Lee M. Liberty Research Professor Boise State University

 Process dataset (e.g. reflection, surface wave, microseismicity, refraction, modeling)  Report – SEG style: Summary, methods, acquisition, processing, interpretation, discussion/conclusions, references  Topic: ◦ Andrew: Seismic refraction from Mt. St. Helens ◦ Tate: BHRS surface wave data ◦ Travis: Rayinvr/Rayfract comparison ◦ Aida: Dry Creek refraction analysis ◦ Marlon: Alaska reflection or modeling ◦ Will and Dmitri: refraction/reflection/surface wave/VSP lab summaries

 Sort (Shots to CMP domain)  Normal moveout correction (NMO)  Stack >> Brute Stack (first look at the data!)

 Preprocessing  Clean up Shot Records  Amplitude recovery  Deconvolution  Sort to CMP  Velocity Analysis – iterative  Residual statics  NMO correction  Mutes  Stack (gains and filters often follow)  Migrate  Convert to depth

 Deconvolution removes “cyclic” noise – anything that repeats itself on a regular basis  2 purposes: ◦ 1) sharpen wavelet and reduce reverberations – SPIKING Deconvolution ◦ 2) remove long-period multiples (i.e. water- bottom multiples) – PREDICTIVE Deconvolution

A mathematical way of combining two signals to achieve a third, modified signal. The signal we record is a set of time series superimposed upon each other. CONVOLUTION

Convolution Seismograms are the result of a convolution between the source and the subsurface reflectivity series (and also the receiver). Mathematically, this is written as: where the operator denotes convolution. source waveletreflectivity seriesoutput series

 The reversal of the convolution process.  By deconvolving the source wavelet, we can obtain the earth's reflectivity.  However, noise (unwanted signal) and other features are also present in the recorded trace and the source wavelet is rarely known with any accuracy.  Convolution in the time domain is represented in the frequency domain by a multiplying the amplitude spectra and adding the phase spectra.

 Airgun bubble pulse ◦ Period depends on gun size and pressure. Use multiple guns synchronized to initial pulse to cancel bubble pulses.  Water multiples ◦ Effect varies with water depth.  For shallow water, multiples are strong but reduce quickly with depth.  For deep water, multiple is below depth of main reflectors.  For slope depths, effect is difficult to eliminate as first (strongest) multiple arrives at main depth of interest.  Peg-leg multiples ◦ Due to interbed multiples which can sometimes be misinterpreted as primaries.

 Make reflections easier to interpret  more like the "real" earth ◦ improve "spikiness" of arrivals ◦ decrease "ringing"  But without decreasing signal relative to noise. ◦ This is one of the main problems

 Deterministic deconvolution - used to remove the effects of the recording system, if the system characteristics are known. This type also can be used to remove the ringing that results from waves undergoing multiple bounces in the water layer, if the travel time in the water layer and the reflectivity of the seafloor are known.  Adaptive deconvolution – when the signature is not known, deconvolution takes on a statistical nature where information comes from an autocorrelation of the seismic trace.  Because the embedded wavelet from the source is repeated at each reflecting interface, this repetition is captured by the autocorrelation and used to design the inverse filter.

 Based on the one-dimensional, plane-wave convolutional model for the removal of the composite wavelet filtering effect in order to uncover the earth reflection coefficient series.  An input acoustic signal is transmitted through the earth and a filtered version of this signal is recorded at a later time.  The earth is assumed to consist of a finite number of horizontal layers upon which the signal is directed at normal incidence (vertically).  The simplest trace representation consists of an average wavelet w(t) convolved with a reflection coefficient series r(t). This noise free trace is: x(t) = w(t)*r(t) Decon_Tutorial.pdf

 The convolutional model is the basic assumption of deconvolution: ◦ Trace = source * reverberations (noise) * reflections (earth) ◦ G(t) = S(t) * N(t) * R(t)  “Spiking” deconvolution shapes the source wavelet.  “Predictive” deconvolution removes reverberations and multiples, but leaves the wavelet mostly untouched.  Deconvolution is implemented using a “least- squares” approach to minimize the difference between the “desired output” and the “actual output”.

 Shortens the embedded wavelet and attempts to make it as close as possible to a spike. The frequency bandwidth of the data limits the extent to which this is possible.  This is also called whitening deconvolution, because it attempts to achieve a flat, or white, spectrum.  This kind of deconvolution may result in increased noise, particularly at high frequencies.

side lobes

 Reverberations are caused by some frequencies being enhanced (constructive interference) while others are diminished (destructive interference).  The result is a frequency spectrum with peaks and troughs.

 BUT: we can shape the frequency spectrum of the source to equalize the frequency components, thus making the bandwidth closer to a “boxcar” function amplitude frequency source bandwidth original after decon

Location 109 Time (ms) DECONVOLVEDNO DECONVOLUTION Location 109 Time (ms)

Processing: deconvolution of the source Seismic profiles before (top) and after (bottom) the deconvolution. Note that the deconvolved signal is spike-like.

S = W  R + N (noise) Five Main Assumptions – #1: R is composed of horizontal layers of constant velocity – #2: W is composed of a compressional plane wave at normal incidence which does not change as it travels, ie is stationary – #3: noise N = 0 – #4: R is random. There is no "pattern" to the set of reflectors R – #5: W is minimum phase Generally #3 is NOT valid – ie. there will always be some noise on our seismic records – We will need to investigate what happens when N ≠ 0 We generally do not know W Convolution Model

 The filter attempts to shape the input seismic trace x(t) into the desired output r(t) by minimizing the mean-squared error between the desired output and the actual filter output y(t).  The actual output is simply the input x(t) convolved with the filter f(t).  The least-squares error is

 Predict and eliminating multiple reflections  How does it work?  Design a filter that recognizes and eliminates repetitions in the signal  Uses the autocorrelation to remove the multiples.  Predictability means that the arrival of an event can be predicted from knowledge of earlier events.

 In the convolutional model, one assumption is that the reflectivity sequence (reflection coefficients) are random. This means that the autocorrelation of the seismic trace is the same as the autocorrelation of the input wavelet, scaled by the amplitude of the reflectivity sequence. A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation of the series on the bottom. A measure of how well a signal matches a time- shifted version of itself, as a function of the amount of time shift.

Short-period reverberations can also be caused by bubble oscillations in airgun sources, shallow water layers, or thin reflective layers near the source or receiver.

“pegleg” multiple

 Regularly-spaced cycles  “predictable” – given a model, we can predict the times of the noise.  We can add the “predictable” noise (reverberations, multiples) to our convolutional model by convolving our original source wavelet with a noise model

Source wavelet The convolutional model

 We can deconvolve the reverberations, as long as we do not touch the original source wavelet. “Predictive” deconvolution We can use “predictive” deconvolution to remove the minimum phase reverberations – we are “predicting” the times and amplitudes of the reverberations. This is called “predictive error filtering” when using least-squares error method to implement it. Remove the spike train

 Preprocessing  Clean up Shot Records  Amplitude recovery  Deconvolution  Sort to CMP  Velocity Analysis – iterative  Residual statics  NMO correction  Mutes  Stack (gains and filters often follow)  Migrate  Convert to depth

 Stacking velocity is the velocity obtained by taking the best-fit hyperbola through a reflector (not necessarily through T 0 ), assuming a constant-velocity model.  T 2 =T The stacking velocity is determined by computer velocity analyses, and is used to correct the CDP data for normal moveout (NMO). x2x2 v stack 2

 For flat layers that are “well-behaved” (only gradual velocity changes):  v stack ≈ v rms ≈ v ave  >>generally within 3%, nearly always within 5%

t 2,v 2 t 3,v 3 t 4,v 4 t 5,v 5 t 1,v 1 v stack

Velocity semblance analysis A quantitative measure of the coherence of seismic data from multiple channels that is equal to the energy of a stacked trace divided by the energy of all the traces that make up the stack. If data from all channels are perfectly coherent, or show continuity from trace to trace, the semblance has a value of unity.seismic tracemake upcoherent

Velocity (m/s) Travel time (s) Velocity semblance analysis

Velocity (m/s) Travel time (s)

Image point Apexes of hyperbola

Portland Hills fault Portland, Oregon Liberty et al., 2003

  Midpoint smearing Flat layer Dipping layer

 Word document  16 steps Shot gather CMP gather

v stack ≈ v rms /cos  ≈ v ave /cos  v stack >> v rms, v ave for dipping layers v stack ≈ v rms ≈ v ave for flat layers

v stack ≈ v rms /cos  ≈ v ave /cos  so, if    flat layer), v stack ≈ v rms ≈ v ave If    vertical layer), v stack =∞

 Often a choice of whether to correctly stack dipping or horizontal reflectors (different velocities for each)  Example: imaging faults versus strata

 Pre-stack migration (time, depth)  DMO (Dip Moveout; partial prestack migration)