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Pet. Sci. (2016) 13:225–236 DOI 10.1007/s12182-016-0092-7 ORIGINAL PAPER Velocity calibration for microseismic event location using surface data 1 1 1 1 1 • • • • Hai-Yu Jiang Zu-Bin Chen Xiao-Xian Zeng Hao Lv Xin Liu Received: 17 July 2015 / Published online: 20 April 2016 The Author(s) 2016. This article is published with open access at Springerlink.com Abstract Because surface-based monitoring of hydraulic samples, and an appropriate number of travel times within fracturing is not restricted by borehole geometry or the the threshold range are chosen. The corresponding velocity difficulties in maintaining subsurface equipment, it is models are then used to relocate the perforation-shot. We becoming an increasingly common part of microseismic use the velocity model with the smallest relative location monitoring. The ability to determine an accurate velocity errors as the basis for microseismic location. Numerical model for the monitored area directly affects the accuracy analysis with exact input velocity models shows that of microseismic event locations. However, velocity model although large differences exist between the calculated and calibration for location with surface instruments is difficult true velocity models, perforation shots can still be located for several reasons: well log measurements are often to their actual positions with the proposed technique; the inaccurate or incomplete, yielding intractable models; ori- location inaccuracy of the perforation is \2 m. Further gin times of perforation shots are not always accurate; and tests on field data demonstrate the validity of this the non-uniqueness of velocity models obtained by inver- technique. sion becomes especially problematic when only perforation shots are used. In this paper, we propose a new approach to Keywords Velocity calibration Microseismic overcome these limitations. We establish an initial velocity monitoring Double-difference RMS error Very fast model from well logging data, and then use the root mean simulated annealing Perforation-shot relocation square (RMS) error of double-difference arrival times as a proxy measure for the misfit between the well log velocity model and the true velocity structure of the medium. 1 Introduction Double-difference RMS errors are reduced by using a very fast simulated annealing for model perturbance, and a Hydraulic fracturing of low-permeability reservoirs gen- sample set of double-difference RMS errors is then selec- erates many microseismic events due to pressure increase ted to determine an empirical threshold. This threshold associated with fluid injection into treatment wells value is set near the minimum RMS of the selected (Warpinski et al. 2005). Fracture development can be characterized by various microseismic monitoring tech- niques (Liang et al. 2015; Wang et al. 2013). Generally & Zu-Bin Chen speaking, when the approximate locations of perforation czb@jlu.edu.cn shots can be resolved, we have the confidence to locate Hai-Yu Jiang nearby microseismic events, and a usable velocity model joyjiang1987@126.com plays an important role to achieve this goal (Usher et al. 2013). At present, because of the convenience of operation, Key Laboratory of Geo-Exploration and Instrumentation of Ministry of Education, College of Instrumentation and surface observations are an effective technique when Electrical Engineering, Jilin University, monitoring wells cannot be used. They are one of the main Changchun 130026, Jilin, China targets for improvement in future microseismic monitoring. Microseismic monitoring with surface observations Edited by Jie Hao 123 226 Pet. Sci. (2016) 13:225–236 requires a well-resolved velocity model, yet many factors double differences (DDrms) (Concha et al. 2010; Wald- can interfere with model calibration, as follows. (1) Well hauser and Ellsworth 2000; Zhang et al. 2009a, b; Zhang logs are influenced by many extraneous factors, such as and Thurber 2003; Zhou et al. 2010). Using the relative pore pressure, stress accumulation, and mud invasion; in differences of the first arrival times of multiple events, addition, seismic wave velocities around the reservoir can DDrms values are minimized using very fast simulated be altered by prior resource extraction, including mining. annealing (VFSA) (Pei et al. 2009). In order to obtain an Consequently, velocity measurements from well logs are optimal velocity model for perforation relocations, we often unsuitable for microseismic event location (Grechka select a subset of DDrms from the results of simulated et al. 2011; Pei et al. 2009; Quirein et al. 2006; Zhang et al. annealing. A threshold is set near the minimum value, and 2013a, b). Moreover, log data may be incomplete, which velocity models with DDrms values between the threshold naturally reduces the accuracy of the initial model. Meth- and the minimum are chosen for further analysis. These ods based on searching for a local optimal solution (Pei models are then used to relocate the perforation shots. We et al. 2008; Tan et al. 2013) are not suitable for this task. choose the velocity model with the smallest perforation (2) A particularly common problem in microseismic shot location errors as the model for locating microseismic monitoring is a combination of little available source events. information (e.g., perforation shots), few receivers, and This paper first introduces the principles of the method, poor network coverage, resulting in a poorly constrained and then conducts tests on synthetic data. We investigate velocity model. (3) Perforations are often not precisely the influences of velocity range constraints and picking timed, so a velocity model cannot always be calibrated errors on the proposed technique. Finally, the proposed using perforation travel times alone. Although seismic technique is applied to data from a perforation shot at a gas tomography is widely used to image earth structure on shale reservoir as an example of velocity model local to global scales, the above limitations mean that we calculation. cannot expect the same high-quality results from micro- seismic monitoring data (Bardainne and Gaucher 2010). Several papers have proposed methods to construct reser- 2 Travel time calculation voir velocity models for microseismic event location, most of which are based on the following steps: (1) A simple This study uses ray tracing to obtain travel times for velocity model, using only a few parameters, is constructed microseismic events and perforation shots. Traditional two- from well logging data. (2) Known positions of perforation point ray tracing algorithms mainly comprise shooting shots are iteratively relocated until a suitable velocity (e.g., Xu et al. 2004) and ray bending algorithms (e.g., Li model is obtained. Pei et al. (2009) and Bardainne and et al. 2013). More recent works use wave front extension Gaucher (2010) developed a fast simulated annealing methods based on the eikonal equation and Huygens’ algorithm to invert for a velocity model, which showed principle (e.g., Zhang et al. 2006a, b); the shortest path little dependence on initial values and outperformed the algorithm (Wang and Chang 2002; Zhang et al. 2006a, b; local optimal solution technique. However, the method still Zhao and Zhang 2014); and the LTI method (Zhang et al. faced the problem that perforation shot origin times are 2009a, b), based on graph theory and Fermat’s principle. generally inaccurate. Tan et al. (2013) proposed an inver- Compared with the above methods, ray tracing based on sion method based on time differences calculated from Snell’s law is not restricted by nodes and can provide picked arrival times, which circumvented the issue of ori- accurate travel time and azimuth information (Zhang et al. gin time inaccuracies. However, their method was still 2013a, b). Traditional shooting methods were improved by sensitive to the initial model. Anikiev et al. (2014) Gao and Xu (1996), who proposed a new type of step-by- described a method in which the initial velocity of each step iterative ray tracing algorithm that greatly improved layer was simultaneously increased or decreased using the computational efficiency. This method can also be used accuracy of perforation shot relocations as an evaluation with a slightly more complicated velocity model than other standard. They obtained a relatively accurate velocity techniques. In this paper, we expand the method to a 3D model by inversion. However, their method still could not layered structure for calculating travel times. satisfy the precision requirements of microseismic event location. 2.1 Ray tracing in a layered medium This paper presents a new method to address the prob- lem of velocity model calibration using surface data. A As shown in Fig. 1, the dichotomy is used to determine the one-dimensional layered model is built, in which the dif- shortest path between two points in difference medium. We ference between theoretical and expected models is char- set the medium interface to Z = z , where P is the launch 2 1 acterized by the root mean square (RMS) errors of time point, P is the receiver, P is the intersection of P and P 3 2 1 3 123 Pet. Sci. (2016) 13:225–236 227 P x y z ( , , ) x ¼ðÞ x þ x =2 3 3 3 3 > 3 2 0 0 y ¼ y þ k x x ð7Þ 2 xy 3 2 3 z ¼ z ' ' ' ' 3 Z P ( x , y , z ) 3 3 3 3 where k = (y - y )/(x - x ) is the slope of the pro- xy 2 1 2 1 θ jection of the line segment onto the plane Z = z . P is then 2 2 θ 0 ' ' ' ' obtained by Eqs. (6) and (7), and P is replaced by P . The P ( x , y , z ) P x y z 2 ( , , ) 2 2 2 2 2 2 2 2 θ steps above are repeated until e is sufficiently small, which yields an estimate of P . 2.2 Step-by-step iterative ray-tracing method In this paper, source–receiver paths in a layered medium P ( x , y , z ) 1 1 1 1 are modified using a step-by-step iterative method. The specific steps (also shown in Fig. 2) are as follows. Fig. 1 Solving the refraction points by dichotomy (1) The starting point P and endpoint P are connected with 0 n a straight line. The intersections of the line with each layer (denoted P , P , P , … P ) are calculated. 1 2 3 n-1 with the medium interface, and P is the end point of the (2) Y is taken as the first interface. A new intermediate test ray path. refraction point P is calculated between P and P 0 2 Beginning with Snell’s law of refraction, 1 using the dichotomy method, and P is replaced by P . sin h v 1 1 P , P , P , …, P can be obtained in the same way. ¼ ð1Þ 1 2 3 n-1 sin h v 2 2 0 (3) Repeat step (2) until t - t \e,where t is the travel time 0 0 of the previous iteration and t is the current travel time. and substituting P , P , P into the equation above, we 1 2 A series of intermediate points is obtained. The line that have qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi connects these points with the two endpoints is taken as 2 2 0 0 v x x þ y y the minimum travel time path. 1 2 2 3 3 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 0 0 0 x x þ y y þ z z 2 2 2 3 3 3 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 v ðÞ x x þðÞ y y 2 1 2 1 2 3 Principle of velocity model perturbance ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2Þ 2 2 2 ðÞ x x þðÞ y y þðÞ z z 1 2 1 2 1 2 3.1 Very fast simulated annealing with DDrms 0 0 If x = x , y = y , then 3 3 3 3 In field data, and particularly for surface observations, the cðÞ 1 b location error of a perforation shot is always very large a ¼ ð3Þ pffiffiffi z ¼ z þ aðz \z Þ 3 1 2 pffiffiffi ð4Þ P z ¼ z aðz [ z Þ 3 1 2 2 2 3 0 0 If c = (x - x ) ? (y - y ) , then 2 2 3 3 P ' qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 v ðÞ x x þðÞ y y 2 1 2 1 2 P Y b ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ 2 2 2 2 2 v ðÞ x x þðÞ y y þðÞ z z 1 1 2 1 2 1 2 P Y We can then solve for P . If the vertical error satisfies 1 1 e = (z - z ) \ 0, or if b [ 1, then x ¼ðÞ x þ x =2 > 1 2 < 2 0 0 y ¼ y þ k x x ð6Þ 2 xy 2 2 2 z ¼ z Fig. 2 Iterative node point adjustment (red solid line represents the On the other hand, if e = (z - z ) [ 0, then 3 ray path after processing) 123 228 Pet. Sci. (2016) 13:225–236 when one adopts a velocity model based on a priori well (c) DDrms value does not decrease after multiple log data. Moreover, part of the data might be missing, iterations. which naturally affects the accuracy of the initial model. Therefore, methods of searching for a local optimal 3.1.1 The objective function velocity model are not applicable. Simulated annealing (SA) is a search algorithm that seeks the global minimum We use the following procedure to construct an objective of an objective function in a given model space. There is no function based on DDrms values: need to solve large matrix equations, and constraints can be 1. Select the reference trace with the highest signal-to- added easily. noise ratio. This is denoted by the subscript M. Compared with other techniques, such as the Gaussian– 2. Compute the differences between the observed first Newton and Levenberg–Marquard methods, SA does not arrival times of all traces and those of trace M: depend on the initial value. As long as the initial annealing obs Dt ¼½ t t ; t t ; ...; t t : temperature is sufficiently high, the method converges 1 k 2 k M k stably to the neighborhood of the global minimum. Ingber 0 0 0 3. Generate an initial velocity model, V ¼ V ; V ; (1989) presented a very fast simulated annealing (VFSA) p1 p2 algorithm based on iterative calculation of an exponent. 0 0 V ; ...; V , from sonic log data. p3 pn Computation was much faster than either the conventional 4. Calculate theoretical time differences for the reference SA algorithm or the standard genetic algorithm (Ingber and cal 0 trace, Dt ¼½ t t ; t t ; ...; t t , based on V . 1 k 2 k M k Rosen 1992). VFSA has already been used for velocity 5. Determine the RMS error of the DDrms value using model estimation based on borehole observations (Pei et al. the equations 2009) by constructing a solution space with six (sets of) obs cal obs cal obs cal parameters: dDt ¼½Dt Dt ; Dt Dt ; ...; Dt Dt 1 1 2 2 n n 1. Velocity vector, V = (V , V , V , …, V ) , where ð9Þ p1 p2 p3 pn rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V denotes the P-wave velocity of layer i. pi 1 n 2. Objective function, E(V). Because perforation shot origin EðVÞ¼ dDt ð10Þ i¼1 times are inaccurate, we use the RMS error of the time double-difference (DDrms) value, which can be com- puted from first arrival time differences. The procedure to 3.1.2 Velocity perturbation vector compute the DDrms value is described below. 3. Initial temperature T . The initial temperature must The velocity vector is perturbed using the equation satisfy the requirement that all proposed models are kþ1 k max min acceptable solutions for the next iteration of the V ¼ V þ xS V V ð11Þ fact i i i i calculation. We choose a small positive number at max min where V and V are the minimum and maximum first, then multiply by a constant value b [ 1, until the i i values of velocity in layer i, respectively, subject to the probability of acceptance of each proposed model min max constraint V 2 [V , V ]; S is a step-size factor that converges to unity. i fact i i guarantees the DDrms value decreases stably; and 4. Temperature annealing parameter, T , which for VFSA x 2 [-1,1] is a random number generated from the obeys the relationship equation 1=2N T ¼ T expðckÞð8Þ k 0 "# jj 2l1 where T is temperature, c is a constant (for this 0 x ¼ sgnðÞ l 0:5 T 1 þ 1 ð12Þ application, c = 0.5 is a suitable value), and N is the total number of layers. where sgn denotes the signum function. A suitable value 5. A random perturbation to the velocity vector, for S is approximately 0.1. fact described below. 6. Termination criteria. In this application, we terminate 3.2 Selecting the optimal velocity model the algorithm the first time one of the following three conditions is satisfied: Before selecting the optimal velocity model, a set of DDrms values and the corresponding velocity models must (a) Temperature T is reduced to a certain value or be obtained. In the simulated annealing process, each time close to zero. we update the DDrms value, both the DDrms value and the (b) DDrms value decreases below a predetermined threshold. corresponding velocity vector V are preserved. In the 123 Pet. Sci. (2016) 13:225–236 229 simulated annealing algorithm, V replaces V if the con- The initial velocity values for each layer are 950, 1300, dition E(V ) \ E(V) is satisfied. On the other hand, if 1800, 2800, and 3300 m/s. The simulation requires 2133 s E(V ) [ E(V), then V is updated using the replacement on a notebook computer with a 2.26-GHz Intel processor. probability. Observed values of first arrival time differences are 0 determined from the true synthetic model using the ray EðÞ V EðÞ V PðÞ V ! V¼ exp a ð13Þ tracing method described above (Fig. 5). When the minimum DDrms value is determined (here, where a is an adjustment parameter. The number of 2.97e-5 s), the iterative calculation stops and a threshold velocity models in the model set is determined by a; the of 3.97e-5 is set. Ten DDrms values are chosen randomly more velocity models are preserved, the greater the like- between the minimum DDrms value and the threshold. The lihood of obtaining reliable results. However, computation velocity models corresponding to these DDrms values are time will increase accordingly. used to relocate the perforation shot, as shown in Fig. 6. The purpose of establishing a velocity model in this The optimal velocity model is then picked. From the above way is to obtain accurate travel times for perforation shots results, we can see that although there are significant dif- and microseismic events. We mainly focus on the rela- ferences between the initial and synthetic velocity models, tionships between DDrms value, absolute travel time RMS the perforation shot can be still relocated to its true posi- (i.e., the differences between travel times calculated with tion; the relocation error is only 1.67 m. the theoretical and synthetic models), and the velocity model RMS for each layer (i.e., the difference between the 4.1 Sensitivity to the constraints theoretical and synthetic layer velocities) (Fig. 3). Here, we consider two main constraints on the viability of adopting a model for use with surface observations. One is 4 Synthetic examples the range of P-wave velocities used in the model. Increasing this range will increase the solution space; if we In this section, the effects of a hydraulic fracture treatment use a simulated annealing algorithm with a larger velocity are simulated to investigate the accuracy of the proposed range and parameters that are otherwise unchanged, then method. We define a synthetic velocity model with five source location accuracy and computational efficiency will layers, and exact velocities are given in Table 1. The both be reduced. If the range of velocity variations is too geophone array geometries and relative perforation shot small, then we probably will not obtain a viable result, as location are shown in Fig. 4. The exact shot position is shown in Fig. 7. It is therefore desirable to choose a rea- X = 830 m, Y = 840 m, Z =-1180 m. This study s1 s1 s1 sonable range of velocity variations in each layer. Gener- uses a star-shaped array (6 lines, 96 geophones), as the aim ally, the range of velocities in the objective layers is mainly is to place as many geophones as possible in a small area. determined from well logging data and local geology. 0.12 (a) (b) 0.1 0.08 0.06 0.04 0.02 0 2 4 6 8 0 2 4 6 8 −3 −3 x 10 x 10 The DDrms value, s The DDrms value, s Fig. 3 Sample velocity model distribution. Each blue circle repre- calculated from the velocity model corresponding to the plotted sents a velocity model corresponding to one DDrms value. a Plot of DDrms value. b Relationship between DDrms value and velocity the relationship between DDrms value and travel time RMS error. model RMS. The model error reflects differences between the The travel time error describes the deviation between the travel time velocity model and the actual medium of the perforation shot calculated from the actual medium and that The RMS error of travel time, s The RMS error of velocity, m/s 230 Pet. Sci. (2016) 13:225–236 Table 1 Synthetic velocity Layer Depth, m Synthetic velocity Velocity constraint range model parameters model, m/s (V - V ), m/s min max 1 0–200 1200 600–1300 2 200–500 1600 1000–1800 3 500–700 2200 1600–2400 4 700–900 3200 2400–3600 5 900–1200 3800 3000–4200 Another constraint is the number of surface geophones, which determines the number of time double-differences available for the inversion. The same termination condi- 1500 tions are used for the SA algorithm, and adding surface geophones improves the convergence of the DDrms value, as shown in Fig. 8. However, the algorithm requires more computation time to converge. Less accurate travel time information is obtained when DDrms is reduced to a small value, and it can be the case that no acceptable velocity model is obtained at all. Figure 8 compares the velocity calibration results with different numbers of surface geo- phones; the termination conditions are the same for all simulations. Using the same line pattern as in Fig. 4, the 0 500 1000 1500 2000 number of geophones increases or decreases uniformly in X, m each line. The minimum DDrms value of Fig. 8a is 1.3e-6. The Fig. 4 Geometry of recording stations and perforation shot. Each station has 4 geophones, for a total of 96 sensors. Black lines minimum DDrms value in Fig. 8b–d is less than 2.5e-6s. represent the arms of the star-patterned array. Blue dots represent As shown in Fig. 8, reliable location results are more likely geophone positions. The green star represents the position of the when a large number of surface geophones are used. perforation shot Y, m 0 1500 X, m 0 1200 -300 1850 -600 2500 -900 -1200 3800 Depth, m Fig. 5 Velocity model and ray paths. The green dot represents the perforation position, red lines represent ray paths, and blue dots represent receivers Y, m Velocity, m/s Pet. Sci. (2016) 13:225–236 231 −1140 The relocation result of velocity model Perforation shot position (a) (b) The relocation result of optimal model The relocation result of initial model 860 −1150 The relocation result of the model corresponds to minimum DDrms value 850 −1160 840 −1170 830 −1180 820 −1190 810 −1200 800 810 820 830 840 850 860 800 810 820 830 840 850 860 X, m X, m Fig. 6 Calculated perforation shot locations using 10 sample velocity models. The selected models corresponded to DDrms values within a certain range of the minimum DDrms value. a The top view, b the side view 50 3000 add a set of random picking errors to the synthetic arrival 40 times at each receiver, ranging from 0 to 5 % of the cal- culated travel time. We use the same stop condition as in the numerical experiments above. The algorithm termi- nates when DDrms value reaches 7.84e-4 s. A threshold of 8.84e-4 s is set; 10 velocity models are selected to relocate the perforation shot, and an optimal velocity model is picked out by the method described above. 200 400 600 800 1000 1200 1400 1600 1800 2000 Figure 9 shows that the perforation shot can still be Velocity range, m/s located close to its true position, despite picking errors. The Fig. 7 Influence of velocity range on the accuracy and efficiency of location inaccuracy is again within 2 m, and relatively the source location. The horizontal axis represents the total range of accurate results can still be obtained. The velocity model P-wave velocities in the synthetic velocity structures of different tests can be considered an ‘‘equivalent’’ velocity model. Because of the large discrepancies between the recovered However, increasing the number of surface arrays arbi- velocity model and the true model, large errors are possible trarily may lead the reduction of DDrms value to be dif- when locating microseismic events far from the ficult. In this case, more computation time is needed; perforation. notably, increasing the number of rays also increases the In Fig. 10, the velocity models used in Fig. 9 are used to forward calculation time. locate a synthetic microseismic event (true hypocenter 534, 532, -1165). This illustrates the relative accuracy of 4.2 The sensitivity to picking errors microseismic event location using these velocity models. Figure 11 illustrates the relationship between first arrival Calibrating a velocity model for microseismic event loca- time picking errors and minimum DDrms values, using the tion requires accurate information about perforation shots. same stop conditions as for the previous tests. In actual situations, seismic signals recorded by geophones Figure 10 confirms that for microseismic events located are usually contaminated by noise, which may cause far from the perforation, the optimal velocity model for the picking errors (Rodriguez et al. 2012; Song et al. 2010; Tan perforation shot introduces an inherent location error. et al. 2014). Compared with borehole observations, the Figure 11 suggests that increasing picking errors will picking errors of P-wave arrivals are relatively large at the increase location errors; for example, if picking errors reach 20 % of computed travel times, locations of micro- surface. This will affect the proposed technique. Therefore, to model our algorithm’s sensitivity to picking errors, we seismic events will be poorly constrained. The main reason Location inaccuracy, m Y, m Elapsed time, s Z, m 232 Pet. Sci. (2016) 13:225–236 0.12 0.14 (a) (b) 0.12 0.1 0.1 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 −3 −3 x 10 x 10 The DDrms value, s The DDrms value, s 0.12 0.14 (d) (c) 0.12 0.1 0.1 0.08 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0 1 2 3 4 5 6 0 1 2 3 4 5 −3 −3 x 10 x 10 The DDrms value, s The DDrms value, s Fig. 8 Comparative plots of tomography inversion results with different constraints. The inversion takes approximately 47 s with 6 geophones in (a); 232 s with 24 geophones in (b); 813 s with 48 geophones in (c); and 3137 s with 96 geophones in (d). Legends are the same as for Fig. 3 870 −1160 (a) (b) −1165 −1170 −1175 −1180 −1185 −1190 −1195 810 −1200 800 810 820 830 840 850 860 800 810 820 830 840 850 860 X, m X, m Fig. 9 Relocation of a perforation shot using data with picking errors, legends are the same as for Fig. 6. a Top view, b Side view for this is that the process of reducing the DDrms value is 5 Field data experiments influenced by the picking errors; when picking errors are large, the DDrms value cannot be reduced to a sufficiently In this section, we test our algorithm’s performance on data small value, and this reduces the chances to obtain a recorded by an experiment in Shanxi province, China. As meaningful velocity model. shown in Fig. 12, six survey lines were deployed in this Y, m The RMS of travel time, s The RMS of travel time, s Z, m The RMS of travel time, s The RMS of travel time, s Pet. Sci. (2016) 13:225–236 233 570 −1140 (a) (b) −1150 −1160 −1170 −1180 −1190 500 510 520 530 540 550 560 500 510 520 530 540 550 560 X, m X, m Fig. 10 The location result of microseismic event using the data with picking errors, legends are the same as for Fig. 6. a Top view, b side view F2 F1 E3 E2 E1 D2 4 D1 C2 C1 B3 0 2 4 6 8 10 12 14 16 18 20 22 B2 Picking errors, % B1 A3 Fig. 11 Relationship between picking errors of first arrival times and relocation inaccuracy. The x-axis represents the maximum values of A2 picking errors added to the synthetic data; the thick black lines A1 indicates the range of relocation inaccuracies after 100 trials 200 400 600 800 1000 Time, ms E3 E2 Fig. 13 Perforation shot monitoring records for the surface geo- E1 D2 phones in Fig. 12. The x-axis represents time since the beginning of D1 the record. The y-axis corresponds to geophone channel numbers F2 F1 Fracturing well A1 experiment, with two or three data loggers per line. Each C1 data logger was equipped with four vertical-component -200 B1 geophones, with a horizontal sensor spacing of 20 m along B2 the line. The first geophone of each survey line was placed A2 C2 B3 -400 at a fixed distance from the center of the array, to ensure A3 that the data loggers were evenly distributed and all sensors were far enough from the injection well to minimize noise -600 from processes related to injection (e.g., mechanical pump -400 -200 0 200 400 600 Y, m noise). The position of the straight well is at the center of the observation system; the wellhead coordinates were Fig. 12 Microseismic monitoring array geometry. Geophones are arranged in a star-like surface array around production wells (-68.025, 107.258, -1.34) under the unified GPS X, m Relocation inaccuracy, m Y, m Z, m Channels 234 Pet. Sci. (2016) 13:225–236 Sonic log (a) −200 −1000 Initial model value Location results of random model sample Inverted value −400 −1050 Actual position of perforation shot Location results of optimal velocity model Well trajectory −1100 −600 Location results of initial velocity model value −1150 −800 −1200 −1250 −1000 −1300 −1200 −1400 0 200 2000 2500 3000 3500 4000 4500 −100 Y, m X, m −200 −100 Velocity, m/s Fig. 14 Inversion results, showing initial and optimal velocity (b) 100 models observation system we defined. The perforation (fracturing point) coordinates are (107.258, -68.025, -1197.8). The maximum geophone elevation is -3.87 m and the mini- mum is -102.73 m. Because the waveforms of Fig. 13 are −50 not in good agreement, we obtain first arrival picks for each −100 geophone manually. Figure 14 shows the initial velocity obtained from well logging data, and the optimal velocity −150 model obtained by the method of this paper. The velocity structure was divided into seven layers, based on sonic logs −200 (Table 2). Layer boundaries corresponded to sudden 50 100 150 200 velocity changes. The number of layers and their respective X, m thicknesses do not need to be a constraint. The perforation positions obtained from the initial velocity model contain (c) −1050 significant errors, as shown in Fig. 15. However, the per- foration could be located close to its true position using −1100 models obtained by inversion. Therefore, we infer that the final velocity model is suitable for microseismic event −1150 locations. The VFSA algorithm reduced the DDrms value from 0.0215 s to 4.4e-4 s. To improve the accuracy of the −1200 inversion, we set a selection threshold of 6.4e-4 s for candidate velocity models. Fifty models with DDrms val- −1250 ues between the threshold and the minimum were selected. −1300 These were used to relocate the perforation shot, and an optimal velocity model was picked based on the results. 40 60 80 100 120 140 160 180 From Fig. 15, compared with the initial velocity model, the X, m perforation shot can be located very close to its actual Fig. 15 Location results based on 50 candidate velocity models. position; the location inaccuracy is 5.23 m. Therefore, we Models are selected if their final DDrms value lies within the range of conclude that the velocity model obtained by our method is the minimum DDrms value; each model is used to locate the perforation suitable for microseismic event location. shot independently. a Three-dimensional figure. b Top view. c Side view perforation shots. The DDrms value is minimized using a 6 Conclusion VFSA algorithm, and velocity model viability is evaluated based on the accuracy of perforation shot relocations. This In this paper, we present a non-linear inversion method for technique can overcome many of the difficulties caused by the calculation of velocity models suitable for locating monitoring hydraulic fractures with surface instruments microseismic events with surface sensor data. The pro- alone. Using tests on synthetic and field data, our inter- posed technique is based on the RMS error of time double- pretations and conclusions are as follows. differences, which are determined from surface records of Depth, m Depth, m Depth, m Y, m Pet. Sci. (2016) 13:225–236 235 Table 2 Stratum velocity Layer Depth, m Starting velocity model, m/s Velocity constraint range (V - V ), m/s min max structure parameters 1 0–200 2954.5 2650–3200 2 200–305 3214.5 3100–3500 3 305–418 3047.8 2800–3200 4 418–517 3348.6 3200–3500 5 517–645 2942.2 2600–3300 6 645–975 2690.1 2400–3000 7 975–1300 3408.2 3000–3800 distribution, and reproduction in any medium, provided you give 1. The proposed technique does not strongly depend on appropriate credit to the original author(s) and the source, provide a the initial velocity model, and can also overcome the link to the Creative Commons license, and indicate if changes were problem of inaccurate perforation shot origin times. made. However, due to complex local geology and a lack of available information, the velocity model inversion is non-unique. Therefore, whether or not a velocity References model is suitable for microseismic event location is Anikiev D, Valenta J, Stane˘ F, et al. Joint location and source determined based on the accuracy of perforation-shot mechanism inversion of micro-seismic events: benchmarking on relocation. seismicity induced by hydraulic fracturing. Geophys J Int. 2. Constraints on velocity structure have an effect on the 2014;198(1):249–58. proposed technique’s results. Reasonable velocity Bardainne T, Gaucher E. 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Petroleum Science – Springer Journals
Published: Apr 20, 2016
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