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## Environmental and Exploration Geophysics II

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**Environmental and Exploration Geophysics II**Static Anomalies and Energy Partitioning tom.h.wilson wilson@geo.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV**Original due dates -**and pb 4.8 Due Today, Oct. 24th Due Tuesday, Oct. 29th Velocity Analysis Problem**Geophone output is often designed to be proportional to**pressure, particle velocity, acceleration or displacement. Land geophone output is typically proportional to particle velocity, while marine geophones record pressure variations.**V**Interval Velocity Particle Velocity v**Pi**PR PT Normal Incidence Raypaths Boundary Conditions**We can rewrite boundary condition 1 as**The subscript P indicates that pressure variations are being considered in this case**From the wave equation, we have that**This allows us to rewrite boundary condition II in terms of the pressures, as - By convention, up is negative, thus**Our two boundary conditions become**which implies As a matrix equation, we have**Part II**Geophone output is often designed to be proportional to pressure, particle velocity, acceleration or displacement. Land geophone output is typically proportional to particle velocity, while marine geophones record pressure variations.**V**Interval Velocity Particle Velocity v**Note that Pv =Vv2**Thus Ev2**We have, as expected, a decrease of energy across the**interface. Energy is conserved!**Compute and plot two-way interval transit times, two-way**total reflection time, layer impedance and boundary reflection coefficients**Density, velocity and impedance plots are usually**represented in step-plot form. The values as listed are constant through an interval and marked by abrupt discontinuity across layer boundaries.**Reflection coefficients exist only at boundaries across**which velocity and density change, hence their value is everywhere 0 except at these boundaries. Stick Plot**Subsurface model**Simplified representation of the source disturbance**Follow the wavefront through the subsurface and consider how**its amplitude changes as a function only of energy partitioning. A. What is the amplitude of the disturbance at point A? B. At point B we have transmission through the interface separating media 1 and 2. At C? We consider only transmission and reflection losses. Geometrical divergence and absorption losses are ignored. Hence PA = 1psi. - hence the amplitude of the wavefront at B is Tp 12 PA.**At C? -**At D? -