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 Common MidPoint (CMP) Records and Stacking

Tom Wilson, Department of Geology and Geography Common Midpoint (CMP) gather, also often referred to as Common Depth Point (CDP)

Tom Wilson, Department of Geology and Geography Doug Smith’s seismic Data Processing site Common Midpoint Gather

Tom Wilson, Department of Geology and Geography Velocity Analysis

Tom Wilson, Department of Geology and Geography 4.1) Determine the velocity and thickness of the material above the first reflecting horizon X (meters)3 meter geophone interval 11 traces 33 meters from 40 to 73 meters

Tom Wilson, Department of Geology and Geography Discussion of problems 4.1 Read over and think about how you are going to solve problems 4.5 and 4.8

Tom Wilson, Department of Geology and Geography If we sum all the noisy traces together - sample by sample - we get the trace plotted in the gap at right. This summation of all 16 traces is referred to as a stack trace. Note that the stack trace compares quite well with the pure signal. Stack Trace Pure signal Greenbrier Huron Onondaga Where i is the trace number and j is a specific time

Tom Wilson, Department of Geology and Geography +1 Noise comes in several forms - both coherent and random. Coherent noise may come in the form of some unwanted signal such as ground roll. A variety of processing and acquisition techniques have been developed to reduce the influence of coherent noise. The basic nature of random noise can be described in the context of a random walk - Random noise can come in the form of wind, rain, mining activities, local traffic, microseismicity... See Feynman Lectures on Physics, Volume 1.

Tom Wilson, Department of Geology and Geography The random walk attempts to follow the progress one achieves by taking steps in the positive or negative direction purely at random - to be determined, for example, by a coin toss. +1

Tom Wilson, Department of Geology and Geography Does the walker get anywhere? Our intuition tells us that the walker should get nowhere and will simply wonder about their point of origin. However, lets take a look at the problem form a more quantitative view. It is easy to keep track of the average distance the walker departs from their starting position by following the behavior of the average of the square of the departure. We write the average of the square of the distance from the starting point after N steps as The average is taken over several repeated trials.

Tom Wilson, Department of Geology and Geography After 1 step will always equal 1 ( the average of +1 2 or -1 2 is always 1. After two steps - which is 0 or 4 so that the average is 2. After N steps

Tom Wilson, Department of Geology and Geography Averaged over several attempts to get home the wayward wonderer gets on average to a distance squared from the starting point. Since=1, it follows that and therefore that

Tom Wilson, Department of Geology and Geography The results of three sets of random coin toss experiments See Feynman Lectures on Physics, Volume 1.

Tom Wilson, Department of Geology and Geography The implications of this simple problem to our study of seismic methods relates to the result obtained through stacking of the traces in the common midpoint gather. The random noise present in each trace of the gather (plotted at left) has been partly but not entirely eliminated in the stack trace. Just as in the case of the random walk, the noise appearing in repeated recordings at the same travel time, although random, does not completely cancel out

Tom Wilson, Department of Geology and Geography The relative amplitude of the noise - analogous to the distance traveled by our random walker- does not drop to zero but decreases in amplitude relative to the signal. If N traces are summed together, the amplitude of the resultant signal will be N times its original value since the signal always arrives at the same time and sums together constructively. The amplitude of noise on the other hand because it is a random process increases as Hence, the ratio of signal to noise isor just where N is the number of traces summed together or the number of traces in the CMP gather.

Tom Wilson, Department of Geology and Geography In the example at left, the common midpoint gather consists of 16 independent recordings of the same reflection point. The signal-to-noise ratio in the stack trace has increased by a factor of  16 or 4. The number of traces that are summed together in the stack trace is referred to as its fold – i.e. 16 fold.

Tom Wilson, Department of Geology and Geography If you had a 20 fold dataset and wished to improve its signal-to-noise ratio by a factor of 2, what fold data would be required? Square root of 20 = Square root of N(?) = 8.94 What’s N To double the signal to noise ratio we must quadruple the fold To double the S/N we have to increase the fold by 2 2 ; to triple it, by 3 2 ; etc.

Tom Wilson, Department of Geology and Geography The reliability of the output stack trace is critically dependant on the accuracy of the correction velocity.

Tom Wilson, Department of Geology and Geography Accurate correction ensures that the same part of adjacent waveforms are summed together in phase. Average Amplitude Stack = Summation

Tom Wilson, Department of Geology and Geography then the reflection response will be “smeared out” in the stack trace through destructive interference between traces in the sum. If the stacking velocities are incorrect ….

Tom Wilson, Department of Geology and Geography The reason for this becomes obvious when you think of the earth as consisting of layers of increasing velocity. At larger and larger incidence angle you are likely to come in at near critical angles and then will travel significant distances at higher than average (or RMS) velocity. Greenbrier Limestone Big Injun Refraction into high velocity layers brings the events in along paths that have non-hyperbolic moveout.

Tom Wilson, Department of Geology and Geography The two-term approximation to the multilayer reflection response is hyperbolic. The velocity in this expression is a root-mean-square velocity. Are they also hyperbolic? The real world: multilayer reflections

Tom Wilson, Department of Geology and Geography The sum of squared velocity is weighted by the two- way interval transit times t i through each layer. A series of infinite terms – but we just ignore a bunch of them

Tom Wilson, Department of Geology and Geography The approximation is hyperbolic, whereas the actual is not. The disagreement becomes significant at longer offsets, where the actual reflection arrivals often come in earlier that those predicted by the hyperbolic approximation.

Tom Wilson, Department of Geology and Geography V RMS, V AV and V NMO are different. V NMO does not equal V RMS. Each of these 3 velocities has different geometrical significance.

Tom Wilson, Department of Geology and Geography The V NMO is derived form the slope of the regression line fit to the actual arrivals. In actuality the moveout velocity varies with offset. The RMS velocity corresponds to the square root of the reciprocal of the slope of the t 2 -x 2 curve for relatively short offsets.

Tom Wilson, Department of Geology and Geography The general relationship between the average, RMS and NMO velocities is shown at right.

Tom Wilson, Department of Geology and Geography Geometrically the average velocity characterizes travel along the normal incidence path. The RMS velocity describes travel times through a single layer having the RMS velocity. It ignores refraction across individual layers.

Tom Wilson, Department of Geology and Geography

Water Bottom Reflection Reflection from Geologic interval Water Bottom Multiple Normal Incidence Time Section ….

Tom Wilson, Department of Geology and Geography DEPTHDEPTH Interbed Multiples

Tom Wilson, Department of Geology and Geography Interbed Multiples

Tom Wilson, Department of Geology and Geography The Power of Stack extends to multiple attenuation

Tom Wilson, Department of Geology and Geography Velocities associated with primary reflections are higher than those associated with multiples. The primaries are flattened out while residual moveout remains with the multiple reflection event. The NMO Corrected CDP gather

Tom Wilson, Department of Geology and Geography Multiple attenuation Multiple Primary Reflections

Tom Wilson, Department of Geology and Geography Buried graben or multiple Examples of multiples in marine seismic data

Tom Wilson, Department of Geology and Geography Multiples are considered “coherent” noise or unwanted signal

Tom Wilson, Department of Geology and Geography Interbed multiples or Stacked pay zones

Tom Wilson, Department of Geology and Geography

Waterbottom and sub-bottom multiples

Tom Wilson, Department of Geology and Geography Other forms of coherent “noise” will also be attenuated by the stacking process. The displays at right are passive recordings (no source) of the background noise. The hyperbolae you see are associated with the movement of an auger along a panel face of a longwall mine.

Tom Wilson, Department of Geology and Geography Multiples Refractions Air waves Ground Roll Streamer cable motion Scattered waves from off line Stacking helps attenuate random and coherent noises

Tom Wilson, Department of Geology and Geography Offset (m)Reflection1Reflection2Reflection3 xt1 (ms)t2 (ms)t3 (ms) Table 1 (right) lists reflection arrival times for three reflection events observed in a common midpoint gather. The offsets range from 3 to 36 meters with a geophone spacing of 3 meters. Conduct velocity analysis of these three reflection events to determine their NMO velocity. Using that information, determine the interval velocities of each layer and their thickness.

Tom Wilson, Department of Geology and Geography Note hyperbolic moveout of the three reflection events.

Tom Wilson, Department of Geology and Geography Recall - The variables t 2 and x 2 are linearly related.

Tom Wilson, Department of Geology and Geography Estimates of RMS velocities can be determined from the slopes of regression lines fitted to the t 2 -x 2 responses. Keep in mind that the fitted velocity is actually an NMO velocity!

Tom Wilson, Department of Geology and Geography Start with definition of the RMS velocity The V i s are interval velocities and the t i s are the two-way interval transit times.

Tom Wilson, Department of Geology and Geography Let the two-way travel time of the n th reflector

Tom Wilson, Department of Geology and Geography hence

Tom Wilson, Department of Geology and Geography Since V n is the interval velocity of the n th layer t n in this case represents the two-way interval transit time through the n th layer

Tom Wilson, Department of Geology and Geography Hence, the interval velocities of individual layers can be determined from the RMS velocities, the 2-way zero - offset reflection arrival times and interval transit times.

Tom Wilson, Department of Geology and Geography the two-way travel time to the n th reflector surface the two-way interval transit time between the n and n-1 reflectors The terms represent the velocities obtained from the best fit lines. Remember these velocities are actually NMO velocities. is the interval velocity for layer n, where layer n is the layer between reflectors n and n-1 See Berger et al. page 173

Tom Wilson, Department of Geology and Geography The interval velocity that’s derived from the RMS velocities of the reflections from the top and base of a layer is referred to as the Dix interval velocity. However, keep in mind that we really don’t know what the RMS velocity is. The NMO velocity is estimated from the t 2 - x 2 regression line for each reflection event and that NMO velocity is assumed to “represent” an RMS velocity. You put these ideas into application when solving problems 4.4

Tom Wilson, Department of Geology and Geography & See page Use dip-moveout approach (pages 197 through 199)

Tom Wilson, Department of Geology and Geography Problem 4.1 is due next Monday Dix interval velocities. We’ll have additional time for questions next Monday 4.4 and 4.8. They will be due the following Monday (March 22). Questions about Exercises IV-V? Exercise VI? Exercises IV-VI due March 17 th