1. Seismic reflection Ali K. Abdel-Fattah Geology Dept.,
Collage of science
King Saud University

2. 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

3. 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 studies
km’s: Oil exploration
10’s km: Crustal structure

4. 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

5. 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

6. Zoeppritz’s equations
R = & T = = 0.85
Time = 2 x 600 / = 0.29s

7. Zoeppritz’s equations

8. 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

9. 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;

10. 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

11. Moveout

12. 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

13. Moveout
The depth is then determined by

14. 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;

15. 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:

16. 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 h

17. 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

18. 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

19. 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

20. 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.

21. Common Mid-Point Gathers