Understanding Cumulative Response Functions in Soil Conductivity Measurement, Slides of Earth Sciences

Download Understanding Cumulative Response Functions in Soil Conductivity Measurement and more Slides Earth Sciences in PDF only on Docsity! McNeill introduces another function, R(z) - the cumulative response function - which he uses to compute the ground conductivity from a given distribution of conductivity layers beneath the surface. RV(z) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 z 0.0 0.2 0.4 0.6 0.8 1.0 C um ul at iv e R es po ns e -R (z ) RH(z) zzzR z zR H V 2)14()( )14( 1)( 2/12 2/12 −+= + = For next time continue your reading of McNeill and develop a general appreciation of the relative and cumulative response functions. R is an integral of φ from some z to ∞ Docsity.com Each point on the RV(z) curve represents the area under the φV(z) curve from z to ∞. The following diagrams are intended to help you visualize the relationship between R(z) and φ(z). Here’s how we get the R’s Docsity.com To get the area between Z, and Z, ... Docsity.com How would you express this integral as a difference of cumulative response functions? How would you get this area? Docsity.com )()0()( 10 1 zRRdzz VV z V −=∫ φ Just the same as before – a difference between two integrals (areas) Docsity.com