Common MidPoint (CMP) Records and Stacking Environmental and Exploration Geophysics II Common MidPoint (CMP) Records and Stacking tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV Tom Wilson, Department of Geology and Geography

Note that the stack trace compares quite well with the pure signal. 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. Greenbrier Huron Onondaga Where i is the trace number and j is a specific time Tom Wilson, Department of Geology and Geography

See Feynman Lectures on Physics, Volume 1. Noise 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. Random noise can come in the form of wind, rain, mining activities, local traffic, microseismicity ... +1 -1 The basic nature of random noise can be described in the context of a random walk - 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 -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

will always equal 1 ( the average After 1 step will always equal 1 ( the average of +12 or -12 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

from the starting point. 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

See Feynman Lectures on Physics, Volume 1. 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

Hence, the ratio of signal to noise is or just 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 is or 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

Question - 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 = 4.472 Square root of N(?) = 8.94 What’s N N=80 To double the signal to noise ratio we must quadruple the fold 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

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

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

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

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

The approximation is hyperbolic, whereas the actual is not 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

Refraction into high velocity layers brings the events in along paths that don’t have hyperbolic moveout. Greenbrier Limestone Big Injun 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. Tom Wilson, Department of Geology and Geography

Different kinds of velocity VRMS VAV and VNMO are different. VNMO does not equal VRMS. Each of these 3 velocities has different geometrical significance. Tom Wilson, Department of Geology and Geography

In actuality the moveout velocity varies with offset. The VNMO 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 t2-x2 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

Other benefits derived from Stacking Seeing double? Tom Wilson, Department of Geology and Geography

Water Bottom Reflection Normal Incidence Time Section …. Water Bottom Reflection Reflection from Geologic interval Water Bottom Multiple Tom Wilson, Department of Geology and Geography

Interbed Multiples DEPTH 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

The NMO Corrected CDP gather 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 Primary Reflections Multiple Multiple Tom Wilson, Department of Geology and Geography

Examples of multiples in marine seismic data Buried graben or multiple 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

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

Problem 4.4 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. Offset (m) Reflection1 Reflection2 Reflection3 x t1 (ms) t2 (ms) t3 (ms) 3 21.4 62.3 79.4 6 25 62.4 79.5 9 30.1 62.6 79.6 12 36.1 62.9 79.9 15 42.5 63.2 80.1 18 49.2 63.6 80.5 21 56.2 64.1 80.9 24 63.3 64.7 81.3 27 70.4 65.4 81.8 30 77.6 66.1 82.4 33 84.9 66.9 83 36 92.2 67.7 83.7 Tom Wilson, Department of Geology and Geography

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

The variables t2 and x2 are linearly related. Recall - 2 2 t - x The variables t2 and x2 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 t2-x2 responses. Keep in mind that the fitted velocity is actually an NMO velocity! Then what? Tom Wilson, Department of Geology and Geography

Dix Interval Velocity Start with definition of the RMS velocity The Vis are interval velocities and the tis are the two-way interval transit times. Tom Wilson, Department of Geology and Geography

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

hence Tom Wilson, Department of Geology and Geography

Vn is the interval velocity of the nth layer Since Vn is the interval velocity of the nth layer tn in this case represents the two-way interval transit time through the nth 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

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

You put these ideas into application when solving problems 4.4 and 4.8 Dix Interval Velocity 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 t2-x2 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 and 4.8 Tom Wilson, Department of Geology and Geography

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

Back to your computer projects Back to your computer projects. Please review the Summary Activities and Report Handout. We are at the mid point in the semester and time will run out quickly. Questions about gridding and math on two maps topics covered in the last lecture? Tom Wilson, Department of Geology and Geography

Conversion to Depth Tom Wilson, Department of Geology and Geography

Average velocity map Tom Wilson, Department of Geology and Geography

Without Extrapolation Tom Wilson, Department of Geology and Geography

With Extrapolation Tom Wilson, Department of Geology and Geography

Increased projection distance Tom Wilson, Department of Geology and Geography

Time Surface Tom Wilson, Department of Geology and Geography

Tom Wilson, Department of Geology and Geography

Wells > Edit > Time Depth Charts Tom Wilson, Department of Geology and Geography

Interval Velocity Tom Wilson, Department of Geology and Geography

Formation top approach (times derived from TD chart and formation top depths from well file) Tom Wilson, Department of Geology and Geography

Time horizon Tom Wilson, Department of Geology and Geography

Conversion to depth Tom Wilson, Department of Geology and Geography

Time vs. Depth Tom Wilson, Department of Geology and Geography

Mark your calendar Problem 4.1 is due today Problems 4.4 and 4.8 are due 1st Wednesday following Spring Break. Look over Exercises IV-V. These will be due 1st Monday after Spring Break. Exercise VI will be due Wednesday after Spring Break For the remainder of today – Conversion to depth and project work. Mid Term Reports are due the Monday March 23rd. Tom Wilson, Department of Geology and Geography