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从数学角度研究入手 ,论证线性和非线性响应测井曲线深度积分面积的守恒关系 :线性响应测井曲线的深度积分面积与曲线的纵向分辨率无关 ,而非线性响应测井曲线的深度积分面积与曲线的纵向分辨率有关 ,且纵向分辨率越高 ,其深度积分面积越大 .然后 ,研究了线性和非线性数学变换对不同分辨率线性和非线性响应测井曲线关系的影响 .最后 ,在一定条件下分析了不同分辨率泥质含量曲线深度积分面积的守恒性 ,并研究了孔隙度曲线积分面积的守恒性问题 .
From the perspective of mathematics, the conservation of the depth integral area of linear and non-linear response logging curves is demonstrated: the depth integral area of linear response logging curve has nothing to do with the longitudinal resolution of the curve, while the depth integral area of nonlinear response logging curve Which is related to the vertical resolution of the curve and the higher the vertical resolution is, the greater the integral area of the depth is.Furthermore, the effects of linear and nonlinear mathematical transformation on the relationship between linear and non-linear response logging curves with different resolutions are studied.Finally, Under certain conditions, the conservation of the depth integral area of the shale content curves at different resolutions was analyzed and the conservation of the integral area of the porosity curve was studied.