Moment Tensor Inversion in Strongly Heterogeneous Media

at Pyhasalmi Ore Mine, Finland

Václav Vavryčuk (Academy of Sciences of the CR)

Daniela Kühn (NORSAR)

Overview

• Introductiono Pyhäsalmi ore mine, Finlando P-wave polarity pattern

• Waveform modellingo 2-D modellingo 3-D modelling

• Homogeneous vs heterogeneous modelo P-wave polaritieso focal mechanisms

• Amplitude vs waveform inversiono selected datao comparison of resultso waveform fit

• Summary

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

• microseismic monitoring: since January 2003 safety of the underground personnel optimisation of mining process

• network: 12 1-C geophones

+ 6 3-C geophones (ISS)

3-D geometry sampling rate: < 3000 Hz

• events: 1500 events /months (including blasting) -2 < Mw < 1.5

Pyhäsalmi ore mine, Finland

owned by Inmet Mining Co.

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

- Down+Up

Earthquake source mechanisms

Focal solution:• shear fracture

Moment tensor:• + volume change

Full moment tensor

mathematical description:• pure double-couple

mathematical description:• nine force couples

isotropic

deviatoric

+

best double couple

CLVD+

Complex polarity pattern of P-wave first onset

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Waveform modelling

620 m

• E3D: viscoelastic 3-D FD code (Larsen and Grieger, 1998)• strong interaction with mining cavities: reflection,

scattering, conversion

Waveform modelling: 2D

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Waveform modelling: 3D

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

- complex waveforms

- strong coda

- complex secondary arrivals

- scattering effects stronger on amplitudes than travel times, since size of heterogeneities (cavities, access tunnels) same order or smaller than wavelengths

- arrival times computed by Eikonal solver still fit (wavefronts heal quickly after passing a cavitiy)

observed seismograms

Waveform modellingsynthetic seismograms

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Homogeneous & heterogeneous models

Geophone network (artificial)

.sourcelocation

source mechanisms

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Comparison 1-D/3-D

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Observed amplitudes

Retrieved source mechanism

Synthetic source mechanism

Moment tensor inversionfor a homogeneous model

ISO = 23 %DC = 37 %CLVD = 40 %

ISO = 0 %DC = 100 %CLVD = 0 %

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Moment tensor inversion: amplitudes versus waveforms

txgtmtxu kinnki ,,*,

Representation theorem:

xGMxU kinnki

,

Moment tensor inversion:

UGM g

point source

Amplitude inversion

tftstd *

Space and time factorization

tdxUtxu ii

,

tfxGtxg kinkin

,,,

tsMtm nknk

GMU matrix notation

generalized linear inversion

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

first maximum amplitude amplitude of the direct wave

Amplitude picking I

direct wave scattered wave

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

first maximum amplitude is not always the amplitude of the direct wave

Amplitude picking II

?

direct wave

waveform complexity(head wave?)

scattered waveIntroduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Representation theorem:

,,, xGmxu kinnki

mG ,, xxu

point source

frequency domain

Waveform inversion

in principle, the same inversion algorithm as for the amplitude inversion, but run repeatedly for many frequencies

time domain

Moment tensor inversion:

matrix notation

txGtmtxu kinnki ,,*,

,, xxg uGm generalized linear

inversion

tsMtm nknk

Time factorization:time-independent moment tensor

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Amplitude inversion:

• homogeneous model of the medium

• Green’s functions calculated using ray theory

• inversion of P-wave amplitudes (20-30 amplitudes)

• frequencies: 250-500 Hz

Waveform inversion:

• 3-D heterogeneous model of the medium

• Green’s functions calculated using the FD code

• inversion of full waveforms (15-20 waveforms)

• frequencies: 50-150 Hz

Amplitude vs. waveform inversion

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

5

17

12

26

Events near cavity: no. 5 no. 17

Events near ore body/host rock transition: no. 12 no. 26

Selected events

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

ch 22

ch 21

ch 15

ch 14 ch 8

ch 7ch 3

ch 2 ch 30

Complex waveforms, strong reflections, difficulty to identify the S wave (in some cases)

Event 12: data

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

amplitude inversion P-wave inversion full wave inversionevent no.

5

12

17

26

ORE

BODY

CAVITY

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

amplitude inversion P-wave inversionevent no.

ORE

BODY

CAVITY

5

12

17

26

full wave inversion

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

amplitude inversion P-wave inversionevent no.

ORE

BODY

CAVITY

5

12

17

26

full wave inversion

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

first rupture second rupture

strike = 105ºdip = 91ºrake = -75ºDC = 38%CLVD = -14%ISO = -48%

strike =90ºdip = 87ºrake = -121ºDC = 24%CLVD = -42%ISO = -34%

Event 17: two rupturesP-wave inversion:

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Event 17: waveform fit

GOOD FIT!ch 7

ch 12

ch 20 ch 21 ch 22

ch 30

ch 11

ch 29ch 28

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Event 17: waveform fitAmplitude misfit

ch 5ch 4ch 3

ch 10ch 8 ch 9

ch 16ch 15

ch 24

ch 14

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Event 17: waveform fit

Phase misfitch 2 ch 13 ch 23

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

structural model in mines usually is very complex

large and abrupt changes in velocity at cavities

the model varies in time

Summary I

earthquake source is complex (single forces, non-DC components, complex source history)

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

inversion in a homogeneous model may lead to:

• incorrect mechanism

• spurious non-DC

Summary II

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

radiated wave field is complex (reflected, converted, scattered waves, head waves)

Amplitude inversion:• simple approach

• limited applicability (simple Green’s functions are not adequate)

• no control on frequency bands

• amplitudes can be wrongly interpreted

Full waveform inversion:• complex Green’s functions can be calculated by 3-D FD codes

• accurate model needed!

• sensitive to time shifts due to mislocation or due to inaccurate model

• frequency band of inverted waves can be easily controlled

• inversion from P-wave only seems to be more reliable than from the whole seismogram (due to multiple scattering)

• promising but computationally demanding and laborious

Summary III

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary

Thank you!

Complexity of velocity model

Introduction

Waveform modelling

1D/3Dmodels

Moment tensor

inversion

Summary