Jian Zhou

Alexandre Bousse

Guanyu Yang

Jean-Jacques Bellanger

Limin Luo

Christine Toumoulin

Jean-Louis Coatrieux

A blob-based tomographic reconstruction of 3D coronary trees from rotational X-ray angiography

Keywords: cone-beam, coronary, reconstruction, X-ray, angiography, blob, maximum a posteriori, expectationmaximization

A method is proposed for a 3D reconstruction of coronary networks from rotational projections that departs from motion-compensated approaches. It deals with multiple views extracted from a time-stamped image sequence through ECG gating. This statistics-based vessel reconstruction method relies on a new imaging model by considering both the effect of background tissues and the image representation using spherically-symmetric basis functions, also called 'blobs' . These blobs have a closed analytical expression for the X-ray transform, which makes easier to compute a cone-beam projection than a voxel-based description. A Bayesian maximum a posteriori (MAP) estimation is used with a Poisson distributed projection data instead of the Gaussian approximation often used in tomography reconstruction. A heavy-tailed distribution is proposed as image prior to take into account the sparse nature of the object of interest. The optimization is performed by an expectationmaximization like (EM) block iterative algorithm which offers a fast convergence and a sound introduction of the non-negativity constraint for vessel attenuation coefficients. Simulations are performed using a model of coronary tree extracted from multidetector CT scanner and a performance study is conducted. They point out that, even with severe angular undersampling (6 projections over 110 degrees for instance) and without introducing a prior model of the object, significant results can be achieved.

INTRODUCTION

Coronary arterial disease is a major cause of mortality especially in Europe and the US. Quantitative and accurate characterization of stenoses (length, cross-sectional area) as well as their location within the whole coronary network is thus of major importance for diagnosis and treatment. The 3D reconstruction of arterial trees enhanced with contrast agent has attracted much attention for years using 2D angiographic image sequences with fairly high time resolution. This problem has been addressed first through computer vision approaches using mono-and bi-plane systems with epipolar techniques and feature matching in order to find corresponding primitives and retrieve their 3D geometry. However, the resolution of this ill-posed problem requires either a prior model, 1 additional views, [START_REF] Venaille | Un algorithme peu contraint d'appariement de primitives par stéréovision trnoculaire[END_REF] or the joint use of motion. [START_REF] Ruan | Three dimensional motion and reconstruction of coronary arteries from biplane cineangiography[END_REF] All the reported methods rely on a robust and accurate detection capable to provide in a first step the vessel centerlines, which is difficult to obtain without a significant user interaction (refer to [START_REF] Coatrieux | Computer vision approaches for the threedimensional reconstruction of coronary arteries: review and prospects[END_REF] for a review). The availability of X-ray C-arm imaging systems opens now new perspectives for this reconstruction. While the clinician already gets more insights into the full 3D anatomy during the rotation of the C-arm (covering up to 180-240 degrees within a 7-8 seconds), the full 3D reconstruction may take benefit of a higher number of projections (150-200) by using tomographic methods. Several options can be considered. One first consists to perform a motion-compensated tomographic reconstruction, inspired from Bonnet's work, [START_REF] Bonnet | Dynamic X-ray computed tomography[END_REF] using the motion of the coronary arteries previously estimated by means of computer vision methods. [START_REF] Blondel | Reconstruction of coronary arteries from a single rotational X-ray projection sequence[END_REF] Such method is highly dependent on a critical pre-processing step and on the reliability of the motion estimate. Another way is to carry out the reconstruction from very few views (typically 5-8), corresponding to a single cardiac phase, selected by ECG-gating. A 3D reconstruction of centerlines has been proposed by exploring the 3D voxelized space, region growing and reprojection. [START_REF] Jandt | Automatic generation of 3D coronary artery centerlines using rotational X-ray angiography[END_REF] A fully iterative method has been reported in [START_REF] Hansis | An iterative method for the reconstruction of the coronary arteries from rotational X-ray angiography[END_REF][START_REF] Movassaghi | 4D coronary reconstruction based on retrospectively gated rotational angiography: first in-human results[END_REF] by minimizing the L1-norm of the reconstructed image and a regularization based on vesselness and Gibbs smoothing priors. This contribution describes an iterative reconstruction using a block sequential regularized EM (expectationmaximization) algorithm (BSREM) [START_REF] De Pierro | Fast scaled gradient decomposition methods for maximum likelihood transmission tomography[END_REF] for maximizing a regularized Poisson likelihood estimation, where the update is multiplicative. Instead of using a voxel basis, we consider a spherically-symmetric basis function (i.e the blob basis), the Kaiser-Bessel (KB), which has shown attractive properties. [START_REF] Lewitt | Multidimensional digital image representation using generalized Kaiser-Bessel window functions[END_REF] A 3D realistic phantom data set has been built using a coronary tree extracted from MDCT volume image. Cone beam projections have been computed from this phantom, with and without a background added coming from real angiographic projections. A performance study has then been conducted in terms of convergence, reconstruction error.

METHOD

The imaging geometry used in most recent rotational X-ray angiography systems is a cone-beam geometry. We consider a monoenergetic X-ray source, the ideal projection function due to this point source is:

Y (u; θ(t)) ∝ exp -µ T (θ(t)) x 0 + s • x d (u) -x 0 x d (u) -x 0 ; t ds (1)
where

u = [u 1 , u 2 ] ′ ∈ R 2 , x 0 = [0, -d, 0] ′ and x d (u) = [u 1 , D -d, u 2 ]
′ (where d is the distance from the source to the center of rotation, and D the source-to-detector distance), • is the standard Euclidean norm. T (θ(t)) is the three-dimensional rotation transform:

T (θ(t)) =   cos(θ(t)) -sin(θ(t)) 0 sin(θ(t)) cos(θ(t)) 0 0 0 1   (2)
where θ(t) gives the projection angle at time t. The term µ(x; t) (x ∈ R 3 ) represents the total linear X-ray attenuation coefficient corresponding to the sum of the contribution of the dyed blood vessels of interest µ and the background tissue µ b , i.e., µ(x; t) = µ(x; t) + µ b (x; t).

In real cases, data acquisition is usually done with several discrete time instances, e.g., {t 1 , . . . , t K }. By letting θ k ≡ θ(t k ) (k = 1, . . . , K), we have a projection sequence {Y (u; θ k )}. From equation (3), we see that both arteries and background tissues are projected. The contribution of background tissues is significant in angiogram, and cannot be ignored. One conceptually simple way is to acquire additional projection images of background tissues, denoted by {Y b (u; θ k )}, and to perform logarithmic subtractions: log Y b (u; θ k )-log Y (u; θ k ). However, this is unrealistic since, at least, it requires that the X-ray system has a very accurate repositioning so that it can provide two spatially matched sequences. In addition, any patient motion between the acquisitions will produce artifacts due to incomplete subtraction. An alternative solution is to numerically approximate the background and then subtract it.

In this paper, we adopt this latter strategy with a slightly different implementation. Suppose we already have virtual background images Ŷb (u; θ k ). Instead of a logarithmic subtraction as shown previously, we propose the following approximation for the kth projection image:

Y (u; θ k ) ∝ Ŷb (u; θ k ) exp -µ T (θ k ) x 0 + s • x d (u) -x 0 x d (u) -x 0 ; t k ds . (4)
The challenge still remains when performing a direct reconstruction using {Y (u; θ k )}. The vessel attenuation coefficient function µ is a function of time, depending on, e.g., the distribution of contrast agent, and much more important, the motion of vessels during the acquisition procedure. These effects lead to the inconsistency in projection data. We will consider in this paper that the attenuation within the vessel is constant over time and that all other motions (due to patient movement or respiration) can be neglected. Since the cardiac motion is relatively regular and periodical, through ECG gating, we are able to choose several projections from a rotational sequence which correspond to the same 3D heart motion. We have limited our reconstruction study to a single instant within a cardiac phase. We assume Y (u; θ k )'s consist of K selected projection images. Further, we can use µ(x) instead of µ(x; t k ) for conciseness. Now the task turns to how these selected angiographic images Y (u; θ k )'s can be utilized to reconstruct µ(x) of interest.

As stated, this problem is close to the conventional static tomography reconstruction with, however, critical features: 1) Since a usual examination of coronary angiography is often taken in a relatively short time period (e.g., typically no more than four or five cardiac cycles), the number of consistent projections is small (i.e., K is small, usually less than 6), and projections may not be equally spaced; 2) For relatively low X-ray exposition, the angular scanning is severely limited (e.g., for a typical C-arm rotational X-ray angiography system, the dynamic angle range is less than 180 • ). This is sharply in contrast to the conventional cone-beam tomography in which a normal scanning covers a full range of 360 • . Therefore, a direct 3D reconstruction of vessel from rotational X-ray angiography is indeed a very ill-posed problem. In the following section, we will discuss our approximation solution.

System Model

We transform the above problem into the discrete domain. A single projection image can be discretized and stored lexicographically in one vector. All projection vectors can be stacked one by one, leading to a large data vector Y = [Y 1 , . . . , Y N ] ′ (where N is the total number of projection data, and the prime represents the vector or matrix transpose). Only noisy data can be obtained and we assume that these data are independent random variables whose ensemble means, according to (4), can be expressed as

Ȳi (u) ∝ Y bi exp {-[Au] i } (5)
for all i = 1, . . . , N , where Y bi is the ith element of the background image vector Y b , u = [µ 1 , . . . , µ J ] ′ (where J is the length of u) is a discrete representation of vessel attenuation coefficient function µ(x), A is the cone-beam projection operator, and [•] i returns the ith entry of a vector in brackets.

Without loss of generality, we study here the vessel reconstruction within a cubic field of view. A typical image representation is to consider the piecewise continuous attenuation function µ(x) defined over the cubic region. It can be written as the superposition of scaled and shifted copies of the basis function Ψ(x), as follows:

µ(x) = J j=1 µ j Ψ(x -x j ) (6)
where {x j } (j = 1, . . . , J) form a set of spatial basis locations (or grid points as well). There are many choices of basis functions, one of which is: Ψ(x) = 1, if x ∞ ≤ 1/2 else Ψ(x) = 0 (assuming that the grid spacing is unitless 1). This is the so-called voxel basis that has a constant density inside the voxels. From a signal processing standpoint, it only provides, however, a poor interpolation. Instead of using voxel basis, we consider in this paper another basis family: the spherically-symmetric basis function (also known as the blob basis) which has the following general form:

Ψ(x) = B( x ) (7)
where B(•) is a circularly symmetric kernel. The concept of blob in tomography has been applied for image reconstruction, e.g., [START_REF] Matej | Practical considerations for 3D image reconstruction using spherically symmetric volume elements[END_REF][START_REF] Daube-Witherspoon | Assessment of image quality with a fast fully 3D reconstruction algorithm[END_REF][START_REF] Wang | 3D RBI-EM reconstruction with spherically-symmetric basis function for SPECT rotating slat collimator[END_REF] etc. It is also widely used in the area of volume visualization, e.g., volume rendering. [START_REF] Muraki | Volumetric shape desciption of range data using 'Blobby Model[END_REF] An important blob basis is known as the Kaiser-Bessel (KB) kernel, which has shown certain attractive properties. [START_REF] Lewitt | Multidimensional digital image representation using generalized Kaiser-Bessel window functions[END_REF] It can be written as

B m,α,R (r) = 1 Im(α) 1 -(r/R) 2 m I m α 1 -(r/R) 2 |r| R 0 otherwise (8)
where I m (•) denotes the modified Bessel function of the first kind of order m, R is the radius of the blob, α is a non-negative real number controlling the shape of the blob. Usually, we take m > 0 so that the blob has m -1 continuous derivatives at the boundary.

A blob-based forward projection operator A can be determined according to the basic definition of X-ray projection (4). For one element a ij , using the X-ray transform of the blob function at location x j along the ith ray path Γ i , we have

a ij = Γi B m,α,R ( x -x j )dℓ. (9)
Since the X-ray transform of a KB kernel leads to another KB like kernel, i.e.,

B m,α,R (r) = R 2π α I m+1/2 (α) I m (α) B m+1/2,α,R (r), |r| ≤ R, (10)
it follows that

a ij = B m,α,R (dist[x j , Γ i ]) (11)
with dist[x j , Γ i ] the distance between the grid point j and the ray Γ i .

Image MAP estimation

The commonly used maximum likelihood (ML) estimation finds an image reconstruction that maximizes the probability distribution of the projections, as well as the likelihood distribution.

i {-Ȳi (u) + Y i log( Ȳi (u))} ( 12
)
where terms independent of u has been ignored. The choice of this model is also due to another interpretation of the log-Poisson likelihood term which is the so-called Kullback-Leiber (KL) distance. The KL distance provides a measure of dissimilarity between two vectors p and q, is defined by

KL(p, q) = i {p i log(p i /q i ) -p i + q i }. (13)
Now letting p i = Y i and q i = Ȳi (u) and also ignoring terms independent of u, it can be shown that log Pr(Y |u) ≡ -KL(Y , Ȳ (u)) where Ȳ (u) = [ Ȳ1 (u), . . . , ȲN (u)] ′ . The proposed Poisson model is not specific: even for non-Poisson data, we are still able to seek a ML solution for which the likelihood term can be represented by Pr(Y |u) ∝ exp{-KL(Y , Ȳ (u))}.

However, due to the typical limits in fidelity of data, ML estimates are often unstable, and have to be improved. Usually a unique and stable estimate is sought by incorporating prior information on the original image u, leading to the well known Bayesian MAP estimation. In the MAP estimation, we are interested in the maximum of the posteriori distribution Pr(u|Y ). Using Bayes's rule, we rewrite Pr(u|Y ) as Pr(u|Y ) ∝ Pr(Y |u) Pr(u) where Pr(u) represents the image prior distribution. Then, the MAP estimation is found as

ûMAP = arg max u {log Pr(Y |u) + log Pr(u)}. ( 14
)
The image prior is certainly the key to any MAP estimation. It can not only provide a stable solution but also improve the quality of reconstruction, e.g., by suppressing artifacts due to limited angle projections. One prior defined over a discrete grid system relates to the discrete Markov random field (MRF) on which a roughness measure can be constructed from local neighborhoods. Typically, Pr(u) has the following generic form Pr(u) ∝ exp{-βU (u)} (15) where U (u) is the energy function, and β an adjustable parameter. Let N j be the neighborhoods of the jth grid.

The energy function can be written as where ω js is the weight for the pair of grid points j and s. φ is the potential function, measuring the interaction between the two grid points. In coronary angiography, vessels having branch-like structures occupies a very small part of the volume, so a sparse object prior is of relevance. Now, consider the distribution of local neighborhood differences, i.e., µ jµ s : it should be sharply peaked around zero, due to the contribution of most smooth areas, and have broad tails representing the contribution of the vessels (in particular their edges). Consequently, a sparse object prior can be modeled by a heavy-tailed distribution. With this in mind, we selected a potential function φ(t) = |t|. The corresponding penalty relates to the Laplacian distribution that belongs to the family heavy-tailed distribution. Another advantage is that the resulting R(µ) is close to the total variational (TV) regularization that is powerful for noise smoothing while edge preserving.

U (u) = j s∈Nj ω js φ(µ j -µ s ) (16)

SIMULATION STUDY

Materials

The experiments have been conducted using phantom data. The reference left coronary arteries were extracted a volume of cardiac MSCT reconstructions. [START_REF] Yang | A multiscale tracking algorithm for the coronary extraction in MSCT angiography[END_REF] Fig. 1 shows three maximum-intensity projections of the phantom along the three axes. Stenotic areas and a simulated catheter were also added.

The imaging protocol used in this paper was adapted from the C-arm rotational X-ray coronary angiography Siemens AXIOM-Artis system. The detector plane, 140 2 mm 2 , which was sampled uniformly into 512 2 pixels. All reconstructions have been performed in a volume of (110 mm) [START_REF] Ruan | Three dimensional motion and reconstruction of coronary arteries from biplane cineangiography[END_REF] . This field of view was also uniformly sampled into 128 3 grid points that served as blob locations. According to our discussion on the choice of blob basis, we have used = 2, α = 6.0, and R = 1.5 blob spacing for the calculation of operator A. Six cone-beam vessel projection images, without background tissues, uniformly spaced over the range 120 • were first generated (the starting angle is -29.0 • ). Then, we used the method of low order polynomials approximation to create the required background images (called later on the "true backgound") from some real angiography images acquired separately on the Siemens device. The mean observation data were produced according to the model (4). Poisson noisy data were then generated, which were used for reconstructions. Fig. 2 shows some examples of noisy projection images at different angular views.

Reconstruction

We focus our study on the iterative reconstruction algorithm. The image reconstruction was performed by BSREM. [START_REF] De Pierro | Fast scaled gradient decomposition methods for maximum likelihood transmission tomography[END_REF] In this algorithm, a fully iteration is divided into a set of subiterations, each being performed sequentially using one of the predetermined blocks of measurement data. In our simulation study, the data within each projection image were grouped into one block. Therefore, this leads to a total number of six blocks. The BSREM algorithm is an extension of RAMLA (row-action maximum likelihood algorithm) [START_REF] Browne | A row-action alternative to the EM algorithm for maximizing likelihood in emission tomography[END_REF] for maximizing a regularized Poisson likelihood estimation as (14). They relate to the well-known algebraic reconstruction technique (ART), [START_REF] Gordon | Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography[END_REF] but the update is multiplicative (rather than additive) and a grouped projection can be performed simultaneously. BSREM has been shown even faster with guaranteed global convergence properties.

Influence of background images

As discussed in Section 2, one can construct a set of new measurement data by using logarithm substraction. Let Ỹ =log (Y / Ŷb ). Then, Ỹ serves as the approximate observations of projections Au. In 6 , 8 the authors have used Ỹ to reconstruct the vessels of interest. This method was evaluated in this paper and compared with our strategy as expressed in (4). While the resulting data Ỹ cannot be Poisson distributed, we still can use the BSREM algorithm but the data fidelity term should be interpreted as the KL distance, yielding a modified BSREM for image reconstruction from the presubtracted measurement data. We named it here the algorithm.

For comparison, we introduced two measures of error: 1) the global mean square error defined by

MSE global (n) = ûn -u ref 2 u ref 2 × 100% (17)
which provides the normalized percentage error between the nth iteration ûn and the reference volume u ref .

2) the vessel mean square error denoted by MSE vessel (n) defined in a similar way except that the error is only measured within the support of vessels instead of the entire field of view.

Tab. 1 shows the global MSE values of the two different algorithms at several selected iteration number. We see that the smaller MSE global can be obtained by the proposed BSREM. This possibly means that the logarithm substraction operation imposed before data processing may destroy the optimality of statistical based iterative algorithm, leading to a suboptimal one in terms of global mean square error. Fig. 3 shows the evolution of MSE vessel during the iteration progress. Again, BSREM without pre-logarithm substraction shows a slight better performance.

As mentioned already, the background images are usually unavailable in practice, and they can only be estimated from the measured data. To obtain virtual projection images of background tissues, we have adapted the method used in. [START_REF] Blondel | Reconstruction of coronary arteries from a single rotational X-ray projection sequence[END_REF][START_REF] Hansis | An iterative method for the reconstruction of the coronary arteries from rotational X-ray angiography[END_REF] First, we created the binary vessel mask. This is can be done by thresholding. Second, a morphological closure operation was applied to the noisy projection images to remove vessels. Here, the structure element was a disk whose radius has been chosen large enough to cover the blood vessels. Then, a virtual background image is obtained by combining the original projection image and the filtered image: the virtual background image takes the pixel value from the filtered image if the pixel belongs to a vessel according to the binary vessel mask images, otherwise we use the value on the original projection image. Fig. 4 shows some results when creating one virtual background image from the projection image at angle -5.4 • .

The estimated background images, denoted by , were combined with either BSREM or PreSub.+BSREM to investigate the effect of background tissues on reconstructions. Fig. 5 compares the maximum intensity projection images with either true or virtual background images. Noise and artifacts are clearly shown and this confirms that the accuracy background images does affect the reconstruction quality. Nevertheless, they are mainly in background regions, and most of the vascular structures can be preserved. Tab. 2 lists some MSE vessel values yielded by the two approaches. The results seem to justify the same fact that the proposed BSREM can behave better than the one with pre-logarithm subtraction. However, it can be observed that the mean square error becomes larger over iterations. This is a common feature of iterative ML estimation that can produce an overfit to noisy data, leading to degeneration of reconstruction. An introduction of regularization (or setting β > 0 as well) should improve the solution and will be discussed next.

Choose image prior

This section evaluates the impact of the prior model on the 3D vessel reconstruction. From our former analysis, here the main task of prior is to reduce the background noise while preserving main vascular structures undestroyed. The comparison has been conducted between a heavy-tailed model and a non-heavy-tailed model.

For the latter, we used the Gaussian quadratic prior model (where φ(t) = |t| 2 ). The choice of parameter β is essential due to its smoothing effects. On the other hand, for a specific prior, the choice of β also can be different. Thus, for a fair comparison, we selected these model-based parameter with the aim to minimize the MSE vessel error. More precisely, we chose several β values and recorded the corresponding the minima MSE vessel value of reconstruction during iterations. We can trace out the relationship on the β and MSE vessel plane. An interpolation between discrete samples is then made to predict a global optimal β. Fig. 6 shows two curves related to different priors. In our experiments, the optimal β for the quadratic prior is close to 10 4.0 while for a TV-like it is about 10 2.62 . Note that the global minimum MSE vessel yielded by a TV-like prior is smaller than a quadratic prior, which points out the advantage of TV-like prior over a quadratic one in terms of reconstruction performance.

The results (MIP images) are displayed in Fig. 7. It is clear that the introduction of prior leads to a successful suppression of background artifacts (Note that here we used the virtual background image instead of the true one). From a visual point of view, we also see that the sparse prior, as well as the TV-like prior, can provide even better result (a clear comparison from the top-to-down MIP images). Fig. 8 shows further visual comparisons by using 3D vessel surface rendering. All surfaces are rendered by using the same isosuface values extracted from various reconstructed volumes. Again a better result is obtained by the proposed TV-like prior. However, it is worth to note that both priors still fail to reconstruct some vessel parts marked with circles in Fig. 8. Thus, the introduction of prior models may not fulfil the requirements due to the incomplete rotational X-ray scanning.

The effect of data inconsistency

Till now, the used projection images were motion free data (i.e., the same cardiac phase). In real case, the key assumption relies on the fact that the coronary network is observed exactly in the same position for different views: The reproducibility of the heart cycle and the temporal sampling may introduce some spatial shift. In other words, some inconsistency may exist. Two main motions were examined: rotation and translation. We simulated this data mismatch to explore how it affects the reconstruction. The heart rotation has been simulated by using a random bias, denoted by ǫ angle , added to the projection angle. For translation, since the cardiac motion is mainly dominated by a up-down movement, we used a random up-down displacement ǫ displacement to change the real vessel position when generating each projection image. We only studied the BSREM algorithm with the TV-like prior, and the virtual background images were estimated according to the same method described before. No pre-subtraction was used. The changes of MSE vessel with ∆ angle when using the proposed BSREM algorithm coupled with a TVlike prior. Here, the β value is 10 2.5 . (b) MSE vessel evolution when varying ∆ displacement using the proposed BSREM algorithm coupled with a TV-like prior. Here, the β value is 10 2.5 . Fig. 9(a) plots about the changes of MSE vessel against the maximum magnitude of ǫ angle , i.e., ∆ angle . Note that ǫ angle is the uniform random number within the range [-∆ angle , +∆ angle ]. We see clearly that the mean square error increases with error in angle. For an amount of 5 • bias in angle, it results in almost three times larger error in reconstruction. Fig. 9(b) shows the relationship between MSE vessel and the object displacement error ǫ displacement (note also that ǫ displacement is the uniform random number within the range [-∆ displacement , +∆ displacement ]). The same behavior can be observed. They both show that if the assumption made does not hold, a significant degeneration in the quality of reconstruction can be anticipated.

DISCUSSION AND CONCLUSION

We have described in this paper a method for the 3D reconstruction of coronary networks from sparse projections acquired through a rotational system within a limited angle rotation. This approach, applied in a first step in static conditions by assuming an error-free ECG gating, is based on a statistical modelling, blob basis functions (Kaiser-Bessel) and makes use of a block iterative algorithm (BSREM, block sequential regularized expectationmaximisation). Simulations have been performed by means of a realistic phantom representing an arterial tree extracted from a MDCT dataset in order to have a ground truth. The performance of the method has been assessed by using global statistics (mean square values over the reconstructed volume or over the vessel spatial support). The reconstructions that have been reported show some promising features. They also allow quantifying the influence of the background and the sensitivity to imprecise synchronization resulting in object misregistration (simulated by small translation and rotation errors).

It must be said that the reconstruction of coronary network remains a difficult problem in X-ray imaging (including the MDCT) for several reasons among which: the small size of the objects (few millimeters), the many structures contributing to the background, the patient movements, the ballistic inaccuracies and the time-varying heart cycle. Although this work-in-progress has been limited to a cone beam static situation, it opens a path to deal with dynamic reconstruction. In contrast to approaches that call first for 3D motion field estimation with feature matching, the solution that we are currently developing is based on a fully homogeneous tomographic frame. The availability of 3D dataset (single volume or time indexed multiple volumes) as shown here should serve as an initialization step for further refinements.

Figure 1 .

 1 Figure 1. Computer simulated phantom. Figures from left to right are maximum intensity projections along three axes, x,y,z respectively.

10

 10

Figure 2 .

 2 Figure 2. Simulated noisy projection images at angle: (a)-29.0 • , (b) 18.2 • , and (c) 65.4 • , respectively.

Figure 3 .

 3 Figure 3. A comparison of MSE vessel for PreSub+BSREM and BSREM (β = 0 for both algorithms) as the function of iteration. Here uses true background images Ŷb .

Figure 4 .

 4 Figure 4. Figures from left to right are 1) the projection image at angle -5.4 • ; 2) the corresponding binary vessel mask where the white color indicates the valid vessel regions. 3) the projection image after a morphological closure filtering with a disk type structure element of radius size 10 pixels; 4) the resulting virtual background image.

Figure 5 .

 5 Figure 5. From top to bottom: maximum intensity projection images of reconstructions by using: BSREM (with Ŷb ), PreSub+BSREM (with Ŷb ), BSREM (with Ȳb ) and PreSub+BSREM (with Ȳb ), respectively. (β = 0 for all algorithms)

Figure 6 .

 6 Figure 6. A comparison of the minimum MSE vessel changes as a function of parameter β yielded by BSREM using different priors: quadratic prior (-×-) and total variation like prior (-•-). These two curves are generated by interpolation where discrete samples are indicated by symbols, i.e., circles and crosses. The optimal β values are approximately β = 10 4.0 for the quadratic prior, and β = 10 2.62 for TV-like prior.

Figure 7 .

 7 Figure 7. A comparison of MIP of image reconstruction from BSREM using: the quadratic prior with β = 10 4.0 (the first row) and the TV-like prior with β = 10 2.62 (the second row).

Figure 8 .

 8 Figure 8. 3D vascular surface rendering using true vessel data (a), and data reconstructed by BSREM with the quadratic prior (b), and the TV-like prior (c).

Figure 9 .

 9 Figure 9. (a) The changes of MSE vessel with ∆ angle when using the proposed BSREM algorithm coupled with a TVlike prior. Here, the β value is 10 2.5 . (b) MSE vessel evolution when varying ∆ displacement using the proposed BSREM algorithm coupled with a TV-like prior. Here, the β value is 10 2.5 .

Table 1 .

 1 Comparison of MSE global values (%) for PreSub+BSREM and BSREM (both with β = 0) at several iterations.

	#Itr.	5	30	70	100
	PreSub+BSREM 36.7 22.3 19.3 18.5
	BSREM	52.1 18.7 16.6 16.5

Table 2 .

 2 Comparison of MSE vessel values (%) yielded by PreSub+BSREM and BSREM (both with β = 0 and estimated background image Ȳb ) over iterations.

	#Itr.	5	30	70	100
	PreSub+BSREM 39.9 27.2 28.8 29.7
	BSREM	57.4 26.1 27.7 27.2

ACKNOWLEDGMENTS

This work was supported by an INSERM postdoctoral grand, a PhD grant from the University of Rennes 1, and the scholarship of "co-tutelle en thèse" by French government.


Ahmed E Radwan
email: radwanae@yahoo.com

Sébastien Rohais

Domenico Chiarella

Combined stratigraphic-structural play characterization in hydrocarbon exploration: a case study of Middle Miocene sandstones, Gulf of Suez basin, Egypt

Keywords: Combined stratigraphic-structural traps, Petrophysics, Petrography, Hydrocarbon, Gulf of Suez, Subsurface analysis, Reservoir characterization. 1.Introduction

As most hydrocarbon discoveries in the Gulf of Suez basin are in structural traps, little research has focused on the evaluation of stratigraphic or combined play in the region. The Badri field represents one of the most prolific oil and gas fields in the Gulf of Suez basin with a large cumulative production from the Miocene Belayim and Kareem Reservoirs. However, Middle Miocene Baba sandstones is still relatively underexplored when compared to other prolific producing reservoir intervals. Recent drilling data from the Badri field has renewed interest in this Member as a reservoir unit due to the lateral facies variations from shale to sandstones recognized in some wells. This study aims to investigate the structural and stratigraphic characterization and hydrocarbon potentiality of Serravalian Baba sandstones. An integrated mineralogical, sedimentological, petrophysical, and reservoir characterization analysis was conducted to obtain and evaluate information about the main reservoir characteristics of Baba sandstones using thin sections, wireline logs (i.e. Resistivity, Density-Neutron, Gamma-ray, and Sonic), and subsurface geologic mapping. Results support that Baba sandstones interval has good 2 reservoir properties and high potentiality to produce hydrocarbon increasing the reserves in the studied area. Moreover, the entrapment style of Baba sandstones interval is due to the combined effect of stratigraphic and structural components. Accordingly, this study recommends more attention for the stratigraphic and combined stratigraphic-structural traps present along the Gulf of Suez basin.

stratigraphic, structural lows, and sequence stratigraphy application (i.e. Miocene half-grabens or sub-basins) between the high blocks, these type of traps is mostly linked to Miocene sandstones [START_REF] Young | Sedimentology and sequence stratigraphy of a transfer zone coarse-grained delta, Miocene Suez Rift, Egypt[END_REF][START_REF] Alsharhan | Petroleum geology and potential hydrocarbon plays in the Gulf of Suez rift basin, Egypt[END_REF]Pivnik et al., 2003;[START_REF] Youssef | Early-Middle Miocene Suez syn-rift-basin, Egypt: a sequence stratigraphy framework[END_REF][START_REF] Sarhan | Geophysical appraisal and oil potential for Rudeis Formation at West Hurghada area, southern Gulf of Suez: detection of stratigraphic trap[END_REF]. However, many risks are still exist for exploring Miocene stratigraphic traps, due to the unpredictable lateral distribution and the limited volume of the clastic reservoirs.

The Badri field contains hydrocarbon in the Miocene Belayim and Kareem Reservoirs [START_REF] Egpc | Gulf of Suez oil fields (a comprehensive overview): Egyptian General Petroleum Corporation[END_REF]Abudeif et al., 2016;Radwan, 2020a-d) The base of the Belayim Formation consists of Baba Member evaporitic sequence. However, some wells show blocky sandstones reported in the literature as Baba sandstones [START_REF] Abudeif | Hydrocarbon type detection using the synthetic logs: A case study, Baba member, Gulf of Suez, Egypt[END_REF][START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF]. Baba sandstones are characterized by high resistivity suggesting good petrophysical characteristics as a potential reservoir in the studied area. However, the facies distribution, hydrocarbon habitat, and trapping mechanism have not been understood and need detailed study.

The main aims of this study are to 1) evaluate the hydrocarbon prospectivity of Baba sandstones through the evaluation of their facies distribution, petrographic, and petrophysical properties, 2) interpret and update the hydrocarbon habitat and petroleum system for the studied unit according to the previous publications and geological based interpretations, 3) enhancing the hydrocarbon recoveries by adding new opportunities in the existing field. The novelty of hydrocarbon prospectivity of Baba sandstones will hopefully provide new insights for exploring the nonstructural plays and focusing on facies or lithology change in the area of Gulf of Suez basin.

Geologic setting

The Gulf of Suez basin is a rift basin that contains the major oil-bearing province in Egypt, and that was formed through the separation of the African and Arabian plates during the Late Oligocene -Early Miocene time [START_REF] Bosworth | Structural and stratigraphic evolution of the Gulf of Suez rift, Egypt: a synthesis[END_REF]Abudeif et al., 2016a,b and[START_REF] Radwan | New petrophysical approach and study of the pore pressure and formation damage in Badri, Morgan and Sidki fields[END_REF][START_REF] Lashin | Seismic data analysis to detect the depositional process environments and structural framework of the east central part of Gharib Province, Gulf of Suez-Egypt[END_REF]Gawthorpe et al., 2033a,b;[START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF][START_REF] Lewis | Tectono-sedimentary development of early syn-rift deposits: The Abura Graben, Suez Rift, Egypt[END_REF][START_REF] Rohais | Pre-salt to salt stratigraphic architecture in a rift basin: insights from a basin-scale study of the Gulf of Suez (Egypt)[END_REF]Radwan et al., 2020a-d;[START_REF] Rohais | Source-to-Sink Analysis of the Plio-Pleistocene Deposits in the Suez Rift (Egypt)[END_REF]. The Badri field is located in the southern area of the Gulf of Suez basin and covers an area of about 12 km 2 (Fig. 1) The Badri structure was first drilled in 1966 by a step-out well from the El Morgan Field, which is located immediately to the west of the Badri field across an NNW-striking fault (Radwan et al., 2019a-d;[START_REF] Radwan | Stress Path Analysis for Characterization of In Situ Stress State and Effect of Reservoir Depletion on Present-Day Stress Magnitudes: Reservoir Geomechanical Modeling in the Gulf of Suez Rift Basin, Egypt[END_REF]) (Fig. 2). The structure is characterized by a main extensional fault that separates the East Badri and Badri fields with a throw of 460 meters at the top of the Belayim Formation [START_REF] Radwan | Petrophysical evaluation for Sidri and Baba members within Belayim Formation in the region of Badri field[END_REF][START_REF] Radwan | New petrophysical approach and study of the pore pressure and formation damage in Badri, Morgan and Sidki fields[END_REF]. In addition, a minor structural element called fault z with a throw of 45 meters at the top of the Belayim Formation is mapped in the northern area of the field (Fig. 3) [START_REF] Radwan | Petrophysical evaluation for Sidri and Baba members within Belayim Formation in the region of Badri field[END_REF][START_REF] Radwan | New petrophysical approach and study of the pore pressure and formation damage in Badri, Morgan and Sidki fields[END_REF]Radwan et al., 2019bRadwan et al., , 2020a,c),c).

Lithostratigraphy

The lithostratigraphic succession of the Gulf of Suez basin has been divided into three different stages (Fig. 1C): 1) Pre-rift units (pre-Oligocene), 2) Syn-rift units (Oligo-Miocene), and 3) Post-rift units (Quaternary). The syn-rift sediments are characterized by their overall excellent oil potentiality as a source, reservoir, and seal rocks [START_REF] Richardson | The Gulf of Suez-northern Red Sea neogene rift: a quantitive basin analysis[END_REF][START_REF] Jackson | Style and sequence of deformation during extensional fault-propagation folding: examples from the Hammam Faraun and El-Qaa fault blocks, Suez Rift, Egypt[END_REF][START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF][START_REF] Lewis | Tectono-sedimentary development of early syn-rift deposits: The Abura Graben, Suez Rift, Egypt[END_REF]Radwan et al., 2019b, c).

The syn-rift Miocene succession is subdivided into the six main formations from base to top:

The Nukhul, Rudeis, Kareem the Belayim, South Gharib, and Zeit Formations (EGPC 1964;Fig. 4). The post-Zeit succession attributed to the Plio-Pleistocene is interpreted as post-rift deposits (Fig. 4).

The syn-rift Belayim Formation (Middle Miocene) consists of four Members: Hammam. Faraun (Top), Feiran, Sidri, and Baba (Bottom) (Fig. 5) [START_REF] Abd-Elshafy | Stratigraphy and correlation of Belayim Cenomanian, Gulf of Suez, Egypt[END_REF][START_REF] Alsharhan | Petroleum geology and potential hydrocarbon plays in the Gulf of Suez rift basin, Egypt[END_REF]Radwan et al., 2019a,b;[START_REF] Nabawy | Hydrocarbon potential, structural setting and depositional environments of Hammam Faraun Member of the Belayim Formation, Southern Gulf of Suez, Egypt[END_REF][START_REF] Ali | Integrated petrophysical and lithofacies studies of lower-middle Miocene reservoirs in Belayim marine oil field, Gulf of Suez, Egypt[END_REF][START_REF] Nabawy | Formation evaluation using conventional and special core analyses: Belayim Formation as a case study, Gulf of Suez, Egypt[END_REF]Radwan, 2020a-d;[START_REF] Radwan | Implementation of Rock Typing on Waterflooding Process During Secondary Recovery in Oil Reservoirs: A Case Study, El Morgan Oil Field, Gulf of Suez, Egypt[END_REF]. The sandstones recognized in the Gulf of Suez basin have a good reservoir quality and petroleum accumulation history. The Hammam Faraun Member is the thickest sandstones Member that reaches up to 100 m in the study area and consists of sandstones intercalated with shale and siltstones [START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF][START_REF] Radwan | Petrophysical evaluation for Sidri and Baba members within Belayim Formation in the region of Badri field[END_REF][START_REF] Radwan | New petrophysical approach and study of the pore pressure and formation damage in Badri, Morgan and Sidki fields[END_REF]. Baba and Feiran Members consist of evaporite deposits, while the Sidri Member is composed of shale with thin sandstones beds intercalated (Fig 5). Baba Member (Serravallian) consists of anhydrite with a thin interbedded clastic marker in the middle part, which allows a subdivision of this Member into three lithologic units. The upper and the lower lithological units are mainly composed of anhydrite in the study area, the middle part is represented by clastic sediments. Each lithological unit is easily laterally correlatable throughout the Badri field. Here, Baba Member varies in thickness from approximately 21 m in the south to almost 91 m in the northern area. In the Badri field, the interbedded clastic unit is less than 15 m thick, and shale represents the main lithology although in some areas wells have penetrated sandstones interval hereafter called Baba sandstones.

Material and Methods

The data sets were provided by the Egyptian General Petroleum Corporation (EGPC), through the Gulf of Suez Petroleum Company (GUPCO). Four wells named Badri (A, B, C, and D) represent the core data set in this work. The data consist of formation evaluation logs including Gamma-ray (GR), Density Logs (RHOB), Neutron Logs (NPHI), Compressional Sonic Logs (CODT), formation Resistivity logs (RT), and formation pressure data (MDT). In addition, composite logs, mud logs, and geological reports were used to evaluate Baba clastic interval within the Badri Field as well as to characterize the facies distribution supported by the petrographic analysis. No core data are available for the studied interval, so we depend on the ditch cutting samples. More than 40 ditch samples and 32 thin sections from the four offset wells were used to define the petrographic characteristics of the studied zone. The thin-sections were studied by using a Nikon polarizing microscope and during this procedure detrital minerals, lithology, grain size, sedimentological features, accessory minerals, visual porosity, and cementation type were determined. The point count method was used for porosity analysis in thin section samples. Sandstones classification was done according to [START_REF] Dott | Wacke, Graywacke and Matrix--What Approach to Immature Sandstones Classification?[END_REF].

Petrophysical investigations used the traditional conventional logs according to the standard procedures available in the literature [START_REF] Dresser | Log interpretation charts[END_REF]Abudeif et al, 2016a and b;Schlumberger, 1986;Darwin, 1987;[START_REF] Alberty | Standard interpretation: Part 4. wireline methods[END_REF][START_REF] Atlas | Introduction to wireline log analysis[END_REF][START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF][START_REF] Asquith | Log Interpretation[END_REF][START_REF] Abudeif | Hydrocarbon type detection using the synthetic logs: A case study, Baba member, Gulf of Suez, Egypt[END_REF]Schlumberger, 1987;Radwan, 2020c). The petrophysical parameters have been analyzed using the Techlog© software. The shale volume has been determined using the density neutron method due to the presence of feldspars in the studied sandstones [START_REF] Asquith | Log Evaluation of Shaly Sandstones: A Practical Guide[END_REF]) (Eq.1)

(Table 1). The density-neutron method was used to calculate the total porosity [START_REF] Serra | Fundamentals of well-log interpretation[END_REF] (Eq.2) (Table 1). Effective porosity was calculated using the volume of clay and neutron porosity of pure shale [START_REF] Hill | Bound water in shaly sands-its relation to Q and other formation properties[END_REF][START_REF] Clavier | Theoretical and experimental bases for the dual-water model for interpretation of shaly sands[END_REF][START_REF] Juhasz | Assessment of the distribution of shale, porosity and hydrocarbon saturation in shaly sands[END_REF][START_REF] Schlumberger | Log interpretation principles/applications manual[END_REF][START_REF] Alberty | Standard interpretation: Part 4. wireline methods[END_REF] (Eq.3) (Table 1). Water saturation was calculated using the Archie equation [START_REF] Archie | The electrical resistivity log as an aid in determining some reservoir characteristics[END_REF] (Eq.4) (Table 1). Permeability was estimated using Wyllie and Rose Approach (Wylie and Rose, 1950) (Eq.5 and 6) (Table 1). Hydrocarbon volume calculation was done using the standard volumetric method for hydrocarbon calculations [START_REF] Bishop | Concepts for estimating hydrocarbon accumulation and dispersion[END_REF][START_REF] Shepherd | Volumetrics[END_REF][START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF] (Eq.7 and 8) (Table 1).

Results

Baba clastics marker distribution

All drilled wells in the study area confirmed that the stratigraphic section of Baba Member consists mainly of two anhydrite units separated by a clastic marker interval (Figs 1 and5).

Anhydrite is characterized by white and tannish white color, and moderately hard. The thickness of the clastic interval ranges from 5 to 15 m, and the facies consists mainly of shale. Towards the north of the field, shales laterally grade into blocky sandstones facies (Fig. 5). The blocky sandstones facies has a thickness ranging between 7 to 12 m (Fig. 5). The lateral evolution of Baba sandstones shows that the sandstones decreases in thickness from the east (wells C and D) to the west (wells A and B) (Table . 2). The geographic distribution of Baba sandstones and wells indicate that they encompass a faulted area (fault z), where two wells were drilled in the hanging block (wells C and D) and the other two wells (A and B) in the down-faulted block (Figs. 3 and6).

Baba deposits (B4 in [START_REF] Rohais | Pre-salt to salt stratigraphic architecture in a rift basin: insights from a basin-scale study of the Gulf of Suez (Egypt)[END_REF] recorded the first disconnection of the entire Gulf of Suez basin rift from the Mediterranean Sea during its rifting stage. Halite deposits were preserved in fault-controlled depocenters (Fig. 7). Sediment supplies along the rift shoulders were very low as suggested by the very small isolated and fan-shaped siliciclastic bodies developed along the Morgan accommodation zone (Fig. 7B). Baba sandstones in the Badri field was probably fed from the El Qaa plain fan bodies, with more sand content to the north, progressively interfingering with shale to the south and southwest.

Petrographic characterization.

Shale is the dominant lithology in the clastics marker of Baba Member. The shale is characterized by different colors including dark grey, light gray, brownish grey, greenish grey, and yellowish grey. The shale firmness is ranging from soft to moderate. The shale reaction with the hydrochloric acid showed slightly calcareous content. Pyrite represents the main accessory mineral. The description of Baba sandstones is mainly based on the thirty-two thin section samples from the studied wells. The average grain-size ranges from coarse to medium-grained sand with rarely fine-grained sand and pebble-sized grains locally present (Table .3). According to the ternary plot, Baba sandstones can be classified as Arkose (Q70 F27 L3) (Fig. 8).

Constituent grains

Baba sandstones consist of four components including quartz, feldspars, lithic fragments, and accessory minerals. The quartz grains of Baba sandstones are dominated by both monocrystalline and polycrystalline quartz ranging from 65% to 74% of the total volume (Table 3). The quartz grains range from sub-rounded to sub-angular in most samples (Table 3). The feldspars component is dominated by plagioclase feldspars while some samples have a significant amount of microcline. The feldspars content ranges from 31% to 24% of the total rock. Some feldspars grains show dissolution and alteration. Lithic fragments and accessory minerals represent a minor component of the total rock volume ( 3%). The accessory minerals include pyrite as the dominant mineral. Authigenic quartz overgrowths were also observed in some samples. Micas (e.g. biotite, chlorite, and muscovite) are rarely present (Fig. 9 & 10).

Cement and Matrix

The quartz and anhydrite cement are the dominant cementation process affecting Baba sandstones. The silica cement is dominant in most samples while the anhydrite cement is increasing in the up-section. Baba sandstones matrix contains silt-sized grains of quartz and clays (Table 3) (Fig. 9 & 10). In addition, amorphous organic materials are observed in most samples.

Texture or Fabric

The investigated samples of Baba sandstones are dominantly by sub-rounded grains, although sub-angular grains are locally recognized with angularity increasing toward the up-section. The average grain size in the investigated samples are variables from fine-grained sand (160 microns) to gravel sizes (Table 3). Sorting is characterized by variable degrees including moderately, well and poor sorting. The moderately sorted texture is dominant in most samples. Well sorted grains are dominant in the middle part of Baba sandstones.

Porosity

The estimated porosity in thin sections images by point count method is (10-15%) along with Baba sandstones interval (Table 3). The porosity in Baba sandstones is characterized by both primary and secondary porosity in most samples. The primary porosity is dominant in most samples representing more than 90% of the total porosity. The secondary porosity represents no more than 8 % of the total porosity. The anhydrite of Baba Member indicates a lagoonal and restricted depositional environment, while the sandstones and shales within Baba Member indicate shallow marine environment [START_REF] Salah | The Miocene Kareem Formation in the southern Gulf of Suez, Egypt: a review of stratigraphy and petroleum geology[END_REF][START_REF] Radwan | Petrophysical evaluation for Sidri and Baba members within Belayim Formation in the region of Badri field[END_REF][START_REF] Tawadros | History of Geology in Egypt[END_REF][START_REF] Rohais | Pre-salt to salt stratigraphic architecture in a rift basin: insights from a basin-scale study of the Gulf of Suez (Egypt)[END_REF][START_REF] Nabawy | Formation evaluation using conventional and special core analyses: Belayim Formation as a case study, Gulf of Suez, Egypt[END_REF][START_REF] Radwan | New petrophysical approach and study of the pore pressure and formation damage in Badri, Morgan and Sidki fields[END_REF]Radwan, 2020a). However, the absence of cores in the studied reservoir, and the unobvious log signatures doesn't allow for taking a step further on defining more facies analysis studies.

Petrophysical evaluation

Based on the petrophysical evaluations of Baba clastics sandstones reservoir in the investigated Badri (A, B, C, and D) wells, the shale volume (Vsh) analysis shows a low shale content with an average ranging from 9 % to 13%, while the maximum estimated value is 18% (Table 2). In general, the higher values of the gamma-ray log in the blocky sandstones unit are due to the presence of feldspars. The effective porosity (Øeff) shows good porosity with average values ranging from 11% to 17%, and a maximum value of 23%. The higher effective porosity is in the two up-dip wells and the relatively lower porosities occur in the down-dip wells. The water saturation (Sw) analysis shows a reverse trend compared to that of the effective porosity. The water saturation ranges from 12% to 21%, with maximum values up to 21%. The higher water saturation is observed in the down-dip wells and the lower water saturation is in the up-dip wells.

The hydrocarbon saturation (Shr) analysis shows high saturation values. The higher hydrocarbon saturation is in the up-dip wells, with the average hydrocarbon saturation was ranged from 79% to 88% (Table . 2). The estimated permeability analysis shows average values ranging from 180 to 220 mD, with a maximum of 400 mD. Fluid type evaluation indicated the presence of oil in BDR (A and B) wells, and gas cap in BDR (C and D) wells (Fig. 11).

Hydrocarbon volume

The last inferred petrophysical parameters have been used to calculate the estimated hydrocarbon on the studied Member. According to the standard oil industry equations (Eq. 7 and 8) in (Table 1), the (STOOIP) in the studied Member is approximately 1,100,000 Stock tank barrels as P50. In addition, small estimated quantities of gas reach up to 1481 (MM SCF) as P50.

Interpretation and synthesis

The primary reservoirs of the Badri Field have been deposited during Middle Miocene just after the rift-climax phase. Rifting formed half-grabens structures that allow the deposition of variable clastic and evaporitic sequence in the Belayim Formation (Fig. 1) [START_REF] Evans | Neogene tectonic and stratigraphic events in the Gulf of Suez rift area, Egypt[END_REF][START_REF] Evans | Miocene sandstones provenance relations in the Gulf of Suez: insights into synrift unroofing and uplift history[END_REF][START_REF] Gawthorpe | Evolution of Miocene footwall-derived coarse-grained deltas, Gulf of Suez, Egypt: implications for exploration[END_REF]Abd El Gawad, 2007;Muravchik et al., 2016;[START_REF] Rohais | Pre-salt to salt stratigraphic architecture in a rift basin: insights from a basin-scale study of the Gulf of Suez (Egypt)[END_REF]. In the late middle Miocene thick evaporites, shales were deposited over Middle Miocene sediments forming South Gharib and Zeit Formations, which act as primary seal rocks in the Gulf of Suez basin [START_REF] A-Rehim | The multi-discipline field study approach -Badri Field case study[END_REF][START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF]. The studied Baba Member is the basal Member of Belayim Formation and consists of anhydrite, and sediment influxes has been forms clastics marker in between the anhydrite layers along the studied field. The shaly facies pass laterally to sandstones in the northern part of the field. The lateral correlation of this blocky sandstones facies indicated that in the different areas they have the same electrical log response (Fig 6). The existence of these facies in four adjacent wells with the same log characteristics supporting the idea that these sandy facies are laterally continuous. Paleo-geographic reconstructions (Fig. 7) suggest that these sandstones were part of a large fan-shaped siliciclastic body extended across EL Morgan Accommodation Zone and supplied from the El Qaa Plain area (Eastern border of the rift). Another fan-shaped siliciclastic body was also developed is a similar pattern in the western part of the Morgan Accommodation Zone (Fig. 7B).

Sedimentological interpretations

Porosity investigations of the arkosic sandstones of Baba Member showed predominantly intergranular porosity, as indicated by the thin section photomicrographs (Fig. 9 & 10). In addition, secondary porosity has been recorded in the thin section samples, which may be resulted from the dissolution of feldspar grains. The petrographic analysis points out that Baba clastic sandstones marker unit in Badri (A, B, C, and D) wells is characterized by a wide range of grain-size, porosity, and sorting. Sorting ranges from good to moderate. The observed organic material filling pore space inter grains which may indicate oil pathways or oil-bearing sandstones. The good reservoir quality of Baba sandstones was suggested to be the result of the presence of secondary dissolution pores interconnected with the primary intergranular network.

Moreover, the clay minerals, cementation, and compaction were identified as the main porosityreducing agents. Polycrystalline and monocrystalline quartz grains are usually mechanically stable during weathering and transportation. Consequently, the preservation and the abundance of angular to sub-rounded polycrystalline and monocrystalline quartz grains suggest that sediments pertaining to Baba sandstones experienced short transport. The study of the detrital grains of Baba reservoir indicates that Baba clastics marker reservoir (Serravallian) was driven mainly from nearby exposures of Red Sea Hills. In addition, the presence of polycrystalline quartz suggests igneous source rocks or metamorphic rocks, particularly (gneisses) [START_REF] El-Ashry | Source and dispersal of reservoir sands in El Morgan field, Gulf of Suez, Egypt[END_REF][START_REF] Salah | The Miocene Kareem Formation in the southern Gulf of Suez, Egypt: a review of stratigraphy and petroleum geology[END_REF][START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF].

Petrophysical interpretations

Baba reservoir shows high gamma-ray, low-density readings, relatively porous zone, and high resistivity values (Fig. 6 & 11). It should be noted that the high gamma-ray of Baba sandstones is related to the K-feldspars content within the reservoir, which increases the gamma-ray response.

The result of the well log analysis showed that the average effective porosity ranges between 12 and 20% with a significant increase towards the BDR (C and D) wells. Hydrocarbon saturation ranging from 79% to 88% and increases towards the BDR (C and D) wells. Low shale volume has been estimated to range from 9% as the lowest up to 13% as the maximum and this amount decreases towards the BDR (C and D) wells. According to the well log analysis, it is inferred that the derived petrophysical parameters exhibited good porosity, low clay content, and high hydrocarbon saturation, which indicates that Baba sandstones facies are excellent sandstones unit or reservoir. The petrophysical investigation inferred that the Net Pay to Gross Ratio (NGR) values are equal to 1, which means that net pay is equal to Gross thickness. These sandy facies characteristics have very high potentiality as a hydrocarbon-bearing reservoir within Baba Member.

Hydrocarbon habitat and petroleum geology

The very high potentiality of the Gulf of Suez basin is related to the fact that the rifting tends to produce both open marine and restricted settings favorable to a source rock accumulation, in addition, the relatively high geothermal gradient [START_REF] Khalil | Hydrocarbon occurrences and structural style of the southern Suez rift basin: Egyptian General Petroleum Corp[END_REF][START_REF] Khalil | Structural architecture of the eastern margin of the Gulf of Suez: field studies and analogue modelling results[END_REF]Dolson, et.al, 2001;[START_REF] Alsharhan | Petroleum geology and potential hydrocarbon plays in the Gulf of Suez rift basin, Egypt[END_REF]Lewis et al., 2016;[START_REF] El Nady | Source rock evaluation for hydrocarbon generation in Halal oilfield, southern Gulf of Suez, Egypt[END_REF].

The hydrocarbon potential of the exanimated area is proved by the successful wells producing from Middle Miocene reservoirs.

The principal source rocks in the Badri field are the Upper Cretaceous Brown Limestone (Senonian) and the Eocene Thebes Formation [START_REF] Egpc | Gulf of Suez oil fields (a comprehensive overview): Egyptian General Petroleum Corporation[END_REF]. These limestones were deposited under a marine environment with anoxic conditions. Limestone facies contain abundant algal and amorphous kerogen of Types II and II/I, and organic richness of 8 wt.% (Table 4) and (Fig. 13) [START_REF] Chowdhary | Geology and habitat of oil in Ras Budran field, Gulf of Suez, Egypt[END_REF][START_REF] Lelek | October Field: The Latest Giant under Development in Egypt's Gulf of Suez: Chapter 15[END_REF][START_REF] Hughes | Miocene biofacies development and geological history of the Gulf of Suez, Egypt[END_REF][START_REF] Egpc | Gulf of Suez oil fields (a comprehensive overview): Egyptian General Petroleum Corporation[END_REF][START_REF] Salah | The Miocene Kareem Formation in the southern Gulf of Suez, Egypt: a review of stratigraphy and petroleum geology[END_REF]. These source rocks are mature and have been generating oil since the latest Miocene to Pliocene times in adjacent deep areas.

The seal rocks in Badri Field consists of evaporites and shales Miocene in age [START_REF] Chowdhary | Geology and habitat of oil in Ras Budran field, Gulf of Suez, Egypt[END_REF]Taha, 1987, EGPC, 1996) (Fig. 12 &13). In the studied area, the upper and lower anhydrite units act as top seal, and the surrounded shale of Baba sandstones facies act as lateral seal. In addition, the structural setting of the field juxtaposed the sandstones facies against the evaporitic seal in the eastern side of the field (Fig. 2 & 12). While Baba shale acts as a lateral seal in the western side of the area (Fig. 12). Oil migrated along the bounding faults, formed after the Mid-Rudeis tectonic event in the late Lower Miocene [START_REF] Egpc | Gulf of Suez oil fields (a comprehensive overview): Egyptian General Petroleum Corporation[END_REF]. Hydrocarbon entrapment seems to have a combined stratigraphic and structural nature. Hence, the studied Baba Member is located between the two principal reservoirs, meaning that the same source rock, migration paths charge the porous zone according to the entrapment and effective seals. The stratigraphic component in Baba sandstones consists of facies change from shale to sandstones. Sediment influx is the key factor that controls the facies change from shale to sandstones in this shallow marine to lagoons deposits. The structural component represents the NW to SE trending anticline with closure of more than 130 meters at the top of Belayim Horizon. To the east, NW to SE trending normal fault bounds the reservoir from the east side with more than one four hundred and fifty meters of throw at the top of Belayim. To the west, the Badri Field is bounded and separated from the North El Morgan Field by NW to SE trending normal fault, dipping NE. This fault juxtaposes the Badri Belayim section against the productive Kareem section in the adjacent El Morgan Field [START_REF] Egpc | Gulf of Suez oil fields (a comprehensive overview): Egyptian General Petroleum Corporation[END_REF]Radwan et al., 2019a, 2020a) (Fig. 2 & 12). Smaller NW to SE trending normal fault with thirty-meter vertical displacement has been detected in the NE portion of Badri Field, which affected the studied Baba sandstones (Fig. 3 & 12). A summary chart of hydrocarbon habitat (source rocks, seals, and reservoirs) and their distribution relative to the formations and geologic ages is shown in (Fig. 13). Accordingly, the trap style for the investigated sandstones facies consists of combined stratigraphic and structural components.

Implications for exploring combined traps in the basin

Exploring stratigraphic and combination traps have had less priority from the beginning of the oil and gas revolution until the twenty century. Stratigraphic traps have historically been viewed as a high risk [START_REF] Stirling | The edges of the wedges: a systematic approach to trap definition and risking for stratigraphic, combination and sub-unconformity traps[END_REF]. Non-structural traps were comprising lower than 20% volume of the structural traps worldwide [START_REF] Dolson | Advances and perspectives on stratigraphic trap exploration-making the subtle trap obvious[END_REF]. Acquiring 3D seismic imaging at the beginning of twenty century has led to an enhancement of the seismic resolution, and develop hydrocarbon system modeling. Moreover, the application of sequence stratigraphy concept in hydrocarbon exploration contributed to look over structural traps. Accordingly, many large stratigraphic or combined prospects have been explored (e.g. offshore Ghana and Mozambique and the Utsira High in the North Sea). The economic success of these traps has spotted the light on these under-explored remains globally (e.g. tight gas in the China Ordos Basin) [START_REF] Attia | Petrophysical analysis and hydrocarbon potentialities of the untested Middle Miocene Sidri and Baba sandstone of Belayim Formation, Badri field, Gulf of Suez, Egypt[END_REF][START_REF] Dolson | Advances and perspectives on stratigraphic trap exploration-making the subtle trap obvious[END_REF][START_REF] Arab | Coupling stratigraphic and petroleum system modeling tools in complex tectonic domains: case study in the North Algerian Offshore[END_REF][START_REF] Nguyen | The forming mechanisms of Oligocene combination/stratigraphic traps and their reservoir quality in southeast Cuu Long Basin offshore of Vietnam[END_REF][START_REF] Hall | Hydrocarbon prospectivity of the Cooper Basin, Australia[END_REF][START_REF] Sladen | Lake systems and their economic importance[END_REF].

Multiple chances for exploring new resources along unconformity surfaces, pinch-out, and carbonate reef could then represent a major opportunity for the Gulf of Suez basin as well. To enhance the exploration effectiveness of stratigraphic and combined traps, companies should increase the use of seismo-stratigraphy, biostratigraphy, and lithostratigraphy approaches along with the sequence stratigraphy one [START_REF] Dolson | Exploring for stratigraphic traps. Exploring for oil and gas traps[END_REF][START_REF] Young | Sedimentology and sequence stratigraphy of a transfer zone coarse-grained delta, Miocene Suez Rift, Egypt[END_REF][START_REF] Alsharhan | Petroleum geology and potential hydrocarbon plays in the Gulf of Suez rift basin, Egypt[END_REF]. In this context, analysis of lateral seals needs large consideration while prospecting risk evaluations using the same approach. In the present study, the paleogeographic maps during the deposition of the Baba Mb. give insight on the potential pinch-out and stratigraphic traps surrounding the known reservoir area. This requires a structural restoration as well as putting the area of interest into perspective in a larger basin-scale context.

In the last decades, non-structural traps have been discovered accidentally in the Gulf of Suez basin [START_REF] Alsharhan | Petroleum geology and potential hydrocarbon plays in the Gulf of Suez rift basin, Egypt[END_REF]. Most of these fields are only small accumulations located in flank positions to the tilted block crests [START_REF] Dolson | Advances and perspectives on stratigraphic trap exploration-making the subtle trap obvious[END_REF]. However, although studies within the last decades have provided a good understanding of the petroleum system of the area, main exploration resources are still focused on the same traditional structural traps, and not exploring the synclinal basins. The study case presented in this work can then highlight the potentiality for further development of near-field exploration in the Gulf of Suez basin and surrounded areas.

Conclusions

Our multidisciplinary analysis allows us to evaluate the reservoir architecture and the structural and stratigraphic characterization of the Middle Miocene Baba sandstones. The main conclusions of our study can be summarized as follows:

 Our sedimentological analysis revealed that there is a correlatable clastic marker within the evaporitic Baba Member, and this unit consists of shale laterally passing into blocky sandstones in the northern part of the Badri Field. The stratigraphic analysis suggests that the Baba sandstones decreases in thickness and pinch-out towards the west.

 The petrographic and petrophysical characteristics of the Middle Miocene sandstones suggests that this unit has a pretty consistent mineralogical composition and it pertains to the same depositional environment throughout the area. Moreveor, the reservoir characteristics suggest that this interval represents a potential reservoir. [START_REF] Wescott | Rift basin sequence stratigraphy: some examples from the Gulf of Suez[END_REF]Bowsorth and McClay, 2001). Sea-level is derived from [START_REF] Haq | Phanerozoic cycles of sea-level change on the Arabian Platform[END_REF]. Stratigraphy and ages are from [START_REF] Hardenbol | Mesozoic and Cenozoic sequence chronostratigraphic framework of European basins[END_REF][START_REF] Gradstein | The Geologic Time Scale[END_REF], respectively.



  Integration of structural and stratigraphic analysis, as well as characterization of the petroleum elements of the Middle Miocene Baba sandstones suggests the presence of a unique combined stratigraphic-structural trapping mechanism.  The result of this study could open up a new direction for the petroleum exploration of potential combined traps in the Gulf of Suez basin. In addition, the lateral facies variability recognized along syn-rift sediments of the Gulf of Suez basin represents an interesting aspect that should be further investigated since it might open a new potential target (i.e. stratigraphic traps) for hydrocarbon exploration and development in the basin.  The combined stratigraphic-structural play characterization presented in this work highlights the hydrocarbon potentiality for further development of near-field exploration in the Gulf of Suez basin and surrounded areas. Accordingly, further studies are needed to extend the knowledge in the adjacent fields, and additional targets such as the Baba and Sidri sandstones must be assessed in further exploration plans.

Fig. 1

 1 Fig. 1 A) Structural map of the Suez rift (after Rohais et al., 2016 and references herein).

Fig. 2

 2 Fig.2Southwest-northeast cross-section through the Suez Rift Basin(after EGPC, 1996). See

Fig. 3

 3 Fig. 3 Structure contour map of Baba Member in the Badri field. Position of the studied wells

Fig. 4

 4 Fig. 4 Stratigraphic scheme of Gulf of Suez for the Miocene to Pliocene interval (modified

Fig. 5 A

 5 Fig. 5 A) Standard composite lithology log of the Belayim Formation used in the Badri Field

Fig. 6

 6 Fig. 6 Stratigraphic correlation of Baba sandstones facies through Badri (A, B, C and D)

Fig. 7

 7 Fig. 7 Paleo-lithological maps for the Belayim Formation (Baba, B4) in the vicinity of the

Fig. 8

 8 Fig. 8 QFL triangular diagram showing the classification of Baba sandstones reservoir.

Fig. 9

 9 Fig. 9 Microphotographs from the A well. (A) Sub-rounded quartz grains with intergranular

Fig. 10

 10 Fig. 10 Microphotograph from the D well. (A) Anhydrite cement between quartz grains;

Fig. 11 A

 11 Fig. 11 A) Computer processed interpretation (CPI) for the well B where, GR is Gamma-ray

Fig. 12

 12 Fig. 12 Cross section through the Badri (A, B, C and D) Wells, (refer to Figure 3 for the line

Fig. 13

 13 Fig. 13 Events chart for the Badri Field. Formations abbreviations: NEZ = Nezzazat, N =

Table 2

 2 Summary of the average petrophysical characteristics for Baba Sandstone in the

	studied wells.
	well	A	B	C	D
	Thickness (ft)	28	20	36	38
	Vsh (%)	12	13	11	9
	PHIE (%)	16	12	17	18
	Sw (%)	17	21	12	14
	Shr (%)	83	79	88	86
	K (mD)	180	183	220	200
	Gross (ft)	28	20	36	38
	Pay(ft)	28	20	36	38
	NGR	1	1	1	1

Table 3

 3 Visual estimates of whole-rock composition for the studied zone samples. Sorting:

	Sample	Constituent grains (%)		Cement/Matrix (%)			Text/ Fabric		Porosity (%)
	number	Quartz	Feldspar	Lithics	accessory	calcite	silica	Anhydite	clay	organics	Average	grain size	sorting	rounding	Total	primary	secondary
	1	67	27	2	1		(1) 1	1	1	400		M	SR	14 12 2
	2	72	25	1					2	2	340		M	SR	15 14 1
	3	70	25	3	2		(1) 2	1	1	460		M/W	SR	13 11 2
	4	69	26	1				2	2		380		M/P	SA	14 12 2
	5	70	25	1	1		(2) 1	2		160		P/M	SR	12 11 1
	6	65	30	2	1				2		280		M	SA	11 9	2
	7	66	28	1	1		(2) 1	1		290		P	SA	15 13 2
	8	72	26						1	1	330		M	SR	13 11 2
	9	70	27		1				1	1	480		W	SA	14 13 1
	10	69	29		1				1		500		W	SR	14 13 1
	11	73	25		1					1	470		W	SR	13 11 2
	12	67	31	1					1		450		M	SA	15 14 1
	13	69	27	2	1			1			380		W	SR	12 10 2
	14	70	24	1	2		(1) 2			520		M	SR	15 14 1
	15	66	27	1	1		(3) 1	2	1	490		M/W	SR	15 13 2
	16	72	26				(1) 1		1	600		M	SA	14 13 1
	17	71	24		1		(2) 1	1	1	560		W	SA	13 11 2
	18	68	27	1	2		(3) 1	1	1	440		M/P	SR	14 12 2
	19	69	28	1			(2) 1		1	420		P	SR	14 13 1
	20	72	26		1		(2)		1		390		M	SR	15 13 2
	21	74	25		1		(2)				520		M	SR	15 14 1
	22	70	26	1	1		(3)		1	1	510		W	SA	15 13 2
	23	71	27				(1) 1		1	490		W	SR	13 11 2
	24	69	27	1			(2) 1	1	1	470		M/W	SA	12 10 2
	25	68	28	1			(2) 1	1	1	390		M	SR	14 12 2
	26	72	26		1		(3)			1	280		M/P	SR	14 12 2
	27	70	28		1		(2) 1			290		M/W	SR	15 13 2
	28	69	29		1		(2)		1		330		M	SR	15 13 2
	29	68	30	1			(2) 1			510		W	SR	11 10 1
	30	71	28				(2)		1		480		M	SR	13 11 2

W= Well; M= Moderate; P= Poor. Roundness: R= Rounded; SR= sub-rounded; SA= subangular. Grain size is in microns. Values in ( ) represent % not included in total percent.

Table 4

 4 Summary of the Source rock parameters for the Badri field, where TOC, total organic carbon; S 2 , hydrocarbons from kerogen cracking; S 3 , organic CO 2 -kerogen derived; T max , pyrolysis temperature at which maximum emission of hydrocarbons occurs, R o , Vitrinite reflectance.

Acknowledgments

The author expresses his thanks to the Egyptian General Petroleum Corporation and Gulf of Suez Petroleum Company GUPCO authorities for their permissions to carry out this study and providing data. Ahmed E. Radwan expresses his deepest thanks to the Narodowa Agencja Wymiany Akademickiej (NAWA) under Project PPN/ULM/2019/1/00305/U/00001 for supporting during this research time as well as deep thanks to Prof. Alfred Uchman for his continuous support during the research period.

CRediT author statement

Ahmed Radwan: Lead, Conceptualization, Methodology, Software, Investigation, Writing-Original draft preparation, Reviewing and Editing, Sébastien Rohais.: Reviewing and Editing, Software. Domenico Chiarella: Reviewing and Editing.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: