Method for testing and extracting paleo-tectonic geostress based on rock core

Abstract

A method for testing and extracting paleo-tectonic geostress based on rock core, including: selecting rock cores in different tectonic periods; preparing standard cylindrical samples from the rock cores in a specific orientation; subjecting the samples to an acoustic emission test to test paleo-stresses of multiple tectonic periods and obtain paleo-tectonic stress data sequence; based on a correlation analysis and an Euclidean distance of the stress data sequence, stripping and extracting multi-level Kaiser stress points of the acoustic emission of rock cores from different formations, so as to calculate and evaluate the ground stress of an evaluated formation in an evaluated paleo-tectonic period.

Claims

1. A method for measuring and extracting paleo-tectonic geostress based on rock core, comprising: (S1) selecting a drilling rock core T1 in a tectonic period to be evaluated and a drilling rock core T0 in a previous tectonic period with respect to the tectonic period to be evaluated; and calibrating a radial direction consistency of the drilling rock cores T0 and T1 to ensure that the drilling rock cores T0 and T1 have the same geographic orientation in a radial direction relative to 0°; (S2) obtaining standard cylindrical samples with a diameter of 25 mm and a length of 50 mm respectively from the drilling rock cores T0 and T1 by drilling; and cutting and grinding both ends of each of the standard cylindrical samples; (S3) subjecting the standard cylindrical samples obtained in step (S2) to an acoustic emission stress test to identify a Kaiser point of acoustic emission of each of the standard cylindrical samples and a corresponding loading stress during a loading process; (S4) calculating an average value of a loading stress data sequence corresponding to the Kaiser point of the acoustic emission of each of standard cylindrical samples in the same orientation to obtain a paleo-stress data sequence of a corresponding formation in a corresponding orientation, expressed as follows: $\begin{array}{cc}{\mathrm{DStri}}_{-j}=\frac{\underset{m}{\overset{M}{.Math.}}{\mathrm{DStri}}_{-\mathrm{jm}}}{M}\left(M\ge 3\right);& \left(1\right)\end{array}$ wherein DStr represents a paleo-stress data; i is 0 or 1, and when i is 0, it represents the drilling rock core T0, and when i is 1, it represents the drilling rock core T1; j represents an orientation of the standard cylindrical sample; M represents the number of the standard cylindrical samples in the same orientation, and M≥3; m represents a m-th stress data sequence, and 1≤m≤M; (S5) setting the number of a stress data of standard cylindrical samples from T0 in a j orientation as N0, and setting the number of a stress data of standard cylindrical samples from T1 in the j orientation as N1; and randomly selecting N1 data from N0 data in a stress data sequence of the standard cylindrical samples from T0, followed by permutation to construct a stress data sequence to be evaluated in the j orientation; (S6) calculating a correlation coefficient and an Euclidean distance between the stress data sequence to be evaluated constructed in step (S5) and a stress data sequence of the standard cylindrical samples from T1 in the same orientation obtained in step (S4) respectively through equations (2) and (3), and calculating a ratio of the correlation coefficient to the Euclidean distance via equation (4): $\begin{array}{cc}{\mathrm{Rt}}_{\mathrm{ij}}=\frac{\underset{k}{\overset{N1}{.Math.}}\left({\sigma }_{\mathrm{ik}}-{\stackrel{\_}{\sigma }}_i\right)\left({\sigma }_{\mathrm{jk}}-{\stackrel{\_}{\sigma }}_j\right)}{\sqrt{\underset{k}{\overset{N1}{.Math.}}{\left({\sigma }_{\mathrm{ik}}-{\stackrel{\_}{\sigma }}_i\right)}^2.Math.\underset{k}{\overset{n}{.Math.}}{\left({\sigma }_{\mathrm{jk}}-{\stackrel{\_}{\sigma }}_j\right)}^2}};& \left(2\right)\\ {\mathrm{Do}}_{\mathrm{ij}}=\sqrt{\underset{k}{\overset{N1}{.Math.}}{\left({\sigma }_{\mathrm{ik}}-{\sigma }_{\mathrm{jk}}\right)}^2};& \left(3\right)\\ R_{\mathrm{ij}}=\frac{{\mathrm{Rt}}_{\mathrm{ij}}}{{\mathrm{Do}}_{\mathrm{ij}}};& \left(4\right)\end{array}$ wherein Rt.sub.ij is a correlation coefficient between a stress data sequence DStri of a formation Ti in a certain orientation and a stress data sequence DStrj of a formation Tj in the same orientation; Do.sub.ij is an Euclidean distance between the stress data sequence DStri of the formation Ti in a certain orientation and the stress data sequence DStrj of the formation Tj in the same orientation; R.sub.ij is a ratio of the correlation coefficient Rt.sub.ij to the Euclidean distance Do.sub.ij; σ.sub.ik is a k-th stress value in the stress data sequence DStri of the formation Ti in a certain orientation; σ.sub.jk is a k-th stress value in the stress data sequence DStrj of the formation Tj in a certain orientation; and σ.sub.i is an average value of σ.sub.ik, and σ.sub.jk is an average value of σ.sub.ik; (S7) based on calculation results obtained in step (S6), obtaining a maximum correlation coefficient Rt and a minimum Euclidean distance Do between stress data sequences to be evaluated in the same orientation and the stress data sequence of the standard cylindrical samples from T1 in the same orientation obtained in step (S4) respectively through equations (5) and (6), and obtaining a maximum ratio R.sub.max of the correlation coefficient to the Euclidean distance through equation (7): $\begin{array}{cc}\mathrm{Rt}=\mathrm{Max}\left({\mathrm{Rt}}_{\mathrm{ij}-t}\right)& \left(5\right)\\ \mathrm{Do}=\mathrm{Min}\left({\mathrm{Do}}_{\mathrm{ij}-t}\right)& \left(6\right)\\ R_{\max }=\mathrm{Max}\left(\frac{{\mathrm{Rt}}_{\mathrm{ij}-t}}{{\mathrm{Do}}_{\mathrm{ij}}-t}\right);& \left(7\right)\end{array}$ wherein Rt.sub.ij-t is a correlation coefficient between a t-th stress data sequence to be evaluated constructed in step (S5) and the stress data sequence of the standard cylindrical samples from T1 in the same orientation in step (S4), and Do.sub.ij-t is an Euclidean distance between the t-th stress data sequence to be evaluated constructed in step (S5) and the stress data sequence of the standard cylindrical samples from T1 in the same orientation in step (S4); (S8) taking a stress data sequence to be evaluated corresponding to the maximum correlation coefficient Rt, the minimum Euclidean distance Do, and the maximum ratio R.sub.max as a stress data sequence memorized in the formation T0 in the same orientation as the formation T1; wherein a stress data removed from a corresponding stress data sequence of the standard cylindrical samples from T0 in step (S4) is possessed by the formation T0 but not in the formation T1 in an orientation, and is a paleo-stress data of the formation T0 in the tectonic period to be evaluated; and realizing stripping and extraction of paleo-stress data in the tectonic period to be evaluated in an analysis orientation; and (S9) calculating a maximum horizontal principal stress, a minimum horizontal principal stress and a vertical principal stress of paleo-tectonic ground stress in the tectonic period to be evaluated by means of equations (8) and (9): $\begin{array}{cc}{\sigma }_V={\sigma }_V{\sigma }_{H1}=\frac{{\sigma }_0+{\sigma }_{90}}{2}+\frac{{\sigma }_0-{\sigma }_{90}}{2}\left(1+{\tan }^{2}2\alpha \right){\sigma }_{h2}=\frac{{\sigma }_0+{\sigma }_{90}}{2}-\frac{{\sigma }_0-{\sigma }_{90}}{2}\left(1+{\tan }^{2}2\alpha \right)& \left(8\right)\\ \tan 2\alpha =\frac{{\sigma }_0+{\sigma }_{90}-2{\sigma }_{45}}{{\sigma }_0+{\sigma }_{90}};& \left(9\right)\end{array}$ wherein σ.sub.H1 is a maximum horizontal principal stress of a formation in the tectonic period to be evaluated; σ.sub.H2 is a minimum horizontal principal stress of the formation in the tectonic period to be evaluated; σ.sub.V is the vertical principal stress of the formation in the tectonic period to be evaluated; and σ.sub.0 is a stress component relative to a 0° orientation, σ.sub.45 is a stress component relative to a 45° orientation, and σ.sub.90 is a stress component relative to a 90° orientation.

2. The method of claim 1, wherein in step (S1), the drilling rock core T1 is collected from a formation in the tectonic period to be evaluated; the drilling rock core T0 is collected from a formation in the previous tectonic period with respect to the tectonic period to be evaluated; and the formation in the tectonic period to be evaluated and the formation in the previous tectonic period both have a gentle structure and a formation dip of no more than 15°; the drilling rock core T1 and the drilling rock core T0 both have a diameter of no less than 65 mm; and the drilling rock core T0 and the drilling rock core T1 are both free of visible fracture and development of a structural plane.

3. The method of claim 1, wherein in step (S2), the standard cylindrical samples are collected from the rock cores T0 and T1 respectively along three radial directions of 0°, 45° and 90° and an axial direction.

4. The method of claim 1, wherein in step (S4), stress data sequences of at least 3 standard cylindrical samples in the same orientation are averaged to eliminate an effect of an uncertain factor on stress test.

5. The method of claim 1, wherein in step (S5), the number of the stress data sequence to be evaluated in the j orientation is N0(N0−1)(N0−2) . . . (N0−N1+1).

6. The method of claim 1, wherein in step (S8), the maximum correlation coefficient Rt and the minimum Euclidean distance Do between N0(N0−1)(N0−2) . . . (N0−N1+1) stress data sequences to be evaluated and the stress data sequence of the standard cylindrical samples from T1 in the same orientation, and the maximum ratio R.sub.max of the correlation coefficient to the Euclidean distance are used to determine a stress data sequence memorized formation T0 that is the same as a stress data sequence of the formation T1 at the same orientation.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The FIGURE is a flowchart of test and extraction of paleo-tectonic geostress based on rock core according to an embodiment of this disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

(2) This application will be described in detail below with reference to embodiments and accompanying drawings to make the objectives, technical solutions, and advantages of this application clearer. Obviously, provided below are merely some embodiments of this application, which are not intended to limit the application. Other embodiments obtained by those of the ordinary skill in the art based on the embodiments provided herein without paying any creative effort shall fall within the scope of the present application.

(3) As shown in the FIGURE, a method for testing and extracting paleo-tectonic geostress based on rock core is provided, which includes the following steps.

(4) 1. Selection of Rock Cores

(5) A drilling rock core T1 in a tectonic period to be evaluated and a drilling rock core T0 in a previous tectonic period with respect to the evaluated tectonic period are selected, where the formation in the tectonic period to be evaluated and the formation in the previous tectonic period both have a gentle structure and a formation dip of no more than 15°. The drilling rock core T1 and the drilling rock core T0 both have a diameter of no less than 65 mm. The drilling rock core T0 and the drilling rock core T1 are both free of visible fracture and development of a structural plane. A radial direction consistency of the drilling rock cores T0 and T1 are calibrated to ensure that the drilling rock cores T0 and T1 have the same geographic orientation in a radial direction relative to 0°.

(6) 2. Preparation of Samples

(7) Standard cylindrical samples T0.sub.−0, T0.sub.−45, T0.sub.−90 and T0.sub.−V with a diameter of 25 mm and a length of 50 mm are obtained respectively from the drilling rock core T0 along three radial directions of 0°, 45° and 90° and an axial direction by drilling. Both ends of each of the standard cylindrical samples are cut and ground. At least 3 samples are obtained in each orientation by drilling, i.e., at least 12 cylindrical samples with a diameter of 25 mm are obtained and prepared from the drilling rock core T0 by drilling. Equally, standard cylindrical samples T1.sub.−0, T1.sub.−45, T1.sub.−90 and T1.sub.−V with a diameter of 25 mm and a length of 50 mm are respectively obtained from the drilling rock core T1 along three radial directions of 0°, 45° and 90° and an axial direction by drilling. At least 3 samples are obtained in each orientation by drilling.

(8) 3. Acoustic Emission Test

(9) Six groups of the standard cylindrical samples T0.sub.−0, T0.sub.−45, T0.sub.−90, T0.sub.−V, T1.sub.−0, T1.sub.−45, T1.sub.−90 and T1.sub.−V (at least 3 samples in each group) prepared by drilling are subjected to continuous loading along the axial direction and the acoustic emission events during a loading process are recorded continuously in real time synchronously. The result of the acoustic emission is analyzed to identify a Kaiser points of acoustic emission of each of the standard cylindrical samples and a corresponding loading stress during the loading process.

(10) 4. Obtaining of Paleo-Stress Data Sequence of Formation

(11) A paleo-stress data sequence is formed by the loading stress corresponding to the Kaiser point of each of the standard cylindrical samples. To eliminate an effect of an uncertain factor in a data, an average value of the paleo-stress data sequence of each standard cylindrical sample in each group (including at least 3 samples) is calculated, which is expressed as follows:

(12) $\begin{array}{cc}{\mathrm{DStri}}_{-j}=\frac{\underset{m}{\overset{M}{.Math.}}{\mathrm{DStri}}_{-\mathrm{jm}}}{M}\left(M\ge 3\right);& \left(1\right)\end{array}$

(13) after that, paleo-stress data sequences of corresponding formations along corresponding orientations are obtained, that is, the stress data sequences DStr0.sub.−0, DStr0.sub.−45, DStr0.sub.−90, DStr0.sub.−V and DStr1.sub.−0, DStr1.sub.−45, DStr1.sub.−90, DStr1.sub.−V of T0.sub.−0, T0.sub.−45, T0.sub.−90, T0.sub.−V, T1.sub.−0, T1.sub.−45, T1.sub.−90 and T1.sub.−V are respectively obtained, which is shown as follow:
DStr0.sub.−0={Str0.sub.−0-1,Str0.sub.−0-2 . . . Str0.sub.−0-i . . . Str0.sub.−0-N0}
DStr0.sub.−45={Str0.sub.−0-1,Str0.sub.−45-2 . . . Str0.sub.−45-i . . . Str0.sub.−45-N0}
DStr0.sub.−90={Str0.sub.−0-1,Str0.sub.−90-2 . . . Str0.sub.−90-i . . . Str0.sub.−90-N0}
DStr0.sub.−v={Str0.sub.−0-1,Str0.sub.−v-2 . . . Str0.sub.−v-i . . . Str0.sub.−v-N0}
DStr1.sub.−0={Str1.sub.−0-1,Str1.sub.−0-2 . . . Str1.sub.−0-i . . . Str1.sub.−0-N0}
DStr1.sub.−45={Str1.sub.−0-1,Str1.sub.−45-2 . . . Str1.sub.−45-i . . . Str1.sub.−45-N0}
DStr1.sub.−90={Str1.sub.−0-1,Str1.sub.−90-2 . . . Str1.sub.−90-i . . . Str1.sub.−90-N0}
DStr1.sub.−v={Str1.sub.−0-1,Str1.sub.−v-2 . . . Str1.sub.−v-i . . . Str1.sub.−v-N0}

(14) TABLE-US-00001 TABLE 1 Stress data sequences of Kaiser points of rock cores in different orientations of each formation Data Sampling Formation sequence direction Level 1 Level 2 Level 3 Level 4 T1 DStr1.sub.−0 0 31.686 54.015 63.888 — DStr1.sub.−45 45 13.982 38.142 44.147 — DStr1.sub.−90 90 20.639 40.862 47.341 — DStr1.sub.−v v 21.837 44.691 52.179 — T0 DStr0.sub.−0 0 33.423 53.056 58.188 65.383 DStr0.sub.−45 45 14.017 36.117 41.047 46.999 DStr0.sub.−90 90 21.143 40.994 47.219 63.873 DStr0.sub.−v v 23.007 43.424 52.377 64.779

(15) 5. Stripping and Analysis of Paleo-Stress Data

(16) 5.1 Stripping and Analysis of Paleo-Stress Data in 0° Orientation

(17) (1) The number N0 of the stress data in the stress data sequence in the orientations of a formation DStr0.sub.−0, and the number N1 of the stress data in the stress data sequence in the orientations of a formation DStr1.sub.−0 are obtained. NN=N0−N1 data are randomly removed from a stress data sequence DStr0.sub.−0 to construct a stress data sequence DStr0l with the same amount of stress as that of a stress data sequence DStr1.sub.−0, i.e., N1 data are extracted from the stress data sequence DStr0.sub.−0 and then subjected to a permutation to construct a stress data sequence, which is expressed as follows:
DStr01.sub.−0={Str1.sub.−0-1,Str1.sub.−0-2 . . . Str1.sub.−0-i . . . Str0.sub.−0-N1};

(18) N0(N0−1)(N0−2) . . . (N0−N1+1) stress data sequences DStr0l with N1 stress data are constructed in total.

(19) As shown in Table 1, there are 3 stress data in a stress data sequence of the formation T1, i.e., N1=3; there are 4 stress data in a stress data sequence of the formation T0, i.e., N0=4. The 3 data are extracted from the stress data sequence DStr0.sub.−0 to form 12 data sequences DStr0l in total, the results of which are shown in Table 2.

(20) TABLE-US-00002 TABLE 2 Stress data sequences DStr01 to be evaluated extracted and constructed from stress data sequences of formation T0 Stress data sequence Sequence Level 1 Level 2 Level 3 Level 4 Notes DStr1.sub.−0 31.686 54.015 63.888 — DStr0.sub.−0 33.423 53.056 58.188 65.383 DStr01 1 33.423 53.056 58.188 Extracted DStr01 2 33.423 58.188 65.383 data DStr01 3 33.423 53.056 65.383 sequences DStr01 4 53.056 58.188 65.383 to be DStr01 5 53.056 58.188 33.423 evaluated DStr01 6 53.056 65.383 33.423 DStr01 7 58.188 65.383 33.423 DStr01 8 58.188 65.383 53.056 DStr01 9 58.188 33.423 53.056 DStr01 10 65.383 33.423 53.056 DStr01 11 65.383 33.423 58.188 DStr01 12 65.383 53.056 58.188

(21) (2) A correlation coefficient and an Euclidean distance between the stress data sequences DStr01 to be evaluated and the stress data sequence DStr1.sub.−0 are calculated respectively through equations (2) and (3), and a ratio of the correlation coefficient to the Euclidean distance is calculated via equation (4):

(22) $\begin{array}{cc}{\mathrm{Rt}}_{\mathrm{ij}}=\frac{\underset{k}{\overset{N1}{.Math.}}\left({\sigma }_{\mathrm{ik}}-{\stackrel{\_}{\sigma }}_i\right)\left({\sigma }_{\mathrm{jk}}-{\stackrel{\_}{\sigma }}_j\right)}{\sqrt{\underset{k}{\overset{N1}{.Math.}}{\left({\sigma }_{\mathrm{ik}}-{\stackrel{\_}{\sigma }}_i\right)}^2.Math.\underset{k}{\overset{n}{.Math.}}{\left({\sigma }_{\mathrm{jk}}-{\stackrel{\_}{\sigma }}_j\right)}^2}}& \left(2\right)\\ {\mathrm{Do}}_{\mathrm{ij}}=\sqrt{\underset{k}{\overset{N1}{.Math.}}{\left({\sigma }_{\mathrm{ik}}-{\sigma }_{\mathrm{jk}}\right)}^2}& \left(3\right)\\ R_{\mathrm{ij}}=\frac{{\mathrm{Rt}}_{\mathrm{ij}}}{{\mathrm{Do}}_{\mathrm{ij}}};& \left(4\right)\end{array}$

(23) where Rt.sub.ij is a correlation coefficient between a stress data sequence DStri of a formation Ti in a certain orientation and a stress data sequence DStrj of a formation Tj in the same orientation; Do.sub.ij is an Euclidean distance between the stress data sequence DStri of the formation Ti in a certain orientation and the stress data sequence DStrj of the formation Tj in the same orientation; is a ratio of the correlation coefficient Rt.sub.ij to the Euclidean distance Do.sub.ij; σ.sub.ik is a k-th stress value in the stress data sequence DStri of the formation T1 in a certain orientation, and the corresponding values can be Stri.sub.|0-k, Stri.sub.−45-k, Stri.sub.−90-k, Stri.sub.−v-k; σ.sub.ik is a k-th stress value in the stress data sequence DStrj of the formation Tj in a certain orientation, and the corresponding values can be Strj.sub.−0-k, Strj.sub.−45-k, Strj.sub.−90-k, Strj.sub.−v-k; and σ.sub.1 is an average value of σ.sub.ik, and σ.sub.jk is an average value of σ.sub.jk.

(24) The correlation coefficient, the Euclidean distance between each stress data sequence DStr01 to be evaluated and the stress data sequence DStr1.sub.−0 shown in Table 2, and a ratio of the correlation coefficient to the Euclidean distance are calculated, and the results are shown in Table 3.

(25) TABLE-US-00003 TABLE 3 Construction of stress data sequence of formation T0 and its correlation analysis with paleo-stress data sequence in 0° orientation of formation T1 Ratio of the correlation Stress Correlation Euclidean coefficient to data coefficient distance the Euclidean sequence Sequence Level 1 Level 2 Level 3 Level 4 Rt.sub.ij Do.sub.ij distance RD DStr1.sub.−0 31.686 54.015 63.888 — — — — DStr0.sub.−0 33.423 53.056 58.188 65.383 — — — DStr01 1 33.423 53.056 58.188 — 0.994 6.035 0.165 DStr01 2 33.423 58.188 65.383 — 0.996 4.761 0.209 DStr01 3 33.423 53.056 65.383 — 0.996 2.484 0.401 DStr01 4 53.056 58.188 65.383 — 0.950 21.825 0.044 DStr01 5 53.056 58.188 33.423 — −0.589 37.446 −0.016 DStr01 6 53.056 65.383 33.423 — −0.422 38.910 −0.011 DStr01 7 58.188 65.383 33.423 — −0.574 41.949 −0.014 DStr01 8 58.188 65.383 53.056 — −0.206 30.805 −0.007 DStr01 9 58.188 33.423 53.056 — −0.405 35.266 −0.011 DStr01 10 65.383 33.423 53.056 — −0.575 40.949 −0.014 DStr01 11 65.383 33.423 58.188 — −0.422 39.900 −0.011 DStr01 12 65.383 53.056 58.188 — −0.744 34.189 −0.022

(26) (3) Based on the correlation coefficient and the Euclidean distance between the two data sequences, the same stress data sequence is identified. A maximum correlation coefficient Rt, and a minimum Euclidean distance Do between the stress data sequences to be evaluated and the stress data sequence DStr1.sub.−0, are obtained respectively through equations (5) and (6), and a maximum ratio R.sub.max of the correlation coefficient to the Euclidean distance is obtained through equation (7):

(27) $\begin{array}{cc}\mathrm{Rt}=\mathrm{Max}\left({\mathrm{Rt}}_{\mathrm{ij}-t}\right)& \left(5\right)\\ \mathrm{Do}=\mathrm{Min}\left({\mathrm{Do}}_{\mathrm{ij}-t}\right)& \left(6\right)\\ R_{\max }=\mathrm{Max}\left(\frac{{\mathrm{Rt}}_{\mathrm{ij}-t}}{{\mathrm{Do}}_{\mathrm{ij}}-t}\right);& \left(7\right)\end{array}$

(28) where Rt.sub.ij-t is a correlation coefficient between a t-th stress data sequence DStr0l to be evaluated and the stress data sequence DStr1.sub.−0, and Do.sub.ij-t is an Euclidean distance between the t-th stress data sequence DStr0l to be evaluated and the stress data sequence DStr1.sub.−0.

(29) A stress data sequence to be evaluated corresponding to the maximum correlation coefficient Rt, the minimum Euclidean distance Do, and the maximum ratio of the correlation coefficient to the Euclidean distance R.sub.max is taken as a stress data sequence memorized in the formation T0 in the same orientation as the formation T1.sub.−0, where a stress data removed from a corresponding stress data sequence DStr0.sub.−0 is possessed by the formation T0 but not in the formation T1 in an orientation, and is a paleo-stress data of the formation T0 in the tectonic period to be evaluated. The paleo-stress data in the tectonic period to be evaluated in an analytical orientation is stripped and extracted through the above steps.

(30) 5.2 Stripping and Analysis of Paleo-Stress Data in 45° Orientation, 90° Orientation and Axial Direction

(31) According to the steps in 5.1, the stress data in the 45° orientation, the 90° orientation and the axial direction orientation in the tectonic period to be evaluated are stripped and extracted.

(32) Table 4 shows a stress data stripped from the stress data sequence of the formation T0 shown in Table 1 the same as the formation T1 and the stress data in the tectonic period to be evaluated

(33) TABLE-US-00004 TABLE 4 Stress data sequence of formation T1 included in stress data sequences of formation T0 in all orientations and stress in tectonic period to be evaluated Ratio RD of correlation Stress of Correlation Euclidean coefficient to evaluated Stress data coefficient distance Euclidean tectonic Orientation sequence Level 1 Level 2 Level 3 Rt.sub.ij Do.sub.ij distance period 0 DStr1.sub.−0 33.423 53.056 65.383 0.996 2.484 0.401 58.188 45 DStr1.sub.−45 14.017 36.117 46.999 0.990 3.498 0.283 41.047 90 DStr1.sub.−90 21.143 40.994 47.219 1.000 0.535 1.869 63.873 v DStr1.sub.−v 23.007 43.424 52.377 0.998 1.736 0.575 64.779

(34) 6. Calculation of Principal Stress

(35) Based on each stripped and extracted stress component, a maximum horizontal principal stress, a minimum horizontal principal stress and a vertical principal stress of paleo-tectonic ground stress in the tectonic period to be evaluated are calculated by means of equations (8) and (9):

(36) $\begin{array}{cc}{\sigma }_V={\sigma }_V{\sigma }_{H1}=\frac{{\sigma }_0+{\sigma }_{90}}{2}+\frac{{\sigma }_0-{\sigma }_{90}}{2}\left(1+{\tan }^{2}2\alpha \right){\sigma }_{h2}=\frac{{\sigma }_0+{\sigma }_{90}}{2}-\frac{{\sigma }_0-{\sigma }_{90}}{2}\left(1+{\tan }^{2}2\alpha \right)& \left(8\right)\\ \tan 2\alpha =\frac{{\sigma }_0+{\sigma }_{90}-2{\sigma }_{45}}{{\sigma }_0+{\sigma }_{90}};& \left(9\right)\end{array}$

(37) where σ.sub.H1 is a maximum horizontal principal stress of a formation in the tectonic period to be evaluated; σ.sub.H2 is a minimum horizontal principal stress of the formation in the tectonic period to be evaluated; σ.sub.V is the vertical principal stress of the formation in the tectonic period to be evaluated; and σ.sub.0 is a stress component relative to an 0° orientation, σ.sub.45 is a stress component relative to an 45° orientation, and σ.sub.90 is a stress component relative to an 90° orientation.

(38) Table 5 shows the results of principal stress calculated based on the principal stress components in the tectonic period to be evaluated stripped and extracted in Table 4.

(39) TABLE-US-00005 TABLE 5 Calculation results of principal stress Stress component (MPa) Principal stress (MPa) 45° 90° Minimum Maximum 0° orien- orien- Axial horizontal horizontal Vertical orientation tation tation direction stress stress stress 58.188 41.047 63.873 64.779 58.188 63.873 64.779

(40) The above-mentioned embodiments are merely illustrative of the disclosure, and are not intended to limit the disclosure. It should be understood that any changes, modifications, replacements, and transformations made by those skilled in the art without departing from the spirit and scope of this disclosure shall fall within the scope of the disclosure defined by the appended claims.