Tom Wilson, Department of Geology and Geography Environmental and Exploration Geophysics II tom.h.wilson Department of Geology and Geography West Virginia University Morgantown, WV Energy Partition in Seismic Waves

Tom Wilson, Department of Geology and Geography Recall Energy partitioning

Tom Wilson, Department of Geology and Geography 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.

Tom Wilson, Department of Geology and Geography Interval Velocity Particle Velocity

Tom Wilson, Department of Geology and Geography PiPi PTPT PRPR Normal Incidence Raypaths

Tom Wilson, Department of Geology and Geography The subscript P indicates that pressure variations are being considered in this case We can rewrite boundary condition 1 as

Tom Wilson, Department of Geology and Geography 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

Tom Wilson, Department of Geology and Geography Our two boundary conditions become which implies As a matrix equation, we have

Tom Wilson, Department of Geology and Geography

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.

Tom Wilson, Department of Geology and Geography Interval Velocity Particle Velocity

Tom Wilson, Department of Geology and Geography

Note that Pv =  Vv 2 Thus E  v 2

Tom Wilson, Department of Geology and Geography

We have, as expected, a decrease of energy across the interface. Energy is conserved!

Tom Wilson, Department of Geology and Geography Compute and plot two-way interval transit times, two-way total reflection time, layer impedance and boundary reflection coefficients

Tom Wilson, Department of Geology and Geography 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.

Tom Wilson, Department of Geology and Geography Reflection coefficients exist only at boundaries across which velocity and density change, hence their value is everywhere 0 except at these boundaries.

Tom Wilson, Department of Geology and Geography Subsurface model Simplified representation of the source disturbance

Tom Wilson, Department of Geology and Geography 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 P A = 1psi. - hence the amplitude of the wavefront at B is T p 12 P A.

Tom Wilson, Department of Geology and Geography At C? - At D? -

Tom Wilson, Department of Geology and Geography Consider for a moment- the general n-layer case.

Tom Wilson, Department of Geology and Geography

…. Solve for the Ps and vs and then plot

Tom Wilson, Department of Geology and Geography The plot portrays the amplitude of the wavelet at subsurface points A, B, C and D. Input wavelet Provide a general representation of wavelet amplitudes measured at points A - D. Do for both the pressure and velocity measurements

Tom Wilson, Department of Geology and Geography Total loss - incorporating divergence, absorption and reflection/transmission effects. We have considered the above factors individually. All of them act to attenuate seismic waves as they propagate through the earth. Recall that divergence and absorption losses were combined into the following equation Each mechanism acts as a factor that scales the amplitude of the propagating wavefield. So the net effect on amplitude determined by taking the product of all effects on source amplitude A S.

Tom Wilson, Department of Geology and Geography Energy partitioning is a step-like function. Wave amplitudes will take a jump to higher or lower amplitude across individual interfaces, however, we can consider the effect of transmission through a series of layers having various average values of reflection and transmission coefficient as shown below. Recall that on the decibel scale the relationship between two amplitudes is expressed as where  A is in decibels

Tom Wilson, Department of Geology and Geography If average reflection coefficient is not too high (for example 0.05 or 0.1) then the effect is relatively constant over a large range of depths and we can represent transmission reductions by a single scale factor - say T. Total amplitude decay at distance r

Tom Wilson, Department of Geology and Geography These amplitude effects are non-geological in a sense. Geologists are interested to have accurate information about the reflection coefficients - not only their position, but their value. The above equation indicates that the amplitude of a reflection from a particular reflector will equal The geologist would like to have

Tom Wilson, Department of Geology and Geography Note amplitude/stratigraphic relationships

Tom Wilson, Department of Geology and Geography Accurate portrayal of reflection coefficients is important in stratigraphic interpretations of seismic data. 10,000 14,000 18,500 19,500 16,500 14,500 21,000 18,500

Tom Wilson, Department of Geology and Geography “True Amplitude” … with some computer glitches Once again note the amplitude relationships

Tom Wilson, Department of Geology and Geography This seismic display has been “gain corrected” Note that some of the lithology dependant amplitude differences have disappeared.

Tom Wilson, Department of Geology and Geography

Note that the amplitudes in the gain corrected trace at right do not accurately portray relative differences in the value of reflection coefficients

Tom Wilson, Department of Geology and Geography From Ylmez Truer amplitude display - amplitude averaging is undertaken over longer time windows Gain incorporates amplitude averaging over short time windows

Tom Wilson, Department of Geology and Geography The basic synthetics exercises handed out today will be due next Friday. Look over them and bring questions to class this Thursday.

Tom Wilson, Department of Geology and Geography Read over the paper I handed out to you last Thursday by Sheriff. A proper understanding of resolution issues is critical to stratigraphic interpretations and also to structural interpretations where the identification of subtle structures, such as faults with small offset may be important. We’ll be studying resolution in forthcoming computer labs and relating resolution limits to your exploration data set.