A method for correcting the occurrence of a paleocurrent indicator

Abstract

The application discloses a method for correcting the occurrence of an ancient water flow direction indicator, and mainly studies the correction of the original occurrence of a inclined bedding exposed on two adjacent sections, and comprises the following steps: measuring and counting all the current stratigraphic and structural occurrences; using the method of the stereographic projection, drawing the current occurrence of the structural elements on the stereographic projection; correcting the strata to be horizontal by rotating the normal line or the circular arc representing the occurrence of the strata on the stereographic projection; using the rotation angle obtained in the previous step, correcting the occurrence of the inclined bedding by rotating the normal line or the circular arc representing the occurrence of the inclined bedding, so as to obtain the original occurrence of the inclined bedding. The corrected original occurrence of the inclined bedding has an indicating significance for the ancient water flow direction, and then the provenance direction can be inferred.

Description

Technical Field

[0001] This invention relates to the field of geological sedimentation and tectonics, specifically to a method for correcting the occurrence of ancient water flow direction indicators. Background Technology

[0002] Some bedding or strata deposits developed on outcrops in the field are good indicators of paleowater flow direction, providing valuable reference for determining provenance location, sedimentary environment, and paleogeographic analysis. Cross-bedding is a typical indicator of paleowater flow direction, frequently observed on stratigraphic profiles during field geological exploration. However, the strata containing these deposits are often affected by tectonic movements, resulting in significant changes in their attitude relative to the original sedimentary attitude. This leads to a deviation in the indicative value of the exposed attitude for paleowater flow direction. Therefore, correcting the attitude of paleowater flow direction indicators to obtain their original attitude is essential for determining paleowater flow direction and thus inferring provenance direction.

[0003] Stratigraphic correction of attitude can determine the original attitude of sedimentary structures by examining structural features and morphology. Using stereographic projection, and based on the relationships between various structural elements indicated by paleowater flow direction, the stratigraphic correction problem is transformed into a mathematical problem. With known relationships such as strike and dip, the original attitude of strata and sedimentary structures can be calculated using formulas.

[0004] Stereoscopic projection is an important tool in astronomy for stellar observation, and it is also widely used in engineering, urban planning, and disaster assessment. Utilizing the Earth's rotation and the perpendicularity of its centerline, stereoscopic projection maintains conformity to angles. Its principle is simple and its applications are broad. In stereoscopic projection, the Earth's North and South Poles are considered the origin of the coordinate axes, intersecting the plane. Perpendicular lines are used to depict all points on the Earth, ensuring that any point on the map is at the same angle to the equator, thus achieving a conformal projection effect. This projection method can effectively represent various regions of the Earth's surface while maintaining angular accuracy. Summary of the Invention

[0005] Existing techniques, which rely on numerous mathematical formulas to correct the attitude of paleowater flow indicative structures in stratigraphy, are computationally intensive and prone to cumulative errors. Therefore, this proposal utilizes stereographic projection to introduce a novel calculation method that more efficiently and accurately obtains stratigraphic correction results and the corrected paleowater flow orientation, thereby indicating the direction of sediment source transport.

[0006] This method primarily addresses the correction of the attitude of cross-bedding exposed in stratigraphic profiles, a common occurrence during field reconnaissance. Sometimes, cross-bedding can be observed on two adjacent faces within a stratigraphic profile. In such cases, the sedimentary strata have often been altered by tectonic movements; therefore, the stratigraphic attitude needs to be corrected to a horizontal level to obtain the original stratigraphic attitude and the original cross-bedding attitude, thereby inferring the paleocurrent direction and provenance direction. Specifically:

[0007] The current stratigraphic and structural attitudes are measured and statistically analyzed, obtaining the stratigraphic attitude, the attitudes of the two cross-bedding surfaces, and the dip direction and dip angle of the cross-bedding on the two surfaces. Using stereographic projection, great circular arcs representing the two surfaces are drawn on the stereographic projection. Based on the measured dip direction and dip angle, points representing the attitudes of the cross-bedding on the two surfaces are drawn on the great circular arcs representing the two surfaces. Connecting these two points yields the great circular arc representing the cross-bedding plane, i.e., the current attitude of the plane containing the cross-bedding.

[0008] Since the attitude of bedding planes changes with the attitude of stratigraphy, the original attitude of the bedding planes can be obtained by correcting the stratigraphy to a horizontal plane. There are two methods for correcting the stratigraphy to a horizontal plane: one is to rotate the normal, determining the normal of the bedding plane based on the stratigraphic attitude, rotating the normal until it is perpendicular to the horizontal plane, and recording the rotation angle; the other is to rotate the great circle representing the bedding plane's attitude, rotating the great circle around the strike until it is horizontal, and determining its rotation angle. Using the first method, rotating the bedding plane normal by the same angle, the attitude of the great circle determined by the rotated normal is the original attitude of the bedding plane. Using the second method, based on the principle of "three points determine a plane," taking three points on the great circle of the bedding plane, rotating them by the same angle, and determining a new great circle based on these three points, the attitude of this new great circle is the original attitude of the bedding plane. The corrected original attitude of the bedding plane is indicative of the direction of paleocurrents, and can therefore be used to infer the source direction.

[0009] Specifically: Step 1: Measure the attitude of the strata containing the cross-bedding, determine the two planes on the stratigraphic profile where the cross-bedding is located and measure its attitude, measure and count the dip direction and dip angle of the cross-bedding on the two planes; Assumptions: Stratigraphic attitude α∠β; The attitude of plane 1 is A∠B, the dip direction of the cross-bedding on plane 1 is a, and the dip angle is b; The orientation of plane 2 is C∠D, the dip direction of the cross-bedding on plane 2 is c, and the dip angle is d; Step 2: Construct great circle arcs AB and CD, representing plane 1 and plane 2 respectively, using stereographic projection; Step 3: Using the measured dip direction and dip angle of the cross-bedding on the two surfaces, determine the attitude of the cross-bedding on the two sections using stereographic projection. On AB, the attitude is a1∠b1; on CD, the attitude is c1∠d1. Step 4: Using stereographic projection, connect the two points representing the two linear structures to obtain the great circle arc EF representing the planar structure. That is, the attitude γ∠θ of the plane in which the two lines are currently located is determined by the attitude of the two lines. Step 5: The current stratigraphic attitude is α∠β. Correcting this stratigraphic attitude to horizontal will yield the attitude of the cross-bedding plane formed in the paleogeographic environment. Only then can the cross-bedding plane indicate the direction of paleowater flow. That is, the cross-bedding plane and the ground plane rotate together around the straight line where the ground plane strikes ((α-90)-(α+90)), i.e., the rotation axis R is rotated to the horizontal of the ground plane. Rotation normal: When the ground plane is horizontal, the ground plane normal should be perpendicular to the horizontal plane. Therefore, when the normal is rotated to be perpendicular to the horizontal plane in stereographic projection, the great circle arc of the ground plane is also rotated to the horizontal at the same time. At the same time, the bedding plane normal also rotates by the same angle as the ground plane normal. The bedding plane attitude determined by the rotated bedding plane normal can indicate the ancient water flow direction. Step 6: Determine the ground surface normal m and the slope surface normal n; project the straight line R ((α-90)-(α+90)) containing the strike line onto the great circle arc, and draw two points m and n representing the normal; Step 7: Rotate R until it coincides with N, and rotate m to point O by an angle of x. Therefore, n should also be rotated in the same direction and angle to n'. Step 8: Based on the stratigraphically corrected normal n' of the cross-bedding plane, determine the original attitude μ / ω of the cross-bedding plane, thus obtaining the paleowater flow direction and azimuth μ. or, Directly rotate the great circle representing the ground plane; rotate the great circle representing the ground plane around the strike line to the horizontal and determine its rotation angle; since three points can determine an arc, take three points on the great circle representing the cross bedding and rotate the points by the same angle. The new arc determined by the three points is the rotated cross bedding plane, and its attitude is the corrected cross bedding attitude. Step 6: Draw a great circle representing the ground plane and rotate it around the traverse line to a horizontal position to obtain a semicircle. At this point, it is found that each point on the great circle representing the ground plane rotates counterclockwise by an angle of β to its new position. Step 7: Draw a great circle representing the bedding plane; rotate the transparent paper so that the strike line coincides with the NS direction; take three points 1, 2, and 3 on the great circle of the bedding plane, and rotate all three points counterclockwise by an angle β to obtain a new great circle. This attitude is the original attitude μ / ω of the bedding plane after stratigraphic correction, which gives the paleowater flow direction and azimuth μ.

[0010] As can be seen from the above technical solution, compared with the prior art, the present invention has the following technical effects: 1. Simple, intuitive and efficient operation: This invention utilizes the geometric rotation principle of stereographic projection to transform stratigraphic correction into an intuitive graphical operation, avoiding complex mathematical formula derivation and a large amount of calculation, significantly reducing workload and calculation costs, and improving the efficiency of attitude correction. 2. High precision and controllable error: The cross-bedding surface is corrected by rotating the normal or rotating the great circle arc, which eliminates the error caused by formula approximation in traditional calculation methods. It can accurately restore the original attitude of the cross-bedding, and the two methods can be mutually verified to ensure the reliability of the results. 3. High adaptability and flexible application: For the common cross-bedding exposed on two adjacent sections in the field, this invention provides two parallel schemes: rotating normal and rotating great circle arc. The scheme can be flexibly selected according to the actual data characteristics and operating habits, and is suitable for the attitude correction needs of different geological conditions. 4. Visual indication of paleocurrent direction: The corrected original attitude of the cross-bedding can be directly used to determine the paleocurrent direction, providing clear and reliable quantitative basis for sediment source analysis and paleogeographic reconstruction. Furthermore, the distribution pattern of paleocurrent can be visually displayed through graphic methods such as rose diagrams.

[0011] In summary, this invention, based on the stereographic projection method, simplifies the process of correcting the orientation of ancient water flow indicators. While ensuring accuracy, it significantly improves the ease of operation and the usability of the results, demonstrating good practical value and promising prospects for wider application. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0013] Figure 1 This is a flowchart illustrating the method execution according to an embodiment of the present invention; Figure 2 These are field photos of the exposed cross-bedding in the Laoshan Pass-Baxiandun area; Figure 3 This is the stereographic projection result of Method 1 in the embodiment; Figure 4 This is the stereographic projection result of Method 2 in the embodiment; Figure 5 It is a rose-shaped diagram depicting the ancient water flow direction in the Laoshan Pass-Baxiandun area. Detailed Implementation

[0014] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Step 1: Measure the attitude of the strata containing the cross-bedding, determine the two planes on the stratigraphic profile where the cross-bedding is located and measure its attitude, and measure and count the dip direction and dip angle of the cross-bedding on the two planes.

[0015] Assumptions: Stratigraphic attitude α∠β; The attitude of plane 1 is A∠B, the dip direction of the cross-bedding on plane 1 is a, and the dip angle is b; The orientation of plane 2 is C∠D, the dip direction of the bedding plane on plane 2 is c, and the dip angle is d.

[0016] Step 2: Use stereographic projection to construct great circle arcs AB and CD, representing plane 1 and plane 2 respectively.

[0017] Step 3: Using the measured dip direction and dip angle of the cross-bedding on the two surfaces, determine the attitude of the cross-bedding on the two sections using stereographic projection. On AB, the attitude is a1∠b1; on CD, the attitude is c1∠d1.

[0018] Step 4: Using stereographic projection, connect the two points representing the two linear structures to obtain the great circle arc EF representing the planar structure. That is, the attitude γ∠θ of the plane in which the two lines are currently located is determined by the attitude of the two lines.

[0019] Step 5: The current stratigraphic attitude is α∠β. Correcting this stratigraphic attitude to horizontal will yield the attitude of the cross-bedding plane formed in the paleogeographic environment. Only then can the cross-bedding plane indicate the paleowater flow direction. That is, the cross-bedding plane and the ground surface rotate together around the straight line ((α-90)-(α+90)) containing the strike of the ground surface (i.e., the rotation axis R) until the ground surface is horizontal.

[0020] (1) Method 1: Rotation of normal. When the ground plane is horizontal, the ground plane normal should be perpendicular to the horizontal plane. Therefore, when the normal is rotated to be perpendicular to the horizontal plane on the stereographic projection, the great circle arc of the ground plane is also rotated to the horizontal at the same time. At the same time, the bedding plane normal is also rotated by the same angle as the ground plane normal. The bedding plane attitude determined by the rotated bedding plane normal can indicate the paleowater flow direction.

[0021] Step 6: Determine the surface normal m and the slope normal n. Project the straight line R ((α-90)-(α+90)) containing the strike line onto the great circle arc, and draw two points m and n representing the normal.

[0022] Step 7: Rotate R until it coincides with N, and rotate m to point O by an angle of x. Therefore, n should also be rotated in the same direction and angle to n'.

[0023] Step 8: Based on the normal n' of the cross-bedding plane after stratigraphic correction, determine the original attitude μ / ω of the cross-bedding plane, thus obtaining the paleowater flow direction and azimuth μ.

[0024] (2) Method 2: Directly rotate the great circle representing the ground plane. Rotate the great circle representing the ground plane around the strike line to the horizontal and determine its rotation angle. Since three points can determine an arc, take three points on the great circle representing the cross-bedding and rotate the points by the same angle. The new arc determined by the three points is the rotated cross-bedding plane, and its attitude is the corrected cross-bedding attitude.

[0025] Step Six: Draw a great circle representing the ground plane and rotate it around the traverse line until it is horizontal, resulting in a semicircle. It is then observed that each point on the great circle representing the ground plane rotates counterclockwise by an angle β to its new position.

[0026] Step 7: Draw a great circle representing the bedding plane. Rotate the transparent paper so that the strike line coincides with the NS direction. Take three points 1, 2, and 3 on the great circle of the bedding plane, and rotate all three points counterclockwise by an angle β to obtain a new great circle. This attitude is the original attitude μ / ω of the bedding plane after stratigraphic correction, which gives the paleowater flow direction and azimuth μ.

[0027] Summarizing the above steps and considering a reasonable error range, both methods can obtain the original attitude of the cross-bedding and the paleocurrent direction it indicates. Statistical measurements of the cross-bedding are performed, and its original attitude is corrected using stereographic projection. This determines the average original attitude of the cross-bedding as μ / ω, thus obtaining the paleocurrent direction and azimuth μ, from which the provenance of the sediment can be inferred.

[0028] Implementation Case: Analysis of the ancient water flow direction of the Laiyang Group in the Laoshan Pass-Baxiandun area of ​​Qingdao City, Shandong Province.

[0029] The Laoshan Pass-Baxiandun area is located along the coastal area from Qingshan Pass to Baxiandun in Laoshan District, Qingdao. Geologically, it lies on the high-pressure to ultra-high-pressure metamorphic belt of the Sulu Orogenic Belt, between the Qianliyan Uplift and the Jiaolai Basin. A series of rocks with an outcrop area exceeding 4 km² are distributed here. 2 The strata, with a total thickness exceeding 2 km, are metamorphic marine clastic rocks. Due to the intrusion of the Laoshan granite during the Cretaceous, they were metamorphosed and mainly consist of alternating layers of grayish-green sandstone and bluish-gray mudstone. Based on previous research, it is inferred that this stratum is a turbidite developed on an active continental margin, belonging to the Upper Ordovician of the Yangtze Plate. It may have been formed by the upper cover of the Yangtze Plate thrusting into the North China Plate during the subduction of the Yangtze Plate into the North China Plate.

[0030] The research content is as follows: Ancient water flow direction indicators in the Laoshan Pass-Baxiandun area ( Figure 1 The presence of cross-bedding planes after tectonic changes in the strata caused a misalignment between the observed attitude and the original attitude. To address this, this study employed stereographic projection to correct and restore the original attitude of the strata in their horizontal state before the tectonic movement, thus indicating the correct direction of paleowater flow.

[0031] The main steps include: 1. Measure the attitude of the strata containing the cross-bedding, determine the two planes on the stratigraphic profile where the cross-bedding is located and measure its attitude, and measure and count the dip direction and dip angle of the cross-bedding on the two planes.

[0032] Statistical measurements show that the stratigraphic attitude is 146°∠22°, the attitude of plane 1 is 208°∠75°, the dip direction of the cross-bedding on plane 1 is 118°, and the dip angle is 10°; the attitude of plane 2 is 257°∠60°, the dip direction of the cross-bedding on plane 2 is 167°, and the dip angle is 27°.

[0033] 2. Construct great circle arcs AB and CD representing plane 1 and plane 2 respectively using stereographic projection.

[0034] 3. Using the measured dip direction and dip angle of the cross-bedding on the two surfaces, the attitude of the cross-bedding on the two sections is determined by stereographic projection. On AB, the attitude is 120°∠10°; on CD, the attitude is 180°∠24°.

[0035] 4. Using stereographic projection, connect the two points representing the two linear structures to obtain the great circle arc EF representing the planar structure. That is, the attitude of the plane where the two lines are located is determined by the attitude of the two lines, which is 186°∠23°.

[0036] 5. The current stratigraphic attitude is 146°∠22°. Correcting this stratigraphic attitude to horizontal will yield the attitude of the cross-bedding plane formed in the paleogeographic environment. Only then can the cross-bedding plane indicate the direction of paleowater flow. That is, the cross-bedding plane and the ground plane rotate together around the straight line (i.e., the rotation axis R) of the ground plane strike (56°-236°) until the ground plane is horizontal.

[0037] (1) Method 1: Rotation of normal. When the ground plane is horizontal, the normal of the ground plane should be perpendicular to the horizontal plane. Therefore, when the normal is rotated to be perpendicular to the horizontal plane on the stereographic projection, the great circle representing the ground plane is also rotated to the horizontal at the same time. At the same time, the normal of the bedding plane is also rotated by the same angle as the normal of the ground plane. The attitude of the bedding plane determined by the rotated bedding plane normal can indicate the direction of paleowater flow.

[0038] Step 6: Determine the ground plane normal m (290°∠68°) and the slope bedding plane normal n (65°∠67°). Project the straight line R (56°-236°) containing the strike line onto the great circle arc, and draw two points m and n representing the normal.

[0039] Step 7: Rotate R until it coincides with N, and rotate m to point O. The rotation method is a counterclockwise rotation of 22°, so n is also rotated in the same direction and at the same angle to n' (83°∠74°).

[0040] Step 8: Based on the normal n' of the cross-bedding plane after stratigraphic correction, determine the original attitude of the cross-bedding plane as 240°∠16°, which means that the paleowater flow direction is SW and the azimuth is 240°.

[0041] (2) Method 2: Rotate the great circle representing the ground plane. Rotate the great circle representing the ground plane around the strike line to the horizontal, and determine its rotation direction and angle. Since three points can determine an arc, take three points on the great circle representing the cross-bedding, and rotate the points in the same way. The new arc determined by the three new points is the rotated cross-bedding plane, and its attitude is the corrected cross-bedding attitude.

[0042] Step 6: Draw a great circle representing the ground plane, and rotate it around the traverse line until it is horizontal, resulting in a semicircle. At this point, it is observed that each point on the great circle representing the ground plane rotates counterclockwise by 22° to its new position.

[0043] Step 7: Draw a great circle representing the bedding plane. Rotate the transparent paper so that the strike line coincides with the NS direction. Take three points 1, 2, and 3 on the great circle of the bedding plane, and rotate each of the three points counterclockwise by 22° to obtain a new great circle. This attitude is the original attitude of the bedding plane after stratigraphic correction, which is 248°∠14°. Therefore, the paleocurrent direction is SW, and the azimuth is 248°.

[0044] Summarizing the above steps and considering a reasonable margin of error, both methods can obtain the original attitude of the exposed crossbedding in the Laoshan Pass-Baxiandun area and the paleocurrent direction it indicates. Statistical measurements were performed on the crossbedding exposed in the Laiyang Group in the Pass-Baxiandun area, and its original attitude was corrected using stereographic projection. This determined that the average original attitude of the statistically measured crossbedding in the Pass-Baxiandun area is 240°∠16°, indicating a paleocurrent direction of SW with an azimuth of 240°. A paleocurrent direction rose diagram for the Pass-Baxiandun area was also drawn. Figure 2 ).

[0045] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to mutually. As for the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and relevant parts can be referred to the method section.

[0046] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention; various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention; therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for correcting the attitude of ancient water flow direction indicators, characterized in that, The current stratigraphic and structural attitudes are measured and statistically analyzed. The attitudes of the stratigraphic layers, the attitudes of the two outcrops of the cross-bedding, and the dip direction and dip angle of the cross-bedding on the two outcrops are measured. Then, using stereographic projection, great circular arcs representing the two outcrops are drawn on the stereographic projection. Based on the measured dip direction and dip angle, points representing the attitudes of the cross-bedding on the two outcrops are drawn on the great circular arcs representing the two outcrops. Connecting these two points yields the great circular arc representing the cross-bedding plane, i.e., the current attitude of the plane containing the cross-bedding. Finally, using the strike line of the stratigraphic layer as the axis of rotation, the stratigraphic layer is rotated to a horizontal state with a rotation angle equal to the dip angle of the stratigraphic layer. By using the method of rotating the normal or rotating the great circular arc representing the stratigraphic layer, the cross-bedding plane is rotated by the same angle as the stratigraphic layer, and the stratigraphic layer is corrected to a horizontal state, thus obtaining the original attitude of the cross-bedding plane. This original attitude is used to indicate the direction of paleocurrent and thus infer the source location.

2. The method according to claim 1, characterized in that, The rotation normal method includes: determining the normal of the ground plane according to the attitude of the strata, rotating the normal until it is perpendicular to the horizontal plane, that is, rotating the ground plane to the horizontal, recording its rotation angle, rotating the normal of the bedding plane by the same angle, and the attitude of the great circle determined by the rotated normal is the original attitude of the bedding plane.

3. The method according to claim 1, characterized in that, The method of rotating the great circle arc to represent the ground plane includes: rotating the great circle arc around the strike to the horizontal, determining its rotation angle, taking three points on the great circle arc of the bedding plane and rotating them by the same angle according to the principle of three points determining a plane, and determining a new great circle arc based on the three points after rotation, the attitude of which is the original attitude of the bedding plane.

4. The method according to claim 1, characterized in that, Specifically, the following steps are included: Step 1: Measure the attitude of the strata containing the cross-bedding, determine the two planes on the stratigraphic profile where the cross-bedding is located and measure its attitude, measure and count the dip direction and dip angle of the cross-bedding on the two planes; Assumptions: Stratigraphic attitude α∠β; The orientation of plane 1 is A∠B, the dip direction of the cross-bedding on plane 1 is a, and the dip angle is b; The orientation of plane 2 is C∠D, the dip direction of the cross-bedding on plane 2 is c, and the dip angle is d; Step 2: Construct great circle arcs AB and CD, representing plane 1 and plane 2 respectively, using stereographic projection; Step 3: Using the measured dip direction and dip angle of the cross-bedding on the two surfaces, determine the attitude of the cross-bedding on the two sections using stereographic projection. On AB, the attitude is a1∠b1; on CD, the attitude is c1∠d1. Step 4: Using stereographic projection, connect the two points representing the two linear structures to obtain the great circle arc EF representing the planar structure. That is, the attitude γ∠θ of the plane where the two lines are currently located is determined by the attitude of the two lines. Step 5: The current stratigraphic attitude is α∠β. Correcting this stratigraphic attitude to horizontal will yield the attitude of the cross-bedding plane formed in the paleogeographic environment. Only then can the cross-bedding plane indicate the direction of paleowater flow. That is, the cross-bedding plane and the ground plane rotate together around the straight line where the ground plane strikes ((α-90)-(α+90)), i.e., the rotation axis R is rotated to the horizontal of the ground plane. Rotation normal: When the ground plane is horizontal, the ground plane normal should be perpendicular to the horizontal plane. Therefore, when the normal is rotated to be perpendicular to the horizontal plane in stereographic projection, the great circle arc of the ground plane is also rotated to the horizontal at the same time. At the same time, the bedding plane normal also rotates by the same angle as the ground plane normal. The bedding plane attitude determined by the rotated bedding plane normal can indicate the ancient water flow direction. Step 6: Determine the ground surface normal m and the slope surface normal n; project the straight line R ((α-90)-(α+90)) containing the strike line onto the great circle arc, and draw two points m and n representing the normal; Step 7: Rotate R until it coincides with N, and rotate m to point O by an angle of x. Therefore, n should also be rotated in the same direction and angle to n'. Step 8: Based on the stratigraphically corrected normal n' of the cross-bedding plane, determine the original attitude μ / ω of the cross-bedding plane, thus obtaining the paleowater flow direction and azimuth μ. or, Directly rotate the great circle representing the ground plane; rotate the great circle representing the ground plane around the strike line to the horizontal and determine its rotation angle; since three points can determine an arc, take three points on the great circle representing the cross bedding and rotate the points by the same angle. The new arc determined by the three points is the rotated cross bedding plane, and its attitude is the corrected cross bedding attitude. Step 6: Draw a great circle representing the ground plane and rotate it around the traverse line to a horizontal position to obtain a semicircle. At this point, it is found that each point on the great circle representing the ground plane rotates counterclockwise by an angle of β to its new position. Step 7: Draw a great circle representing the bedding plane; rotate the transparent paper so that the strike line coincides with the NS direction; take three points 1, 2, and 3 on the great circle of the bedding plane, and rotate all three points counterclockwise by an angle β to obtain a new great circle. This attitude is the original attitude μ / ω of the bedding plane after stratigraphic correction, which gives the paleowater flow direction and azimuth μ.

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