| 王辉,冯明伸,程昊,覃保锏,宋曙光,覃晓燕,梁兴东.带状地物压覆固体矿产范围的空间投影变换计算作图方法讨论[J].矿产勘查,2024,15(S2):104-113 |
| 带状地物压覆固体矿产范围的空间投影变换计算作图方法讨论 |
| Discussion on the calculation and mapping method for spatial projection transformation of the solid mineral covered by the belt shaped terrain |
| 投稿时间：2024-10-13 |
| DOI：10.20008/j.kckc.2024s2014 |
| 中文关键词: 压覆矿产资源 安全岩柱 压矿边界 水平投影 垂直纵投影 空间投影变换 带状地物 |
| 英文关键词: covering mineral resources safety rock pillar mining boundary horizontal projection vertical vertical projection spatial projection transformation belt shaped terrain |
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| 中文摘要: |
| 在带状地物压覆陡倾矿体范围的空间投影变换过程中，因作图与计算方法不正确，常常会造成压覆矿体边界范围和压覆矿产资源储量就会出现偏差，探求能正确圈定压覆矿体水平投影范围和垂直纵投影范围的计算方法，以期达到正确估算压覆重要固体矿产资源储量的目的。按照由简单情形至复杂情形的递进研究思路，分规则带状地物垂直投影基准线、规则带状地物斜交投影基准线、不规则带状地物斜交投影基准线三种情形，基于投影基准线的压矿边界范围水平投影 /倾斜投影 /垂直纵投影间的三角函数关系，推导其空间投影变换过程中的数学计算公式，为科学圈定压矿边界范围，正确估算压覆资源储量提供数学基础。设带状地物长轴延伸方向长度为 L，α为矿体倾角， β为基岩移动角 /裂缝角， γ为带状地物长轴延伸方向与投影基线间的交角，在空间投影变换过程中，通过其空间三角函数关系的推导，其结果是:在水平投影图上，安全岩柱沿投影基线方向的宽度 W水平 1=L.sinγtanαcotβ，沿带状地物长轴延伸方向的宽度 W水平 2=L .sinγtanαsin(90-β)cos(arctan(tanαsinγ)) /sin(β-arctan(tanαsinγ))；在垂直纵投影图上，安全岩柱沿投影基线方向的宽度( W垂直 1)与其在水平投影图上的宽度相同( W水 1)沿带状地物长轴延伸方向的宽度 W垂直 2= L.sin2γtan2αsin(90-β)cos(arctan(tanαsinγ)) /sin(β-arctan(tanαsinγ)。分别在水平投影图和垂直纵投影)，图上，依次编联安全岩柱拐点，即可得到水平压覆范围和垂直纵投影压覆范围。利用空间投影变换过程中的三角函数关系，通过数学方法求算编联地表不规则带状物压覆陡倾矿体的水平投影和垂直投影的边界范围，为压覆矿产资源评估提供了正确的计算作图思路与具体方法，方便地质技术人员在计算作图直接引用，具有很强的实践意义。避免地质技术人员在实际作图过程中，因错误地理解空间投影变换和繁琐的计算公式推导，常常导致的压矿边界范围错误编联和压覆资源储量估算结果出现偏差问题。利用本文研究结果，可进行空间投影变换三维可视化计算成图软件开发，提高作图效率和准确度，起到事半功倍的作用。 |
| 英文摘要: |
| Due to incorrect mapping and calculation methods，the boundary range of the ore body and the reserves of the mineral resources are often deviated during the transformation of the space projection of the area ofthe steeply-sloping ore body in the zonal ground features. A calculation method that can correctly delineate thehorizontal projection range and vertical longitudinal projection range of the ore body is sought to achieve thepurpose of correctly estimating the reserves of the important mineral resources. According to the progressive research idea from simple case to complex case，three cases are divided into vertical projection datum line of regular strip surface objects，oblique projection datum line of regular strip surface objects and oblique projectiondatum line of irregular strip surface objects. Based on the projection datum line，the trigonometric function relation. ship between horizontal projection，oblique projection and vertical longitudinal projection of ore mining boundary range is obtained. The mathematical calculation formula in the process of space projection transformation is derived，which provides mathematical basis for scientifically delineating the boundary range of compressed ore andcorrectly estimating the reserves of compressed resources. The length of the long axis extension direction of the zonal surface object is L，α is the dip Angle of the ore body，β is the bedrock movement Angle/crack Angle，and γ is the intersection Angle between the extension direction of the zonal surface object's long axis and the projectionbase line. In the process of spatial projection transformation，through the derivation of its spatial trigonometric function relationship，the results are as follows:On the horizontal projection diagram，the width of the safety pillar along the projection base direction Whorizontal1 =L .sinγtanα coβ，The Whorizontal2 =L .sinγtanαsin(90-β)cos(arctan(tanαsinγ)) /sin(β-arctan(tanαsinγ)) along the long axis of the strip；On the vertical vertical projection chart， the width of the safety pillar along the projection base direction(Wvertical1)is the same as that on the horizontal projection chart(Whorizontal1). Width Wvertical2 =L . sin2γtan2αsin(90-β) cos(arctan(tanαsinγ)) /sin(β -arctan(tanαsinγ)) along the long axis of the strip. The inflection points of the safety pillar can be sequentially linked onthe horizontal projection diagram and the vertical longitudinal projection diagram respectively，and the horizontal and vertical longitudinal projection can be obtained. By using the triangular function relation in the process of spatial projection transformation，the plane projection range and vertical projection range of the irregular belt on thesurface of the surface are realized by mathematical method，which provides a correct mapping idea and a reliablemapping method for the assessment of the resource and reserves. In the process of actual mapping，the geologicaltechnicians will avoid the wrong delineation of the overburden area and the wrong evaluation result of resourcereserves due to the wrong understanding of the spatial projection transformation. In the future work process，the development of three dimensional visual display and spatial projection transformation program can be further car.ried out to save the cumbersome calculation process and improve the efficiency and accuracy of mapping. |
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