Seismic MethodsGeoph 465/565

ERB 5104Lecture 9 – Sept 28, 2015

Lee M. LibertyResearch 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

Final Project - seismic data analysis

Processing steps - Simple version

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

Additional Processing Stepsstack-migrate in time

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 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

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 wavelet reflectivity series output series

seismogram = source reflectivity ,

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.

DECONVOLUTION

Sources of reverberations

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.

What we want to achieve with deconvolution 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.

Deconvolution

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

Deconvolution 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.

Spiking deconvolution

Deconvolution “whitens” the spectrum, boosting high frequencies and flattening the amplitude spectrum.

side lobes

What are reverberations, really? 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.

Bandwidth is limited by the source BUT: we can shape the frequency spectrum of the

source to equalize the frequency components, thus making the bandwidth closer to a “boxcar” function

am

plit

ude

frequency

source bandwidth

original

after decon

Spiking Deconvolution

Deconvolution ResultsLocation 109

Tim

e (

ms)

DECONVOLVEDNO DECONVOLUTION

Location 109

Tim

e (

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

Least-squares deconvolution filter

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.

Predictive deconvolution

Autocorrelation 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.

Ghosts (short-period reverberations)

Long-period reverberations (multiples)

“pegleg” multiple

Characteristics of reverberations/multiples/bubbles 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

Sourcewavelet

The convolutional model

Reverberations and multiples are minimum phase

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 thespike train

Autocorrelation and decon

Spiking decon on shot gathers

Deconvolution

Additional Processing Stepsstack-migrate in time

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

For flat layers without large velocity changes, the RMS velocity is nearly the same as the stacking velocity (vst )

Stacking velocity is the velocity obtained by taking the best-fit hyperbola through a reflector (not necessarily through T0), assuming a constant-velocity model.

T2=T02 +

The stacking velocity is determined by computer velocity analyses, and is used to correct the CDP data for normal moveout (NMO).

x2

vstack2

RMS vs average vs stacking velocity For flat layers that are “well-behaved” (only

gradual velocity changes):

vstack ≈ vrms ≈ vave

>>generally within 3%, nearly always within 5%

We will use vstack to flatten reflectors on the CDPs

t2,v2

t3,v3

t4,v4

t5,v5

t1,v1

vstack

Normal Moveout correction

Normal Moveout correction

Normal Moveout correction

Normal Moveout correction

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.

Velocity (m/s)

Travel ti

me (

s)

Velocity semblance analysis

Velocity semblance analysisVelocity (m/s)

Travel ti

me (

s)

reflection from a dipping layer

Image point

Apexes ofhyperbola

Portland Hills fault Portland, Oregon

Liberty et al., 2003

CDPs over dipping layers

a

a

Midpointsmearing

Flat layer

Dipping layer

Word document 16 steps

Dipping reflectors – 0, 20, 40, 60 degrees

Shot gather CMP gather

Stacking velocity changes with dip angle

vstack ≈ vrms /cosa ≈ vave /cosa

vstack >> vrms , vave for dipping layers

vstack ≈ vrms ≈ vave for flat layers

Stacking velocity changes with dip angle

vstack ≈ vrms /cosa ≈ vave /cosa

so, if =0a o(flat layer), vstack ≈ vrms ≈ vave

If =90a o(vertical layer), vstack=∞

Dipping versus flat layers Often a choice of whether to correctly stack

dipping or horizontal reflectors (different velocities for each)

Example: imaging faults versus strata

To resolve conflict of imaging different dips: Pre-stack migration (time, depth) DMO (Dip Moveout; partial prestack migration)