Statistical characteristics of the internal structure of the seismic background over a hydrocarbon deposit

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Abstract

The fine structure of seismic background in the territory of an oil field was studied using polyspectral analysis and surrogate models. Statistical test for Gaussianity and linearity showed that natural seismic background in the frequency range of 1–50 Hz is a nonlinear process. Bicoherence graphs revealed statistically significant peaks of phase-related triplets with a characteristic geometry of peak clustering in the main triangular region. To analyze the quasi-noise component of the seismic background, surrogate time series with a randomized phase spectrum were generated, the bispectra of which are free of triplet peaks. Bispectral analysis of surrogate series showed the presence of a non-Gaussian quasi-noise component in the seismic background in the frequency range of 1–6 Hz. Previously, the results of the analysis of the used set of records by two completely different methods, each of which extracts information from different components of the seismic background — quasi-noise and regular, were published. These studies showed that each of the two components contains information sufficient to estimate the total thickness of the productive intervals under the recording point. Based on the results of the bispectral analysis and the features of the algorithms of the two methods, a conclusion was made that the quadratically phase-related triplets and the non-Gaussian quasi-noise component in the field territory are manifestations of endogenous seismic emission and are generated by the same nonlinear process developing in the vicinity of an oil-saturated reservoir. The mechanism of seismic emission should be sought in the class of phenomena with quadratic nonlinearity. The statistical characteristics of the internal structure of the seismic background near oil wells have similar features that differ greatly from the statistical characteristics of the seismic record near a “dry” well located outside the reservoir and not producing oil. Previously unknown prognostic features of the oil/water saturation type of rocks have been identified.

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I. Ya. Chebotareva

Oil and Gas Research Institute, Russian Academy of Sciences

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Email: irinache@inbox.ru
Russian Federation, Moscow, 119333

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2. Fig. 1. Information on previous studies: (a) — scheme of the field work site with the location of wells (black triangles) and the grid of tectonic faults; linear dependences on the total thickness of productive intervals in wells NPZ of the values ​​of dimensionless quantitative indicators of productivity (b) — TI for the TI method and (c) — RHI for the IPDS method [6, 8].

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3. Fig. 2. Dependence on the number of the sliding time window N of the probability P of correct acceptance of the hypothesis H0 (upper row) — on Gaussianity using the Dg statistics, surrogate series type FT; (lower row) — on linearity using the Dl statistics, surrogate series type AAFT. Types of model time series: stochastic (C1) — Gaussian and (C2) — non-Gaussian, linear (C3) — Gaussian and (C4) — non-Gaussian, (C5, C6) — non-linear.

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4. Fig. 3. Probability P of correct acceptance of hypothesis H0 about Gaussianity (upper row) and hypothesis H0 about linearity (middle row) depending on the number of the sliding time window N for seismic background records near wells N1, N2, N0; (lower row) — values ​​of time series dispersion D normalized to the maximum. The dashed line marks the boundary of the critical region P* = 1 − α at the significance level α = 0.06.

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5. Fig. 4. Bi-coherence plots calculated based on the seismic background record near well N2 (left) — for the original seismic record and (right) — for surrogate time series. Normalized to the maximum.

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6. Fig. 5. Statistical characteristic of the second order of the structure of the quasi-noise component of the seismic background near oil wells. Averaged along the direction f1+f2 = const values ​​of the bi-coherence matrices for seismic noise records near oil wells (upper row) — for the original seismic records and (lower row) — for surrogate time series. Normalized to the common maximum for each type of series. The position of the wells is shown in Fig. 1. The dashed line is the average value for Gaussian noise.

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7. Fig. 6. Statistical characteristics of the second order of the structure of the regular component of the seismic background near oil wells. Statistically significant peaks of the bicoherence matrix corresponding to phase-related triplets. Top and bottom: results of two different methods of rejecting smaller values. Description in text. The location of the wells is shown in Fig. 1.

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8. Fig. 7. Statistical characteristics of the second order of the structure of the quasi-noise and regular components of the seismic background: (a) — results averaged over the recording points for the quasi-noise component of the seismic background near oil wells, shown in Fig. 5, and (b) — calculated based on the seismic background record near a “dry” well; (top) — results for the original records, (bottom) — for surrogate time series. Matrices of peaks caused by phase-related triplets: (c) — calculated based on the seismic background records near oil wells, Fig. 6, and summed, (g) — calculated from the seismic background recording near the “dry” well; (top) and (bottom) — results of two different methods of rejecting smaller values. The vertical line marks the 6 Hz boundary. The dashed line — the average values ​​for Gaussian noise. The inclined lines are described by equation (14).

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