Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Inversion of horizontal in situ stress field based on wide-azimuth seismic data

Inversion of horizontal in situ stress field based on wide-azimuth seismic data In situ stress is a significant rock mechanics parameter, which is widely used in many aspects of the petroleum industry. Horizontal in situ stress is an important part of in situ stress.Hence,how to obtain accurate information as to horizontal stress can vary with azimuth has been widely explored. A new prediction method for in situ stress on a horizontal plane is proposed here. This new method analyses the relationship between seismic data, fracture orientation and a horizontal in situ stress field. Through a series of actual data, it is found that azimuth seismic data and azimuth elastic modulus can effectively point o ut the direction of the horizontal stress. Meanwhile, the magnitude of horizontal stress is shown to be closely related to a combination of rock elastic modulus and seismic amplitude according to a further analysis of log and wide-azimuth seismic data. Under this premise, an objective function of horizontal in situ stress field inversion using azimuth seismic data is established. Finally, the inversion of a horizontal in situ stress field based on wide-azimuth seismic data is realized. This inversion method can simultaneously invert the maximum horizontal stress, minimum horizontal stress and their orientations, which optimizes the prediction process of a horizontal in situ stress field and establish a new method for the prediction of horizontal in situ stress fields. The application of actual data also veries fi the prediction accuracy of this method. Keywords: wide-azimuth seismic data, elastic modulus, seismic amplitude, direct inversion, horizontal stress field 1. Introduction determines the fracturing ability of reservoir and indicates the engineering ‘sweet spot’. The in situ tress prediction of a subsurface medium is an im- In general, in situ stress can be expressed on the basis of the portant step in the process of petroleum exploration and de- magnitude and orientation of three mutually perpendicular velopment. From the geological point of view, in situ stress stresses. Among them, vertical stress (𝜎 ) is equal to the sum provides the driving force for the formation, migration and of the gravity above it, which can be predicted by the gravity accumulation of petroleum, and ultimately controls the lo- integral of the overlying rock (Lei & Sinha 2012). The magni- cation of reservoirs. In the process of logging, in situ stress tude and orientation of horizontal in situ stress (HISS, includ- provides a basis for calculating wellbore stability (Raoof ing maximum horizontal in situ stress 𝜎 , minimum horizon- et al. 2015). During the development stages, in situ stress tal in situ stress 𝜎 and their orientations) are affected by many © The Author(s) 2022. Published by Oxford University Press on behalf of the Sinopec Geophysical Research Institute. This is an Open Access article distributed under the terms of 131 the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. factors such as rock gravity, pore pressure, tectonic stress and thermal stress (Mallick et al. 1998;Wu et al. 2009): so, the prediction is more complex and less accurate. Therefore, how to obtain accurate HISS information is an urgent problem to be solved. Many scholars have investigated the prediction methods of HISS (Yin et al. 2018). These methods can be roughly divided into four categories: laboratory measurement, well- log analysis, numerical simulation and seismic data predic- tion. Among them, laboratory measurement methods can only obtain small amounts of data. Well-log analysis can only reflect the in situ stress distribution near the well locations, Figure 1. Azimuth seismic data indicating fracture strike. which is not suitable for stress prediction in a large-scale sur- vey (Campbell-Stone et al. 2012). The numerical simulation lative error of the inversion process, a new HISS inversion method has high requirements for the construction of the method driven by wide-azimuth seismic data is proposed. model and the application of loads and boundary conditions, First, according to the statistical analysis, a stress-related at- leading to poor feasibility. Compared with the other three tribute Q is constructed to indicate the characteristics of methods, seismic data are less difficult to obtain and cover HISS changing with azimuth. Then, based on the analysis more information. Thus, the method of using seismic data of rock mechanics, the objective equation of direct inversion to predict stress in reservoir develops. Dillen (2000)inves- of HISS field (including 𝜎 and 𝜎 and their orientations) tigatedthe seismiccharacteristicchangewithstressfieldand H h are derived. The equation establishes the direct relationship researched the earthquake mechanisms by observing time- between seismic elastic information and rock mechanics in- lapse seismic data. This thesis set up the foundation for pre- formation, which makes it possible to directly inverse the dicting in situ stress with seismic data. Hunt et al. (2011) HISS field of underground medium. Finally, the inversion of obtained elastic modulus and curvature characteristics from HISS field is realized by this new inversion method. Work- seismic data, and built relevant models to realize an HISS ing area data application illustrates that accurate information prediction. Gray et al. (2012) used 3D seismic data to calcu- of horizontal stress field can be obtained from this inversion late the magnitude and orientation of 𝜎 and 𝜎 .Based on a H h method. transversely isotropic medium, a new stress prediction model was established by calculating the medium stiffness matrix (Zhang et al. 2015). Information about elastic parameters 2. Orientation of horizontal stress indicated by and anisotropic parameters of underground media was ob- wide-azimuth seismic data tained by using the elastic impedance inversion of prestack seismic data (Ma et al. 2018). Then they built the HISS pre- In the last few years, acquisition and processing technology of diction model of relevant parameters, and realized the HISS wide-azimuth seismic data has been greatly developed, and prediction. wide-azimuth seismic data have been gradually applied to The HISS prediction methods based on seismic data are many aspects of seismic inversion (Pan et al. 2018). Wide- mainly model-driven prediction methods, such as the Nick azimuth data expand the azimuth of the observation system, empirical equation, Andersen model, Huang’s model etc. (Ge and obtain rich information about the reflection waves of a et al. 1998). These prediction methods invert various pa- subsurface medium varying with the azimuth, which is in- rametersrelatedtostressthrough seismicdata, andthen feasible for narrow-azimuth seismic data. Therefore, wide- substitute these parameters into the prediction model to re- azimuth seismic data have a signicant fi advantage in identify- alize the prediction of HISS. The limitations of these meth- ing geological information with horizontal anisotropy (Pan ods include, on the one hand, according to the structure of et al. 2017). Fracture detection technology based on azimuth stress model, restrictions to the applicable scope. For exam- seismic data is a good example, which reflects its advantages ple, some models do not distinguish between maximum and (Mallick & Frazer 1991). As gfi ure 1 shows, fracture detec- minimum horizontal stress, so they are unsuitable for an area tion technology uses an ellipse tfi ting method (Mitchell & where tectonic movement is obvious. On the other hand, Van 2016) to analyze the seismic amplitude attributes vary- due to the uncertainty of the inversion method itself, the er- ing with azimuth, and obtains information about major and ror generated in the inversion process will be transferred and minor axes of the amplitude attributes ellipse, which can be multiplied through the model (Zhang et al. 2020), and ulti- used to indicate the azimuth of fractures. mately affect the prediction accuracy of HISS. To get rid of Fracture occurs when the stress of subsurface medium ex- the limitation of the prediction model and reduce the cumu- ceeds its own bearing capacity. As a result, there is a close 132 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 2. Indication effect of fractures on in situ stress orientation. relationship between the extension direction of natural frac- tures in subsurface media and the orientation of horizontal stress (Hubbert & Willis 1957;Mallick et al. 2017;Zhang et al. 2021). As gfi ure 2 shows, the direction of fracture ex- tension can indicate the orientation of 𝜎 :inthe twomain typesofrock fracturemechanism,thetensilefractureispar- allel to the orientation of the 𝜎 and the acute angle bisector Figure 3. (a) FMI result of wellbore breakout. (b) Rose diagrams of the of a group of shear fractures is also consistent with the orien- wellbore breakout’s azimuth. (c) Azimuth amplitude ellipse tfi ting results. tation of 𝜎 (Haimson 2006). Logically, the long axis direc- tion of azimuth seismic amplitude attribute can also indicate the orientation of 𝜎 as figures 1 and 2 show. Formation micro-scanner image (FMI) gets the distribu- tion of horizontal stress around the wellbore by scanning and analyzing the surrounding resistivity (Huang et al. 2012). Wellbore breakout and induced fractures are common in drilling, which can be observed by FMI. These events occur becauseoftheimbalancebetweentheconnfi ingpressureand the pressure of drilling fluid during drilling. The orientation of horizontal stress at the drilling position can be indicated by analyzing the azimuth of these events (Zoback 2007). At the wellbore breakout, the 𝜎 is perpendicular to the long axis of the wellbore, and the induced fractures are parallel to the 𝜎 (Nian et al. 2016). Figures 3aand 4a are two imaging logging profiles with ob- Figure 4. (a) FMI result of an induced fracture. (b) Rose diagrams of the vious wellbore breakout and induced fractures, respectively, induced fracture’s azimuth. (c) Azimuth amplitude ellipse tfi ting results. in the survey. Figures 3band 4bare therosediagramsofthe wellbore breakout (or induced fracture) azimuth of FMI pro- files. Figures 3cand 4c show the ellipse tfi ting results of az- &Gray 2006). However, the different combination of the imuth amplitude attributes at corresponding well locations. properties of the media above and below the stratigraphic in- Through analysis, it can be found that the wellbore break- terface leads to the difference of reflection characteristics. Ig- out in gfi ure 3a is about 160–180° and the orientation of noring this difference and considering that the major and mi- 𝜎 is perpendicular to it, about 70–90°, which is consistent nor axes indicate the orientations of 𝜎 and 𝜎 ,respectively, H H h with the long axis orientation of ellipse tfi ting in gfi ure 3c. increases the uncertainty of HISS eld fi prediction, that is, the In gfi ure 4b, the orientation of induced fracture is about 90– so-called 90° ambiguity (Li 2013). Therefore, it is controver- 110°, indicating the orientation of 𝜎 , about 90–110°, which sial to obtain the orientation of horizontal stress only by using matches the long axis of the amplitude ellipse in gfi ure 4c azimuthal amplitude attribute. The elastic modulus is an in- well. These gfi ures demonstrate the ratiocination that the herent characteristic of rock that describes its deformation amplitude attribute of azimuth seismic data can indicate the resistance. It depends on the internal structure of the rock, orientation of horizontal stress mentioned before. mineral composition, density and arrangement of pores. It is universal to describe formation anisotropy by using Therefore, the elastic modulus has obvious azimuth charac- the ellipse characteristics of azimuth seismic data (Downton teristics. Normally, the azimuth elastic modulus parallel to 133 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 5. Statistical analysis cross plot of stress, elastic modulus and amplitude in: (a) well 13 and (b) well 133. the orientation of 𝜎 is larger than the azimuth elastic modu- lus and the measured stress, respectively. The scatter points lus parallel to the orientation of 𝜎 (Sayers 2013). Obviously, of different colors in the gfi ure represent the data of differ- in the process of HISS prediction, adding azimuth elastic ent layers in the well logs. The straight lines in different col- modulus can effectively avoid the uncertainty and make the ors are the statistical regression results of the corresponding prediction result more reasonable. color scatters. It can be seen that the scatter points of different colors are distributed near the straight line. From gfi ure 5a and b, it is clear that there is a linear relation 3. Magnitude of horizontal stress predict by between normal stress and elastic modulus. However, differ- wide-azimuth seismic data ent lines (represent different layers) have different intercepts and gradients. Taking seismic amplitude into consideration, According to Hooke’s law, the magnitude of stress is related to we get a more uniefi d result which is shown in gfi ure 6aand the elastic modulus and strain. Meanwhile, the amplitude at- b. In these gfi ures, the x-axis is replaced by a product of elas- tribute of seismic data reflects the displacement of a medium tic modulus and amplitude, the y-axis remains unchanged. under stress. In the process of energy transfer of seismic wave, –8 Here, 10 makes the x-and y-axesvalueshavethesameunits, rock displacement is caused by overcoming the confining MPa. Figure 6 reflects that the gradients of different regres- pressure. Therefore, the information of seismic amplitude sion lines become generally consistent. Also, through anal- and elastic modulus can be used to represent the magnitude yses of the intercept P and the travel time of correspond- of horizontal stress indirectly. ing layers, it is found that P increases linearly with the travel To avoid the interference of positive and negative transfor- time. Table 1 shows the travel time interval of different layers mation of seismic amplitude, the root mean square (RMS) and P. amplitude attribute is used in this study, and the RMS Therefore, it is assumed that stress can be expressed amplitude can be obtained by equation (1). All descrip- by seismic and rock elastic information as shown in tions of amplitude in the following paper refer to RMS equation (2): amplitude. t=1 𝜎 = P + k ⋅ A ⋅ E, (2) A = , (1) where A represents RMS amplitude, n represents the number where 𝜎 is the normal stress; E, A represent elastic modulus of signal and a represents amplitude of the ith signal. and amplitude, respectively; k is the scale factor to uniefi d the –8 To further clarify the relationship between amplitude, demotions, which in this study is 10 ,and P is the intercept, elasticmodulusand in situ stress, some log and seismic data in which increases as the layers become deeper. Through equa- the working area were analyzed. Figure 5aandbshowsthere- tion (2), we can use the information of seismic amplitude and gression analysis cross plot of wells 13 and 133 in the survey. elastic modulus to indirectly express the magnitude of hori- The x-and y-axes in the figures represent the elastic modu- zontal stress. 134 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 6. Statistical analysis cross plot of stress and the product of elastic modulus and amplitude in: (a) well 13 and (b) well 133. Table 1. Statistical regression P and the travel time of corresponding 2012). Then the theory is extended to azimuth seismic data layers of wells 13 and 133. and constructed the inversion equation to obtain azimuthal elastic modulus (Wang et al. 2021): Layer name Time (ms) P Well 13 H3 2191–2205 54.29 Δ𝜇 Δ𝜌 ΔE R(𝛼 , 𝜙 ) = a(𝛼 ) + b(𝛼 ) + c(𝛼 ) H2 2205–2216 55.26 E 𝜇 𝜌 H1 2225–2236 56.18 Well 133 H3 2288–2304 64.89 + d(𝛼 , 𝜙 )𝛿 + e(𝛼 , 𝜙 )𝜀 + f (𝛼 , 𝜙 )𝛾. (4) H2 2304–2317 65.15 H1 2328–2341 66.58 Define 2 2 a(𝛼 ) = sec 𝛼 − 2psin 𝛼 , 4. Inversion of horizontal in situ stress field from wide-azimuth seismic data (2p − 3)(2p − 1) 1 − 2p 2 2 b(𝛼 ) = sec 𝛼 + 2psin 𝛼 , Under equation (2), a new stress attribute Q varying with az- 4 p(4p − 3) 3 − 4p imuth data is defined here: 1 1 c(𝛼 ) = − sec 𝛼 , Q 𝜙 = P + k ⋅ A(𝜙 ) ⋅ E(𝜙 ) = 𝜎 (𝜙 ), (3) 2 4 ( ) 2 2 2 2 2 d(𝛼 , 𝜙 ) = sin 𝛼 cos 𝜙 (1 +sin 𝛼 )(1 −sin 𝛼 cos 𝜙 ), where 𝜙 is the azimuth of the data. In equation (3), P can be regarded as a kind of low- 4 4 2 frequency model that increases linearly with the increase in e(𝛼 , 𝜙 ) = sin 𝛼 cos 𝜙 (1 +sin 𝛼 ), layer travel time. It can be obtained through well data inter- f (𝛼 , 𝜙 ) =−4psin 𝛼 cos 𝜙 , polation over the interpreted horizons. Azimuth amplitude attribute can be obtained from wide-azimuth seismic data ΔE Δ𝜇 Δ𝜌 where , , are the reflection coefficients of elas- according to equation (1). Meanwhile, the azimuthal elas- E 𝜇 𝜌 tic modulus is obtained by inversion of prestack azimuthal tic modulus, Poisson’s ratio and density, 𝛿 , 𝜀 , 𝛾 are three seismic data. Ruger (1996) deduces the approximate equa- anisotropic parameters (Thomsen 1986), p is square of the tion of the relationship between P-wave azimuth reflection ratio of P- and S-wave velocity and 𝛼 , 𝜙 represent the angle coefficient and P- and S-wave velocity, density and three of incidence and azimuth, respectively. According to equa- anisotropy coefficients. Based on this, AVAZ technology de- tion (4), at least six azimuthal P-wave reflection coefficient velops rapidly and is widely used in anisotropic analysis (Xu data volumes are required for inversion, and n fi ally the az- &Li 2001;Shaw&Sen 2006). According to the connec- imuthal elastic modulus information is obtained. After ob- tion between seismic elastic parameters and rock mechan- taining the amplitude and elastic modulus, the azimuthal Q ics parameters, the reflection coefficient equation related to attribute volume is constructed using equation (3) and then Poisson’s ratio and elastic modulus is established (Zong et al. the Q attribute can characterize the horizontal stress well. 135 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 7. Diagram of a 2D stress Mohr circle. In Mohr’s circle theory, the normal stress 𝜎 and shear stress 𝜏 inanydirection canbeexpressedbythe rfi st andsec- Figure 8. Relationship between azimuth seismic data and orientation of ond principal stresses on the plane, as gfi ure 7 shows. 𝜃 is horizontal stress. the angle between the stress and normal phase of principal plane. In terms of horizontal stress distribution, the rst fi and According to trigonometric transformation, we can get second principal stresses are 𝜎 , 𝜎 . Then, the normal stress H h Q(𝜙 ) = 𝜎 + 𝜎 ⋅ cos 2𝜙 ⋅ cos 2𝜑 + 𝜎 ⋅ sin 2𝜙 ⋅ sin 2𝜑. of subsurface medium along any horizontal direction can be + − − (9) expressed as (King et al. 2008;Shahri et al. 2016): Then define 𝜎 + 𝜎 𝜎 − 𝜎 H h H h 𝜎 = + ⋅ cos 2𝜃. (5) M = 𝜎 ⋅ cos 2𝜑 , 2 2 (10) N = 𝜎 ⋅ sin 2𝜑. According to equations (3) and (5), the relationship be- Substitute in to equation (9), then tween HISS and Q attribute of any azimuth is Q(𝜙 ) = 𝜎 + M ⋅ cos 2𝜙 + N ⋅ sin 2𝜙. (11) 𝜎 + 𝜎 𝜎 − 𝜎 H h H h Q(𝜙 ) = + ⋅ cos 2𝜃. (6) 2 2 In equation (11), there are three unknown parameters 𝜎 ,M,N. At least three different sets of az- In equation (6), a nonlinear equation is constructed that con- + imuth data are required to solve this problem. tainsall theparametersusedinHISSexpression. Then alin- Finally, the HISS can be expressed as: earization process is applied to optimize the nonlinear equa- tion as follows. 2 2 𝜎 = 𝜎 + 𝜎 = 𝜎 + M + N , H + − + Define 2 2 𝜎 + 𝜎 𝜎 = 𝜎 − 𝜎 = 𝜎 − M + N , H h h + − + 𝜎 = , 1 N 𝜑 = ⋅ arctan . (12) 𝜎 − 𝜎 H h 2 M 𝜎 = . Equation (11) establishes the potential relationships be- Then equation (6) can be written as tween azimuth seismic amplitude and 𝜎 , 𝜎 and their ori- H h entations. The direct inversion of HISS field can be realized Q(𝜙 ) = 𝜎 + 𝜎 ⋅ cos 2𝜃. (7) + − to benefit from this equation. When applied to a data volume, assuming there are m az- In gfi ure 8, there is a certain azimuthal seismic data, and imuth seismic data, the equation (11) is written in matrix the included angle in the x direction is 𝜙 . In the same coordi- form: nate system,weassumethe anglebetween the 𝜎 and the x direction is 𝜑 . Thus, the angle between the data and the ⎛Q(𝜙 )⎞ ⎛1 cos 2𝜙 sin 2𝜙 ⎞ 1 1 1 ⎜ ⎟ ⎜ ⎟ stress orientation is defined as 𝜃 ,and 𝜃 =∅ − 𝜑 according to Q(𝜙 ) 1 cos 2𝜙 sin 2𝜙 2 2 2 ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ 𝜎 gfi ure 8. Therefore, . . . . ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ = ⋅ M (13) . . . . ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Q(𝜙 ) = 𝜎 + 𝜎 ⋅ cos 2(𝜙 − 𝜑 ). (8) + − ⎝ ⎠ ⎜ ⎟ ⎜ ⎟ . . . . ⎜ ⎟ ⎜ ⎟ Q(𝜙 ) 1 cos 2𝜙 sin 2𝜙 ⎝ m ⎠ ⎝ m m⎠ 136 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 9. Q attribute slices of dier ff ent azimuths: (a) 0–30 ° slice, (b) 30–60° slice, (c) 60–90° slice, (d) 90–120° slice, (e) 120–150° slice and (f) 150–180° slice. Furthermore, for n samples of each seismic trace, there is Equation (14) can be simpliefi d as Q = C ⋅ R (16) ⎛Q ⎞ ⎜ ⎟ where ⎜ ⎟ ⎜ ⎟ Q = (Q Q ...Q ) , ⎜ ⎟ 1 2 m ⎜ ⎟ 1 1 1 1 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 ⎜ ⎟ ⎛ ⎞ 1 1 1 1 Q n n n ⎝ m⎠ ⎜ ⎟ 2 2 2 2 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 1 1 1 1 ⎜ ⎟ 1 1 1 1 n n n 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 ⎛ 1 1 1 1 ⎞ ⎜ ⎟ n n n . . . . . . . . . . . . . . . . . . 2 2 2 2 ⎜ ⎟ ⎜ ⎟ . . . . . . . . . 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 1 1 1 1 ⎜ n n n ⎟ ⎜ ⎟ n n n n 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 C = 1 1 1 1 , ⎜ ⎟ ⎜ ⎟ n n n . . . . . . . . 1 1 1 1 ⎜. . . . . . . . ⎟ ⎜ ⎟ . . . . . . . . 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 2 2 2 2 ⎜ ⎟ ⎜ n n n ⎟ n n n n = 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 ⎜ 1 1 1 1 ⎟ ⎜ ⎟ . . . . . . . . . n n n . . . . . . . . . . . . . . . . . . ⎜ 1 1 1 1⎟ ⎜ ⎟ 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 2 2 2 2 n n n n ⎜ ⎟ n n n ⎜ ⎟ 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 m m m m ⎝ ⎠ ⎜ ⎟ n n n . . . . . . . . . . . . . . . . . . T ⎜. . . . . . . . . ⎟ R = (R R R ) . 𝜎 M N ⎜ n n n n⎟ 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 (17) m m m m ⎝ ⎠ n n n The n fi al inversion objective function is established by the ⎛R ⎞ damping least-square method to realize the inversion of HISS ⎜ ⎟ ⋅ R (14) ⎜ ⎟ field (Wang 2016;Zhang &Dai 2016): ⎝ ⎠ T −1 T R = (C C + 𝜆 ⋅ I) C ⋅ Q . (18) where R is the solution, and 𝜆 is the damping factor or weighting 1 2 n T Q = (Q ,Q , ...Q ) , factor, which is used to enhance the accuracy of the inversion 1 1 1 (15) 1 2 n T R = (𝜎 , 𝜎 , ...𝜎 ) . result. 𝜎 + + + 137 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 10. Inversion result of horizontal stress: (a) maximum horizontal stress and (b) minimum horizontal stress. Figure 11. Magnitude and orientation of maximum horizontal stress: (a) horizontal stress slice, (b) one partial enlarged result and (c) another partial enlarged result. The direct inversion process of HISS eld fi is as follows: parameters 𝜎 ,M,N. Finally, the HISS field is inversed by the damping least-square method. (i) Obtain the amplitude attribute information of each az- imuth from the wide-azimuth seismic data. Meanwhile, 5. Actual data application the azimuthal elastic modulus is inverted from the same seismic data. To verify the feasibility and accuracy of the direct inversion (ii) According to equation (3), the amplitude attribute with method, actual data are applied. Six different azimuth an- azimuth information is combined with the azimuthal gles of actual seismic data are selected to test the HISS field elasticmodulustoobtainthe Q attribute of seismic inversion method in this paper. Figure 9 shows the Q at- data. tribute slice of different azimuths at the T2 horizon. Figure 9a (iii) The relationship equation between the azimuthal Q exhibits a 0–30° slice, gfi ure 9b exhibits a 30–60° slice, gfi - attribute and HISS field is established by equation ure 9c exhibits a 60–90° slice, gfi ure 9d exhibits a 90–120° (11). An objective function with at least three seismic slice, gfi ure 9e exhibits a 120–150° slice and gfi ure 9fexhibits azimuth-stack gathers is found to predict the unknown a 150–180° slice. 138 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 12. Inversion profile of maximum horizontal stress. Figure 13. Inversion profile of minimum horizontal stress. Overall, the value of the Q attribute in gfi ure 9aand fis the Q attribute slices, proving the reliability of the inversion relatively larger than other slices, which indicates that the method in predicting HISS. in situ stress orientation of the actual data is mainly east to Figure 11 shows the orientation of 𝜎 at T2 horizon ob- west. However, in some local positions, gfi ure 9cand dshow tained by inversion. The direction of the short line in the larger Q values, indicating that the stress orientation at these gfi ure represents the orientation of 𝜎 , and the different col- positions is mainly south to north, and the value of Q in ors of the lines represent the magnitude of the maximum the north of the work area is larger than other areas, indi- horizontal stress values. Figure 11 parts b and c are enlarged cating that stress has an obvious high value here. The slices views of the position of the red rectangle in gfi ure 11a. It is of Q attribute with different azimuth show pre-inversion in- clear that the stress orientation in gfi ure 11b is mainly east formation that can provide us a general understanding of to west, while the Q values of the 0–30° and 150–180° az- HISS. imuths in the corresponding positions in gfi ure 9 are larger Figure 10a and b shows the maximum and minimum hor- than other azimuths, so they are consistent. The maximum izontal stress slices of the T2 horizon obtained by the hori- horizontal stress orientation in gfi ure 11cismainlyinthe zontal stress inversion method mentioned previously. These north to south orientation, while the Q values in the cor- gfi ures show that the stress distribution is consistent with responding position of azimuths 60–90° and 90–120° in 139 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. gfi ure 9 are larger than other azimuth data, which is consis- dicting HISS eld fi is derived by using the relationship tent with the results in gfi ure 11c. These results further prove equation. the accuracy of the horizontal stress inversion method. (iv) The 𝜎 , 𝜎 and their orientations of actual data are H h Figures 12 and 13 are the profiles of the 𝜎 and the 𝜎 in predicted by the direct inversion method. The slices of H h the same working area, respectively. The stress logs of well 𝜎 , 𝜎 exhibit a tight connection with Q both in mag- H h Arepresent 𝜎 rmand 𝜎 are overlapped on the correspond- nitude and orientation, which meet theoretical expec- H h ing stress prediction profile separately. Through observing tations. Meanwhile, the prediction results of 𝜎 , 𝜎 . H h the profile shape and numerical distribution, it is clear that profiles demonstrate great corresponding to the actual the inversion results of 𝜎 and 𝜎 reflect a certain degree well logs, proving the feasibility of this method in pre- H h of heterogeneity in the transverse direction. In the vertical dicting an HISS eld. fi direction, the inversion results are in good agreement with the actual well logs, which reflects the accuracy of the direct The method of direct inversion of a horizontal stress eld fi inversion method in horizontal stress prediction. from wide-azimuth seismic data overcomes the limitation of the stress prediction model and avoids the generation of ac- cumulated errors in the process of indirect inversion. Applied 6. Conclusion to the actual data, the expected prediction effect is achieved. The prediction of an in situ stress field is a dicult ffi problem in the integration of geological engineering. At present, the pre- diction methods of in situstressarestilllimitedtocoreexper- Acknowledgements iments, logging and other methods. These methods not only This research is supported by the National Natural Science Foun- have high cost, but also obtain less in situ stress information, dation Project of China (grant no. 41874146) and Shandong which has difficulty in meeting the needs of exploration and Province Foundation for Qingdao National Laboratory of marine development. Wide-azimuth seismic data integrate different science (grant no. 2021QNLM020001). pieces of azimuth information and contain sucffi ient infor- mation for analyzing and prospecting. The attribute parame- Conflict of interest statement: None declared. ters varying with azimuth can be predicted by using the differ- ences between different azimuth information. Based on this References characteristic, a new prediction process is proposed, which sets up a new method for the prediction of HISS fields. Campbell-Stone, E., Shafer, L. & Mallick, S., 2012. Subsurface geomechan- Through the study, we found that: ical analysis, comparison with prestack azimuthal AVO analysis, and im- plication for predicting subsurface geomechanical properties from 3-D seismic data, in Proceedingsofthe 9thBiennialConference&Exposition, (i) Seismic amplitude ellipse fitting is an effective way to SEG, Expanded Abstracts, P501. exhibit the orientation of stress subsurface, but the Dillen, M., 2000. Time-lapse seismic monitoring of subsurface dynamics, thesis, results are not always accurate and may deviate by Delft University of Technology, Delft. 90°. The azimuth elastic modulus information is intro- Downton, J. & Gray, D., 2006. AVAZ parameter uncertainty estimation, duced into the orientation prediction of HISS. Through SEG Technical Program Expanded Abstracts, 25, 234–238. Gray, D., Anderson, P. & Logel, J., 2012. Estimation of stress and geome- a combination of azimuthal amplitude and azimuthal chanical properties using 3D seismic data,First Break, 30, 59–68. elastic modulus, the uncertainty of using only the seis- Ge, H.K., Lin, Y.S. & Wang, S.C., 1998. In-situ stress measurement and its mic amplitude to predict the orientation of stress is application in exploration and development, Journal of Petroleum Uni- avoided. versity (natural science edition), 22, 97–102. (ii) Through the statistical analyses of logging data and Haimson, B., 2006, True triaxial stresses and the brittle fracture of rock, azimuthal seismic data, the potential associations be- Pure & Applied Geophysics, 163, 1101–1130. Huang, J., Griffiths, D.V. & Wong, S.W., 2012. Initiation pressure, location tween HISS, azimuthal seismic amplitude and az- and orientation of hydraulic fracture, International Journal of Rock Me- imuthal elastic modulus are obtained and presented in chanics and Mining Sciences, 49, 59–67. theformofequation(3),and then anew stress-related Hubbert, M.K. & Willis, D., 1957. Mechanics of hydraulic fracturing, attribute Q is constructed. The azimuthal Q attribute Transactions of the AIME, 210, 153–168. not only indicates the orientation of stress, but also Hunt, L., Reynolds, S. & Hadley, S., 2011. Causal fracture prediction: cur- vature, stress, and geomechanics, The Leading Edge, 30, 1274–1286. forms a reliable substitute for the magnitude of stress, King, R.C., Hillis, R.R. & Reynolds, S.D., 2008. In situ stresses and natu- which can be obtained from wide-azimuth seismic data. ral fractures in the Northern Perth Basin, Australia, Australian Journal of (iii) On the basis of rock mechanics analysis, stress in any Earth Sciences, 55, 685–701. azimuth can be expressed by HISS. And the stress in Lei, T. & Sinha, B., 2012. Estimation of horizontal stress magnitudes and any azimuth can be represented as the azimuthal Q at- stress coefficients of velocities using borehole sonic data, Geophysics, 77, tribute. Then, the inversion objective function of pre- 181–196. 140 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Li, C. P., 2013. Research on Fractured Reservoir Prediction with Azimuthal Sayers, C.M., 2013. The effect of anisotropy on the Young’s moduli and Seismic Data, China University of Petroleum, Qingdao, Shandong. Poisson’s ratios of shale. Geophysical Prospecting, 61, 416–426. Ma, N., Yin, X.Y. & Sun, C.Y., 2018. Inversion for crustal stress based Shahri, M.P., Chok, H. & Huang, J., 2016. Stress inversion via borehole im- on azimuthal seismic data, Chinese Journal of Geophysics, 61, 697– age log and fracturing data: integrated approach, in Unconventional Re- 706. sources Technology Conference, 2718–2740. Mallick, S., Craft, K.L. & Meister, L.J., 1998. Computation of principal di- Shaw, R.K. & Sen, M.K., 2006. Use of AVOA data to estimate fluid indica- rections of azimuthal anisotropy from P-wave seismic data, Geophysics, tor in a vertically fractured medium, Geophysics, 71, C15–C24. 63, 692–706. Thomsen, L., 1986. Weak elastic anisotropy, Geophysics, 51, 1954–1966. Mallick, S. & Frazer, L.N., 1991. Reflection/transmission coefficients and Wang, J.H., Zhang, J.M. & Wu, G.C., 2021. Wide azimuth Young’s modulus azimuthal anisotropy in marine seismic studies, Geophysical Journal In- inversion and fracture prediction method and its application – taking the ternational, 28, 241–252. exploration of H structural buried hill in Bozhong Sag as an example, Oil Mallick, S., Mukherjee, D. & Shafer, L., 2017. Azimuthal anisotropy anal- Geophysical Prospecting, 56, 593–602 (in Chinese). ysis of P-wave seismic data and estimation of the orientation of the in Wang, Y., 2016. Seismic Inversion: Theory and Application.Wiley Blackwell. situ stress fields: An example from the Rock-Springs uplift, Wyoming, Wu, C., Chen, M. & Jin, Y., 2009. A prediction method of borehole stability USA, Geophysics Journal of the Society of Exploration Geophysicists, 82, based on seismic attribute technology, Journal of Petroleum Science and B63-B77. Engineering, 65, 208–216. Mitchell, D. & Van, D., 2016. Development of an ellipse tfi ting method Xu, Y. & Li, Y., 2001. Uncertainties in azimuthal AVO analysis, SEG, Ex- with which to analyse selected area electron diffraction patterns, Ultra- panded Abstracts, 24–27. microscopy, 160, 140–145. Yin, X.Y., Ma, N. & Ma, Z.Q., 2018. Review of in-situ stress prediction tech- Nian, T., Wang, G. & Xiao, C., 2016. Determination of in-situ stress orien- nology, Geophysical Prospecting for Petroleum, 57, 488–504. tation and subsurface fracture analysis from image-core integration: an Zhang, M.L., Yang, Y. & Gao, L.S., 2021. A study on the geometric effects example from ultra-deep tight sandstone (BSJQK Formation) in the Ke- of a concrete filling body in remaining roadways with fully mechanised lasu Belt, Tarim Basin, Journal of Petroleum Science and Engineering, 147, caving, JournalofGeophysicsand Engineering, 18, 681–690. 495–503. Zhang, F.C. & Dai, R.H., 2016. Nonlinear inversion of pre-stack seismic Pan, X.P., Zhang, G.Z. & Yin, X.Y., 2017. Azimuthal seismic amplitude data using variable metric method, Journal of Applied Geophysics, 129, 111–125. variation with offset and azimuth inversion in weakly anisotropic media with orthorhombic symmetry, Surveys in Geophysics, 39, 1–25. Zhang, F.C., Yang, J.Y. & Li, C.H., 2020. Direct inversion for reservoir pa- Pan, X.P., Zhang, G.Z. & Yin, X.Y., 2018. Azimuthally pre-stack seismic rameters from prestack seismic data, Journal of Geophysics and Engineer- inversion for orthorhombic anisotropy driven by rock physics. Science ing, 17, 993–1004. China (Earth Sciences), 61, 425–440. Zhang, G.Z., Chen, J.J. & Chen, H.Z., 2015. Prediction for in-situ forma- Raoof, G., Vamegh, R., Bernt, A. & Ramin, M., 2015. Application of in situ tion stress of shale based on rock physics equivalent model, Chinese Jour- stress estimation methods in wellbore stability analysis under isotropic nalofGeophysics, 58, 2112–2122. and anisotropic conditions, Journal of Geophysics and Engineering, 12, Zoback, M., 2007. Reservoir Geomechanics, Cambridge University Press. 657–673. Zong, Z.Y., Yin, X.Y. & Zhang, F., 2012. Reflection coefficient equation Ruger, A., 1996. Reflection Coefficients and Azimuthal AVO Analysis in and pre-stack seismic inversion with Young’s modulus and Poisson ra- Anisotropic Media. Colorado School of Mine, Colorado. tio, Chinese Journal of Geophysics, 55, 3796–3794. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Geophysics and Engineering Oxford University Press

Inversion of horizontal in situ stress field based on wide-azimuth seismic data

Download PDF
11 pages

Loading next page...
 
/lp/oxford-university-press/inversion-of-horizontal-in-situ-stress-field-based-on-wide-azimuth-BTE1djxG4y

References (52)

Publisher
Oxford University Press
Copyright
© The Author(s) 2022. Published by Oxford University Press on behalf of the Sinopec Geophysical Research Institute.
ISSN
1742-2132
eISSN
1742-2140
DOI
10.1093/jge/gxac006
Publisher site
See Article on Publisher Site

Abstract

In situ stress is a significant rock mechanics parameter, which is widely used in many aspects of the petroleum industry. Horizontal in situ stress is an important part of in situ stress.Hence,how to obtain accurate information as to horizontal stress can vary with azimuth has been widely explored. A new prediction method for in situ stress on a horizontal plane is proposed here. This new method analyses the relationship between seismic data, fracture orientation and a horizontal in situ stress field. Through a series of actual data, it is found that azimuth seismic data and azimuth elastic modulus can effectively point o ut the direction of the horizontal stress. Meanwhile, the magnitude of horizontal stress is shown to be closely related to a combination of rock elastic modulus and seismic amplitude according to a further analysis of log and wide-azimuth seismic data. Under this premise, an objective function of horizontal in situ stress field inversion using azimuth seismic data is established. Finally, the inversion of a horizontal in situ stress field based on wide-azimuth seismic data is realized. This inversion method can simultaneously invert the maximum horizontal stress, minimum horizontal stress and their orientations, which optimizes the prediction process of a horizontal in situ stress field and establish a new method for the prediction of horizontal in situ stress fields. The application of actual data also veries fi the prediction accuracy of this method. Keywords: wide-azimuth seismic data, elastic modulus, seismic amplitude, direct inversion, horizontal stress field 1. Introduction determines the fracturing ability of reservoir and indicates the engineering ‘sweet spot’. The in situ tress prediction of a subsurface medium is an im- In general, in situ stress can be expressed on the basis of the portant step in the process of petroleum exploration and de- magnitude and orientation of three mutually perpendicular velopment. From the geological point of view, in situ stress stresses. Among them, vertical stress (𝜎 ) is equal to the sum provides the driving force for the formation, migration and of the gravity above it, which can be predicted by the gravity accumulation of petroleum, and ultimately controls the lo- integral of the overlying rock (Lei & Sinha 2012). The magni- cation of reservoirs. In the process of logging, in situ stress tude and orientation of horizontal in situ stress (HISS, includ- provides a basis for calculating wellbore stability (Raoof ing maximum horizontal in situ stress 𝜎 , minimum horizon- et al. 2015). During the development stages, in situ stress tal in situ stress 𝜎 and their orientations) are affected by many © The Author(s) 2022. Published by Oxford University Press on behalf of the Sinopec Geophysical Research Institute. This is an Open Access article distributed under the terms of 131 the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. factors such as rock gravity, pore pressure, tectonic stress and thermal stress (Mallick et al. 1998;Wu et al. 2009): so, the prediction is more complex and less accurate. Therefore, how to obtain accurate HISS information is an urgent problem to be solved. Many scholars have investigated the prediction methods of HISS (Yin et al. 2018). These methods can be roughly divided into four categories: laboratory measurement, well- log analysis, numerical simulation and seismic data predic- tion. Among them, laboratory measurement methods can only obtain small amounts of data. Well-log analysis can only reflect the in situ stress distribution near the well locations, Figure 1. Azimuth seismic data indicating fracture strike. which is not suitable for stress prediction in a large-scale sur- vey (Campbell-Stone et al. 2012). The numerical simulation lative error of the inversion process, a new HISS inversion method has high requirements for the construction of the method driven by wide-azimuth seismic data is proposed. model and the application of loads and boundary conditions, First, according to the statistical analysis, a stress-related at- leading to poor feasibility. Compared with the other three tribute Q is constructed to indicate the characteristics of methods, seismic data are less difficult to obtain and cover HISS changing with azimuth. Then, based on the analysis more information. Thus, the method of using seismic data of rock mechanics, the objective equation of direct inversion to predict stress in reservoir develops. Dillen (2000)inves- of HISS field (including 𝜎 and 𝜎 and their orientations) tigatedthe seismiccharacteristicchangewithstressfieldand H h are derived. The equation establishes the direct relationship researched the earthquake mechanisms by observing time- between seismic elastic information and rock mechanics in- lapse seismic data. This thesis set up the foundation for pre- formation, which makes it possible to directly inverse the dicting in situ stress with seismic data. Hunt et al. (2011) HISS field of underground medium. Finally, the inversion of obtained elastic modulus and curvature characteristics from HISS field is realized by this new inversion method. Work- seismic data, and built relevant models to realize an HISS ing area data application illustrates that accurate information prediction. Gray et al. (2012) used 3D seismic data to calcu- of horizontal stress field can be obtained from this inversion late the magnitude and orientation of 𝜎 and 𝜎 .Based on a H h method. transversely isotropic medium, a new stress prediction model was established by calculating the medium stiffness matrix (Zhang et al. 2015). Information about elastic parameters 2. Orientation of horizontal stress indicated by and anisotropic parameters of underground media was ob- wide-azimuth seismic data tained by using the elastic impedance inversion of prestack seismic data (Ma et al. 2018). Then they built the HISS pre- In the last few years, acquisition and processing technology of diction model of relevant parameters, and realized the HISS wide-azimuth seismic data has been greatly developed, and prediction. wide-azimuth seismic data have been gradually applied to The HISS prediction methods based on seismic data are many aspects of seismic inversion (Pan et al. 2018). Wide- mainly model-driven prediction methods, such as the Nick azimuth data expand the azimuth of the observation system, empirical equation, Andersen model, Huang’s model etc. (Ge and obtain rich information about the reflection waves of a et al. 1998). These prediction methods invert various pa- subsurface medium varying with the azimuth, which is in- rametersrelatedtostressthrough seismicdata, andthen feasible for narrow-azimuth seismic data. Therefore, wide- substitute these parameters into the prediction model to re- azimuth seismic data have a signicant fi advantage in identify- alize the prediction of HISS. The limitations of these meth- ing geological information with horizontal anisotropy (Pan ods include, on the one hand, according to the structure of et al. 2017). Fracture detection technology based on azimuth stress model, restrictions to the applicable scope. For exam- seismic data is a good example, which reflects its advantages ple, some models do not distinguish between maximum and (Mallick & Frazer 1991). As gfi ure 1 shows, fracture detec- minimum horizontal stress, so they are unsuitable for an area tion technology uses an ellipse tfi ting method (Mitchell & where tectonic movement is obvious. On the other hand, Van 2016) to analyze the seismic amplitude attributes vary- due to the uncertainty of the inversion method itself, the er- ing with azimuth, and obtains information about major and ror generated in the inversion process will be transferred and minor axes of the amplitude attributes ellipse, which can be multiplied through the model (Zhang et al. 2020), and ulti- used to indicate the azimuth of fractures. mately affect the prediction accuracy of HISS. To get rid of Fracture occurs when the stress of subsurface medium ex- the limitation of the prediction model and reduce the cumu- ceeds its own bearing capacity. As a result, there is a close 132 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 2. Indication effect of fractures on in situ stress orientation. relationship between the extension direction of natural frac- tures in subsurface media and the orientation of horizontal stress (Hubbert & Willis 1957;Mallick et al. 2017;Zhang et al. 2021). As gfi ure 2 shows, the direction of fracture ex- tension can indicate the orientation of 𝜎 :inthe twomain typesofrock fracturemechanism,thetensilefractureispar- allel to the orientation of the 𝜎 and the acute angle bisector Figure 3. (a) FMI result of wellbore breakout. (b) Rose diagrams of the of a group of shear fractures is also consistent with the orien- wellbore breakout’s azimuth. (c) Azimuth amplitude ellipse tfi ting results. tation of 𝜎 (Haimson 2006). Logically, the long axis direc- tion of azimuth seismic amplitude attribute can also indicate the orientation of 𝜎 as figures 1 and 2 show. Formation micro-scanner image (FMI) gets the distribu- tion of horizontal stress around the wellbore by scanning and analyzing the surrounding resistivity (Huang et al. 2012). Wellbore breakout and induced fractures are common in drilling, which can be observed by FMI. These events occur becauseoftheimbalancebetweentheconnfi ingpressureand the pressure of drilling fluid during drilling. The orientation of horizontal stress at the drilling position can be indicated by analyzing the azimuth of these events (Zoback 2007). At the wellbore breakout, the 𝜎 is perpendicular to the long axis of the wellbore, and the induced fractures are parallel to the 𝜎 (Nian et al. 2016). Figures 3aand 4a are two imaging logging profiles with ob- Figure 4. (a) FMI result of an induced fracture. (b) Rose diagrams of the vious wellbore breakout and induced fractures, respectively, induced fracture’s azimuth. (c) Azimuth amplitude ellipse tfi ting results. in the survey. Figures 3band 4bare therosediagramsofthe wellbore breakout (or induced fracture) azimuth of FMI pro- files. Figures 3cand 4c show the ellipse tfi ting results of az- &Gray 2006). However, the different combination of the imuth amplitude attributes at corresponding well locations. properties of the media above and below the stratigraphic in- Through analysis, it can be found that the wellbore break- terface leads to the difference of reflection characteristics. Ig- out in gfi ure 3a is about 160–180° and the orientation of noring this difference and considering that the major and mi- 𝜎 is perpendicular to it, about 70–90°, which is consistent nor axes indicate the orientations of 𝜎 and 𝜎 ,respectively, H H h with the long axis orientation of ellipse tfi ting in gfi ure 3c. increases the uncertainty of HISS eld fi prediction, that is, the In gfi ure 4b, the orientation of induced fracture is about 90– so-called 90° ambiguity (Li 2013). Therefore, it is controver- 110°, indicating the orientation of 𝜎 , about 90–110°, which sial to obtain the orientation of horizontal stress only by using matches the long axis of the amplitude ellipse in gfi ure 4c azimuthal amplitude attribute. The elastic modulus is an in- well. These gfi ures demonstrate the ratiocination that the herent characteristic of rock that describes its deformation amplitude attribute of azimuth seismic data can indicate the resistance. It depends on the internal structure of the rock, orientation of horizontal stress mentioned before. mineral composition, density and arrangement of pores. It is universal to describe formation anisotropy by using Therefore, the elastic modulus has obvious azimuth charac- the ellipse characteristics of azimuth seismic data (Downton teristics. Normally, the azimuth elastic modulus parallel to 133 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 5. Statistical analysis cross plot of stress, elastic modulus and amplitude in: (a) well 13 and (b) well 133. the orientation of 𝜎 is larger than the azimuth elastic modu- lus and the measured stress, respectively. The scatter points lus parallel to the orientation of 𝜎 (Sayers 2013). Obviously, of different colors in the gfi ure represent the data of differ- in the process of HISS prediction, adding azimuth elastic ent layers in the well logs. The straight lines in different col- modulus can effectively avoid the uncertainty and make the ors are the statistical regression results of the corresponding prediction result more reasonable. color scatters. It can be seen that the scatter points of different colors are distributed near the straight line. From gfi ure 5a and b, it is clear that there is a linear relation 3. Magnitude of horizontal stress predict by between normal stress and elastic modulus. However, differ- wide-azimuth seismic data ent lines (represent different layers) have different intercepts and gradients. Taking seismic amplitude into consideration, According to Hooke’s law, the magnitude of stress is related to we get a more uniefi d result which is shown in gfi ure 6aand the elastic modulus and strain. Meanwhile, the amplitude at- b. In these gfi ures, the x-axis is replaced by a product of elas- tribute of seismic data reflects the displacement of a medium tic modulus and amplitude, the y-axis remains unchanged. under stress. In the process of energy transfer of seismic wave, –8 Here, 10 makes the x-and y-axesvalueshavethesameunits, rock displacement is caused by overcoming the confining MPa. Figure 6 reflects that the gradients of different regres- pressure. Therefore, the information of seismic amplitude sion lines become generally consistent. Also, through anal- and elastic modulus can be used to represent the magnitude yses of the intercept P and the travel time of correspond- of horizontal stress indirectly. ing layers, it is found that P increases linearly with the travel To avoid the interference of positive and negative transfor- time. Table 1 shows the travel time interval of different layers mation of seismic amplitude, the root mean square (RMS) and P. amplitude attribute is used in this study, and the RMS Therefore, it is assumed that stress can be expressed amplitude can be obtained by equation (1). All descrip- by seismic and rock elastic information as shown in tions of amplitude in the following paper refer to RMS equation (2): amplitude. t=1 𝜎 = P + k ⋅ A ⋅ E, (2) A = , (1) where A represents RMS amplitude, n represents the number where 𝜎 is the normal stress; E, A represent elastic modulus of signal and a represents amplitude of the ith signal. and amplitude, respectively; k is the scale factor to uniefi d the –8 To further clarify the relationship between amplitude, demotions, which in this study is 10 ,and P is the intercept, elasticmodulusand in situ stress, some log and seismic data in which increases as the layers become deeper. Through equa- the working area were analyzed. Figure 5aandbshowsthere- tion (2), we can use the information of seismic amplitude and gression analysis cross plot of wells 13 and 133 in the survey. elastic modulus to indirectly express the magnitude of hori- The x-and y-axes in the figures represent the elastic modu- zontal stress. 134 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 6. Statistical analysis cross plot of stress and the product of elastic modulus and amplitude in: (a) well 13 and (b) well 133. Table 1. Statistical regression P and the travel time of corresponding 2012). Then the theory is extended to azimuth seismic data layers of wells 13 and 133. and constructed the inversion equation to obtain azimuthal elastic modulus (Wang et al. 2021): Layer name Time (ms) P Well 13 H3 2191–2205 54.29 Δ𝜇 Δ𝜌 ΔE R(𝛼 , 𝜙 ) = a(𝛼 ) + b(𝛼 ) + c(𝛼 ) H2 2205–2216 55.26 E 𝜇 𝜌 H1 2225–2236 56.18 Well 133 H3 2288–2304 64.89 + d(𝛼 , 𝜙 )𝛿 + e(𝛼 , 𝜙 )𝜀 + f (𝛼 , 𝜙 )𝛾. (4) H2 2304–2317 65.15 H1 2328–2341 66.58 Define 2 2 a(𝛼 ) = sec 𝛼 − 2psin 𝛼 , 4. Inversion of horizontal in situ stress field from wide-azimuth seismic data (2p − 3)(2p − 1) 1 − 2p 2 2 b(𝛼 ) = sec 𝛼 + 2psin 𝛼 , Under equation (2), a new stress attribute Q varying with az- 4 p(4p − 3) 3 − 4p imuth data is defined here: 1 1 c(𝛼 ) = − sec 𝛼 , Q 𝜙 = P + k ⋅ A(𝜙 ) ⋅ E(𝜙 ) = 𝜎 (𝜙 ), (3) 2 4 ( ) 2 2 2 2 2 d(𝛼 , 𝜙 ) = sin 𝛼 cos 𝜙 (1 +sin 𝛼 )(1 −sin 𝛼 cos 𝜙 ), where 𝜙 is the azimuth of the data. In equation (3), P can be regarded as a kind of low- 4 4 2 frequency model that increases linearly with the increase in e(𝛼 , 𝜙 ) = sin 𝛼 cos 𝜙 (1 +sin 𝛼 ), layer travel time. It can be obtained through well data inter- f (𝛼 , 𝜙 ) =−4psin 𝛼 cos 𝜙 , polation over the interpreted horizons. Azimuth amplitude attribute can be obtained from wide-azimuth seismic data ΔE Δ𝜇 Δ𝜌 where , , are the reflection coefficients of elas- according to equation (1). Meanwhile, the azimuthal elas- E 𝜇 𝜌 tic modulus is obtained by inversion of prestack azimuthal tic modulus, Poisson’s ratio and density, 𝛿 , 𝜀 , 𝛾 are three seismic data. Ruger (1996) deduces the approximate equa- anisotropic parameters (Thomsen 1986), p is square of the tion of the relationship between P-wave azimuth reflection ratio of P- and S-wave velocity and 𝛼 , 𝜙 represent the angle coefficient and P- and S-wave velocity, density and three of incidence and azimuth, respectively. According to equa- anisotropy coefficients. Based on this, AVAZ technology de- tion (4), at least six azimuthal P-wave reflection coefficient velops rapidly and is widely used in anisotropic analysis (Xu data volumes are required for inversion, and n fi ally the az- &Li 2001;Shaw&Sen 2006). According to the connec- imuthal elastic modulus information is obtained. After ob- tion between seismic elastic parameters and rock mechan- taining the amplitude and elastic modulus, the azimuthal Q ics parameters, the reflection coefficient equation related to attribute volume is constructed using equation (3) and then Poisson’s ratio and elastic modulus is established (Zong et al. the Q attribute can characterize the horizontal stress well. 135 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 7. Diagram of a 2D stress Mohr circle. In Mohr’s circle theory, the normal stress 𝜎 and shear stress 𝜏 inanydirection canbeexpressedbythe rfi st andsec- Figure 8. Relationship between azimuth seismic data and orientation of ond principal stresses on the plane, as gfi ure 7 shows. 𝜃 is horizontal stress. the angle between the stress and normal phase of principal plane. In terms of horizontal stress distribution, the rst fi and According to trigonometric transformation, we can get second principal stresses are 𝜎 , 𝜎 . Then, the normal stress H h Q(𝜙 ) = 𝜎 + 𝜎 ⋅ cos 2𝜙 ⋅ cos 2𝜑 + 𝜎 ⋅ sin 2𝜙 ⋅ sin 2𝜑. of subsurface medium along any horizontal direction can be + − − (9) expressed as (King et al. 2008;Shahri et al. 2016): Then define 𝜎 + 𝜎 𝜎 − 𝜎 H h H h 𝜎 = + ⋅ cos 2𝜃. (5) M = 𝜎 ⋅ cos 2𝜑 , 2 2 (10) N = 𝜎 ⋅ sin 2𝜑. According to equations (3) and (5), the relationship be- Substitute in to equation (9), then tween HISS and Q attribute of any azimuth is Q(𝜙 ) = 𝜎 + M ⋅ cos 2𝜙 + N ⋅ sin 2𝜙. (11) 𝜎 + 𝜎 𝜎 − 𝜎 H h H h Q(𝜙 ) = + ⋅ cos 2𝜃. (6) 2 2 In equation (11), there are three unknown parameters 𝜎 ,M,N. At least three different sets of az- In equation (6), a nonlinear equation is constructed that con- + imuth data are required to solve this problem. tainsall theparametersusedinHISSexpression. Then alin- Finally, the HISS can be expressed as: earization process is applied to optimize the nonlinear equa- tion as follows. 2 2 𝜎 = 𝜎 + 𝜎 = 𝜎 + M + N , H + − + Define 2 2 𝜎 + 𝜎 𝜎 = 𝜎 − 𝜎 = 𝜎 − M + N , H h h + − + 𝜎 = , 1 N 𝜑 = ⋅ arctan . (12) 𝜎 − 𝜎 H h 2 M 𝜎 = . Equation (11) establishes the potential relationships be- Then equation (6) can be written as tween azimuth seismic amplitude and 𝜎 , 𝜎 and their ori- H h entations. The direct inversion of HISS field can be realized Q(𝜙 ) = 𝜎 + 𝜎 ⋅ cos 2𝜃. (7) + − to benefit from this equation. When applied to a data volume, assuming there are m az- In gfi ure 8, there is a certain azimuthal seismic data, and imuth seismic data, the equation (11) is written in matrix the included angle in the x direction is 𝜙 . In the same coordi- form: nate system,weassumethe anglebetween the 𝜎 and the x direction is 𝜑 . Thus, the angle between the data and the ⎛Q(𝜙 )⎞ ⎛1 cos 2𝜙 sin 2𝜙 ⎞ 1 1 1 ⎜ ⎟ ⎜ ⎟ stress orientation is defined as 𝜃 ,and 𝜃 =∅ − 𝜑 according to Q(𝜙 ) 1 cos 2𝜙 sin 2𝜙 2 2 2 ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ 𝜎 gfi ure 8. Therefore, . . . . ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ = ⋅ M (13) . . . . ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ Q(𝜙 ) = 𝜎 + 𝜎 ⋅ cos 2(𝜙 − 𝜑 ). (8) + − ⎝ ⎠ ⎜ ⎟ ⎜ ⎟ . . . . ⎜ ⎟ ⎜ ⎟ Q(𝜙 ) 1 cos 2𝜙 sin 2𝜙 ⎝ m ⎠ ⎝ m m⎠ 136 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 9. Q attribute slices of dier ff ent azimuths: (a) 0–30 ° slice, (b) 30–60° slice, (c) 60–90° slice, (d) 90–120° slice, (e) 120–150° slice and (f) 150–180° slice. Furthermore, for n samples of each seismic trace, there is Equation (14) can be simpliefi d as Q = C ⋅ R (16) ⎛Q ⎞ ⎜ ⎟ where ⎜ ⎟ ⎜ ⎟ Q = (Q Q ...Q ) , ⎜ ⎟ 1 2 m ⎜ ⎟ 1 1 1 1 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 ⎜ ⎟ ⎛ ⎞ 1 1 1 1 Q n n n ⎝ m⎠ ⎜ ⎟ 2 2 2 2 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 1 1 1 1 ⎜ ⎟ 1 1 1 1 n n n 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 ⎛ 1 1 1 1 ⎞ ⎜ ⎟ n n n . . . . . . . . . . . . . . . . . . 2 2 2 2 ⎜ ⎟ ⎜ ⎟ . . . . . . . . . 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 1 1 1 1 ⎜ n n n ⎟ ⎜ ⎟ n n n n 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 C = 1 1 1 1 , ⎜ ⎟ ⎜ ⎟ n n n . . . . . . . . 1 1 1 1 ⎜. . . . . . . . ⎟ ⎜ ⎟ . . . . . . . . 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 2 2 2 2 ⎜ ⎟ ⎜ n n n ⎟ n n n n = 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 ⎜ 1 1 1 1 ⎟ ⎜ ⎟ . . . . . . . . . n n n . . . . . . . . . . . . . . . . . . ⎜ 1 1 1 1⎟ ⎜ ⎟ 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 2 2 2 2 n n n n ⎜ ⎟ n n n ⎜ ⎟ 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 m m m m ⎝ ⎠ ⎜ ⎟ n n n . . . . . . . . . . . . . . . . . . T ⎜. . . . . . . . . ⎟ R = (R R R ) . 𝜎 M N ⎜ n n n n⎟ 1 ... 1 cos 2𝜙 ... cos 2𝜙 sin 2𝜙 ... sin 2𝜙 (17) m m m m ⎝ ⎠ n n n The n fi al inversion objective function is established by the ⎛R ⎞ damping least-square method to realize the inversion of HISS ⎜ ⎟ ⋅ R (14) ⎜ ⎟ field (Wang 2016;Zhang &Dai 2016): ⎝ ⎠ T −1 T R = (C C + 𝜆 ⋅ I) C ⋅ Q . (18) where R is the solution, and 𝜆 is the damping factor or weighting 1 2 n T Q = (Q ,Q , ...Q ) , factor, which is used to enhance the accuracy of the inversion 1 1 1 (15) 1 2 n T R = (𝜎 , 𝜎 , ...𝜎 ) . result. 𝜎 + + + 137 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 10. Inversion result of horizontal stress: (a) maximum horizontal stress and (b) minimum horizontal stress. Figure 11. Magnitude and orientation of maximum horizontal stress: (a) horizontal stress slice, (b) one partial enlarged result and (c) another partial enlarged result. The direct inversion process of HISS eld fi is as follows: parameters 𝜎 ,M,N. Finally, the HISS field is inversed by the damping least-square method. (i) Obtain the amplitude attribute information of each az- imuth from the wide-azimuth seismic data. Meanwhile, 5. Actual data application the azimuthal elastic modulus is inverted from the same seismic data. To verify the feasibility and accuracy of the direct inversion (ii) According to equation (3), the amplitude attribute with method, actual data are applied. Six different azimuth an- azimuth information is combined with the azimuthal gles of actual seismic data are selected to test the HISS field elasticmodulustoobtainthe Q attribute of seismic inversion method in this paper. Figure 9 shows the Q at- data. tribute slice of different azimuths at the T2 horizon. Figure 9a (iii) The relationship equation between the azimuthal Q exhibits a 0–30° slice, gfi ure 9b exhibits a 30–60° slice, gfi - attribute and HISS field is established by equation ure 9c exhibits a 60–90° slice, gfi ure 9d exhibits a 90–120° (11). An objective function with at least three seismic slice, gfi ure 9e exhibits a 120–150° slice and gfi ure 9fexhibits azimuth-stack gathers is found to predict the unknown a 150–180° slice. 138 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Figure 12. Inversion profile of maximum horizontal stress. Figure 13. Inversion profile of minimum horizontal stress. Overall, the value of the Q attribute in gfi ure 9aand fis the Q attribute slices, proving the reliability of the inversion relatively larger than other slices, which indicates that the method in predicting HISS. in situ stress orientation of the actual data is mainly east to Figure 11 shows the orientation of 𝜎 at T2 horizon ob- west. However, in some local positions, gfi ure 9cand dshow tained by inversion. The direction of the short line in the larger Q values, indicating that the stress orientation at these gfi ure represents the orientation of 𝜎 , and the different col- positions is mainly south to north, and the value of Q in ors of the lines represent the magnitude of the maximum the north of the work area is larger than other areas, indi- horizontal stress values. Figure 11 parts b and c are enlarged cating that stress has an obvious high value here. The slices views of the position of the red rectangle in gfi ure 11a. It is of Q attribute with different azimuth show pre-inversion in- clear that the stress orientation in gfi ure 11b is mainly east formation that can provide us a general understanding of to west, while the Q values of the 0–30° and 150–180° az- HISS. imuths in the corresponding positions in gfi ure 9 are larger Figure 10a and b shows the maximum and minimum hor- than other azimuths, so they are consistent. The maximum izontal stress slices of the T2 horizon obtained by the hori- horizontal stress orientation in gfi ure 11cismainlyinthe zontal stress inversion method mentioned previously. These north to south orientation, while the Q values in the cor- gfi ures show that the stress distribution is consistent with responding position of azimuths 60–90° and 90–120° in 139 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. gfi ure 9 are larger than other azimuth data, which is consis- dicting HISS eld fi is derived by using the relationship tent with the results in gfi ure 11c. These results further prove equation. the accuracy of the horizontal stress inversion method. (iv) The 𝜎 , 𝜎 and their orientations of actual data are H h Figures 12 and 13 are the profiles of the 𝜎 and the 𝜎 in predicted by the direct inversion method. The slices of H h the same working area, respectively. The stress logs of well 𝜎 , 𝜎 exhibit a tight connection with Q both in mag- H h Arepresent 𝜎 rmand 𝜎 are overlapped on the correspond- nitude and orientation, which meet theoretical expec- H h ing stress prediction profile separately. Through observing tations. Meanwhile, the prediction results of 𝜎 , 𝜎 . H h the profile shape and numerical distribution, it is clear that profiles demonstrate great corresponding to the actual the inversion results of 𝜎 and 𝜎 reflect a certain degree well logs, proving the feasibility of this method in pre- H h of heterogeneity in the transverse direction. In the vertical dicting an HISS eld. fi direction, the inversion results are in good agreement with the actual well logs, which reflects the accuracy of the direct The method of direct inversion of a horizontal stress eld fi inversion method in horizontal stress prediction. from wide-azimuth seismic data overcomes the limitation of the stress prediction model and avoids the generation of ac- cumulated errors in the process of indirect inversion. Applied 6. Conclusion to the actual data, the expected prediction effect is achieved. The prediction of an in situ stress field is a dicult ffi problem in the integration of geological engineering. At present, the pre- diction methods of in situstressarestilllimitedtocoreexper- Acknowledgements iments, logging and other methods. These methods not only This research is supported by the National Natural Science Foun- have high cost, but also obtain less in situ stress information, dation Project of China (grant no. 41874146) and Shandong which has difficulty in meeting the needs of exploration and Province Foundation for Qingdao National Laboratory of marine development. Wide-azimuth seismic data integrate different science (grant no. 2021QNLM020001). pieces of azimuth information and contain sucffi ient infor- mation for analyzing and prospecting. The attribute parame- Conflict of interest statement: None declared. ters varying with azimuth can be predicted by using the differ- ences between different azimuth information. Based on this References characteristic, a new prediction process is proposed, which sets up a new method for the prediction of HISS fields. Campbell-Stone, E., Shafer, L. & Mallick, S., 2012. Subsurface geomechan- Through the study, we found that: ical analysis, comparison with prestack azimuthal AVO analysis, and im- plication for predicting subsurface geomechanical properties from 3-D seismic data, in Proceedingsofthe 9thBiennialConference&Exposition, (i) Seismic amplitude ellipse fitting is an effective way to SEG, Expanded Abstracts, P501. exhibit the orientation of stress subsurface, but the Dillen, M., 2000. Time-lapse seismic monitoring of subsurface dynamics, thesis, results are not always accurate and may deviate by Delft University of Technology, Delft. 90°. The azimuth elastic modulus information is intro- Downton, J. & Gray, D., 2006. AVAZ parameter uncertainty estimation, duced into the orientation prediction of HISS. Through SEG Technical Program Expanded Abstracts, 25, 234–238. Gray, D., Anderson, P. & Logel, J., 2012. Estimation of stress and geome- a combination of azimuthal amplitude and azimuthal chanical properties using 3D seismic data,First Break, 30, 59–68. elastic modulus, the uncertainty of using only the seis- Ge, H.K., Lin, Y.S. & Wang, S.C., 1998. In-situ stress measurement and its mic amplitude to predict the orientation of stress is application in exploration and development, Journal of Petroleum Uni- avoided. versity (natural science edition), 22, 97–102. (ii) Through the statistical analyses of logging data and Haimson, B., 2006, True triaxial stresses and the brittle fracture of rock, azimuthal seismic data, the potential associations be- Pure & Applied Geophysics, 163, 1101–1130. Huang, J., Griffiths, D.V. & Wong, S.W., 2012. Initiation pressure, location tween HISS, azimuthal seismic amplitude and az- and orientation of hydraulic fracture, International Journal of Rock Me- imuthal elastic modulus are obtained and presented in chanics and Mining Sciences, 49, 59–67. theformofequation(3),and then anew stress-related Hubbert, M.K. & Willis, D., 1957. Mechanics of hydraulic fracturing, attribute Q is constructed. The azimuthal Q attribute Transactions of the AIME, 210, 153–168. not only indicates the orientation of stress, but also Hunt, L., Reynolds, S. & Hadley, S., 2011. Causal fracture prediction: cur- vature, stress, and geomechanics, The Leading Edge, 30, 1274–1286. forms a reliable substitute for the magnitude of stress, King, R.C., Hillis, R.R. & Reynolds, S.D., 2008. In situ stresses and natu- which can be obtained from wide-azimuth seismic data. ral fractures in the Northern Perth Basin, Australia, Australian Journal of (iii) On the basis of rock mechanics analysis, stress in any Earth Sciences, 55, 685–701. azimuth can be expressed by HISS. And the stress in Lei, T. & Sinha, B., 2012. Estimation of horizontal stress magnitudes and any azimuth can be represented as the azimuthal Q at- stress coefficients of velocities using borehole sonic data, Geophysics, 77, tribute. Then, the inversion objective function of pre- 181–196. 140 JournalofGeophysicsand Engineering (2022) 19, 131–141 Yang et al. Li, C. P., 2013. Research on Fractured Reservoir Prediction with Azimuthal Sayers, C.M., 2013. The effect of anisotropy on the Young’s moduli and Seismic Data, China University of Petroleum, Qingdao, Shandong. Poisson’s ratios of shale. Geophysical Prospecting, 61, 416–426. Ma, N., Yin, X.Y. & Sun, C.Y., 2018. Inversion for crustal stress based Shahri, M.P., Chok, H. & Huang, J., 2016. Stress inversion via borehole im- on azimuthal seismic data, Chinese Journal of Geophysics, 61, 697– age log and fracturing data: integrated approach, in Unconventional Re- 706. sources Technology Conference, 2718–2740. Mallick, S., Craft, K.L. & Meister, L.J., 1998. Computation of principal di- Shaw, R.K. & Sen, M.K., 2006. Use of AVOA data to estimate fluid indica- rections of azimuthal anisotropy from P-wave seismic data, Geophysics, tor in a vertically fractured medium, Geophysics, 71, C15–C24. 63, 692–706. Thomsen, L., 1986. Weak elastic anisotropy, Geophysics, 51, 1954–1966. Mallick, S. & Frazer, L.N., 1991. Reflection/transmission coefficients and Wang, J.H., Zhang, J.M. & Wu, G.C., 2021. Wide azimuth Young’s modulus azimuthal anisotropy in marine seismic studies, Geophysical Journal In- inversion and fracture prediction method and its application – taking the ternational, 28, 241–252. exploration of H structural buried hill in Bozhong Sag as an example, Oil Mallick, S., Mukherjee, D. & Shafer, L., 2017. Azimuthal anisotropy anal- Geophysical Prospecting, 56, 593–602 (in Chinese). ysis of P-wave seismic data and estimation of the orientation of the in Wang, Y., 2016. Seismic Inversion: Theory and Application.Wiley Blackwell. situ stress fields: An example from the Rock-Springs uplift, Wyoming, Wu, C., Chen, M. & Jin, Y., 2009. A prediction method of borehole stability USA, Geophysics Journal of the Society of Exploration Geophysicists, 82, based on seismic attribute technology, Journal of Petroleum Science and B63-B77. Engineering, 65, 208–216. Mitchell, D. & Van, D., 2016. Development of an ellipse tfi ting method Xu, Y. & Li, Y., 2001. Uncertainties in azimuthal AVO analysis, SEG, Ex- with which to analyse selected area electron diffraction patterns, Ultra- panded Abstracts, 24–27. microscopy, 160, 140–145. Yin, X.Y., Ma, N. & Ma, Z.Q., 2018. Review of in-situ stress prediction tech- Nian, T., Wang, G. & Xiao, C., 2016. Determination of in-situ stress orien- nology, Geophysical Prospecting for Petroleum, 57, 488–504. tation and subsurface fracture analysis from image-core integration: an Zhang, M.L., Yang, Y. & Gao, L.S., 2021. A study on the geometric effects example from ultra-deep tight sandstone (BSJQK Formation) in the Ke- of a concrete filling body in remaining roadways with fully mechanised lasu Belt, Tarim Basin, Journal of Petroleum Science and Engineering, 147, caving, JournalofGeophysicsand Engineering, 18, 681–690. 495–503. Zhang, F.C. & Dai, R.H., 2016. Nonlinear inversion of pre-stack seismic Pan, X.P., Zhang, G.Z. & Yin, X.Y., 2017. Azimuthal seismic amplitude data using variable metric method, Journal of Applied Geophysics, 129, 111–125. variation with offset and azimuth inversion in weakly anisotropic media with orthorhombic symmetry, Surveys in Geophysics, 39, 1–25. Zhang, F.C., Yang, J.Y. & Li, C.H., 2020. Direct inversion for reservoir pa- Pan, X.P., Zhang, G.Z. & Yin, X.Y., 2018. Azimuthally pre-stack seismic rameters from prestack seismic data, Journal of Geophysics and Engineer- inversion for orthorhombic anisotropy driven by rock physics. Science ing, 17, 993–1004. China (Earth Sciences), 61, 425–440. Zhang, G.Z., Chen, J.J. & Chen, H.Z., 2015. Prediction for in-situ forma- Raoof, G., Vamegh, R., Bernt, A. & Ramin, M., 2015. Application of in situ tion stress of shale based on rock physics equivalent model, Chinese Jour- stress estimation methods in wellbore stability analysis under isotropic nalofGeophysics, 58, 2112–2122. and anisotropic conditions, Journal of Geophysics and Engineering, 12, Zoback, M., 2007. Reservoir Geomechanics, Cambridge University Press. 657–673. Zong, Z.Y., Yin, X.Y. & Zhang, F., 2012. Reflection coefficient equation Ruger, A., 1996. Reflection Coefficients and Azimuthal AVO Analysis in and pre-stack seismic inversion with Young’s modulus and Poisson ra- Anisotropic Media. Colorado School of Mine, Colorado. tio, Chinese Journal of Geophysics, 55, 3796–3794.

Journal

Journal of Geophysics and Engineering – Oxford University Press

Published: Mar 21, 2022

Keywords: wide-azimuth seismic data; elastic modulus; seismic amplitude; direct inversion; horizontal stress field

There are no references for this article.