismic section with an accurate velocity model, which enhances the resolution as well as the structural clarifications.

Further,Appl. Sci. 2020 the, three10, 4391 major faults are interpreted accurately, as the resolution of the data is quite 12good. of 15 One of the unconformities was produced because of erosion in the geological time scale change at the depth of 2.5 km. These types of structures make imaging more complex; for example, below the fracturewhere τ (thex, y ,intervalz) is the velocity travel time and from migration the source of data to the might receiver be wrong. point with Using coordinates the hybrid (x, ytravel,z) and time n is methodthe slowness provides at that accurate point (thevelocity velocity determination v equal to 1 for/n) [migration.31]. The target of our imaging was the reservoirThis, methodwhich at calculates 2.5 km has each an travel anticlinal time tablestructure using. This paraxial was raytracing,imaged properly then in, theas shown shadow in zone the interpreted(Figure 10) thesection travel in timesFigure are 12b. computed by solving the eikonal equation. The amplitude spectrum of the data is generally used to predict reservoir productivity by seismic 3.5. Diffraction Separation and Imaging using Correct Velocity Model imaging, as shown in Figure 13a. his approach uses the data in the time domain, while the output is the amplitudeAfter careful spectrum consideration using a of Fourier the velocity transform. analysis Furthermor and stackinge, a process frequency (Figure spectrum 11a), the is dataplotted are againstready for the DFF three as data an input. sets for Figure quantitative 11b shows evaluation: the separated (a) input diff ractionshot gather with data; an enhanced (b) diffraction amplitude, data; (whichc) migrated allows data the hyperbola (Figure 13b). to be This observed demonstrates more accurately. a low-frequency For quality enhancement control (QC) with purposes, higher amplitudefull-wave and(blue) di,ff whichraction is diveryfference important sections for imaging. are generated A targeted to ensure zone the below accuracy 2.5 km of is the resolved algorithm, and canas shown be interpreted in Figure for 11 c.structural clarifications and for further reservoir characterization.

Figure 11. (a) Common Mid Point (CMP) stacked section after careful processing, including sorting of the gather data from the CMP gather data, amplitude correction, and NMO correction. (b) Diffraction section after application of dip frequency filtering with high amplitude display. Diffracted events are enhanced. (c) Difference or reflection section, showing that consideration of the diffraction is quite important for successful subsurface imaging, especially for faults and fractures.

We considered two methods to compare the results of imaging using different velocity modeling techniques. Figure 12a shows the image section using semblance velocity analysis, which was used because of uncertainties in picking the velocity, as this is an interactive process and the chance of error is greater. In this analysis, the three major faults are not imaged and interpretation is difficult. Further, the aim of migration was to delineate the reservoir below 2.5 km, which was not resolved because of velocity error. The second method used for migration is the hybrid travel time method, which incorporates both the eikonal solver and the paraxial raytracing algorithm to calculate the velocity. It also handles the shadow zone and multipathing effects in the data. Figure 12b is a migrated seismic section with an accurate velocity model, which enhances the resolution as well as the structural clarifications. Further, the three major faults are interpreted accurately, as the resolution of the data is quite good. One of the unconformities was produced because of erosion in the geological time scale change at the depth of 2.5 km. These types of structures make imaging more complex; for example, below the fracture the interval velocity and migration of data might be wrong. Using the hybrid travel time method provides accurate velocity determination for migration. The target of our imaging was the reservoir, which at Appl. Sci. 2020, 10, 4391 13 of 15

2.5 km has an anticlinal structure. This was imaged properly, as shown in the interpreted section in Figure 12b. The amplitude spectrum of the data is generally used to predict reservoir productivity by seismic Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 15 Appl.imaging, Sci. 2020 as, 10 shown, x FOR PEER in Figure REVIEW 13 a. his approach uses the data in the time domain, while the13 output of 15 is theFigure amplitude 11. (a) spectrum Common Mid using Point a Fourier (CMP) stacked transform. section Furthermore, after careful processing a frequency, including spectrum sorting is plotted Figure 11. (a) Common Mid Point (CMP) stacked section after careful processing, including sorting againstof thethe three gather data data sets from for the quantitative CMP gather evaluation: data, amplitude (a) input correction shot gather, and NMO data; correction(b) diﬀraction. (b) data; of the gather data from the CMP gather data, amplitude correction, and NMO correction. (b) (c) migratedDiffraction data section (Figure after 13 applicationb). This demonstrates of dip frequency a low-frequency filtering with high enhancement amplitude display. with higher Diffracted amplitude Diffraction section after application of dip frequency filtering with high amplitude display. Diffracted (blue),events which are isenhanced very important. (c) Difference for imaging.or reflection A section, targeted show zoneing that below consideration 2.5 km is of resolved the diffraction and can be events are enhanced. (c) Difference or reflection section, showing that consideration of the diffraction interpretedis quite forimportant structural for successful clariﬁcations subsurface and for imaging, further especially reservoir for characterization. faults and fractures. is quite important for successful subsurface imaging, especially for faults and fractures.

FigureFigure 12.12. ((aa)) SeismicSeismic migration using prestack prestack Kirchhoff Kirchhoﬀ migration.migration. A A velocity velocity model model was was updated updated Figure 12. (a) Seismic migration using prestack Kirchhoff migration. A velocity model was updated usingusing semblance semblance velocity velocity analysis. analysis. Faults Faults and and anticlinal anticlinal structures structures that that were were our targets our targets are not are imaged. not using semblance velocity analysis. Faults and anticlinal structures that were our targets are not (imaged.b) Migrated (b) M seismicigrated data seismic using data Kirchho usingﬀ depth Kirchhoff migration, depth with migration the hybrid, with travel the hybrid time calculatedtravel time by imaged. (b) Migrated seismic data using Kirchhoff depth migration, with the hybrid travel time thecalculated eikonal by equation the eikonal and equation paraxial and raytracing. paraxial Faultsraytracing. and anticlineFaults and sections anticline in sections the deeper in the section deeper are calculated by the eikonal equation and paraxial raytracing. Faults and anticline sections in the deeper imagedsection are properly. imaged properly. section are imaged properly.

Figure 13. (a) The amplitude spectrum of the migrated data shows a linear distribution of the FigureFigure 13. (a) The The amplitude amplitude spectrum spectrum of theof the migrated migrated data data shows shows a linear a distributionlinear distribution of the amplitude of the amplitude energy. (b) Frequency spectrum of input data (purple), diffraction data (green), and amplienergy.tude (b ) energy Frequency. (b) Frequency spectrum of spectrum input data of (purple), input data di ff (purple),raction data diffraction (green), data and (green), migrated and data migrated data using hybrid travel time (blue). migratedusing hybrid data travelusing timehybrid (blue). travel time (blue). In addition to providing high-resolution seismic data and a better signal-to-noise ratio, velocity InIn addition addition to to providing providing high high-resolution-resolution seismic seismic data data and and a better a better signal signal-to-noise-to-noise ratio, ratio, velocity velocity information about the subsurface provide critical results. For this reason, an extensive velocity informationinformation about the the subsurface subsurface provide provide critical critical results. results. For For this this reason, reason, an extensive an extensive velocity velocity analysis analysis was performed to select and prove the best method of velocity estimation. The hybrid travel analysiswas performed was performed to select to and select prove and prove the best the method best method of velocity of velocity estimation. estimation. The The hybrid hybrid travel travel time time equation can successfully assess velocity, especially in the shadow zone and multipathing areas, timeequation equation can successfullycan successfully assess assess velocity, velocity especially, especially in the in shadow the shadow zone zone and and multipathing multipathing areas, area whichs, which was proven by the results. whichwas proven was proven by the by results. the results. 4. Conclusions 4.4. Conclusions Conclusions This paper shows the importance and behavior of seismic diffraction with respect to velocity ThisThis paper paper shows the importance andand behaviorbehavior ofof seismicseismic di diffractionffraction with with respect respect to to velocity velocit andy and depth, which follows the Zoeppritz equation by considering the angle of incidence and not the anddepth, depth, which which follows follows the Zoeppritzthe Zoeppritz equation equation by consideringby considering the the angle angle of incidence of incidence and and not not the the offset. offset. We found that three parameters have essential effects on diffraction behavior, namely the offset.We found We foundthat three that parametersthree parameters have essentialhave essential effects effects on diff onraction diffraction behavior, behavior namely, namely the velocity, the velocity, depth, and frequency of the seismic wave. Further, the need for a diffraction separation velocity, depth, and frequency of the seismic wave. Further, the need for a diffraction separation method was studied and a DFF filtering technique was introduced for diffraction separation and method was studied and a DFF filtering technique was introduced for diffraction separation and imaging. imaging. Finally, two methods of velocity model-building were used for the Marmousi dataset to Finally, two methods of velocity model-building were used for the Marmousi dataset to demonstrate the importance of velocity modeling. The hybrid travel time method for calculating the demonstrate the importance of velocity modeling. The hybrid travel time method for calculating the velocity model was more accurate than the semblance method because it uses both an eikonal solver velocity model was more accurate than the semblance method because it uses both an eikonal solver Appl. Sci. 2020, 10, 4391 14 of 15 depth, and frequency of the seismic wave. Further, the need for a diffraction separation method was studied and a DFF filtering technique was introduced for diffraction separation and imaging. Finally, two methods of velocity model-building were used for the Marmousi dataset to demonstrate the importance of velocity modeling. The hybrid travel time method for calculating the velocity model was more accurate than the semblance method because it uses both an eikonal solver and paraxial raytracing to calculate the velocity in the shadow zones, such as for fractures. Use of the correct velocity model is the key to seismic depth imaging. The model enhanced the preserved energy through the recovery of low frequencies in the final image and helped us to interpret the fractures and deeper events that contribute to reservoir delineation in oil and gas exploration.

Author Contributions: Y.B. developed the algorithms, performed the research, and obtained the results. N.M.M. performed the geological studies on the area. S.Y.M.A. reviewed the final results and technically reviewed the geological aspects of the area. S.H.A. performed the regional geology of the study area. D.P.G. technically reviewed the work and helped to improve the results. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: We are thankful to Universiti Sains Malaysia (USM) and Universiti Teknologi PETRONAS (UTP) for providing the facility used for this research. This work is supported by the USM short-term research Grant. In this work, we used MATLAB and Seismic Unix from Colorado School of Mines (CSM). Conflicts of Interest: The authors declare no conflict of interest.

References

1. Fomel, S.; Landa, E.; Taner, M.T. Diffraction imaging for fracture detection. In Proceedings of the 69th EAGE Conference and Exhibition-Workshop Package, London, UK, 11–14 June 2007. 2. Landa, E. Diffractions–yesterday, today and tomorrow. In Proceedings of the 72nd EAGE Conference & Exhibition Incorporating SPE EUROPEC 2010, Barcelona, Spain, 14–17 Jun 2010. 3. Bin Waheed, U.; Alkhalifah, T.; Stovas, A. Diffraction traveltime approximation for TI media with an inhomogeneous background. Geophysics 2013, 78, WC103–WC111. [CrossRef] 4. Coimbra, T.A.; Faccipieri, J.H.; Speglich, J.H.; Gelius, L.-J.; Tygel, M. Enhancement of diffractions in prestack domain by means of a finite-offset double-square-root traveltime. Geophysics 2019, 84, V81–V96. [CrossRef] 5. Bashir, Y.; Ghosh, D.P.; Janjuhah, H.; Sum, C.W. Diffraction Enhancement Through Pre-Image Processing: Applications to Field Data, Sarawak Basin, East Malaysia. Geosciences 2018, 8, 74. [CrossRef] 6. Schwarz, B.; Gajewski, D. Accessing the diffracted wavefield by coherent subtraction. Geophys. J. Int. 2017, 211, 45–49. [CrossRef] 7. Dell, S.; Abakumov, I.; Kashtan, B.; Gajewski, D.; Popovici, A.M.; Fomel, S. Utilizing diffractions in full-wave inversion for a detailed model building. SEG Tech. Program Expand. Abstr. 2017, 2017, 1033–1037. [CrossRef] 8. Bashir, Y.; Ghosh, D.P.; Sum, C.W. Influence of seismic diffraction for high-resolution imaging: Applications in offshore Malaysia. Acta Geophys. 2018, 66, 305–316. [CrossRef] 9. Berryhill, J.R. Diffraction response for nonzero separation of source and receiver. Geophysics 1977, 42, 1158–1176. [CrossRef] 10. Hilterman, F.J. Amplitudes of seismic waves—a quick look. Geophysics 1975, 40, 745–762. [CrossRef] 11. Bansal, R.; Imhof, M.G. Diffraction enhancement in prestack seismic data. Geophysics 2005, 70, V73–V79. [CrossRef] 12. Berkovitch, A.; Belfer, I.; Hassin, Y.; Landa, E. Diffraction imaging by multifocusing. Geophysics 2009, 74, WCA75–WCA81. [CrossRef] 13. Fomel, S. Applications of plane-wave destruction filters. Geophysics 2002, 67, 1946–1960. [CrossRef] 14. Claerbout, J.F. Earth soundings analysis: Processing versus inversion, vol. Blackwell Scientific Publications: Cambridge, MA, USA, 1992. 15. Klem-Musatov, K.D.; Hron, F.; Lines, L.R.; Meeder, C.A. Theory of Seismic Diffractions; Society of Exploration Geophysicists: Tulsa, OK, USA, 1994. 16. Trorey, A.W. A simple theory for seismic diffractions. Geophysics 1970, 35, 762–784. [CrossRef] Appl. Sci. 2020, 10, 4391 15 of 15

17. Harlan, W.S.; Claerbout, J.F.; Rocca, F. Signal/noise separation and velocity estimation. Geophysics 1984, 49, 1869–1880. [CrossRef] 18. Landa, E.; Keydar, S. Seismic monitoring of diffraction images for detection of local heterogeneities. Geophysics 1998, 63, 1093–1100. [CrossRef] 19. Söllner, W.; Yang, W. Diffraction response simulation: A 3D velocity inversion tool. In Proceedings of the SEG Technical Program Expanded Abstracts 2002; Society of Exploration Geophysicists: Tulsa, OK, USA, 2002; pp. 2293–2296. 20. Li, J.-Y.; Chen, X.; Hao, Z.-J.; Rui, Z.-H. A Study on Multiple Time-Lapse Seismic AVO Inversion. Chin. J. Geophys. 2005, 48, 974–981. [CrossRef] 21. Fourier, J. Sine and Cosine Series for an Arbitrary Function in Joseph Fourier 1768-1830 Ed. and Annotated by I; Grattan-Guinness MIT Press: Cambridge, MA, USA, 1807. 22. Birch, K.G. A Spatial Frequency Filter to Remove Zero Frequency. Opt. Acta: Int. J. Opt. 1968, 15, 113–127. [CrossRef] 23. Ghosh, D.; Halim, M.F.A.; Brewer, M.; Viratno, B.; Darman, N. Geophysical issues and challenges in Malay and adjacent basins from an E & P perspective. Geophysics 2010, 29, 436–449. [CrossRef] 24. Madon, M. Geological setting of Sarawak. Pet. Geol. Resour. Malays. 1999, 1, 273–290. 25. Gudmundsson, A. Rock Fractures in Geological Processes by Agust Gudmundsson; Cambridge University Press (CUP): Cambridge, UK, 2009. 26. Park, R. Foundation of Structural Geology; Informa UK Limited: London, UK, 2013. 27. Aki, K.; Richards, P.G. Quantative seismology: Theory and methods; Freeman Company, LLC: New York, NY, USA, 1980; Volume 801. 28. Kadir, M.B. Fractured Basement Exploration Case Study in Malay Basin. In PGCE 2010; Vols. I and II; EAGE: Merida, Mexico, 2010. [CrossRef] 29. Bashir, Y.; Ghosh, D.; Sum, C. Preservation of Seismic Diffraction to Enhance the Resolution of Seismic Data. Soc. Explor. Geophys. 2017, 2017, 1038–1043. [CrossRef] 30. Rawlinson, N.; Hauser, J.; Sambridge, M. Seismic ray tracing and wavefront tracking in laterally heterogeneous media. Adv. Geophys. 2008, 49, 203–273. [CrossRef] 31. Fomel, S. Traveltime computation with the linearized eikonal equation. SEP 1997, 94, 123–131.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).