(Guangzhou Marine Geological Survey Guangzhou 5 10760)
About the author: Zhao Zhongquan, male, (1983—), master, mainly engaged in the investigation and research of marine oil and gas resources, e-mail: zzqhello @163.com.
Using seismic numerical simulation technology combined with actual data, we can establish seismic identification models of various geological bodies, effectively avoid the multiplicity of seismic phenomena, and thus improve the interpretation accuracy. This paper introduces the method flow of two-dimensional geological modeling and two simulation methods-convolution method and PSPI wave equation method. The former is the earliest seismic wave field simulation method because of its simplicity, easy operation, stable calculation and wide application. By solving the wave equation, the latter contains abundant wave field information, which can fully reflect the dynamic and kinematic characteristics of seismic waves. In practical application, the convolution method is used to simulate the three-dimensional tidal channel model and the simplified multi-cycle inclined thin interbedded sedimentary model of carbonate rocks. The zero offset frequency wave number domain wave equation method is used to simulate the seismic response of reefs, and the results have certain guiding significance for the identification of carbonate reefs.
Geological modeling; Numerical simulation; Convolution method; PSPI method
Different geological bodies have different seismic reflection characteristics, including internal structure, external morphology, amplitude, frequency and other parameters, due to their differences in lithology, physical properties, oil and gas bearing properties, internal structure and rock combination. Due to the complexity of seismic wave propagation in underground soil and various interferences, there are multiple solutions of various reflection phenomena on seismic profile, which greatly increases the difficulty of seismic interpretation. Using seismic numerical simulation technology combined with actual data, the seismic identification models of different geological bodies are established, which can effectively avoid the multiplicity of seismic phenomena and improve the interpretation accuracy.
1 geological modeling
The foundation of seismic numerical simulation technology is the establishment of geological geophysical model, which can be summed up as the mathematical description of geological geophysical model structure.
Two-dimensional closed structure model is used to establish complex geological model. The two-dimensional closed structural model defines the same geological attribute as an independent closed geological unit, divides the geological model into several independent closed geological units according to the geological attribute, and arranges all the independent closed geological units in an orderly manner in space, thus constructing a two-dimensional geological model. The closed structure model defines the underground geological structure through building blocks, which can describe very complex geological bodies. The two-dimensional closed structure model is described as an organic combination of geological units with the same geological attributes (speed, density, etc.). ) and surrounded by stratum interface, fault interface or model boundary. The description of closed structure model actually describes the relationship between closed geological units and closed geological units. The former includes the description of the attributes and boundaries of closed geological units. The latter is the description of the spatial relationship of geological units, that is, the description of the boundary connection relationship and stratigraphic attributes of closed geological units [1].
In the process of numerical simulation, in order to verify the wave field characteristics of some complex geological bodies, it is necessary to draw various geological models. Usually, with the help of conventional drawing software (drawing board, Photoshop, CorelDraw, AutoCAD, etc.), two-dimensional closed structural surfaces can be drawn. ), and then according to the region filling algorithms in image processing (seed filling and scanning conversion filling), different two-dimensional closed structural surfaces are filled with different colors. Among them, different colors represent different two-dimensional closed structural plane attributes (speed, density, etc.). ); The closed surfaces with the same attributes are merged to form the final two-dimensional closed structure model [1]. So as to obtain properties (speed, density, etc. The model of two-dimensional closed structure model needs to convert the color map of two-dimensional closed structure model into speed pixel space and attribute space. According to the mutual mapping between color space and attribute space, attributes (speed, density, etc. ) model, as shown in figure 1, creates a flow chart for the model.
Figure 1 Flow chart for establishing two-dimensional closed structure model
2 Two numerical simulation methods
2. 1 convolution model
In convolution model, we regard seismic reflection signal s(t) as the convolution of seismic wavelet w(t) and underground reflectivity r(t). Seismic wavelet w(t) is the waveform reflected by a single underground reflection interface recorded by the actual seismic system (as shown in Figure 2, ideal noiseless convolution process). The reflectivity r(t) represents an ideal noiseless seismic record. The recorded seismic trace s(t) can be regarded as the sum of seismic signal w(t)* r(t) and additive noise n(t), so the seismic trace can be regarded as the deformation of filtered underground reflectivity with noise interference.
In noiseless convolution model, we regard seismic signal S(t) as the convolution of seismic wavelet w(t) and underground reflection coefficient r(t):
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Where: s (t)-synthetic seismic record;
R(t)- reflection coefficient;
W(t)- seismic wavelet.
Figure 2 Convolution process
2.2 PSPI wave equation method
By solving the wave equation, the numerical simulation method can fully reflect the dynamic and kinematic characteristics of seismic waves, with rich wave field information and accurate simulation results. This paper only introduces the wave field continuation method of phase shift interpolation in frequency-wave number domain [2], which is suitable for the drastic change of lateral velocity.
The basic idea of phase-shifting interpolation wave field continuation method, called PSPI method for short, is to divide the wave field continuation into two parts in each depth step Δ z of wave field downward continuation. Firstly, the wave field p(x, zi, ω) at the depth zi is extended to zi+ 1 = zi with l reference velocities. Secondly, according to the relationship between the actual migration velocity V(x, z) and the reference velocity V 1, V2…, VL, the wavefield p(x, zi+ 1, ω) at zi+ 1 is obtained through wavefield interpolation, and zi+65438+ is obtained according to the same steps.
For isotropic media, the two-dimensional scalar acoustic wave equation is taken as the basic continuation equation:
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Where p = p (x, z, t) is the value of two-dimensional seismic wave field; X and z are the coordinate axes in the horizontal and vertical directions, respectively; T is the time axis; V(x, z) is the propagation velocity of seismic waves, which is variable in both vertical and horizontal directions. Formula (2) Fourier transforms X and T respectively, considering and considering? 2/? The correspondence between x2 sum and (-ikx)2 and (iw)2 can be obtained as follows:
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Where is the two-dimensional Fourier transform of p(x, z, t); V is the seismic wave velocity; W is the circumferential frequency; Kx is the horizontal wave number; Kz is the vertical wave number. The seismic record simulation with zero offset only considers one-way wave, so the continuation formula of phase displacement wave field can be obtained as follows:
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Where (kx, zi, w) is the wavefield value in the frequency wavenumber domain; δ z is the depth continuation step; Kx is the wave number in the survey line direction; Kz is the depth wave number. Formula (4) is the forward formula of two-dimensional wave field, and its continuation direction is from underground to ground; Equation (5) is a two-dimensional wave field migration formula, and its continuation direction is from the surface to the underground.
In order to meet the requirement that the velocity of underground seismic wave field can be changed in both vertical and horizontal directions, several different seismic wave velocities are used to phase shift in the same extension depth, and then Lagrange interpolation formula is used to interpolate, so that all the extended wave field values P(x, zi+ 1, t) propagating at different velocities can be obtained, and the wave field extension problem with lateral velocity change can be approximately solved [3].
3 Simulation example
3. 1 numerical simulation of three-dimensional tidal channel
A simple three-dimensional tidal channel model is established by using convolution principle. This three-dimensional tidal channel is actually formed by arranging a plurality of (128) two-dimensional sections. The sampling point of the three-dimensional model is 128× 128, which is realized by MATLAB. Choose the wavelet as Rick wavelet, and its formula is:
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Where fp is the main frequency. In the process of machining, the main frequency is FP = 40 Hz, the sampling interval is 2 ms, and the number of symmetrical sampling points is 24. The wavelet waveform is shown in Figure 3.
Fig. 3 Lake wavelet
Fig. 4 Plan of Tidal Channel
Fig. 4 is a plan view of the tidal channel, which only reflects the plan shape of the tidal channel. As the boundary control of three-dimensional modeling realized by computer, the abscissa represents the vertical line and the ordinate represents the xline (crossing line). Fig. 5 is a schematic diagram of a three-dimensional geological model. The model is simple, and the whole tidal channel is composed of three layers. The tidal channel shown in fig. 4 is embedded between the second layer and the third layer, and the inflow direction of the tidal channel is not considered. According to this geological model, computer seismic forward modeling can be carried out and the corresponding three-dimensional seismic data volume can be obtained. As can be seen from the figure, the yellow dashed line (upper) and the blue dashed line (lower) respectively span three tidal channel branches and two tidal channel branches, that is to say, the two survey lines at the corresponding two dashed lines should have three and two tidal channels respectively, and the corresponding two sections are extracted as shown in Figures 6 and 7:
Fig. 5 3D geological model
Figure 6 XLine = 100 (yellow dotted line)
Figure 7 XLine = 100 (blue dotted line)
Then slice along the horizontal direction in the three-dimensional data volume, that is, extract the time slice. Fig. 8 is a schematic diagram of the position of the time slice on the seismic section. The five marking lines in the figure are white solid line, yellow dotted line, white solid line, red dotted line and white solid line from top to bottom, and the corresponding time is 70 ms, 85 ms, 95 ms, 99 ms, 1 10 ms (the time range is 0 ~ 128 ms). Figures 9 ~ 13 show the corresponding slices. As can be seen from the figure, with the increase of slicing time (depth), the distribution range of tidal channels gradually decreases. Because the stratum is horizontally layered, time slicing is equivalent to stratum slicing and slicing along the stratum, and its slicing effect is very obvious. The shape of tidal channel is well shown in the slice, but it is found in many slices. The time range from the visible tidal channel shape to the disappearance of tidal channel is between 70 ~ 65438+80~ 100 ms, while the real range of tidal channel is between 80~ 100 ms. The range of tidal channel delineated according to the slice is obviously wider than the real range. The reason is that no matter which wavelet is chosen, it has a certain duration and limited bandwidth, which limits the synthesis. Therefore, when interpreting actual seismic data and identifying geological anomaly boundaries, the influence of seismic wavelet should be considered instead of pulse wave.
Fig. 8 is a schematic sectional view
Fig. 9 Slice t = 70 ms
Figure 10 slice t = 85ms
Figure 1 1 slice t = 95ms.
Figure 12 slice t = 99ms
Figure 13 slice T = 1 10 ms
3.2 Thin Interlayer Deposition Model
Figure 14 is a simplified multi-cycle inclined thin interbed sedimentary model of carbonate rocks (Zeng, 2003). In order to better highlight the relationship between wave impedance structure controlled by lithofacies and seismic signals, it is simplified. All the dip angles of the model are the same, and the vertical time thickness of each layer is the same (5 ms or 15 m, the speed is 6000 m/s). The wave impedance differences between mudstone and low porosity granular limestone, and between low porosity granular limestone and high porosity granular limestone are the same. All high porosity granular limestones have the same depth range, forming a horizontal lithologic stratigraphic unit.
In the time-domain seismic response (figure 15), in the case of high frequency (60 Hz lake wavelet), the seismic reflection is constructively tuned to the time stratigraphic unit, so the seismic in-phase axis is distributed along the time stratigraphic unit (figure 15a). When the wavelet frequency is reduced to 40 Hz, seismic reflection responds to both time stratigraphic units and lithologic stratigraphic units (Figure 15b). When using 30 Hz lake wavelet (figure 15c), the seismic event axis is destructively tuned to the time stratigraphic unit and constructively tuned to the lithologic stratigraphic unit, so the reflection of the time stratigraphic unit is further weakened, and the seismic event axis is controlled by the lithofacies reflection [4].
This simulation process emphasizes the importance of understanding the geological framework, time stratigraphic unit and thickness scale of lithostratigraphic facies belt. Imaging of time horizon (Figure 15a) and lithologic horizon (Figure 15c) is useful. The former is used for correlation and the latter is used for rough reservoir evaluation. However, these two reactions cannot be confused. Two sets of contradictory earthquake events in figure 15b will cause earthquake illusion [4].
Figure 14 Simplified Model of Multi-cycle Inclined Thin Interlayer Deposition of Carbonate Rock
3.3 Numerical simulation of reefs [5 ~ 7]
Frequency-wavenumber domain phase shift plus interpolation migration (PSPI) uses multiple reference velocities for migration at each depth interval, and generates the final migration profile by interpolating multiple migration results. The more interpolation speed is used, the more it can reflect the speed change of the actual medium. This method has great advantages in imaging accuracy and lateral speed change adaptability, but the processing time is a little longer. In view of the fact that the two-dimensional post-stack modeling in this paper does not need too much processing time, PSPI method is used for forward simulation.
Figure 16 shows the original seismic profile of a block passing through the reef, and Figure 17 shows the reef velocity model based on this profile: the model velocity varies from 5600 m/s to 5980 m/s, and it can be seen from Figure 16 that the bottom interface of the reef is clearly identifiable, the surrounding rock is covered and the internal reflection is chaotic. In order to verify the correctness of geological modeling, PSPI method is used to simulate the wave field of the model, and the simulation section is shown in Figure 18. Because the reef is deeply buried, the reflection radian at the top and bottom of the reef is large, and the diffracted waves at irregular points are messy, so the velocity model in Figure 15 is used for post-stack time migration, and the migration profile (Figure 19) is obtained, which shows 256 seismic traces horizontally and zero offset reflection time vertically, as shown in Figure 19. There is a certain gap between the top boundary of the reef in the simulated record and the original profile, but the bottom boundary reflection, internal reflection and flank reflection of the reef are basically consistent with the original profile, and the shapes of other stratigraphic interfaces are also in good agreement with the original profile. This verifies the correctness of the geological model to some extent, and shows that when there is a certain wave impedance difference between the reef and the surrounding rock, abnormal reflection will appear on the seismic profile, which can be distinguished by effective structure and parameter inversion. It is believed that by improving the model and adjusting the parameters in the algorithm, it can be better consistent with the original profile, thus providing a powerful verification tool for seismic interpretation of reefs.
Figure 15 Figure 14 Seismic Response of Time Domain Model
4 conclusion
Seismic numerical simulation (forward simulation) technology is based on the establishment of geophysical model, using the method of establishing conceptual two-dimensional closed structural geological model to obtain the mathematical model of complex geological body, and simulating with various algorithms can verify the seismic wave field characteristics of the corresponding geological body. Establishing seismic identification models of different geological bodies combined with actual data can effectively reduce the multiplicity of seismic phenomena and improve the interpretation accuracy; Convolution method has no boundary condition constraint and signal loss in frequency domain, which is simple and easy to operate, stable in calculation and widely used. The pseudo three-dimensional tidal channel model and inclined thin interbed model simulated by this method have achieved good results. The numerical simulation method for solving wave equation contains abundant wave field information, which can fully reflect the dynamic and kinematic characteristics of seismic waves. PSPI wave field continuation method is one of them. The seismic response characteristics of reefs are simulated by combining forward modeling and migration, which verifies the correctness of the interpretation results and provides a powerful test tool for seismic interpretation of reefs.
Figure 16 Original Section
Figure 17 Geological Velocity Model of Reef (256×256)
Figure 18 forward recording (wavelet main frequency is 30Hz)
Figure 19 migration profile (main frequency of wavelet is 30Hz)
refer to
Liu. Seismic facies analysis and numerical simulation of carbonate rocks [D]. Chengdu: Chengdu University of Technology, 2009.
Han Jianyian. Seismic forward modeling and migration of complex geological bodies [D]. Chengdu: Chengdu University of Technology, 2008.
Zhenhua He, Wang Caijing, et al. Migration processing and inversion method of reflected seismic data [M]. Chongqing: Chongqing University Press, 1989.
Zeng and Kerens. Seismic frequency control in carbonate seismic stratigraphy; Bulletin of the American Association of Petroleum Geologists, August 7, 2003, 273~293.
Zhenhua He, Huang, Wen Xiaotao, et al. Multi-scale and high-precision seismic identification technology for carbonate reef and beach reservoirs [R]. Chengdu: Key Laboratory of Earth Exploration and Information Technology, Ministry of Education, Chengdu University of Technology, 2009.
Xiong Xiaojun, Zhenhua He, Huang. Numerical simulation of seismic response characteristics of reefs [J]. acta petrolei sinica, 2009,30 (1): 7 ~ 65.
Xiong Zhong, Zhenhua He, Huang. Seismic numerical simulation and response characteristics analysis of reef reservoirs [J]. Journal of Petroleum and Natural Gas, 2008,30 (1): 75 ~ 78
Application and analysis of two seismic numerical simulation methods based on two-dimensional geological modeling
Zhao zhongquan
(Guangzhou Marine Geological Survey, Guangzhou, 5 10760)
Abstract: Using the seismic numerical simulation technology combined with the actual seismic data, the seismic identification models of various geological bodies can be established, which can effectively avoid the multiplicity of seismic phenomena and improve the interpretation accuracy. This paper introduces the method of 2D geological modeling process and two simulation methods, namely, seismic convolution method and PSPI wave equation method. The former is the earliest simulation method of seismic wave field, which has no boundary conditions and signal loss in frequency domain, is simple, easy to operate, stable in calculation and widely used, while the latter is based on wave equation and contains rich wave field information, which can fully reflect the dynamic and kinematic characteristics of seismic waves. In practical application, we adopt the evolution model in the three-dimensional tidal channel model and the multi-cycle simplified sedimentary model of thin interbedded carbonate rocks. We simulated the seismic response of reefs in frequency and wave number domain by wave equation method with zero offset, and confirmed that the results are of certain significance to the identification of reefs.
Keywords: Geological modeling numerical simulation convolution PSPI method