sinusoidal

Elementary Theory V Elementary Theory V

y

Electromagnetic equations in an isotropic and homogeneous media

H w H iw H

e H H

E w E iw E

e E E

iwt iwt

G G

G G

G G

G G

με μσ

με μσ

2 2

0 2 2

0

) (

)

(

variation

Elementary Theory VII Elementary Theory VII

y

Attenuation of electromagnetic waves

2 2

i ωμσ ω με

∇

E

=

E E

∇²

H

=

iωμσ H

ω με²

H

x For a poor conductor (ε=10ε₀, μ=μ₀, and σ=10^-3S/m poor conductor)

x For a good conductor (ε=10ε₀, μ=μ₀, and σ=10³S/m good conductor)

i ωμσ ω με

∇

E

=

E

−

E

∇

H

=

iωμσ H

−ω με

H

11

0 F

10 9 10

ε= ε = × ⁻ m ₀ 1.3 10⁶H

μ μ= = × ⁻ m equation) (Laplace 0 ) 10 6 . 4 10 6 . 2

( ^{5 8}

2 = × − × ≈

∇ E i ^{− −} E

) 10 6 4 25

( ⁸

2E i × E

∇ ⁻

) equation (diffusion

25

) 10 6 . 4 25 (

2E iw E 만족

iE

E i

E μσ

=

∇

=

×

−

=

∇

y

Diffusion equation

A h h l d h l d

2 i

ωμσ μσ^∂t

∇ = =

∂

E E E ² i

ωμσ μσ^∂t

∇ = =

∂

H H H

x

Assume that the wave is polarized in the xy plane and propagates along the z axis

mz iwt

mz iwt mz

iwt y

mz iwt x

e wH t i

H

e m z H

H z

H y

H x

H H

e E t z H H

e E t z E E

+

+ +

+

∂ =

∂

∂ =

= ∂

∂ + ∂

∂ + ∂

∂

= ∂

∇

=

=

=

=

0

2 2 0

2 2 2 2 2 2 2 2

0 0

) , (

) , (

μσ μσ

az az wt i

az i iwt

e e H H

H z

e H H

a w i

i i m

i

w i t m

H H

−

− +

±

=

→

∞

→

=

+

= +

± + =

=

∂ =

= ∂

∇

) ( 0

) 1 ( 0

2

2 2

0

) 1 2 ( ) 1 ( 2

) 1 (

이므로 면

인데 이용하면 를

하므로 여야

μσ μσ μσ

Elementary Theory VIII Elementary Theory VIII

y

Attenuation of electromagnetic waves

• cos(ωt-az) indicates that waves are propagating as a sinusoid in

the z direction.

• e

^-azindicates that waves decay, or attenuate in the z direction.

• Skin Depth (δ) defined

as the depth at which wave amplitude has decayed to 1/e its original value.

f f

w z w

z a az e ^az e

ρ πμ πμ

ρ μ

ρ μσ

1 2

2 1 1

1

=

=

=

=

=

=

=

−

y

Skin depth

Principles of EM survey Principles of EM survey

◦ Electromagnetic methods use the response of the ground to the propagation of incident alternating electromagnetic waves which are made up of two orthogonal vector components, an electric intensity (E) p g p , y ( ) and a magnetic force (H) in a plane perpendicular to the direction of travel.

◦ For geophysical applications, frequencies of the primary alternating field are usually less than a few thousand hertz. The wavelength of the primary wave is of the order of 10-100 km while the typical source-receiver separation is much smaller (4 – 100 m). Æ The propagation of the primary wave and associated wave attenuation can be disregarded (Figure 10.8).

( g )

Principles of EM survey Principles of EM survey

Primary field

Primary field + secondary field

Primary field 에 의해

생긴 전기장(와전류)

Principles of EM survey Principles of EM survey

90 도 의 위상차

약간의 위상차 (전도체에 의해서)

(A)+(C) Primary field + Secondary field

Principles of EM survey Principles of EM survey

Conductor 에 의한 위상차 (전도도가 높을수록 커진다) R

의

P : Primary magnetic field

(A), (B)와의 위상차 이

상 성 분

R의 동상성분

y g

S : Secondary magnetic field R : Resultant magnetic field

Principles of EM survey Principles of EM survey

<전도도>

A > B > C

길이: field 의 세기를 나타냄

탄성파탐사 탄성파탐사

Seismic method

Introduction I Introduction I

y Seismic method (exploration seismology) is widely used in petroleum exploration, civil engineering, groundwater searches S i i th d hi h hi h l ti d t

y Seismic method: high accuracy, high resolution, and great penetration.Æ popular in petroleum exploration

y Exploration seismology is an offspring of earthquake seismology.

When an earthquake occurs, the earth is fractured and the rocks move Æ Such a rupture generates seismic waves

y The objective of seismic exploration is to deduce information about the rocks, especially about the attitudes of the beds, from the

b d i l ti d f i ti i lit d f

observed arrival times and from variations in amplitude, frequency, phase, and wave shape.

y Reflection, Refraction, Surface wave methods

Introduction II Introduction II

Basic Theory I Basic Theory I

y Stress

◦

The ratio of the force to area

◦

Stress can be resolved into two components, one at right-angles to the surface ( ) and one in the plane of the surface ( ).

◦

Stress at a point:

y Strain

◦

The stressed body undergoes strain

◦

The stressed body undergoes strain

◦

The strain is the amount of deformation expressed as the ratio of the change in length (or volume) to the original length (or volume).

Basic Theory II Basic Theory II

y Elasticity

◦

The size and shape of a solid body can be changed by applying

f h l f f h b d Th l f

forces to the external surface of the body. These external forces are opposed by internal forces that resist the changes in size and shape

◦

As a result, the body tends to return to its original condition when the external forces are removed.

◦

The property of resisting changes in size and shape and of returning to the original condition when the external forces are

d removed

Basic Theory III Basic Theory III

y Elasticity

◦

Stress and strain are linearly d d d h b d b h dependent and the body behaves elastically until the yield point (elastic limit or proportional limit) is reached.

◦ Below the yield point, on relaxation of stress, the body reverts to its pre-stressed shape and size.

◦ At stresses beyond the yield point At stresses beyond the yield point, the body behaves in a plastic or ductile manner and permanent damage results.

◦ If further stress is applied, the body is strained until it fractures

Basic Theory IV Basic Theory IV

y Elastic moduli

◦ The relationship between stress and strain for any material is defined by i l ti d li

various elastic moduli.

◦ Young’s modulus (영률) & Poisson’s ratio (포아송의 비)

Basic Theory V Basic Theory V

y Elastic moduli

◦ Bulk modulus (체적탄성률)

Basic Theory VI Basic Theory VI

y Elastic moduli

◦ Shear (rigidity) modulus (a Lamé constant): 전단계수, 강성률

◦ Axial modulus

Seismic waves I Seismic waves I

y Types of seismic waves

◦

Seismic waves travel away from any seismic source at speeds d d b l d l d h d f h d determined by elastic moduli and the densities of the media through which they pass

◦

There are two main types of seismic waves: body waves and surface waves

◦

Body waves: waves that pass through the bulk of a medium are known as body waves

◦

Surface waves: waves confined to the interfaces between media with contrasting elastic properties, particularly the ground surface, are called surface waves

◦

Guided waves: are encountered in some applications, which are confined to particular thin bands sandwiched between layers with higher seismic velocities by total internal reflection.

Seismic waves II Seismic waves II

y Body waves

◦ In unbounded homogeneous isotropic media, body waves only exist.

◦ Two types of body waves can travel through an elastic medium.

◦ P-wave

x Material particles oscillate about fixed points in the direction of wave propagation by compressional and dilatational strain

x Primary, longitudinal, dilatational, irrotational, or compressional waves (for example, sound waves)

x Velocity

Seismic waves III Seismic waves III

y Body waves

◦ S-wave

x Particle motion is at right-angles to the direction of wave propagatio n and occurs by pure shear strain

x Secondary, transverse, rotational, or shear waves

x When particle motion is confined to one plane only, the S-wave is sai d to plane-polarized (SH and SV waves)

x Velocity

Seismic waves IV Seismic waves IV

y Surface waves

◦ In an infinite homogeneous isotropic medium, only P and S wave exist.

H h th di d t t d t i fi it i ll di ti However, when the medium does not extend to infinity in all directions, other types of waves can be generated. They are called surface waves.

◦ The waves do not penetrate deep into subsurface media. They are confi ned to the interfaces.

◦ Large amplitude and low frequency waves

◦ Rayleigh, Love, Stoneley waves

Seismic waves V Seismic waves V

y Surface waves

◦ Rayleigh waves

x The combination of P and SV waves.

x Travel along the free surface of the Earth with amplitudes that decrea se exponentially with depth

x Particle motion is in a retrograde elliptical sense in a vertical plane with respect to the surface

Seismic waves VI Seismic waves VI

y Surface waves

◦ Rayleigh waves

x Velocity depends upon the elastic constants near the surface and is always less than the S wave velocity β. When the Poisson’s ratio is 0.25, the Rayleigh wave velocity is 0.92β

x Because the elastic constants change with depth, the velocity of Rayleigh waves varies with wavelength. Æ A variation of velocity with wavelength (or frequency) is called dispersion.

x Rayleigh waves are dispersive in layered media, whereas they are not dispersive in semi-infinite homogeneous media.

x Groundroll which can mask reflections on a seismic record x Assessment of stability of structure such as dam and road (Spectral

analysis of the surface waves: SASW). The SASW employs the dispersive features of Rayleigh waves.

Seismic waves VII Seismic waves VII

y Surface waves

◦ Love waves

x Love waves occur only where a medium with a low S-wave velocity overlies a half space with a higher S-wave velocity

x Velocities are intermediate between the S-wave velocity at the surface and that in deeper layers.

x Particle motion is at right-angles to the direction of wave propagation but parallel to the surface

x These are polarized shear waves

Seismic waves VIII Seismic waves VIII

y Surface waves

◦

Stoneley waves

x

Similar to Rayleigh waves

x

Propagate along the interfaces between fluid and solid media

◦

Surface waves have the characteristic that their waveform changes as they travel because different frequency components propagate at different rates, a phenomenon known as wave dispersionp

◦

The dispersion patterns are indicative of the velocity structure through which the waves travel, and thus surface waves generated by earthquakes can be used in the study of the lithosphere and asthenosphere

Seismic wave & Fourier series

Seismic wave & Fourier series

Velocity & Density Velocity & Density

음파의

음파의 전파 전파

음파의

음파의 전파 전파

1.

2.

1.

3.

4.

음파의

음파의 전파 전파

1.

2.

3.

탄성파의

탄성파의 전파 전파

탄성파의

탄성파의 전파 전파

Vp = 2000 m/s Vs=1000 m/s 2 km

0.3 km

Vp=4000 m/s Vs=2500 m/s

0.7 km

Direct waves

P -Reflection

PS-Reflection

SS-Reflection Rayleigh

Seismic exploration Seismic exploration

y Refraction method

◦ 선두파(임계굴절파 이용)

◦ 비교적 천부구조에 대한 정보 제공

◦ 지반조사 등에 활용

◦ 반사법 탐사자료 해석시 보조자료로 이용

y Reflection method

◦ 반사파

◦ 심부구조에 대한 정보 제공

◦ 석유, 가스, 메탄가스하이드레이트 탐사석유, 가 , 메탄가 하이 레이 탐사

◦ 지반조사에도 활용

y Surface method

◦ 표면파의 분산 특성 이용

◦ 지반 조사 및 구조물의 안정성 평가에 활용

육상송신원 육상송신원

종류 원리 비고

중력추 낙하에너지 해머, 중력추

스윕 연속 주파수 바이브레이터

화약 폭발에너지 폭약,샷파이프

전기뇌관

Source (Wacker Rammer)

육상수진기 육상수진기

종류 원리 비고

지오폰 자 석 과

코일

10-100Hz,

지오폰 코일 3성분 측정가능

하 이 드 로폰

압전 소자

P파만 측정 물이 필요

해양탄성파탐사

해양탄성파탐사 모식도 모식도

해상

해상 송신원 송신원 및 및 수진기 수진기

굴절법

굴절법 탐사 탐사 모식도 모식도

기록장치 케이블 음원

1층 : 직접파

굴절파 반사파

2층 :

9 굴절법 탐사에서는 타겟 깊이의3-5배 정도로 수진기를 벌려줘야 함

9 따라서 반사법 탐사에 비해 수진기 간격이 넓음

9 파가 먼거리를 전파해 가므로 반사법 탐사보다 저주파의 송신원 및 저주파 대역의 수진기 필요

수평층

수평층 구조 구조

t

i

V T = X +

2

수평층

수평층 굴절파 굴절파 주시 주시

굴절파

굴절파 주시 주시 예시 예시

굴절파

굴절파 주시곡선의 주시곡선의 예시 예시

호주 동부 붕괴된 돌리네에서 얻은 주시곡선

주시곡선의

주시곡선의 이상 이상

y 초동의 부정확한 발췌로 인한

초동 돌출이상

y 천부의 속도 또는 두께의 변

화

y 지표 지형의 변화

y 지중에 다른 속도층 존재

y 국부적인 불규칙한 지형구조

y 굴절면 속도의 수평적인 변화

반사파

반사파 탐사 탐사 모식도 모식도

기록장치 케이블 음원

1층 : 2층 : 거리

직접파

굴절파

투과파 반사파

시간

반사파

반사파 주시 주시

y 수평2층구조 반사파 주시

반사법탐사자료

반사법탐사자료 예시 예시

반사계수 반사계수

y 수직입사에 대한 반사계수

2 2

v

1 1

v R ρ

_{2 2}

− ρ

_{1 1}

2 2 1 1

R ⁼ ρ v + ρ v

1/2 1

출력 반사계수 시계열

에너지원 파형

1/2

1

*

현장자료 현장자료

깊이

1/2

1/2 자료처리자료처리 ^시간

시간 시간

-1/2 1/2

자료처리

자료처리 모식도 모식도

자료처리

자료처리 모식도 모식도

탄성파탐사

자료변환 속도분석

자료편집

Geometry설정

CDP gather

속도분석

NMO보정

중합

디컨벌루션 CDP gather

뮤팅

디컨벌루션

구조보정

자료해석

자료처리

자료처리 FF--K filter K filter

자료처리

자료처리 FF--K filter K filter

자료처리

자료처리 CDP gather CDP gather

y CMP gather

◦ 지하의 각 점이 여러 차례

샘플링 되도록 하여 자료 샘플링 되도록 하여 자료 처리 과정에서 일정한 보 정작업과 이들을 합침으 로써 신호성분은 강화시 키고 잡음은 약화시켜 궁 극적으로 양호한 S/N을 얻는 기법

F ld수 C

y Fold수 & Coverage

자료처리

자료처리 NMO NMO보정 보정

y NMO보정

Constant

Constant--velocity velocity moveout moveout correction correction

Constant

Constant--velocity velocity moveout moveout correction correction

Constant

Constant--velocity stacks of 24 CMP velocity stacks of 24 CMP gathers

gathers

자료처리

자료처리 속도분석 속도분석

속도분석

속도분석 및 및 NMO NMO보정 보정 예시 예시

속도분석

속도분석 및 및 NMO NMO보정 보정 예시 예시

NMO stretches

NMO stretches

Dix equation Dix equation

Migration

Migration

Migration Migration

탄성파

탄성파 자료해석 자료해석

y 지질학적 고려사항

◦ 근원암(Source rock): 탄화수소 생성, 흑색셰일이나 세립질의 흑색 석회암

◦ 저류암(Reservoir rock): 탄화수소가 잘 이동할 수 있도록 충분한 공

극과 투수성을 가진 암석. 공극률이 높은 사암, 파쇄나 공동이 잘 발

달되어 있는 석회암이나 돌로마이트 등의 탄산염암

◦ 트랩(Trap): 구조적 트랩 (습곡, 단층, 부정함, 암염돔)과 층서적 트랩 (퇴적환경의 영향)

◦ 덮개암(caprock): 집적된 탄화수소가 빠져 나갈 수 없도록 불투수성

암석이 덮고 있어야 함. 셰일이나 증발잔류암

y 석유와 가스가 함께 존재하는 경우

◦ 비중에 의하여 가스가 위쪽, 석유와 지층수가 하부에 존재

퇴적구조 퇴적구조

y 탄화수소 트랩을 형

성하는 퇴적구조

문서에서 지구물리학 지구물리학 (페이지 47-82)