Doctoral training, Solid Earth - Part 3: Array Seismology ...and Earth Structure. With increasing period, surface waves become sensitive to deeper velocity structure. (Similar in magneto-tellurics)

Seismology

Doctoral training on internal Earth

Part 3: Array Seismology,

Resolution issues

Christine Thomas

Barcelonnette, October 19, 20161

Array Seismology


Seismic Arrays


GERESS

Rost and Thomas, 2002

Seismic Arrays


Seismic Arrays



Seismic Arrays


Backazimuth and slowness


often: S = u

Thomas, 2008

ray parameter p and horizontal slowness u:

uRv

iR

v

irp 0

0

00 sinsin

Backazimuth and slowness


at source: azimuth measured

from north to gcp

at receiver: backazimuth

(baz) measured from N to

gcp.

slowness related to angle of

incidence at array


Horizontal slowness


appapp

yxvv

uuucos

,sin

),(

horizontal slowness

angle of incidence

apparent velocity


Beamforming


Delay and sum technique

hori

N

i

i

N

i

i urtnN

tstxN

tb

11

1)()(~1

)(

Advantages

•phase with appropriate slowness amplified

•suppression of noise

noise suppression dependent of number of stations

Disadvantages

•works only for discrete values of u and baz

•waveforms must be coherent!

Beamforming


Vespagram


vespa=slant stack

beam trace for fixed azimuth:

N

i

uiiu ttxN

tv1

, )(1

)(

Advantages:

•only either u or baz needs to be known

•noise reduction

Disadvantages:

•structure influences results

•coherency required

•theoretical baz must be known correctly

•resolution not great for small arrays

Vespagram


vespagram

slowness or backazimuth versus time

slownesses

Vespagram


Rost and Thomas 02

theoretical backazimuth (or

slowness) needs to be

accurate.

otherwise changes in

slowness (or backazimuth)

due to interdependence of

slowness and backazimuth

misleading slowness

values or disappearing of

signal

correct baz

4th root stacking (vespagram)


Nu

NuN

NuNu

i

i

NM

i

iuiNu

v

vvv

tx

txttx

Mv

,'

,'

,'

,

/1

1

,,'

)(

)()(

1

Advantages

•incoherent noise suppressed efficiently

•coherent phases amplified

•slowness enhanced

Disadvantages

•waveform distortion (non-linear technique)

•useless for waveform studies

4th root process


traces4th root traces

linear stack4th root stack

4th root


linear stack:

waveforms ok, other-

non-coherent phases

are also visible,

slowness resolution

poorer

4th root stack:

coherency more

important than

amplitude.

Stacked amplitude

smaller, waveforms

unusable, polarities ok.

4th root process

Barcelonnette, October 19, 201618Rost and Thomas 02

linear stack:

waveforms ok, other-

non-coherent phases

are also visible,

slowness resolution

poorer

4th root stack:

coherency more

important than

amplitude.

Stacked amplitude

smaller, waveforms

unusable, polarities ok.Rost and Thomas 02

Source stack


)()(1

),(1

jij

K

j

ji txtaK

tuS

with time delays urrjj

)( 0

Advantages

•cheap

•known structure

•identical response

Disadvantages:

•source parameter must be known

•multiples enhanced

if only one station available (with source array)

Double beam


Rost and Thomas 02

Combines source

and receiver

stacks (e.g.,

Krüger et al.,

1993)

Better resolution

same problems as

source-stacks and

receiver stacks

Krüger et al., 1995

Phase weighted stack


)()()( tietAtS

nN

j

tiN

i

ipwsje

Nts

Ntv

1

)(

1

1)(

1)(

Another method to improve resolution:

phase weighted stack

(Schimmel and Paulssen, 1997)

complex trace

instantaneous phase

Rost and Thomas 02

"slowaz" analysis


Simultaneous

measuring of

slowness and

backazimuth.

stacks over all

slowness and

backazimuth values

for a (small) time

window

Rost and Thomas 02

f-k (frequency wavenumber) analysis


Jahnke 99

Advantages: can be used to find baz and u

Disadvantages: only applicable to small time windows

assumes plane wave

simultaneous

measurement of

slowness and

backazimuth.

In frequency

domain.

uses wavenumber

uk

ckkkk zyx

222||

f-k (frequency wavenumber) analysis


deN

XdttbkkEN

i

kkri

oi

2

1

)(22 01

)()()(

shifted trace )()(~0uurtxtx iii

beam:

N

i

ii uurtxN

tb1

0 ))((1

)(

using Parceval’s theorem

and shift theorem

the beam energy can be written as

dBN

dttbbeamE

2

2 )(1

)()(

with:)(

10

1

)( 0 kkAeN

N

i

kkri i

the array response

function (ARF)

ARF (f-k analysis)


Array response function of

Yellowknife array, YKA, (left)

and Gräfengberg array GRF (bottom)

ARF also serves as measure of coherency

Rost and Thomas 02

Array methods


Thomas 2008

Array methods


Aligned seismogram

(distance dependent)

beam

vespa

F-k

Thomas 2008

Migration


•calculates delay times from point at depth.

•shifts traces back with these delay times

•stacks traces

•3D grids with appropriate spacing

Migration

Ampl. at b.p.Rost and Thomas, 2009

Migration


Advantages: no plane wave

approximation

project energy back to origin

good spatial resolution (steep rays)

good depth resolution (shallow

rays)

Disadvantages: velocities must be

known exactly

poor spatial resolution (shallow

rays, high frequencies)

poor depth resolution (steep rays)

Many other migration methods exist

(e.g. Hutko et al., 2004)

Thomas et al 1999

Resolution issues

30Barcelonnette, October 19, 2016

31

The Earth

After Strobach, 1991


32

Resolution issues/Fresnel zone

How much can a wave "see"? How accurate is the observation?

view from top

Fresnel volume

around a ray. For

reflection, the cut

through the FV is the

Fresnel zone.


33


e.g.: P-waves reflected at D”: 2 x 4 degrees (1Hz)

S-waves reflected at D”: 3.5 x 7 degrees (6 s)

PP

What does that mean? If we deal with a strictly layered (1D) Earth

our resolution is only as good as the size of the Fresnel zone!


34


The Fresnel zone can be

reduced:

One possible way is the use of

arrays - only what is common

for all rays for the array

contributes to the Fresnel

Zone

(also commonly used in

Exploration seismics!)


35

Resolution issues/ Map views of observations

We need suitable source receiver combinations to study different

structures. This is not always possible for all the regions of the Earth!


36

Banana-Doughnut

If dealing with

waves rather than

rays:

Sensitivity to wave

around position of

ray, no sensitivity

along the ray.

Information from

area around ray!

Not from the path

assumed for the ray.


37

Sensitivity kernels (surface waves)

Sensitivity kernels (surface

waves) show relationship

between dispersion velocities

and Earth Structure.

With increasing period,

surface waves become

sensitive to deeper velocity

structure.

(Similar in

magneto-tellurics)


38

Sensitivity kernels (surface waves)

Sensitivity

kernels differ

between

Rayleigh and

Love waves.

Need to calculate

kernels for best

resolution.


39

Places of reflection

Interpretation of

reflection point in

a 1D model.

(Mid-point

between source

and receiver)


40


But for a slanted

receiver, the mid

point is not

necessarily the

reflection point

(Snell's law

applies).

This is similar to

the migration

principle:


41


But for a slanted receiver, the mid

point is not necessarily the reflection

point (Snell's law applies).

This is similar to the migration

principle:

The reflector moves "uphill" and

becomes steeper.

A way to find true reflection is

migration of waves.

=Array seismology


42

Resolution issues/Array response function


43

When interpreting

stacks of seismic

data the array

response function

can produce

"spatial aliasing"

This leads to

spurious energy

that should not be

interpreted.

Resolution issues/Array response function


44

Resolution issues/tomography

REGULARIZATIONDamping parameter

Dat

a M

isfi

t

DampingRawlinson et al. [2010]

Regularisation:

How much can the

data misfit be

reduced without

increasing the run

time (for small

damping only

marginal changes to

misfit).

Usually point closest

to zero (in bend of L-

shaped curve) is

taken for best fit.


45

Resolution issues/tomographySources and receivers

Ray density

Number of paths in each cell

Sensitivity

Sensitivity of dt to the velocity in each cell

sampling of the region should be

uniform, but also sensitivity of rays to

structure should be taken into account


46

Resolution issues/tomographySources and receivers

15x15 25x25

35x35 45x45

Many crossing paths are needed to find

the true model (not always possible).

Resolution also depends on the

gridding (cells)


47

Resolution issues/tomography

Rawlinson et al, 2010

Rays are not straight lines

any more but may be

deviated in strikingly

heterogeneous media. This

leads to travel time

variations for the

theoretical travel times


48

Resolution issues/receiver function analysisDeconvolution

issues

Effects of

frequency.

Some

reflectors

may be

missed


49

Resolution issues/receiver function analysis

How do we find reflectors in this? How believable are reflectors?

Especially in poorly sampled regions?


What can we interpret?


Measuring amplitudes and polarities



52

travel times

amplitudes

polarities

waveforms

frequency content

t1 t2 t3

amplitude

frequencycontent

polarityandwaveform

traveltime



53

Amplitude

one of the most difficult measurements because

amplitude is affected by many things:

source effects

receiver effects

attenuation - intrinsic and scattering

energy partitioning

structure/topography

discontinuity versus gradient

.....


Amplitude - Topography

54

Snell's law

Ray parameter p = sin (i)/v

Reflected waves: angle is the

same as for incident wave.

Measured w.r.t vertical.



55

Snell's law

Ray parameter p = sin (i)/v

Reflected waves: angle is the

same as for incident wave.

Measured w.r.t vertical.

Focussing and defocussing

effects!

= amplitude variations!


56


Focussing and

defocussing effects

modelled with a

simple model:

strong effects in

amplitude and more

than one apparent

reflector visible in

places.

Misinterpretations

possible


57

Focussing and

defocussing effects

modelled with a

simple model:

strong effects in

amplitude and more

than one apparent

reflector visible in

places.

Misinterpretations

possible



58

Amplitude - Source effects

when interpreting

amplitudes and polarities:

Knowledge of the source

is important!

N

E

largest amplitude (downswing)

largest amplitude (upswing)


59

Amplitude - Stacking=averaging

sum sum

stacking a number of travel

will give an average

waveform.

This does not necessarily

describe the structure

correctly as reflections in

different places are added

(without correcting for the

pace of reflection).

changes in apparent

frequency possible

v v


60

Amplitude - Unknown mineralogy

Seismologists often work with standard Earth models (PREM, ak135...)

When interpreting depths, these are based on ak135/PREM etc values

of discontinuities. Often this means interpretations in the ol-wd-rg-

pv+mw system only

Cobden et al (2008)

showed that depending

on mineralogy, the

discontinuities change

(depth and velocity/

density increase).


61

Amplitude - discontinuity versus gradient

Sharp discontinuities reflect (or transmit) energy different from

gradient zones. Often calculations are done with sharp discontinuities

and then amplitudes are interpreted in terms of gradients.

Measuring gradients is difficult - frequency might help (but difficult)

vel

de

pth

vel

de

pth

vel

de

pth

vel

de

pth

these gradients will produce different seismic waveforms

but the interpretation will be non-unique!



62

travel time

travel times of seismic waves can be affected by:

structures (fast and slow velocities)

deviations from the assumed path

topography (for reflections off discontinuities)

attenuation

.....


Travel times - velocity variations

63

+-

t+

t-

t-t

t

travel time deviations due to

velocity variations.

and due to deviations from the

great circle path.


also: need to consider out-of-plane propagation!

(Fermat's principle)


64

polarities

polarities of seismic waves can be affected by:

source effects (different parts of radiation pattern)

energy partitioning (Zoeppritz equations) due to velocity and

density changes

.....


Polarities - energy partitioning

65

Energy partitioning

We have to consider

SV

P

SV

P

SH reflected

SH transmitted

and they depend on

velocities (P and S) and

density

reflected

transmitted


Polarities - Zoeppritz equations

66

Zoeppritz equations

wave from below


Polarities and Amplitudes

67

Zoeppritz equations - polarity and amplitude variations due to

changes in velocity and/or density are possible



68

travel times

amplitudes

polarities

waveforms

frequency content

t1 t2 t3

amplitude

frequency

content

polarity

and

waveformtravel

time


Documents

Doctoral training, Solid Earth - Part 3: Array Seismology ...and Earth Structure. With increasing period, surface waves become sensitive to deeper velocity structure. (Similar in magneto-tellurics)