Module 03 Seismic Reflection

7/27/2019 Module 03 Seismic Reflection

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Seismic

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Module 3

Seismic Reflection

Learning Objectives

Know ledge Level:

Properties of seismic traces

Vertical and horizontal resolution

Amplitude behavior and recovery

Factors affecting amplitudes, detection, and

resolution


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TOPICS

Reflection Coefficients

Convolutional Model

Zero Phase Wavelet

Vertical and Horizontal Resolution

Thin Bed Tuning

Geometric Spreading

Factors that affect Recorded Amplitudes


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WHY IMPORTANT

Interaction of propagating source wavelet withinhomogeneous subsurface is fundamental

Understanding resolution is critical to final

interpretation and in design/QC of acquisition andprocessing

Quantitative amplitude analysis is based onunderstanding amplitude changes duringpropagation


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Normal Incidence Reflection Coefficient

A

AR12

1V12V2

A(1-R12)

2V2 - 1V12V2 + 1V1

V = Acoustic impedance

Where = density in gm/cc and V= velocity unit length/sec

R12 =


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Ideal Seismogram

The seismic data recorded should give us the

Earths reflectivity sequence:

Surface

Depth

Time

Reflection Coefficient


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Definitions and Basic Relationships

for Sinusoids

Phase refers to position

of zero crossing.


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Exercise

Given the above wavelet,

1. What is the frequency of the wavelet?

2. What is the wavelength in a layer of velocity 3800 m/sec?


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Exercise

Most of the energy in a seismic wavelet is contained in a band of

frequencies centered about the dominant frequency. The dominant

period can be defined as the time between two major crests. The

dominant frequency is the reciprocal of the dominant period. The

equation for wavelength, , is:

= velocity/frequency

Calculate wavelengths for the following cases:a. Shallow rocks: V=2000 m/s, f=50 Hz;

b. Deep rocks: V=6000 m/s, f=25 Hz.


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Convolutional Model

Source Input Earth Noise Seismic traces

+ =

Time

*


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Normal Incidence Synthetic

Wavelet contains

source pulse, instrument

distortion, near surface effects

Rocks V LogRC Log

(depth)

RC Log

(time)

Z

t

Reflectivity R(t)

Plus

The Wavelet


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Composing a Wavelet by Superposition


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Synthetic Seismogram by Superposition


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Constructing the Synthetic Trace

REFLECTIVITY

WAVELET

REFLECTIVITY

WAVELET

SUPERIMPOSED

REPLACEMENTS

EACH REFLECTION STICK

IS REPLACED BY A

PROPORTIONAL VERSIONOF THE WAVELET

THE OVER-LAPPED WAVELETSARE SUMMED TO PRODUCE

THE SEISMIC TRACE

t

t

t

R1 R4 R6

R2R4

R5


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Constructing the Synthetic Trace

Zero Phase


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TOTAL SEISMIC

RESPONSE

(SYNTHETIC SEISMOGRAM)

INDIVIDUAL

RESPONSE

100 MS

ACOUSTICIMPEDANCE

WATER

GAS

WATER

LITHOLOGY

Mixed Phase


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Pinchout?


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Wavelets & Spectra

Mixed PhaseZero Phase

Wavelets can be decomposed into amplitude

and phase spectra using the Fourier Transform


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The Zero Phase Wavelet

Zero phase is optimum

Strongest peak

Symmetry optimizes resolution

Peak at zero reference time

Closest to reflection coefficient spike


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Common Types of Seismic Wavelets

Name Shape Spectrum Features

RickerNo side-lobe

overshoot

KlauderWhite from

f1 to f2

Texas

Doublef3 = 4 f2

Ormsby

Controllable

side-loberipple

f1

f1 f2

f1 f2 f3

f1 f2 f3 f4

S


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Klauder Wavelet

S i i


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Vertical or Temporal Resolution

Seismic ability to define top and

bottom of a rock layer

In general, reflections are composites of thin layer effects.

S i i R l ti Li it


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Resolution Limits

Full Wavelength

Resolved Layer

Half Wavelength

Resolved Layer

Quarter Wavelength

Unresolved Layer

(Detected)

Single Reflection

No Layer

Seismic


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Ideal Threshold For Vertical Resolution

Dominant Wavelength of Seismic Wave =

Where: V is the velocity in unit distance per second and

f is the dominant frequency in Hz

f

V

V(m/sec) F(Hz) / 4 (m)

2000 50 10

3000 40 19

4000 30 33

5000 20 62.5

Seismic P ti l V ti l R l ti


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Practical Vertical Resolution

estimateveconservat idatanoisy2

12=N

estimatenominaldataaverage313=N

est imateopt imist icdatamodel4

14=N

qualitydataondepending4and2betweenisNWhere

fthanveconservat imoreffBANDWIDTHmaxm inmax

BandwidthN

VR intv

Seismic


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Vertical Resolution Exercise (N=3)

A shallow feature with velocity of 2000 m/s and

bandwidth of 50 Hz can be resolved if it is as thin

as_______meters.

A deep feature with 5000 m/s velocity and

bandwidth of 20 Hz can be resolved if it is as thin as_________meters.

The thickness of a deep feature must

be__________(greater, less) than that of a shallowfeature in order to be resolvable.

Seismic Lateral Effects


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Lateral Effects

Fresnel Zone

Lateral Resolution Before Migration

Lateral Resolution After Migration

Seismic


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Fresnel Zone

frequencydominantf

f

t

2

V

R

V

Z2t

wave.aofphasecoherent

common,areflecting

areacirculartheof

radiustherepresentsR

o

oo

Velocity = V

Reflections come from areas (not points) on interfaces. Seismic

wavelength and wavefront travel time result in an area of

constructive interference on the reflector.

Seismic Fresnel Zone


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Fresnel Zone

Where:

V : is the velocity in unit distance per secondT : is time in second

F : is the frequency in HZ

T(sec) V(m/sec) F(hz) R(m)

1 2000 50 141

2 3000 40 355

3 4000 30 632

4 5000 20 1118

f

t

2

V

RRadiusZoneFresnel

Seismic


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Fresnel Zone in 3-D

Map View

3-D Migration reduces (but does not eliminate) fresnel zone in

both x and y dimensions

Seismic


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Implications of Fresnel Zones

Seismic Lateral Resolution


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Lateral Resolution

After migration, lateral resolution (RL) depends upon

the maximum frequency contributing to the migrated

image. This can be computed from the verticalresolution (RV) and maximum ray angle.

angle)raym ax

angleraym ax

sin(BandwidthN

VR

sinRR

intL

VL

Seismic Lateral Resolution


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Lateral Resolution

Lateral resolution after migration

Point diffractors, 30m separation, 10m traceinterval, 3000m/s velocity

Hz100maxf Hz50maxf

After Kirchhoff Migration After Kirchhoff Migration

After Cordsen, Galbraith and Peirce

Planning Land 3-D Seismic Surveys, 2000

Geophysical Development Series, V. 9

RLRL

Seismic Lateral Resolution Concept Based


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p

on Diffraction Properties

Seismic

R fl ti Practical Lateral Resolution


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Practical Lateral Resolution

A pragmatic definition depends upon the interpreters ability to visually

detect the seismic response of the target. An empirical threshold of 3

consecutive traces is often used as the minimum detectable response.

Minimum Detectable Size

Rv = Vertical ResolutionDiffractions Prior to Migration

angle)raymax

angleraymax

sin(BandwidthN

V3R

sin

R3R

intL

VL

3 traces * Rv / sin(max ray angle)

Seismic

R fl ti Exercise


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Exercise

Calculate the size of a feature that is

detectable under the following circumstances: Trace spacing = 25m

Interval velocity Vint = 3000 m/s

Dominant frequency = 40 hz

Maximum ray angle = 30 degrees

angle)raymaxsin(

R3R

BandwidthN

VR

VL

intV

Seismic

Reflection Wedge Model and Tuning


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Wedge Model and Tuning

Horizontal Distance (x)

Depth(Z)

Seismic

Reflection Wedge Model and Tuning


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Tuning alignment at:

bed thickness = /4

wavelet time delay = 1/(2*fdom)

Bed thickness as a % of dominant wavelength

Wedge Model and Tuning

Seismic

Reflection Tuning Amplitude Behavior


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Tuning Amplitude Behavior

AMP

Bed Thickness

1.0

Seismic

Reflection Spherical Divergence and Geometric


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p g

Spreading

Spherical Geometric

Divergence Spreading

CONSTANT

Seismic

ReflectionDecrease in Amplitude and


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Frequency with Time

Amplitude is equal to 100

Amplitude is equal to 10-6

Time

High frequency signal 0.5 sec

Low frequency signal 6.0 sec

Raw observed

seismic data

Seismic

Reflection Changes During Propagation


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Changes During Propagation

Decay in amplitude:

divergence due to geometric spreading - v2t

Loss of high frequencies due to earth's

attenuation - Q effect

Seismic

ReflectionGeometric Spreading Correction


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Spherical Divergence:

Constant Velocity = Vc

Ar= A0(r0/r) = A0(VcT0/VcTr)= A0(T0/Tr)

A0

r2 Ar2

r1 Ar1

Source Source

0

2

0

2

000

t

t

V

)t(VS

SSpreadingGeometric

TV

TVAA

V(t)timeand

depthwithincreasesVelocity

:SpreadingGeometric

gs

gs

rrr

Seismic

Reflection Amplitude Recovery


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p y

Seismic

Reflection Absorption and Scattering


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p g

Rock Fragments

Seismic

Reflection High Frequency Attenuation


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A shot record after

correction for geometric

spreading loss is shown

at left

The far left record is not

filtered but narrow passband filters were applied

to the next four

The amplitude is seen to

decay with both time and

frequency

Seismic

Reflection Inelastic Attenuation


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(Absorption and Scattering)

A(x) = A0e-ax

where A(x) = amplitude as a function of distance

A0 = reference amplitude

x = seismic path length

e = base of natural logarithms = 2.718...a = attenuation constant

= p/Q pf/QV

where Q = Quality Factor, = wavelength,

f = frequency, and V = velocity


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Reflection Factors That Affect Seismic Amplitudes


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Superimposed

Noise

Geophone Sensitivity

and Coupling

Instrument

Balance

SourceStrength

and

coupling

Geometrical

Spreading

Reflection

CoefficientVariation of Reflection

Coefficient with angle

of Incidence

Interference of

Different Events

Interbed Multiples

in Thin Beds

Absorption

ArrayDirectivity

Scattering

Reflector Curvatureand Rugosity

Seismic

Reflection Summary


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Properties of seismic waveforms and traces , f, velocity

Vertical resolution Zero phase wavelet

Resolution limits

Tuning Lateral resolution

Fresnel zones

Detectable object size

Amplitude effects Geometric spreading

Absorption

Seismic

Reflection


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Answer

40 ms

m

Hz

15225

3800

Frequency

VelocityWavelength

25040.0

1

Period

1Frequency

Seismic

Reflection Answer


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Shallow rocks: V=2000 m/s, f=50 Hz;

Deep rocks: V=6000 m/s, f=25 Hz.

m4050

2000

m24025

6000

Seismic

ReflectionVertical Resolution Exercise

Answers


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Answers

A shallow feature with velocity of 2000 m/s and bandwidth of 50 Hz can

be resolved if it is as thin as_______meters.

A deep feature with 5000 m/s velocity and bandwidth of 20 Hz can be

resolved if it is as thin as _________meters.

The thickness of a deep feature must be__________(greater, less) than

that of a shallow feature in order to be resolvable.

m3.13503

2000

BandwidthN

VR intv

m3.83203

5000

BandwidthN

VR intv

Greater

Seismic

Reflection Answer


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m150)30sin(

253

sin(

R3

m25403

3000

v

angle)raymaxRresolutionlateral

Rresolutionvertical

L

v

Assume N = 3 for normal data

Minimum

Number

of Traces

(empirical constant)

Vertical

Resolution

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Module 03 Seismic Reflection