THE EXPERIMENTAL MODEL TPDOT&TWSM APPROACH COMPUTATION RESULTS

COMPUTATION OF DIFFRACTED WAVEFIELDS BELOW

LEVANT BASIN MULTI-LAYERED EVAPORITIC SUCCESSION ON GPUs

N. ZYATKOV1, A. AYZENBERG2, A.M. AIZENBERG3, O.E. ERUTEYA4, K. OMOSANYA5

Across the Mediterranean basins, the Messinian salinity crisis resulted in the deposition of up to 2 km thick multi-layered evaporitic succession consisting of alternating layers of halite and clastics [2, 3]. Such geological objects obscure seismic imaging and may even be over pressurized posing

potential drilling hazards, which are often hard to predict [4]. We demonstrate TPDOT&TWSM approach developed in IPGG SB RAS by example of evaluating the interference wavefields wave fragment into the shadow zone for real geological case from the Levant Basin, offshore Israel. Using of

GPUs allowed accelerating TWSM algorithm based on multiple large size matrix-vector operations in hundreds and more times.

We analyzed complex intra-salt structures within the Messenian evaporites from a three-dimensional, depth-migrated, seismic reflection volume from the Levant Basin, offshore Israel (Figure 1).

In the black circle, we have identified the clastics under consideration and the corresponding seismic blanking spot. Structure of the experimental model includes five layers: 3 clastic and 2 halite layers in between (Figure_2, left). We assumed that all layers are homogeneous and of severe curvature (Figure 2, right).

Medium and geometrical properties were taken from borehole data analyzed in [2]. We put a plane wave source at the sea surface and receivers line beneath the source. The edges E1, E2 and E3 of interfaces C1, C2 and C3, respectively, cause the edge diffraction waves. Similarly to optics, the seismic blanking in ME1 occurs due to the interference of the wavefield: the transmitted wave through C1, C2 and C3 and the edge-diffracted waves at E1, E2 and E3 all together give very weak wave amplitude; the image based on the low amplitude wave is therefore unclear (Figure 2). By that reason we observe the shadow in ME1.

Using TPDOT&TWSM, we obtained the reflected wave from ME1 (Figure_5). The modelling result confirms that in the middle of the seismogram the amplitudes are very weak (we had to zoom the seismogram 500 times for the traces to become visible; the red circle in Figure 5). It is obvious that the inversion of such a wavefield resulted in the shadow zone in ME1 of Figure 1. Therefore, in order to obtain a better image, the diffracted wave must be extracted from the interference wavefield. Since it has high amplitude its inversion will give enough illumination in the shadow.

Table below shows model computation time at 8 kernels of Intel Xeon 2.53 GHz CPUs in comparison to computation times on 3, 12, 24 and 30 NVIDIA Tesla M2090 GPUs with Fermi-architecture.

Figure 5. The seismogram representing the low amplitude wave in the shadow.

Intel Xeon

2.53 GHz (8 kernels) 3 GPUs 12 GPUs 24 GPUs 30 GPUs

Computation time (min) 720 20.4 5.8 3.2 2.8

1 Novosibirsk State University, Novosibirsk, Russia, nikolay.zyatkov@gmail.com

2 University of Bergen, Bergen, Norway, alena.ayzenberg@gmail.com 3 Institute of Petroleum Geology and Geophysics, Novosibirsk, Russia, AizenbergAM@ipgg.sbras.ru

4 University of Haifa, Haifa, Israel, oeruteya@campus.haifa.ac.il 5 Norwegian University of Science and Technology, Norway, kamaldeen.o.omosanya@ntnu.no

ACKNOWLEDGMENTS We are thankful to NTNU and the Research Centres Bergen and Trondheim of Statoil ASA. We thank Nicolas Waldmann, Milana Ayzenberg, Jan Pajchel, Ola-Petter Munkvold and Kees Wapenaar. We also thank Schlumberger for granting Petrel-E&P Software to the University of Haifa. REFERENCES [1] Aizenberg, A and Ayzenberg, A. (2015). Wave Motion, 53:66–79. [2] Feng, Y.E., Yankelzon, A., Steinberg, J., Reshef, M. (2016). Mar. Geol. doi:10.1016/j.margeo.2016.04.004 [3] Roveri, M. et al. (2014), Mar. Geol., 352(0), 25–58. [4] Van Gent, H., Urai, J.L., de Keijzer, M. (2011). Journal of Structural Geology, 33, 292–311. doi:10.1016/j.jsg.2010.07.005 [5] Zyatkov N., Ayzenberg A., Omosanya, K.O, Romanenko A., Aizenberg M. A. (2016). ICAIT-2016.

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Figure 3. TWSM matrix-vector multiplication scheme adapted for GPUs.

Figure 4. Scalability of the TWSM algorithm.

Transmission-Propagation-Diffraction Operator Theory (TPDOT) [1] describes in explicitly analytic form propagation of the seismic wavefields in 3D block-layered geologic media by action of two operators: 1) transmission operator (reflection/refraction) at curved interface, 2) propagation operator inside block/layer. Tip-Wave Superposition Method (TWSM) [5] being the mid-frequency range approximation of TPDOT. TWSM computes the wave amplitude functions at receivers by multiple multiplication of large scale matrices and and wave amplitude function for source wavefield at interface C3. For model at Figure 2 wave amplitude function at receivers reflected from ME1 can be represented as matrix-vector multiplication:

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Matrix describe propagation from elements of clastic interface Ci to elements of clastic interface Cj. Matrix describes propagation from elements of clastic interface C3 to receivers x. Matrices describe refraction from halite layer hl in layer hk through the clastic layer. Matrix kjhkjdescribes reflection from clastic layer ME1. Each wave amplitude vector in the frequency domain demands to repeat matrix-vector multiplications (1) for each discrete frequency of some frequency array ______ . Acceleration of each matrix-vector multiplication is realized on GPUs with help of scheme, shown at Figure 3. Each GPU accelerator processes multiplication of group of matrix strips corresponding to frequencies . by group of wave amplitude vectors. Finally GPUs gather new transformed group of wave amplitude vectors via exchange by computed data. Since matrix dimension is , then TWSM algorithm adapted for GPUs can potentially keep any number of available GPUs but no more than . Curve of scalability the TWSM algorithm is demonstrated at Figure_4.

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Figure 1. Left: Map of Levant Basin Province, Eastern Mediterranean. Right: 2D seismic profile showing the stratigraphy of the Levant Basin, the structure of

interest and a seismic blanking spot in ME1.

Figure 2. Left: experimental model for TPDOT&TWSM with three edge-shaped diffractors. Right: 3D interfaces of multi-layered evaporitic succession.