Seismic reflection

Ali K. Abdel-Fattah

Geology Dept.,

Collage of science

King Saud University

• The seismic signal is reflected back to the surface at layer interfaces, and

• The signal is recorded at distances less than depth of investigation

• Sensitive to impedance contrasts

• Use near-normal incidence i.e. P-waves

Applications

• Detection of subsurface cavities

• Shallow stratigraphy

• Site surveys for offshore installations

• Hydrocarbon exploration

• Crustal structure and tectonics

Target scale:10’s m: Ground water, engineering and environmental studieskm’s: Oil exploration10’s km: Crustal structure

Reflection at normal incidence• Consider the figure• A P-wave with amplitude Ai reaches the

interface at normal incidence angle• Produces reflected P-wave in layer 1 and

transmitted P-wave in layer 2• The amplitude of the reflected and

transmitted waves can be calculated as a function of the incidence angle using Zoeppritz’s equations

• Reflection coefficient– is the ratio of the amplitudes of the reflected and

incident waves

• Transmission coefficient– Is the ratio of the amplitudes of the transmitted

and incident waves

Zoeppritz’s equations

• The equations show that the reflection and transmission coefficients depend on the difference in impedance (the product of velocity and density) between the two layers

• If Z1 = Z2, there is no reflection. All energy is transmitted into the second layer.

– This does not mean that ρ1=ρ2 and v1= v2 but ρ1v1= ρ2v2.

• R can have a value of +1 to -1.

– R will be negative when Z1 > Z2.

– A negative value means that there will be a phase change of 180° in the phase of the reflected wave (a peak becomes a trough).

– This is called a negative polarity reflection.

– Generally, R ±0.2 for the Earth with maximum values of ±0.5.

– Most energy is transmitted, not reflected

• T is always positive

– transmitted waves have the same phase as the incident wave

– T can be larger than 1

Zoeppritz’s equations

R = 0.15 & T = = 0.85Time = 2 x 600 / 4100 = 0.29s

Zoeppritz’s equations

Reflection time- distance plots

• The ray path in the figure tells us that

• We may re-arrange this to yield

• where to = 2h=v is the “zero-offset" time. Note that it is not the same as the intercept time for refracted wave

Reflection time- distance plots

• This hyperbolic equation is usually re-arranged in its approximate (parabolic) form:

• Since is less than 1, the square root can be expanded with the binomial expansion. Keeping only the first term in the expansion the following expression for the travel time is obtained:

• Equation (4.41) is known as the “Normal MoveOut" equation. From the NMO equation we can see that the moveout;

ovtx /

Moveout

• The Movout is a useful parameter for characterizing and interpreting reflection arrivals

• The Movout is measured as the difference in travel times to two offset distances

• The plot shows how to measure the moveout, Δt, for two small offsets

Moveout

Moveout

• Using the small offset travel time expression for x1 and x2 yields the

• The normal moveout (NMO), Δtn, is a special term used for the moveout when x1 is zero. The NMO for an offset x is then:

• With the value of the intercept time, to , the velocity is determined via

otv

xxt

2

21

22

2

mnoo tt

xv

2

Moveout

• The depth is then determined by

2ovt

h

Reflection times in multi-layered media

• In multi-layered media with horizontal interfaces, homogeneous layer, the NMO equation needs only a small modication

• The correct average is the root-mean-square velocity

– where to is the zero oset time at the bottom of the Nth layer and vi and ti are the velocities and two-way travel times in each ith layer

• The correct NMO equation can be shown to be;

The Dix equation

• The last equation predicts that the normal moveout for a given reflection depends only on the zero offset time “to” and the rms velocity down to the reflector

• Measuring the moveout for the nth reflector therefore amounts to measuring the value of vrmsn down to this reflector

• By measuring the values of vrms down to diefrent reflectors we may use the equation of root-mean-square velocity to extract the “interval velocity" of the interveaning layer:

Dip moveout

• If the interface is dipping, the up-dip and down-dip travel times are changed by an amount dependant on the dip angle θ

• The binomial expansion for the travel time for small offsets becomes:

• The dip moveout is defined as

22

222

2

sin41

sin44

oo

tv

xhxt

v

xhhxt

h

v

xttt xxd

sin2

Dip moveout

• t(x) is greater than t(-x) and the travel time curve is asymmetric about x = 0

• The minimum travel time does not occur at x = 0

• Also note that the reflection received at x = 0 did not originate beneath x = 0

h

Common Mid-Point Gathers

• There are two disadvantages to using only a shot gather for analysis:

– Reflections tend to have a low amplitude

• This means that noise in the seismic data can obscure reflections.

– Each reflection occurs at a different point on the interface

• The analysis of shot gathers assumes uniform horizontal layers. If there are significant lateral variations in structure, this will result in errors

Common Mid-Point Gathers

• This can be overcome by using multiple shot points and multiple receivers.

• From the total dataset, a set of rays are then chosen that have a common reflection point.

• This technique is called both common-mid point (CMP) or common depth point (CDP) profiling.

• The shot and receiver are located equal distances from the CMP.

• The reflection point is taken to be halfway in between the shot and the detector.

• In a dipping interface, this is an approximation, but does not introduce large errors

Common Mid-Point Gathers

• The collection of traces with the same reflection point is called a common mid-point gather (CMP gather) or common depth point (CDP) gather.

Common Mid-Point Gathers