CN104200039A - Quantitative forecasting method of tectonic fissure occurrence - Google Patents

Abstract

The invention relates to the field of oil-gas field exploration and development, particularly to a quantitative forecasting method of tectonic fissure occurrence. The quantitative forecasting method includes firstly determining a fissure mechanical property and rock mechanics parameters in a research area and restoring a paleotectonic map; secondly performing a numerical simulation of a paleostress field; thirdly selecting an appropriate rock failure principle according to the simulated paleostress field and the fissure mechanical property, and forecasting the best occurrence and the second-best occurrence of paleofissures on the basis of plane shearing strength distribution or profile shearing strength distribution of the stress field in the research area; coupling spatial positions of the paleorock stratum and the current rock stratum based on the simulated ant tracing technique, and then establishing a spatial switching theoretical model of the paleorock stratum and the current rock stratum; performing the quantitative analysis of fissure kinematics characteristics, and forecasting the occurrence of the current fissures according to that of the paleofissures.

Description

A kind of tectoclase occurrence quantitative forecasting technique

Technical field

The present invention relates to oilfield prospecting developing field, especially a kind of tectoclase occurrence quantitative forecasting technique.

Background technology

Long-term exploration and practice confirm, utilize tectonic stress field method for numerical simulation to carry out Reservoir Tectonic Fracture prediction and there is good theoretical foundation, and be a kind of reliable crack prediction method.Tectonic stress Numerical Simulation and geological foundation work are combined closely, formation and development a set ofly take numerical simulation as basis, application criterion in rock is carried out the research method of crack quantitative forecast.The method had both strictly been considered Causes of Cracking mechanism, can combine with production of hydrocarbons static data, dynamic data again, therefore, had obtained good effect in oil field.Quantity research shows greatly, and high angle tectoclase often be take as main in the crack in low permeability reservoir, and it forms the co-controlling that is subject to many geologic agents such as stress field, tectonic position, petrologic make-up, depth of stratum, sedimentary micro, pore fluid with distribution.Domestic scholars Dai Junsheng, Wang Bifeng, Sun Yeheng, Ji Zong town and Feng Jianwei etc. start with from affecting the geologic agent of Reservoir Tectonic Fracture formation and development, at tectoclase, form on the basis of palaeostress field numerical simulation in period, in conjunction with criterion in rock and individual well crack, achievement is described, utilize fracture faces energy theoretical, rock strain energy theory and law of conservation of energy, set up the quantitative mathematical relation between stress field and Reservoir Tectonic Fracture parameter at all times, and apply it in the crack quantitative forecast of a plurality of oily blocks of China the western and eastern, obtained good effect.

The tendency in crack and inclination angle play a decisive role in quantizing fractured reservoir anisotropy, also be the prerequisite of fracture aperture, factor of porosity, Permeability Parameters Accurate Prediction now, the effect of crack tendency is fracture parameters anisotropy to be split on each coordinate direction in surface level minute; The effect of fracture dip is fracture parameters anisotropy to be split on surface level and vertical plane minute.But while using in practice numerical simulation for stress field method to predict tectoclase occurrence, do not consider the transformation effect of tectonic activities fracture occurrence, cause and when the later stage quantizes fracture parameters anisotropy, occur larger error, be difficult to meet the requirement of the reasonable Efficient Development in oil field.

Summary of the invention

The present invention is intended to address the above problem, a kind of tectoclase occurrence quantitative forecasting technique is provided, and it has solved the problem that tectoclase occurrence cannot Accurate Prediction.

Technical scheme of the present invention is: a kind of tectoclase occurrence quantitative forecasting technique, and concrete steps are as follows:

The first step is determined the mechanical mechanism that crack, study area forms

By rock core observation, well logging interpretation, thin slice observation, in conjunction with stress field, develop, determine the mechanical mechanism that individual well crack forms, for stress loading in numerical simulation for stress field provides foundation.According to the mechanical condition that forms crack, tectoclase can be divided into shearing crack, a property crack and cutting a property seam.In rock core, thin slice crack observation process, the mechanical property in crack can judge according to the smooth degree of fracture plane and filling operation, and shearing crack face is more straight, common scratch, step, antistep etc., shearing crack filling operation is lower, Chang Weiwei filling-half filling crack.Open property fracture plane and often bend, fracture plane is rough, and filling operation is higher, mostly is half filling-full-filling crack.If two kinds of features have concurrently, can think cutting a property crack, log interpretation technology crack identification can make up the deficiency of the aspects such as in rock core, the observation of thin slice crack, coring bed is complete, cored interval is discontinuous, can full well section crack mechanical property be analyzed, and concrete analysis judgement is as follows:

Shearing crack occurrence is very stable, and trend, inclination angle is relatively fixing, all extends on horizontal and vertical far, but when through the lithology rock stratum that there were significant differences, crack occurrence can change.It is smooth that fracture plane is more straight, and the distance between two walls is less, and form is identical, the micro-structures such as the scratch that on fracture plane, common two wall relative motions produce, friction minute surface or step.Usually cut and wear rock particles, crack occurrence is substantially constant.General intensive growth, the distance between crack is less, and is equidistant distribution, is conventionally density interphase and distributes when larger in fracture development region.Conventionally grow in groups, form " X " type conjugated fissures system, can make the well-developed network of fracture of rock.There are folding tail, rhombus knot ring and 3 kinds of forms of joint fork.Can occur that plumage splits, major fracture face is close and form with the pinniform microfracture face of major fracture face by certain angle by a large amount of occurrence.

Open property crack occurrence unstable, extended distance is very short, and fracture plane is not straight, is bending or zigzag.Fracture plane is coarse, and two walls are concavo-convex alternate shape, between distance also larger, in vertically oriented fracture direction, often have slight splitting, but a micro-structure such as general agensis scratch on fracture plane.Usually walk around rock particles, minority can be cut and be worn, but the plane of fracture is irregular, and crack occurrence often changes.General growth is sparse, and fracture interval is larger, uneven even if a large amount of growth is also density, and rare close integrated belt is grown.Grow irregularly, not generally being group is output, also can occur conformation of rules under certain condition.There are dendroid bifurcated and 2 kinds of forms of amygdaloidal knot ring.

Second step is determined study area rock mechanics parameters

In numerical simulation for stress field, required definite rock mechanics parameters comprises Young's modulus of elasticity, Poisson ratio, cohesion, shearing strength, tensile strength and density etc.The corresponding distribution in the field of force of reservoir rock mechanics parameter is, the distribution of break (failure mode) and the tectoclase of rock is closely related, be the Main Basis that oil gas well drilling design, reservoir reconstruction measure are formulated, this is also numerical simulation for stress field of the present invention and the definite basis of palaeotectonics crack occurrence.

The parameters such as mechanics such as the elastic modulus of rock calculating by Rock Mechanics Test And, Poisson ratio are called rock static state mechanics parameter, and the mechanics parameters such as the elastic modulus of rock that well-log information calculates, Poisson ratio are called rock dynamic mechanics parameter.Comprehensive utilization Rock Mechanics Test And and well-log information calculate, and proofread and correct by the correction of single shaft-tri-axle and dynamic-static, determine the rock mechanics parameters of zone of interest position, study area; Rock Under Uniaxial Compression-triaxial compression test directly utilizes underground rock core, so accuracy, with a high credibility, but because test sample spot is few, acquired results is directly used in numerical simulation and lacks sufficient theoretical foundation.And near zone of fracture, rock failure is serious, cannot carry out single shaft-triaxial compression test, the rock mechanics parameters of zone of fracture is also difficult to obtain by Rock Mechanics Test And.According to rock mechanics correlation theory, think, the mechanics parameters such as the elastic modulus E of rock, Poisson ratio μ can be by acoustic logging compressional wave time difference Δ t _p, shear wave slowness Δ t _sand rock density ρ tries to achieve.Well-log information has advantages of that continuity is good, with low cost, can make up the deficiency of Rock Mechanics Test And.

First uniaxial compression experimental result is corrected to the result under triaxial compression test condition, result is demarcated on logging trace, by dynamic mechanics parameter and the static mechanical parameter fitting demarcated, obtain fitting function, by continuous result of log interpretation plane section correction, it is continuous static rock mechanics section, and get the mean value in objective interval, as numerical simulation for stress field and Reservoir Fractures rock mechanics parameters used.

The 3rd step is recovered the paleostructural map of study area, recondition, definite factor that affects palaeostress field distribution as first deposited tomography, tectonic relief, faults distribution etc.

At present, along with the development of computer technology, the softwares such as 3Dmove, IATR have been obtained better effects in basin palaeotectonics is recovered, and palaeotectonics recovery technology also reaches its maturity, on the comprehensive basis of analyzing to study area geologic background, choose suitable software and carry out palaeotectonics recovery.

In palaeostress field numerical simulation, palaeotectonics is recovered the main factor of considering to affect Stress Field Distribution, such as first depositing tomography, tectonic relief, faults distribution etc., palaeotectonics height value and position analysis can be restored in structural map different measuring points in palaeotectonics height value and the position of geologic epoch with diverse ways.For example: on key section, choose some reference mark and also directly from structural evolution sectional view, obtain palaeotectonics height value and the position at these reference mark.In rock stratum, tomography both sides erosion sediment thickness hour, also can be according to classic method or the balanced section technique of establishment " pagoda figure ", utilize structure contour map and the bed boundary underlying formation erosion sediment thickness figure at Different Strata interface now to calculate the palaeotectonics height value of different measuring points, then according to structural deformation pattern, the position of measuring point is proofreaied and correct.Recover accurately palaeotectonics form, also need, according to the compaction correction tables of data of study area formation porosity-depth relationship establishment Yi Geneng image study district formation compaction rate, to carry out compaction correction.

The 4th step, to study area palaeostress field timing, directed, quantitative, is carried out palaeostress field numerical simulation

Calmodulin binding domain CaM structural evolution, tectonic stress field develop, and analyze activity, the activity intensity of tomography, and the intensity that evaluation structure develops each period, determines mainly making the seam phase of study area.

The directed Main Basis rock core crack of palaeostress field, observed result and the Image Logging Data in thin slice crack, and the occurrence of calmodulin binding domain CaM active fault, the mechanical property of fracture, the micro-little structure of the fold in seismic data, the seismic properties of extraction and thin slice is determined the direction of principle stress.

Palaeostress field size is determined the method that can adopt acoustic-emission, microstructure estimation algorithm, mathematical analysis, in numerical simulation for stress field, can adopt the ancient stress of a kind of equivalence, according to criterion in rock, judge, in Present Stress Field, rock can not produce obvious gross fracture, also there is stress relief effect in the crack simultaneously forming under palaeostress field effect, therefore terrestrial stress mainly makes existing crack further extend, expand now, generally no longer form new crack, but may form a small amount of micro-crack.Determining of the ancient stress of equivalence is mainly to guarantee under the prerequisite that stress types is consistent with the stress types that forms crack, the individual well Reservoir Fracture parameter of take is constraint condition, relation between stress and Reservoir Fracture parameter, realizes by constantly inverting, matching in combination.

To palaeostress field regularly, directed, quantitatively after, according to the paleostructural map recovering and rock mechanics parameters, set up the ancient geology-mechanical model in study area, the palaeostress field numerical simulation to study area.

The 5th step criterion in rock preferably

Reservoir rock produces while breaking being subject to effect of stress, follows certain mathematics criterion.The stressed generation of rock destroys available following general formula and represents:

σ ₁＝f(σ ₂,σ ₃) (1)

Formula (1) is called fracture criteria, and coulomb-More's (Mohr-Coulomb) criterion and Florence Griffith (Griffith) criterion are the most frequently used fracture criterias of friable sandstone.

If the crack that rock stress destruction forms is shear property or take shear property as main, applicable coulomb-mohr criterion:

In formula (2), σ ₁and σ ₃be respectively major principal stress and least principal stress, MPa; C ₀for rock cohesion, MPa; for internal friction angle of rock, (°).

If what form is a property or with Zhang Xingwei master's crack, applicable griffith criterion is expressed as under triaxiality condition:

As (σ ₁+ 3 σ ₃) during > 0, fracture criteria is:

$\left\{\begin{array}{c}{({\mathrm{\σ}}_1-{\mathrm{\σ}}_2)}^2+{({\mathrm{\σ}}_2-{\mathrm{\σ}}_3)}^2+{({\mathrm{\σ}}_3-{\mathrm{\σ}}_1)}^2=24{\mathrm{\σ}}_T({\mathrm{\σ}}_1+{\mathrm{\σ}}_2+{\mathrm{\σ}}_3)\\ \cos 2\mathrm{\θ}=\frac{{\mathrm{\σ}}_1-{\mathrm{\σ}}_3}{2({\mathrm{\σ}}_1+{\mathrm{\σ}}_3)}\end{array}\right.---\left(3\right)$

As (σ ₁+ 3 σ ₃)≤0 o'clock, fracture criteria can be reduced to:

θ＝0，σ ₃＝-σ _T (4)

In formula (3)-(4), σ ₁and σ ₃be respectively major principal stress and least principal stress, MPa; σ _tfor the tensile strength of Rocks under Uniaxial Tension test, MPa; θ is angle of rupture, (°).

Under extruding condition, rock can only produce shear fracture, but under tensile stress state, and the rock crack character different researchers viewpoint producing of breaking differs.There is scholar to think that shearing crack can only form under extruding condition, but the actual observation situation from rock core crack and outcrop crack, also there is a kind of transitional type between shear crack and tension gash, open cutting property seam (or seam turned round in title), not only there is the tension distortion along fracture plane normal direction in crack two dishes, also exists along the tangential slip distortion of fracture plane.All there is growth in this class crack in the stretching, extension basin of western part extruding foreland basin and east, mainly results from the structure reversion phase (tension type is opened shear crack) or lasting three-dimensional extrusion stress state period (expanding is opened shear crack) that by stretching, to extruding, change.BISHOPAW, when Dai Zihang etc. have analyzed in practice tension stress and have existed, the impact of rock generation shear fracture on stability of soil slope, think that traditional M-C criterion over-evaluated the resistance to tension of rock-soil material, when tension stress exists, can first by tensile fracture criterion, judge whether rock tension fracture occurs, if reach rock tension fracture strength condition, rock generation tension is broken; If can not reach the tension of the rock condition of breaking, then judge whether shear fracture can occur by M-C criterion, be referred to as tension-shearing combined rupture criterion:

In formula (5), F ^tfor rock generation tension rupture stress condition, MPa; F ^sfor there is to occur after tension is broken the stress condition of shear fracture, MPa in rock.

Li Junying etc. have inquired into theoretically when tension stress exists, the quantitative relationship of rock shearing angle of rupture and principle stress size, and when minimax principle stress is in " one draws a pressure " situation, normal stress tension and compression half-convergency χ is depended at the shear fracture angle of rock:

In formula (6), θ _lfor the position angle of shear fracture trend surface, (°);

The prediction of the ancient crack occurrence of the 6th step

6-A) the conversion of stress field coordinate system and earth coordinates

In numerical simulation for stress field, when crack forms, the unit normal vector of place plane is n ', and inclination angle is η ', is inclined to into γ ' (occurrence in ancient crack).According to criterion in rock, can obtain stress field coordinate system (σ ₁, σ ₂, σ ₃direction represents respectively three change in coordinate axis direction) in the occurrence in crack, the angle of principal direction of stress and earth coordinates X-Y-Z axle is expressed as:

1. σ ₁angle with X-Y-Z axle: α ₁₁, α ₁₂, α ₁₃;

2. σ ₂angle with X-Y-Z axle: α ₂₁, α ₂₂, α ₂₃;

3. σ ₃angle with X-Y-Z axle: α ₃₁, α ₃₂, α ₃₃.

The rock shearing of take breaks as example, and the normal vector of two groups of fracture planes that produce in stress field coordinate system can be expressed as:

$\left[\begin{array}{c}{n^{\′\′}}_x\\ {n^{\′\′}}_y\\ {n^{\′\′}}_z\end{array}\right]=\left[\begin{array}{c}\sin \mathrm{\θ}\\ 0\\ \cos \mathrm{\θ}\end{array}\right]$ Or $\left[\begin{array}{c}{n^{\′\′}}_x\\ {n^{\′\′}}_y\\ {n^{\′\′}}_z\end{array}\right]=\left[\begin{array}{c}\sin \mathrm{\θ}\\ 0\\ -\cos \mathrm{\θ}\end{array}\right]---\left(7\right)$

In earth coordinates, the normal vector of fracture plane is expressed as:

$\left[\begin{array}{c}{n^{\′}}_x\\ {n^{\′}}_y\\ {n^{\′}}_z\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\α}}_{11}& \cos {\mathrm{\α}}_{21}& \cos {\mathrm{\α}}_{31}\\ \cos {\mathrm{\α}}_{12}& \cos {\mathrm{\α}}_{22}& \cos {\mathrm{\α}}_{32}\\ \cos {\mathrm{\α}}_{13}& \cos {\mathrm{\α}}_{23}& \cos {\mathrm{\α}}_{33}\end{array}\right]\left[\begin{array}{c}{n^{\′\′}}_x\\ {n^{\′\′}}_y\\ {n^{\′\′}}_z\end{array}\right]---\left(8\right)$

According to formula (8), obtain ancient crack occurrence n ' at the component n ' of three coordinate axis _x, n ' _y, n ' _z, calculate inclination angle η ', the tendency γ ' in ancient crack:

$\left\{\begin{array}{c}\tan {\mathrm{\η}}^{\′}=\frac{\sqrt{{n^{\′}}_x^2+{n^{\′}}_y^2}}{{n^{\′}}_z}\\ \tan {\mathrm{\γ}}^{\′}=\frac{{n^{\′}}_x}{{n^{\′}}_y}\end{array}\right.---\left(9\right)$

Ancient fracture dip can be expressed as:

${\mathrm{\η}}^{\′}=\arctan \frac{\sqrt{{n^{\′}}_x^2+{n^{\′}}_y^2}}{{n^{\′}}_z}---\left(10\right)$

Ancient crack tendency needs a minute quadrant to discuss:

1. n ' _x>=0 and n ' _y>0, ancient crack tendency for east northeast to, now:

${\mathrm{\γ}}^{\′}=\arctan \left(\frac{{n^{\′}}_x}{{n^{\′}}_y}\right)---\left(11\right)$

2. n ' _x≤ 0 and n ' _y>0, ancient crack tendency for the southeast to, now:

${\mathrm{\γ}}^{\′}=\arctan \left(\frac{{n^{\′}}_x}{{n^{\′}}_y}\right)+\mathrm{\π}---\left(12\right)$

3. n ' _x<0 and n ' _y≤ 0, ancient crack tendency for southwest to, now:

${\mathrm{\&gamma;}}^{\&prime;}=\arctan \left(\frac{{n^{\&prime;}}_x}{{n^{\&prime;}}_y}\right)+\mathrm{\&pi;}---\left(13\right)$

4. n ' _x>=0 and n ' _y<0, ancient crack tendency for northwest (NW) to, now:

${\mathrm{\&gamma;}}^{\&prime;}=\arctan \left(\frac{{n^{\&prime;}}_x}{{n^{\&prime;}}_y}\right)+2\mathrm{\&pi;}---\left(14\right)$

6-B) shear crack advantage trend-trend analysis

According to coulomb fracture criteria, the ability of rock opposing shear failure is not only relevant with the shear stress on acting surface, also relevant with normal stress.Its surface of stress accumulation stage that breaks at plastic deformation there will be micro-fold, and volume also can slightly expand, and shear displacemant occurs subsequently in the weak face direction along rock interior and slide, and forms the potential shear fracture grid that X-type conjugation cross network distributes; Then in stress relief, break the stage, when stress surpasses the ultimate strength of rock, will on the basis of potential break grid, form the X-type cross shear fracture of a pair of conjugation, two groups of shear failure planes have conjugacy, when major principal stress is horizontal direction, in plane strain ellipse, two groups of conjugated shear rupture lines represent the trend line in two groups of cracks.Shear crack occurs with the form of two groups of conjugated shear in theory, but is subject to the impact of the factors such as the strong nonuniformity in rock stratum, regional stress field, conventionally can suppress wherein one group of growth, and only leave another group.

In hydrocarbon reservoir crack is described, at different tectonic positions, the development degree in two groups of cracks is conventionally different, and the present invention mainly controls the angle of shear crack dominant orientation from regional stress field, the development degree of two groups of shear cracks of judgement.Under region shear stress is controlled, the development degree of micro cracks in oil of a certain group of rotation direction is high, is advantage crack, and the development degree of micro cracks in oil of another group rotation direction is low, is inferior advantage crack.

As shown in Fig. 2-a, somewhere least principal stress is north-south, when major principal stress is the horizontal compressive stress of East and West direction, adopt the advantage trend in area planar shear stress judgement crack: under the left-handed plane shear stress condition of region, easily grow northwest strike crack, under region dextrorotation plane shear stress condition, easily grow east northeast and move towards crack.As shown in Fig. 2-b, if least principal stress is north-south, when major principal stress is vertical direction compressive stress, adopt the advantage tendency in section shear stress judgement crack, north-south, region: under the left-handed section shear stress condition of region, easily grow the crack of inclining, north, under region dextrorotation section shear stress condition, easily grow the crack of inclining, south.

The 7th step design and simulation ant tracer technique, realizes the coupling of locus, rock stratum at all times

Realize the coupling of rock mechanics sheaf space position at all times, what mainly adopt is emulation ant tracer technique, on the basis of the corresponding mathematical algorithm of design, works out corresponding program, and its principle is as follows:

Conventionally ant is cooked irregular walking near ant cave, once find food, moves back to alone ant cave and on the way leaves pheromones to attract more ant to come to carry food.In fact, each ant has only been cooked very simply and has worked: check and within the scope of certain, have or not food, and gradually to the dense direction motion of pheromones.Adopt such thinking, in locus, rock stratum coupling at all times, the attitude of rocks now of take is " food ", by in stress field simulation data volume, extract carry in a large number ancient attitude of rocks information stress node as " ant body ", to locus, rock stratum coupling at all times, (pheromones) preserved in the path of following the trail of simultaneously, convene other stress node ant body in certain limit according to similar path finding " food ".

Although cannot realize the accurate coupling of rock stratum at all times by emulation ant tracer technique at local location, but as a whole, this algorithm can improve the precision of rock stratum coupling at all times, in programming implementation procedure, need to arrange following key parameter (Fig. 3): 1. initial search frequency range refers to the scope that a stress node ant body can relate in initial ranging, by initial search radius R and two parameters of searcher parallactic angle ψ, determine, the ancient drop of Ant Search radius R Main Basis fracture, the inclination angle of fracture and rock stratum are determined in the combined factors such as horizontal stretching rate of different times:

R＝(1+sinδ ₁)·H+I (15)

In formula (15), H comprehensively determines according to the ancient drop of tomography and inclination angle, m; δ ₁for making the inclination angle now of seam institute in period sedimentary type formations, (°); I is for affecting the other factors Reliability equivalence factor of ant body search radius, m.

Searcher parallactic angle ψ with make seam phase and tectonic stress field afterwards and develop relevant.

2. the iteration angle degree ⊿ Φ that increase to overflow is mainly larger, simultaneously also relevant with attitude of rocks variation range on ant algorithm impact operation time of design, and attitude of rocks difference hour can be selected bigger numerical at all times.

3. (area is S in ant source ₁) after ant body once follows the trail of, the scope by other stress node ant body of this path walking, in order to programme conveniently, is defaulted as regular rectangular shape by this scope.

4. ant body tracing path tolerance angle Φ and accommodation zone tolerance angle Φ make ant body can search out faster abundant food when search; The initial area that accommodation zone is set is identical with ant source area, and the width L of accommodation zone can be expressed as:

$L=\frac{S_1}{2R\&CenterDot;\tan \mathrm{\&Phi;}}---\left(16\right)$

5. the illegal attitude of rocks and the legal attitude of rocks refer to the attitude of rocks now that ant body captures in accommodation zone, when its number is less than 3, think that the attitude of rocks now catching is the illegal attitude of rocks, need to increase tolerance angle Φ (step-length Wei ⊿ Φ), until the number of the attitude of rocks now capturing is more than or equal at 3 o'clock, judgement captures the discrete type of the attitude of rocks, will remain numerical value as the legal attitude of rocks after rejecting abnormalities value.

6. stop macroscopical scope of activities (first depositing tomography or study area scope is border) of threshold value ant body, when ant body runs into certain border, will lose the confidence to the attitude of rocks of following the trail of, thereby finish follow the trail of, and to take the attitude of rocks of this boundary vicinity be the legal attitude of rocks.

The 8th step is set up crack space, rock stratum replacement theory model at all times by rock mechanics layer

Subterranean strata is subject to terrestrial stress effect break and produce behind crack, and tectonic movement can be studied by means of suitable theoretical model the transformation effect of the crack occurrence in later stage.The control that is mainly subject to rock mechanics layer is grown in the formation in crack.So-called rock mechanics layer refers to the rock stratum that a set of mechanical behaviors of rocks is close or mechanical properties of rock is consistent, and rock mechanics layer is equal one deck of lithology always generally but not.Therefore, can set up fracture spaces transformation model (Fig. 4) by rock mechanics layer at all times, quantitatively characterizing crack is subject to kinematics character under the stress field effect of many phases in the later stage.In order to meet research needs, model is made the following assumptions under the prerequisite of suitably simplifying:

1. mainly grow in single rock mechanics layer in crack, and crack is not cut and worn different rock mechanics layers on plane, section;

2. in tectonic activities, crack does not produce relative sliding, rotates relative to rock mechanics layer at all times, and crack keeps relative static with rock mechanics layer, and " minor fault " do not developed in crack;

3. when theoretical model enough little (cell cube in numerical simulation for stress field), the motion feature of rock mechanics layer can be split as spatial translation-rotation combination;

4. the occurrence of rock mechanics layer has inheritance on vertical, simulation among a small circle in, think that the occurrence of rock mechanics layer is consistent vertical.

The 9th step crack movement Epidemiological Analysis

Setting up crack at all times on the basis of space, rock stratum replacement theory model, the kinematics character quantitative test of fracture.

If the unit normal vector of rock mechanics layer (hereinafter to be referred as rock stratum now) place plane is m now, inclination angle is δ, is inclined to as ω; The unit normal vector of forming periods of fractures rock mechanics layer (hereinafter to be referred as ancient rock stratum) place plane is m ', and inclination angle is δ ', is inclined to as ω '; The unit normal vector of place, crack plane is n now, and inclination angle is η, is inclined to as γ.

Three components of the normal vector m of unit of place, rock stratum plane in earth coordinates are now:

$\left\{\begin{array}{c}{m}_x=\sin \mathrm{\&delta;}\sin \mathrm{\&omega;}\\ m_y=\sin \mathrm{\&delta;}\cos \mathrm{\&omega;}\\ m_z=\cos \mathrm{\&delta;}\end{array}\right.---\left(17\right)$

Three components of the normal vector m of unit of place, ancient rock stratum plane in earth coordinates are:

$\left\{\begin{array}{c}{m_x}^{\&prime;}=\sin {\mathrm{\&delta;}}^{\&prime;}\sin {\mathrm{\&omega;}}^{\&prime;}\\ {m_y}^{\&prime;}=\sin {\mathrm{\&delta;}}^{\&prime;}\cos {\mathrm{\&omega;}}^{\&prime;}\\ {m_z}^{\&prime;}={\cos \mathrm{\&delta;}}^{\&prime;}\end{array}\right.---\left(18\right)$

9-A) non-horizontal stratum kinematics analysis at all times

When rock stratum is non-horizontal stratum at all times, it is as follows that crack movement is learned feature:

Three representation in components of the normal vector p ' of vector m, m ' place plane in earth coordinates are:

$\left\{\begin{array}{c}{p^{\&prime;}}_x={m^{\&prime;}}_y{m}_z-{m^{\&prime;}}_z{m}_y\\ {p^{\&prime;}}_y={m^{\&prime;}}_z{m}_x-{m^{\&prime;}}_x{m}_z\\ {p^{\&prime;}}_z={m^{\&prime;}}_x{m}_y-{m^{\&prime;}}_y{m}_x\end{array}\right.---\left(19\right)$

In formula (19), p ' _zduring <0, three representation in components of vector p ' in earth coordinates are:

$\left\{\begin{array}{c}{p^{\&prime;}}_x={m^{\&prime;}}_z{m}_y-{m^{\&prime;}}_y{m}_z\\ {p^{\&prime;}}_y={m^{\&prime;}}_x{m}_z-{m^{\&prime;}}_z{m}_x\\ {p^{\&prime;}}_z={m^{\&prime;}}_y{m}_x-{m^{\&prime;}}_x{m}_y\end{array}\right.---\left(20\right)$

Three representation in components of the normal vector p of unit of vector m, m ' place plane in earth coordinates are:

$\left\{\begin{array}{c}{p}_x=\frac{{p^{\&prime;}}_x}{\sqrt{{{p^{\&prime;}}_x}^2+{{p^{\&prime;}}_y}^2+{{p^{\&prime;}}_z}^2}}\\ p_y=\frac{{p^{\&prime;}}_y}{\sqrt{{{p^{\&prime;}}_x}^2+{{p^{\&prime;}}_y}^2+{{p^{\&prime;}}_z}^2}}\\ p_z=\frac{{p^{\&prime;}}_z}{\sqrt{{{p^{\&prime;}}_x}^2+{{p^{\&prime;}}_y}^2+{{p^{\&prime;}}_z}^2}}\end{array}\right.---\left(21\right)$

By rotating vector p, it is overlapped with a certain coordinate axis, after around the rotation of this coordinate axis, finally the thinking of the reverse cycle of coordinate axis is realized to the ancient attitude of rocks to the three dimensions conversion of the attitude of rocks now.

As shown in Figure 5, vector p is rotated around X-axis, be located on XOZ face, work as p _y>=0 o'clock, rotation angle ξ ₁for on the occasion of; Work as p _yduring < 0, rotation angle ξ ₁for negative value (rotation angle positive and negative pressed right hand rule judgement, be negative value clockwise, be counterclockwise on the occasion of, lower together), so rotation matrix T ₁can be expressed as:

$T_1=\left[\begin{array}{ccc}1& 0& 0\\ 0& \frac{p_z}{\sqrt{{p_y}^2+{p_z}^2}}& -\frac{p_y}{\sqrt{{p_y}^2+{p_z}^2}}\\ 0& \frac{p_y}{\sqrt{{p_y}^2+{p_z}^2}}& \frac{p_z}{\sqrt{{p_y}^2+{p_z}^2}}\end{array}\right]---\left(22\right)$

Vector p is rotated around Y-axis, it is overlapped, rotation angle ξ with X-axis ₂>=0, rotation matrix T ₂be expressed as:

$T_2=\left[\begin{array}{ccc}{p}_x& 0& \sqrt{{p_y}^2+{p_z}^2}\\ 0& 1& 0\\ -\sqrt{{p_y}^2+{p_z}^2}& 0& p_x\end{array}\right]---\left(23\right)$

Vector m, m ' are through twice rotation, and postrotational vector is respectively h, h ', and three representation in components of vector h in earth coordinates are:

$\left[\begin{array}{c}{h}_x\\ h_y\\ h_z\end{array}\right]=\left[\begin{array}{ccc}{p}_x& p_y& p_z\\ 0& \frac{p_z}{\sqrt{{p_y}^2+{p_z}^2}}& -\frac{p_y}{\sqrt{{p_y}^2+{p_z}^2}}\\ -\sqrt{{p_y}^2+{p_z}^2}& \frac{p_x{p}_y}{\sqrt{{p_y}^2+{p_z}^2}}& \frac{p_x{p}_z}{\sqrt{{p_y}^2+{p_z}^2}}\end{array}\right]\left[\begin{array}{c}{m}_x\\ m_y\\ m_z\end{array}\right]---\left(24\right)$

Three representation in components of vector h ' in earth coordinates are:

$\left[\begin{array}{c}{h_x}^{\&prime;}\\ {h_y}^{\&prime;}\\ {h_z}^{\&prime;}\end{array}\right]=\left[\begin{array}{ccc}{p}_x& p_y& p_z\\ 0& \frac{p_z}{\sqrt{{p_y}^2+{p_z}^2}}& -\frac{p_y}{\sqrt{{p_y}^2+{p_z}^2}}\\ -\sqrt{{p_y}^2+{p_z}^2}& \frac{p_x{p}_y}{\sqrt{{p_y}^2+{p_z}^2}}& \frac{p_x{p}_z}{\sqrt{{p_y}^2+{p_z}^2}}\end{array}\right]\left[\begin{array}{c}{m_x}^{\&prime;}\\ {m_y}^{\&prime;}\\ {m_z}^{\&prime;}\end{array}\right]---\left(25\right)$

As shown in Figure 6, establish the position angle ξ of vector h and Y-axis positive dirction ₃, the position angle ξ of vector h ' and Y-axis positive dirction ₄, ξ ₃can be expressed as:

$\left\{\begin{array}{cc}{\mathrm{\&xi;}}_3=\arccos \left(h_y\right)& (h_z\&GreaterEqual;0)\\ {\mathrm{\&xi;}}_3=360-\arccos \left(h_y\right)& (h_z<0)\end{array}\right.---\left(26\right)$

In like manner, ξ ₄can be expressed as:

$\left\{\begin{array}{cc}{\mathrm{\&xi;}}_4=\arccos \left({h_y}^{\&prime;}\right)& ({h_z}^{\&prime;}\&GreaterEqual;0)\\ {\mathrm{\&xi;}}_4=360-\arccos \left({h_y}^{\&prime;}\right)& ({h_z}^{\&prime;}<0)\end{array}\right.---\left(27\right)$

The rotation angle ξ that vector h ' is overlapped with vector h can be expressed as:

ξ＝ξ ₃-ξ ₄ (28)

Adopt formula (28), both can determine the size of rotation angle, can also determine that ancient rock stratum is converted to the sense of rotation of rock stratum now simultaneously.

Around X-axis, rotate ξ below, the normal vector m of rock stratum face is now overlapped with the normal vector m ' of ancient rock stratum face, rotation matrix is expressed as:

$T_3=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\&xi;}& -\sin \mathrm{\&xi;}\\ 0& \sin \mathrm{\&xi;}& \cos \mathrm{\&xi;}\end{array}\right]---\left(29\right)$

Then make vector P go back to original position, first by vector P around rotate-ξ of Y-axis ₂, rotation matrix T ₄be expressed as:

$T_4=\left[\begin{array}{ccc}{p}_x& 0& -\sqrt{{p_y}^2+{p_z}^2}\\ 0& 1& 0\\ \sqrt{{p_y}^2+{p_z}^2}& 0& p_x\end{array}\right]---\left(30\right)$

Again by vector P around rotate-ξ of X-axis ₁, rotation matrix T ₅be expressed as:

$T_5=\left[\begin{array}{ccc}1& 0& 0\\ 0& \frac{p_z}{\sqrt{{p_y}^2+{p_z}^2}}& -\frac{p_y}{\sqrt{{p_y}^2+{p_z}^2}}\\ 0& -\frac{p_y}{\sqrt{{p_y}^2+{p_z}^2}}& \frac{p_z}{\sqrt{{p_y}^2+{p_z}^2}}\end{array}\right]---\left(31\right)$

Aggregative formula (21)-(31), ancient rock stratum is converted to the rotation matrix T of rock stratum now and can be expressed as:

T＝T ₅·T ₄·T ₃·T ₂·T ₁ (32)

Arrangement obtains:

$T=\left[\begin{array}{ccc}(1-{P_x}^2)\cos \mathrm{\&xi;}+{P_x}^2& P_x{P}_y(1-\cos \mathrm{\&xi;})+P_z\sin \mathrm{\&xi;}& P_x{P}_z(1-\cos \mathrm{\&xi;})-P_y\sin \mathrm{\&xi;}\\ P_x{P}_y(1-\cos \mathrm{\&xi;})-P_z\sin \mathrm{\&xi;}& (1-{P_y}^2)\cos \mathrm{\&xi;}+{P_y}^2& P_y{P}_z(1-\cos \mathrm{\&xi;})+P_x\sin \mathrm{\&xi;}\\ P_x{P}_z(1-\cos \mathrm{\&xi;})+P_y\sin \mathrm{\&xi;}& P_y{P}_z(1-\cos \mathrm{\&xi;})-P_x\sin \mathrm{\&xi;}& (1-{P_z}^2)\cos \mathrm{\&xi;}+{P_z}^2\end{array}\right]---\left(33\right)$

9-B) horizontal stratum kinematics analysis at all times

While there is horizontal stratum in rock stratum at all times, i.e. p _z=0 o'clock, formula (28) was difficult to determine accurately rotation angle ξ, and it is large to ask for process computation amount, and now rotation angle ξ asks for process and can be optimized for:

First, vector p is rotated around Z axis, make it to overlap with X-axis, rotation angle ξ 5 is expressed as:

$\left\{\begin{array}{cc}{\mathrm{\&xi;}}_5=-\arccos \left(p_x\right)& (p_y\&GreaterEqual;0)\\ {\mathrm{\&xi;}}_5=\arccos \left(p_x\right)& (p_y<0)\end{array}\right.---\left(34\right)$

Vector p and X-axis coincidence rotation matrix can be expressed as:

$T_6=\left[\begin{array}{ccc}\cos {\mathrm{\&xi;}}_5& -\sin {\mathrm{\&xi;}}_5& 0\\ \sin {\mathrm{\&xi;}}_5& \cos {\mathrm{\&xi;}}_5& 0\\ 0& 0& 1\end{array}\right]---\left(35\right)$

When the level of ancient rock stratum, rotation angle ξ can be expressed as:

$\left\{\begin{array}{cc}\mathrm{\&xi;}=\arccos \left(m_z\right)& (m_y\cos {\mathrm{\&xi;}}_5+m_x\sin {\mathrm{\&xi;}}_5<0)\\ \mathrm{\&xi;}=-\arccos \left(m_z\right)& (m_y\cos {\mathrm{\&xi;}}_5+m_x\sin {\mathrm{\&xi;}}_5>0)\end{array}\right.---\left(36\right)$

When rock stratum level now, rotation angle ξ can be expressed as:

$\left\{\begin{array}{cc}\mathrm{\&xi;}=\arccos \left({m_z}^{\&prime;}\right)& ({m_y}^{\&prime;}\cos {\mathrm{\&xi;}}_5+{m_x}^{\&prime;}\sin {\mathrm{\&xi;}}_5>0)\\ \mathrm{\&xi;}=-\arccos \left({m_z}^{\&prime;}\right)& ({m_y}^{\&prime;}\cos {\mathrm{\&xi;}}_5+{m_x}^{\&prime;}\sin {\mathrm{\&xi;}}_5<0)\end{array}\right.---\left(37\right)$

Equally, ancient rock stratum is converted to the rotation matrix T of rock stratum now and can be expressed as:

$T=\left[\begin{array}{ccc}(1-{P_x}^2)\cos \mathrm{\&xi;}+{P_x}^2& P_x{P}_y(1-\cos \mathrm{\&xi;})& -P_y\sin \mathrm{\&xi;}\\ P_x{P}_y(1-\cos \mathrm{\&xi;})& (1-{P_y}^2)\cos \mathrm{\&xi;}+{P_y}^2& P_x\sin \mathrm{\&xi;}\\ P_y\sin \mathrm{\&xi;}& -P_x\sin \mathrm{\&xi;}& \cos \mathrm{\&xi;}\end{array}\right]---\left(38\right)$

The tenth step, according to the ancient occurrence in the kinematics character of place, crack rock mechanics layer and crack, is asked for the occurrence in crack now

The normal vector n ' of ancient fracture plane can be expressed as in the projection of three coordinate axis:

$\left(\begin{array}{c}{n^{\&prime;}}_x=\sin {\mathrm{\&eta;}}^{\&prime;}\sin {\mathrm{\&gamma;}}^{\&prime;}\\ {n^{\&prime;}}_y=\sin {\mathrm{\&eta;}}^{\&prime;}\cos {\mathrm{\&gamma;}}^{\&prime;}\\ {{n^{\&prime;}}_z=\cos \mathrm{\&eta;}}^{\&prime;}\end{array}\right.---\left(39\right)$

According to formula (33), (38), the unit normal vector of fracture plane can be expressed as in the projection of three coordinate axis now:

$\left[\begin{array}{c}{n}_x\\ n_y\\ n_z\end{array}\right]=T\&CenterDot;\left[\begin{array}{c}{n^{\&prime;}}_x\\ {n^{\&prime;}}_y\\ {n^{\&prime;}}_z\end{array}\right]---\left(40\right)$

According to formula (9)-(14), can calculate the occurrence of crack in earth coordinates now.

The invention has the beneficial effects as follows: the present invention is determining on the basis of crack, study area mechanical property, rock mechanics parameters, recovery paleostructural map, carry out palaeostress field numerical simulation, according to the palaeostress field of simulation, select suitable criterion in rock, and calmodulin binding domain CaM stress field midplane shear stress or section shearing stress distribution, to the dominant orientation in ancient crack, the prediction of inferior dominant orientation.By design and simulation ant tracer technique, realize the coupling of locus, rock stratum at all times, on this basis, set up space, rock stratum replacement theory model at all times, quantitative test crack movement is learned feature, in conjunction with the occurrence in ancient crack, predicts the occurrence in crack now.The present invention is derived and is formed by strict mathematical algorithm, after corresponding geological information digitizing, can utilize computer programming language to develop corresponding calculation procedure, realizes the quantitative forecast of Recent Structural crack occurrence.The present invention has higher practical value for the Accurate Prediction of tectoclase occurrence, and forecast cost is cheap, workable, predict the outcome to determining fault block permeability predominant direction, reasonably dispose well pattern, determining that the spatial relation of water injection well and producing well has certain directive significance, can improve the precision of Reservoir Tectonic Fracture aperture, factor of porosity and Permeability Prediction simultaneously.

Accompanying drawing explanation

Fig. 1 is tectoclase occurrence quantitative forecast process flow diagram.

Fig. 2 is plane strain ellipse and section strain ellipse schematic diagram.

Fig. 3 is emulation ant tracer technique design diagram.

Fig. 4 is crack space, rock stratum replacement theory illustraton of model at all times.

Fig. 5 is rotation angle ξ ₁, ξ ₂determine schematic diagram.

Fig. 6 is rotation angle ξ ₃, ξ ₄determine schematic diagram.

Fig. 7 is Tongcheng fault zone east wing construction location figure.

Fig. 8 is wing rock core crack, Tongcheng fault zone east mechanical property distribution histogram.

Fig. 9 is Tongcheng fault zone LN281 survey line seismic cross-section.

Figure 10 is that the Tongcheng fault zone east wing is made abundant two sections of palaeotectonics aspect graphs of seam phase.

Figure 11 is Tongcheng fault zone faulting speed comparison diagram in each in period.

Figure 12 is that Tongcheng fault zone Funing County active fault in late period moves towards rose.

Figure 13 is the abundant two sections of fracture strike roses of the Tongcheng fault zone east wing.

Figure 14 is Tongcheng fault zone Dong Yi Funing County least principal stress in late period distribution plan.

Figure 15 is the Y-Z in late period of Tongcheng fault zone Dong Yi Funing County section shearing stress distribution figure.

Figure 16 is the abundant two sections of bottom surface structural maps now of the Tongcheng fault zone east wing.

Figure 17 is Tongcheng fault zone east wing crack advantage tilt profiles figure now.

Figure 18 be the Tongcheng fault zone east wing now crack advantage move towards distribution plan.

Figure 19 is Tongcheng fault zone east wing crack time advantage tilt profiles figure now.

Figure 20 be the Tongcheng fault zone east wing now crack time advantage move towards distribution plan.

Figure 21 is Tongcheng fault zone east wing rock core and numerical Simulation Prediction fracture strike rose comparison diagram.

Figure 22 is Tongcheng fault zone east wing rock core and numerical Simulation Prediction fracture dip comparison diagram.

In Fig. 3, R is initial search radius, and ψ is searcher parallactic angle, the width that L is accommodation zone, and Φ is ant body tracing path tolerance angle, and E-W represents east-west direction, and S-N represents North and South direction.

In Fig. 4,1. ancient rock mechanics layer, 2. rock mechanics layer now, 3. ancient shear crack, 4. ancient tension gash, 5. shear crack now, 6. tension gash now.

In Fig. 5, vector p is the unit normal vector of vector m, m ' place plane, S ₁for p subpoint on XOZ face, S ₂for vector p subpoint in X-axis, ξ ₁, ξ ₂be respectively the rotation angle of vector p in twice rotary course.

In Fig. 6, ξ ₃for the position angle of vector h and Y-axis positive dirction, ξ ₄for the position angle of vector h ' with Y-axis positive dirction.

In Figure 14, negative value represents extrusion stress, on the occasion of representing tensile stress (unit: Pa).

In Figure 15, negative value represents dextrorotation, on the occasion of representing left-handed (unit: Pa).

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described:

Take the quantitative forecast of two sections of Subei Basin Jinhu Depression Tongcheng fault zone Dong Yi Funing County groups (being called for short abundant two sections) tectoclase occurrence as example illustrates concrete technical scheme of the present invention:

Tongcheng fault zone is located in Jinhu border of the county, and study area is mainly positioned at the eastern wing of Subei Basin-Dongtai Depression-Jinhu Depression-Tongcheng fault zone.Copper city tomography is a typical strike-slip fault, and south is intersected in border-Yangchuan village tomography of Jinhu Depression, disappears to area, copper city (Fig. 7) northwards.Study area main force pay sand is abundant two sections, and reservoir properties is poor, and lithology be take hyposmosis siltstone as main.

Tongcheng fault zone, since abundant two sections of depositions, has mainly experienced Wubao and three buttress two phases tectonic movements.It is the Wubao phase that the seam phase is mainly made on abundant two sections of stratum, study area, this in period tomography intense activity, main manifestations is the tension of nearly north-south, has formed the fracture system of concave interior complexity.Calmodulin binding domain CaM geologic information, as follows to the step of Tongcheng fault zone east wing Recent Structural crack occurrence quantitative forecast:

The first, by rock core observation, well logging interpretation, thin slice observation combined structure stress field, develop, determine that wing individual well crack, Tongcheng fault zone east forms mechanical mechanism, for stress loading in numerical simulation for stress field provides foundation.In core observation, mainly by fracture plane, extending length, scratch, step, arteries and veins bulk-growth situation and stuff judges.All there is growth (Fig. 8) in the crack of the three kinds of character in study area, and wherein shear crack is main, accounts for 87%, and its seam face is generally straight, mostly is not filling seam; Tension gash, cut seam and grow a little less than, respectively account for approximately 7%.

The second, by Rock Mechanics Test And and well-log information, calculate, and proofread and correct by the correction of single shaft-tri-axle and dynamic-static, determined the rock mechanics parameters of zone of interest position, study area, uniaxial tension test is 2.4MPa; It is 6.5MPa that the cohesion of material is approximately equal to single shaft shearing strength, and other rock mechanics parameters is as listed in table 1:

The mechanics parameter that table 1 Tongcheng fault zone east wing numerical simulation for stress field is chosen

	Poisson ratio	Elastic modulus (GPa)	Density (g/cm3)
				Sand layers	0.15	5.6	2.21
Distributed fault	0.2	5	2.2
				Shale layer	0.23	4.5	2.1
Country rock	0.15	5.5	2.22

The 3rd, the Tongcheng fault zone east wing is successive sedimentation from abundant two sections to abundant four sections, there is not the intensive denudation on stratum, therefore on key section, choose some reference mark and directly from seismic cross-section (Fig. 9) obtain structure height value and the position of abundant two sections, abundant four sections, adopt the thinking of balanced cross section to recover the ancient height of abundant two sections.In order to recover accurately palaeotectonics form, according to study area formation porosity-depth relationship, establishment can image study district formation compaction rate compaction correction tables of data, carry out compaction correction, finally obtain Tongcheng fault zone and make abundant two sections of palaeotectonicss of seam phase rise and fall (Figure 10).

The 4th, to Tongcheng fault zone east wing palaeostress field numerical simulation.

The Tongcheng fault zone east wing is carried out to palaeostress field numerical simulation and mainly rely on ANSYS software.According to Tongcheng fault zone structural evolution, tectonic stress field, develop, analyze activity, the activity intensity of tomography, the intensity that evaluation structure develops each period, determines mainly making the seam phase of study area.Due to Wubao motion, established sedimentary fault is further movable.From abundant first phase to abundant fourth phase faulting speed, strengthen gradually, in the abundant fourth phase, reach mxm., abundant fourth phase fault activity is the strongest; Wear the south phase, three buttress phase fault activities weaken gradually, therefore, substantially determine main Zao Fengqiwei Funing County late period (Figure 11) of study area.

To the observed result in the directed Main Basis rock core of Tongcheng fault zone Funing County palaeostress field in late period, thin slice crack and in conjunction with making the occurrence of seam phase active fault, the mechanical property of fracture, determine the direction of principle stress.The abundant two sections of fracture strike roses (Figure 13) of the Tongcheng fault zone east wing that move towards rose (Figure 12) and Tongcheng fault zone rock core Fracture orientation is obtained according to Tongcheng fault zone Funing County active fault in late period, determine the tensile stress that Funing County's least principal stress in late period is nearly north-south, major principal stress is vertical direction, mainly by gravitational stresses, is produced.

Palaeostress field size is determined the ancient stress of a kind of equivalence of employing, according to criterion in rock, judge, in Present Stress Field, rock can not produce obvious gross fracture, also there is stress relief effect in the crack simultaneously forming under palaeostress field effect, therefore terrestrial stress mainly makes existing crack further extend, expand now, generally no longer forms new crack, but may form a small amount of micro-crack.Determining of the ancient stress of equivalence is mainly to guarantee under the prerequisite that stress types is consistent with the stress types that forms crack, the individual well Reservoir Fracture parameter of take is constraint condition, relation between stress and Reservoir Fracture parameter in combination, by constantly inverting, matching, realize, finally determine that the border, north and south at Tongcheng fault zone east wing model applies the tensile stress of 4.5MPa, thing border applies 1.5MPa tensile stress, and vertical stress is generated by ANSYS software automatically by acceleration of gravity is set.

To palaeostress field regularly, directed, quantitatively after, according to the paleostructural map recovering and rock mechanics parameters, set up the ancient geology-mechanical model in study area, to the palaeostress field numerical simulation of study area (Figure 14, negative value represents extrusion stress, on the occasion of representing tensile stress).

The 5th, according to palaeostress field numerical simulation result, choose the mechanical property that suitable criterion in rock judges whether crack forms and form.

According to Tongcheng fault zone rock core crack, the definite crack of well logging interpretation, form mechanical mechanism, the crack that rock stress destruction forms is shear property or take shear property as main, applicable coulomb-mohr criterion; What form is a property or with Zhang Xingwei master's crack, applicable griffith criterion, when tension stress exists, judges by tensile fracture criterion whether rock tension fracture occurs, if reach rock tension fracture strength condition, rock generation tension is broken; If can not reach the tension of the rock condition of breaking, then judge whether shear fracture can occur by M-C fracture criteria, as shown in formula (1)-(6).

The 6th, the prediction of the ancient crack occurrence of the Tongcheng fault zone east wing.

ANSYS software carries out palaeostress field numerical simulation, obtains the stress numerical of great deal of nodes, easily obtains size and the region Y-Z section shear stress of principle stress, σ ₁angle with X-Y-Z axle: α ₁₁, α ₁₂, α ₁₃; σ ₂angle with X-Y-Z axle: α ₂₁, α ₂₂, α ₂₃; σ ₃angle with X-Y-Z axle: α ₃₁, α ₃₂, α ₃₃.Size, direction and rock mechanics parameters in conjunction with stress, three components of the normal vector that can ask for crack according to formula (1)-(6) in stress field coordinate system, then ask for the occurrence of ancient crack in earth coordinates according to formula (7)-(14).

The advantage tendency in judgement Tongcheng fault zone crack: it is vertical direction that Funing County's Tongcheng fault zone in late period is subject to north-south tensile stress and biggest principal stress direction, for the formed shear crack in study area, using the cell cube stress field that in ANSYS stress field simulation, a plurality of nodes form as regional stress field, and utilize north-south section (Y-Z section) figure of shear stress (Figure 15, negative value represents dextrorotation, left-handed on the occasion of representing) easily tomography inclines in growth north under the advantage tendency-region left-handed section shear stress condition in wing crack, judgement Tongcheng fault zone east, under region dextrorotation section shear stress condition, easily grow the south tomography that inclines.It is main utilize north-south, region section shearing stress distribution to judge inclining to the north of the tendency of the ancient crack of the wing, Tongcheng fault zone east.

The 7th, design and simulation ant tracer technique, realizes locus, rock stratum coupling at all times.

Recovering, on the basis of Tongcheng fault zone east wing paleostructural map (Figure 10), to read respectively the occurrence of the abundant two sections of rock stratum of Figure 10, Figure 16, by design and simulation ant tracer technique, realizing the coupling of rock mechanics sheaf space position at all times:

1. initial search radius R and searcher parallactic angle ψ determine basis abundant four sections of reservoir end face structural maps now, read the inclination angle of rock stratum, i.e. δ in formula (15) ₁, according to the ancient drop in the inclination angle of Tongcheng fault zone east wing active fault and Funing County late period, the scope of setting different fault block H is 100-150m.

According to the trend (approximately EW) of study area Funing County-Dai Nan active fault in period, determine that the fault block later stage is stretched to master with nearly north-south, therefore, searcher parallactic angle ψ is set to North and South direction.

2. according to computer hardware-software conditions, the required precision of binding district crack quantitative forecast, it is 5 ° that research district iteration increases the Jiao Du ⊿ Φ that overflows.

3. the spacing that ant source (square) length of side is seismic line is set, and ant source area is S ₁=25m * 25m=625m ².

4. ant body tracing path tolerance angle Φ is set is 15 °, according to formula (16), writes the original width L that corresponding algorithm can be asked for accommodation zone.

5. stopping threshold value, to take Tongcheng fault zone Dong Yi Funing County active fault in late period, aged fault be border, by the boundary digitizing of each fault block, usings that this stops threshold value as ant body.

According to the emulation ant tracer technique parameter arranging, by each fault block digitizing, utilize the emulation ant tracer technique parameter arranging, write corresponding computer program to attitude of rocks coupling at all times, the attitude of rocks at all times, geodetic position coordinate after output coupling, as shown in table 2:

Table 2 adopts after emulation ant tracer technique the correspondence table (part) of rock stratum at all times

X coordinate/m	Y coordinate/m	Ancient formation dip/°	Ancient rock stratum tendency/°	Now formation dip/°	Now rock stratum tendency/°
						682025.63	3634941.50	20.06	69.09	31.61	117.66
682105.56	3635278.50	17.00	157.23	32.56	112.73
						682593.69	3636213.25	10.79	91.19	25.30	111.97
682850.31	3636588.25	12.84	137.62	20.05	141.00
						682787.19	3636777.75	25.05	168.07	23.85	109.60
683940.06	3638121.00	16.01	104.70	24.04	117.51
						684638.50	3638584.25	19.01	221.46	29.32	89.90
685757.69	3638390.50	10.08	158.14	29.51	122.57
						686216.31	3638386.25	3.91	179.27	25.45	124.81
685742.50	3637977.75	15.73	91.80	31.96	112.45
						685390.44	3637202.50	14.74	63.01	36.10	85.02
684594.00	3636024.00	1.77	251.61	27.19	121.67
						684491.38	3635759.25	4.73	40.60	28.99	118.80
683775.06	3634835.00	14.24	95.85	26.25	118.75
						683757.50	3634381.75	17.34	49.21	30.07	111.05
683287.00	3633995.25	4.39	169.69	31.93	109.76
						682967.50	3633197.50	2.38	161.87	29.56	114.35
680639.44	3633105.25	12.56	96.98	20.21	196.27
						681091.56	3633009.75	5.12	177.45	22.70	180.67
681515.38	3633048.75	13.76	91.10	31.57	117.89
						682197.13	3633073.50	5.51	68.31	28.22	128.13
682370.19	3633105.25	5.93	121.64	27.95	127.63
						680824.94	3633621.50	19.17	89.25	20.89	199.45
680905.88	3633432.50	8.38	187.31	18.51	190.80
						681772.69	3633992.75	12.20	98.83	31.61	124.37
682752.50	3633745.75	8.02	76.72	24.92	165.72
						682567.19	3634105.50	17.30	103.94	29.36	117.60
682129.88	3634157.50	14.48	112.89	32.38	119.07
						682685.75	3634365.25	7.71	122.56	31.41	123.84
683045.25	3634098.25	13.72	80.84	33.85	109.76
						683323.19	3634406.00	12.02	39.58	32.67	105.95
683519.63	3634469.00	6.68	187.25	33.32	107.57
						683334.31	3634847.50	10.12	124.73	31.99	117.77
683174.94	3634777.00	13.93	106.52	37.43	110.86
						682290.94	3634844.25	21.52	92.71	33.83	113.95
682344.00	3634664.50	17.60	101.42	32.53	118.61
						682907.13	3634872.75	25.29	108.98	35.42	107.91
683111.19	3634942.25	13.65	99.95	37.44	108.16

X coordinate/m	Y coordinate/m	Ancient formation dip/°	Ancient rock stratum tendency/°	Now formation dip/°	Now rock stratum tendency/°
						683462.06	3635113.75	23.01	57.55	33.35	112.87
683711.00	3634999.50	9.91	88.47	28.74	117.92
						683592.69	3635371.00	31.70	140.98	30.86	116.87
683751.81	3635456.75	8.89	205.23	30.62	115.96
						683119.31	3636482.00	13.55	151.08	31.36	118.94
683033.63	3636674.00	14.62	136.58	28.76	118.03
						684339.44	3636122.50	14.20	123.78	29.14	118.12
683449.88	3636649.50	21.90	106.97	32.12	117.66
						683160.13	3636914.75	19.80	103.18	29.37	108.50
683339.69	3637012.75	17.01	94.82	39.81	98.12
						684212.94	3636486.00	8.89	135.66	27.23	162.63
683731.44	3636506.50	16.07	87.07	35.62	115.44
						683645.75	3637319.25	19.04	124.74	26.64	92.99
683274.38	3637601.00	6.95	137.51	17.82	90.64
						685055.38	3638558.75	20.24	110.58	32.36	113.08
685320.50	3638466.25	15.61	162.88	35.28	112.79
						684887.06	3638504.00	29.50	115.27	33.95	109.08
684816.88	3637601.25	6.90	171.88	35.64	159.25

The 8th, according to the result of rock stratum coupling at all times, set up crack space, rock stratum replacement theory model at all times.

By observing five mouthfuls of core holes of the Tongcheng fault zone east wing, the crack of growing on rock core is not cut and is worn different rock mechanics layers on plane, section, thinks that crack forms the control that growth is mainly subject to rock mechanics layer; Relative rock mechanics layer, in tectonic activities, crack does not produce relative sliding, rotation; Study area area is less than 100km ², by ANSYS software, in numerical simulation for stress field, divided altogether tens0000 grid cell body, think that each grid cell body is enough little, the motion feature of rock mechanics layer can be split as spatial translation-rotation combination; By comparative study district seismic section, abundant one section, abundant two sections, abundant three sections of attitudes of rocks have inheritance on vertical, can think that the occurrence of rock mechanics layer is consistent vertical.

Therefore, from integral body, see in the scope of simulation, be applicable to setting up crack space, rock stratum replacement theory model at all times.

The 9th, Tongcheng fault zone east wing crack movement Epidemiological Analysis.

Setting up wing crack, Tongcheng fault zone east at all times on the basis of space, rock stratum replacement theory model, the kinematics analysis to ancient crack:

When if rock stratum is non-horizontal stratum at all times, adopt formula (17)-(33) to analyze the kinematics character in ancient crack; When if rock stratum exists horizontal stratum at all times, adopt formula (34)-(38) to analyze ancient crack movement and learn feature;

The tenth, according to the occurrence in the kinematics character in crack and ancient crack, ask for the occurrence in crack now.

After stress field simulation, according to criterion in rock, ask for the occurrence in ancient crack, dominant orientation, inferior dominant orientation according to north-south, region section shear stress judgement crack, after adopting emulation ant tracer technique to locus, rock stratum coupling at all times, according to formula (39)-(40), ask for the projection of normal vector three coordinate axis in earth coordinates of fracture plane now, according to formula (9)-(14), calculate the occurrence (Figure 17-20) of crack in earth coordinates now.

By rock core, observe crack occurrence and prediction occurrence contrast (Figure 21-22), can draw, in error range, crack occurrence and the rock core observed result of prediction are basically identical, cause the reason of both othernesses to be:

1. rock core Fracture orientation adopts attitude of rocks method, and the true occurrence of the crack occurrence that orientation obtains and crack exists error;

2. a small amount of crack may form in other earth history period, has caused the difference of rock core crack with prediction crack occurrence result.

As a whole, the present invention has improved the precision of crack occurrence prediction, has higher practical value.

With way of example, describe the present invention above, but the invention is not restricted to above-mentioned specific embodiment, all any changes of doing based on the present invention or modification all belong to the scope of protection of present invention.

Claims (7)

1. a tectoclase occurrence quantitative forecasting technique, described step is as follows:

1) by rock core observation, well logging interpretation, thin slice observation, in conjunction with stress field, develop, determine that crack, study area forms mechanical mechanism;

2) in conjunction with Rock Mechanics Test And and well-log information, rock mechanics parameters is carried out to the correction of single shaft-tri-axle and dynamic-static correction, determine the rock mechanics parameters of zone of interest position, study area;

3) recover the paleostructural map of study area, considering emphatically affects the factor that palaeostress field distributes, as first deposited tomography, tectonic relief, faults distribution etc.;

4) geologic information such as calmodulin binding domain CaM structural evolution, tectonic stress field evolution and rock core, well logging, earthquake, to palaeostress field regularly, directed, quantitatively, and then modeling effort district makes seam phase palaeostress field;

5) select suitable criterion in rock, if the crack that rock stress destruction forms is shear property or take shear property as main, applicable coulomb-mohr criterion, if what form is a property or with Zhang Xingwei master's crack, applicable griffith criterion, when tension stress exists, can first by tensile fracture criterion, judge whether rock tension fracture occurs, if reach rock tension fracture strength condition, rock generation tension is broken, if can not reach the tension of the rock condition of breaking, then judge whether shear fracture can occur by coulomb-More's fracture criteria;

6) according to criterion in rock, the occurrence of ancient crack is predicted, first ask for the occurrence in crack in stress field coordinate system, the occurrence in crack in stress field coordinate system is transformed into the occurrence in crack in earth coordinates, if the crack forming is shear crack, stress types in combination, select area planar shear stress or section shearing stress distribution, the advantage trend of prediction shear crack or advantage tendency;

7) design and simulation ant tracer technique, realizes locus, rock stratum coupling at all times;

8) on the basis of rock mechanics sheaf space position coupling at all times, set up crack space, rock stratum replacement theory model at all times;

9) setting up crack at all times on the basis of space, rock stratum replacement theory model, fracture Kinematics Analysis;

10) according to crack movement, learn the occurrence in feature and ancient crack, ask for the occurrence in crack now.

2. a kind of tectoclase occurrence quantitative forecasting technique according to claim 1, is characterized in that:

The occurrence step that in described stress field coordinate system, crack occurrence is transformed in earth coordinates is as follows:

In numerical simulation for stress field, obtain the angle of principal direction of stress and earth coordinates X-Y-Z axle:

1. σ ₁angle with X-Y-Z axle: α ₁₁, α ₁₂, α ₁₃;

2. σ ₂angle with X-Y-Z axle: α ₂₁, α ₂₂, α ₂₃;

3. σ ₃angle with X-Y-Z axle: α ₃₁, α ₃₂, α ₃₃;

Take rock shear fracture as example, and the unit normal vector of two groups of fracture planes that crack produces in stress field coordinate system can be expressed as:

$\left[\begin{array}{c}{n^{\&prime;\&prime;}}_x\\ {n^{\&prime;\&prime;}}_y\\ {n^{\&prime;\&prime;}}_z\end{array}\right]=\left[\begin{array}{c}\sin \mathrm{\&theta;}\\ 0\\ \cos \mathrm{\&theta;}\end{array}\right]$ Or $\left[\begin{array}{c}{n^{\&prime;\&prime;}}_x\\ {n^{\&prime;\&prime;}}_y\\ {n^{\&prime;\&prime;}}_z\end{array}\right]=\left[\begin{array}{c}\sin \mathrm{\&theta;}\\ 0\\ -\cos \mathrm{\&theta;}\end{array}\right]---\left(7\right)$

In formula (7), θ is angle of rupture, (°);

N " _xfor the component of unit normal vector biggest principal stress direction in stress field coordinate system in ancient crack, dimensionless;

N " _yfor the component of unit normal vector intermediate principal stress direction in stress field coordinate system in ancient crack, dimensionless;

N " _zfor the component of unit normal vector least principal stress direction in stress field coordinate system in ancient crack, dimensionless;

Three representation in components of fracture plane unit's normal vector in earth coordinates are:

$\left[\begin{array}{c}{n^{\&prime;}}_x\\ {n^{\&prime;}}_y\\ {n^{\&prime;}}_z\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\&alpha;}}_{11}& \cos {\mathrm{\&alpha;}}_{21}& \cos {\mathrm{\&alpha;}}_{31}\\ \cos {\mathrm{\&alpha;}}_{12}& \cos {\mathrm{\&alpha;}}_{22}& \cos {\mathrm{\&alpha;}}_{32}\\ \cos {\mathrm{\&alpha;}}_{13}& \cos {\mathrm{\&alpha;}}_{23}& \cos {\mathrm{\&alpha;}}_{33}\end{array}\right]\left[\begin{array}{c}{n^{\&prime;\&prime;}}_x\\ {n^{\&prime;\&prime;}}_y\\ {n^{\&prime;\&prime;}}_z\end{array}\right]---\left(8\right)$

N ' _xfor the component of unit normal vector X-direction in earth coordinates in ancient crack, dimensionless;

N ' _yfor the component of unit normal vector Y direction in earth coordinates in ancient crack, dimensionless;

N ' _zfor the component of unit normal vector Z-direction in earth coordinates in ancient crack, dimensionless;

According to formula (7)-(8), obtain three components of ancient crack unit normal vector in earth coordinates, just can ask for the occurrence in ancient crack.

3. a kind of tectoclase occurrence quantitative forecasting technique according to claim 1, is characterized in that:

Described stress types in combination, selects area planar shear stress or section shearing stress distribution, the advantage trend of prediction shear crack or advantage tendency, and principle is as follows:

From region shear stress field, control the angle of shear crack dominant orientation, judge the development degree of two groups of shear cracks, the development degree of micro cracks in oil of a certain group of rotation direction is high, for advantage crack, the development degree of micro cracks in oil of another group rotation direction is low, is inferior advantage crack, when somewhere major principal stress is horizontal direction, adopt the advantage trend in area planar shear stress judgement crack, if when somewhere major principal stress is vertical direction, adopt the advantage tendency in section shear stress judgement crack, region.

4. a kind of tectoclase occurrence quantitative forecasting technique according to claim 1, is characterized in that:

Described emulation ant tracer technique refers in locus, rock stratum coupling process at all times, the attitude of rocks now of take is " food ", by in stress field simulation data volume, extract carry in a large number ancient attitude of rocks information stress node as " ant body ", to locus, rock stratum coupling at all times, (pheromones) preserved in the path of following the trail of simultaneously, convene other stress node ant body in certain limit according to similar path finding " food ", in implementation procedure, need to arrange following key parameter:

1. initial search frequency range refers to the scope that a stress node ant body can relate in initial ranging, this scope is definite by initial search radius R and two parameters of searcher parallactic angle ψ, and the ancient drop of Ant Search radius R Main Basis fracture, the inclination angle of fracture and rock stratum are determined in the combined factors such as horizontal stretching rate of different times:

R＝(1+sinδ ₁)·H+I (15)

In formula (15), H is comprehensively definite according to the ancient drop of tomography and inclination angle, and unit is m;

δ ₁for making the inclination angle now of seam sedimentary type formations in period, unit is °;

I is for affecting the other factors Reliability equivalence factor of ant body search radius, and unit is m;

Searcher parallactic angle ψ (unit for °) with make the seam phase and the evolution of tectonic stress field is afterwards relevant;

2. iteration increase to be overflow the ant algorithm operation time of angle degree ⊿ Φ (unit be °) major effect design, simultaneously also relevant with attitude of rocks variation range, and attitude of rocks difference is compared with hour selecting bigger numerical at all times;

3. (area is S in ant source ₁) after ant body once follows the trail of, by the scope of other stress node ant body of this path walking;

4. ant body tracing path tolerance angle Φ (unit for °) and accommodation zone tolerance angle Φ make ant body can search out faster abundant food when search; The initial area that accommodation zone is set is identical with ant source area, and the width L of accommodation zone can be expressed as:

$L=\frac{S_1}{2R\&CenterDot;\tan \mathrm{\&Phi;}}---\left(16\right)$

5. the illegal attitude of rocks and the legal attitude of rocks refer to the attitude of rocks now that ant body captures in accommodation zone, when its number number is less than three, think that the attitude of rocks now catching is the illegal attitude of rocks, need to increase tolerance angle Φ (step-length Wei ⊿ Φ), until the number of the attitude of rocks now capturing is more than or equal at 3 o'clock, the discrete type of the attitude of rocks that judgement captures, will remain numerical value as the legal attitude of rocks after rejecting abnormalities value;

6. stop macroscopical scope of activities (first depositing tomography or study area scope is border) that threshold value refers to ant body, when ant body runs into certain border, will lose the confidence to the attitude of rocks of following the trail of, thereby finish follow the trail of, and to take the attitude of rocks of this boundary vicinity be the legal attitude of rocks.

5. a kind of tectoclase occurrence quantitative forecasting technique according to claim 1, is characterized in that:

Described crack at all times space, rock stratum replacement theory model refer to by rock mechanics layer at all times, set up, in order to the model of quantitatively characterizing crack kinematics character in later structural activity, in order to meet research needs, model is made the following assumptions under the prerequisite of suitably simplifying:

1) mainly grow in single rock mechanics layer in crack, and crack is not cut and worn different rock mechanics layers on plane, section;

2) in tectonic activities, crack does not produce relative sliding, rotates relative to rock mechanics layer at all times, and " minor fault " do not developed in crack;

3), enough hour of theoretical model, the motion feature of rock mechanics layer can be split as spatial translation-rotation combination;

4) occurrence of rock mechanics layer has inheritance on vertical, simulation among a small circle in, think that the occurrence of rock mechanics layer is consistent vertical.

6. a kind of tectoclase occurrence quantitative forecasting technique according to claim 1, is characterized in that:

It is as follows that described crack movement is learned signature analysis step:

1) motion feature of non-horizontal stratum can be expressed as:

$T=\left[\begin{array}{ccc}(1-{P_x}^2)\cos \mathrm{\&xi;}+{P_x}^2& P_x{P}_y(1-\cos \mathrm{\&xi;})+P_z\sin \mathrm{\&xi;}& P_x{P}_z(1-\cos \mathrm{\&xi;})-P_y\sin \mathrm{\&xi;}\\ P_x{P}_y(1-\cos \mathrm{\&xi;})-P_z\sin \mathrm{\&xi;}& (1-{P_y}^2)\cos \mathrm{\&xi;}+{P_y}^2& P_y{P}_z(1-\cos \mathrm{\&xi;})+P_x\sin \mathrm{\&xi;}\\ P_x{P}_z(1-\cos \mathrm{\&xi;})+P_y\sin \mathrm{\&xi;}& P_y{P}_z(1-\cos \mathrm{\&xi;})-P_x\sin \mathrm{\&xi;}& (1-{P_z}^2)\cos \mathrm{\&xi;}+{P_z}^2\end{array}\right]---\left(33\right)$

$\left[\begin{array}{c}{n}_x\\ n_y\\ n_z\end{array}\right]=T\&CenterDot;\left[\begin{array}{c}{n^{\&prime;}}_x\\ {n^{\&prime;}}_y\\ {n^{\&prime;}}_z\end{array}\right]---\left(40\right)$

2) horizontal stratum motion feature can adopt formula (38) and formula (40) to represent:

$T=\left[\begin{array}{ccc}(1-{P_x}^2)\cos \mathrm{\&xi;}+{P_x}^2& P_x{P}_y(1-\cos \mathrm{\&xi;})& -P_y\sin \mathrm{\&xi;}\\ P_x{P}_y(1-\cos \mathrm{\&xi;})& (1-{P_y}^2)\cos \mathrm{\&xi;}+{P_y}^2& P_x\sin \mathrm{\&xi;}\\ P_y\sin \mathrm{\&xi;}& -P_x\sin \mathrm{\&xi;}& \cos \mathrm{\&xi;}\end{array}\right]---\left(38\right)$

In formula (33), (38), (40), ξ is rotation angle, and unit is °;

N ' _xfor the component of unit normal vector X-direction in earth coordinates in ancient crack, dimensionless;

N ' _yfor the component of unit normal vector Y direction in earth coordinates in ancient crack, dimensionless;

N ' _zfor the component of unit normal vector Z-direction in earth coordinates in ancient crack, dimensionless;

N _xfor the component of unit normal vector X-direction in earth coordinates in crack now, dimensionless;

N _yfor the component of unit normal vector Y direction in earth coordinates in crack now, dimensionless;

N _zfor the component of unit normal vector Z-direction in earth coordinates in crack now, dimensionless;

P _xfor ancient rock mechanics layer normal and the component of unit normal vector X-direction in earth coordinates of rock mechanics layer normal place plane now, dimensionless;

P _yfor ancient rock mechanics layer normal and the component of unit normal vector Y direction in earth coordinates of rock mechanics layer normal place plane now, dimensionless;

P _zfor ancient rock mechanics layer normal and the component of unit normal vector Z-direction in earth coordinates of rock mechanics layer normal place plane now, dimensionless.

7. a kind of tectoclase occurrence quantitative forecasting technique according to claim 6, is characterized in that:

Described rotation angle ξ size and the method for orientation determination are:

1) process of asking for of the rotation angle ξ of non-horizontal stratum can be expressed as:

$\left[\begin{array}{c}{h}_x\\ h_y\\ h_z\end{array}\right]=\left[\begin{array}{ccc}{p}_x& p_y& p_z\\ 0& \frac{p_z}{\sqrt{{p_y}^2+{p_z}^2}}& -\frac{p_y}{\sqrt{{p_y}^2+{p_z}^2}}\\ -\sqrt{{p_y}^2+{p_z}^2}& \frac{p_x{p}_y}{\sqrt{{p_y}^2+{p_z}^2}}& \frac{p_x{p}_z}{\sqrt{{p_y}^2+{p_z}^2}}\end{array}\right]\left[\begin{array}{c}{m}_x\\ m_y\\ m_z\end{array}\right]---\left(24\right)$

$\left[\begin{array}{c}{h_x}^{\&prime;}\\ {h_y}^{\&prime;}\\ {h_z}^{\&prime;}\end{array}\right]=\left[\begin{array}{ccc}{p}_x& p_y& p_z\\ 0& \frac{p_z}{\sqrt{{p_y}^2+{p_z}^2}}& -\frac{p_y}{\sqrt{{p_y}^2+{p_z}^2}}\\ -\sqrt{{p_y}^2+{p_z}^2}& \frac{p_x{p}_y}{\sqrt{{p_y}^2+{p_z}^2}}& \frac{p_x{p}_z}{\sqrt{{p_y}^2+{p_z}^2}}\end{array}\right]\left[\begin{array}{c}{m_x}^{\&prime;}\\ {m_y}^{\&prime;}\\ {m_z}^{\&prime;}\end{array}\right]---\left(25\right)$

In formula (24)-(25), m ' _xfor the component of unit normal vector X-direction in earth coordinates of ancient rock mechanics layer, dimensionless;

M ' _yfor the component of unit normal vector Y direction in earth coordinates of ancient rock mechanics layer, dimensionless;

M ' _zfor the component of unit normal vector Z-direction in earth coordinates of ancient rock mechanics layer, dimensionless;

M _xfor the component of unit normal vector X-direction in earth coordinates of rock mechanics layer now, dimensionless;

M _yfor the component of unit normal vector Y direction in earth coordinates of rock mechanics layer now, dimensionless;

M _zfor the component of unit normal vector Z-direction in earth coordinates of rock mechanics layer now, dimensionless;

ξ ₃can be expressed as:

$\left\{\begin{array}{cc}{\mathrm{\&xi;}}_3=\arccos \left(h_y\right)& (h_z\&GreaterEqual;0)\\ {\mathrm{\&xi;}}_3=360-\arccos \left(h_y\right)& (h_z<0)\end{array}\right.---\left(26\right)$

In like manner, ξ ₄can be expressed as:

$\left\{\begin{array}{cc}{\mathrm{\&xi;}}_4=\arccos \left({h_y}^{\&prime;}\right)& ({h_z}^{\&prime;}\&GreaterEqual;0)\\ {\mathrm{\&xi;}}_4=360-\arccos \left({h_y}^{\&prime;}\right)& ({h_z}^{\&prime;}<0)\end{array}\right.---\left(27\right)$

Rotation angle ξ can be expressed as:

ξ＝ξ ₃-ξ ₄ (28)

2) process of asking for of the rotation angle ξ of horizontal stratum can be expressed as:

Rotation angle ξ ₅be expressed as:

$\left\{\begin{array}{cc}{\mathrm{\&xi;}}_5=-\arccos \left(p_x\right)& (p_y\&GreaterEqual;0)\\ {\mathrm{\&xi;}}_5=\arccos \left(p_x\right)& (p_y<0)\end{array}\right.---\left(34\right)$

When the level of ancient rock stratum, rotation angle ξ can be expressed as:

$\left\{\begin{array}{cc}\mathrm{\&xi;}=\arccos \left(m_z\right)& (m_y\cos {\mathrm{\&xi;}}_5+m_x\sin {\mathrm{\&xi;}}_5<0)\\ \mathrm{\&xi;}=-\arccos \left(m_z\right)& (m_y\cos {\mathrm{\&xi;}}_5+m_x\sin {\mathrm{\&xi;}}_5>0)\end{array}\right.---\left(36\right)$

When rock stratum level now, rotation angle ξ can be expressed as:

$\left\{\begin{array}{cc}\mathrm{\&xi;}=\arccos \left({m_z}^{\&prime;}\right)& ({m_y}^{\&prime;}\cos {\mathrm{\&xi;}}_5+{m_x}^{\&prime;}\sin {\mathrm{\&xi;}}_5>0)\\ \mathrm{\&xi;}=-\arccos \left({m_z}^{\&prime;}\right)& ({m_y}^{\&prime;}\cos {\mathrm{\&xi;}}_5+{m_x}^{\&prime;}\sin {\mathrm{\&xi;}}_5<0)\end{array}\right.---\left(37\right)$

According to formula (24)-(28) and formula (34), (36), (37), can determine size, the direction of rotation angle ξ.