Critical and head waves - critical angle i_c intersects and travels at 90^o. If they are more oblique they are reflected.

so: sini_c/V₁ = sin90^o/V₂

==> sini_c = V₁/V₂(sin90^o) = V₁/V₂ ==> q_c = sin^-1(V₁/ V₂)

Huygen's principle: each point on a wave front acts as a new source for waves.

Diffraction - bending of waves into shadows. Radial scattering of incident seismic energy.

• Edges of faulted layers
• Small isolated object
  e.g., boulder in a homogeneous layer

Fermat's Principle - a ray that reaches a particular point does so in a minimum time.

Head Waves:
sini_head = V₁/V₂ = sini_c

So head waves are the same as the critical refraction. The refracted rays are than the measurements of the time to receivers for head waves.

Travel time diagram

• head wave
• direct wave - travels just below the interface
• reflected waves

The direct wave is measured by 1/V₁
The refracted wave is measured by 1/V₂

The refracted wave starts at the criticak distance. This is where the reflection and refraction coincide.

=>

Reflected ray: 2h_i/V₁ - never first arrivals

First arrivals for near surface distances are direct rays whereas beyond a certain distance (the crossover distance) are the fastest.

Source - shot point

Locating the first arrival is called picking

The calculation between the picks and distance to source will yield velocities

To calculate the depth of an interface can use:

=>

For Muiltiple Layers:

This continues for each interface.

Dipping Interfaces:

• There is no way by looking at the ray that it is coming off of a dipping layer. So velocities calculated from these interfaces are apparent velocities.
• Reversed lines: this becomes very important. By reversing the line the travel time curve shows the dipping interface.
• If the interface has a small dip <5^o than the approximation is calculated: 1/V₂ ~= 1/2(slope_2f + slope_2r)
• The interfaces are calculated differently as well:
  

  

Flat Layers vs. Dipping Layers

1. The slope of the refraction line is less steep up dip, steeper down dip
2. The intercept is less at the up-dip than down-dip end
3. The slopes for direct rays (first sections on the travel time plot) are unchanged

The true dip

• Shooting along strike gives is a parrallel view. The structure appears horizontal.
• Obliquely the dip will be too low
• True dip can be obtained by using two line perpendicular to eachother
  
  
  where q is the angle between the dip direction and the seismic line from a

Seismic Velocity

• Generally velocity increases with depth
• The best measurement is in boreholes
• Weathering of rocks will lower the velocity of rocks

Hidden Layers

• Thin layer of strata
• Low Velocity Layer (LVL)

A seismic interface is not necessarily a geologic boundary. Some rocks may be to similar in type. So velocity would not seperate these interfaces out.

Survey

• Various scales
• Need:
  • Source
  • line of receivers
  • Timing
• Hammer seismics
  • strike a plate on the ground with a hammer, a switch closes, and the recording unit starts.
  • Distance of profile is dependent on:
    • the system
    • size of the hammer
    • rocks
    • noise - to reduce noise you can bury the cables and/or lay the cable flat
  • Can stack data by hitting the hammer several times in the same location
  • typically goes ~ 100m distance for such profiles
  • shallow surveys rule of thumb:
    10x the depth to interface in 100 m line = recording depth of 10 m
• Explosion seismics
  • want energy to go down not up, so bury the charges
  • drill holes are expensive, the best holes are below the water table for better coupling. can try to take advantage of a water body as well. Shooting in water is cheaper as well.
  • this type of survey is just a hammer survey on steriods
• Land surveying in general
  Have to think about station spacing. Two far apart and you may miss varying layers.
• Marine seismics
  • use explosives, but most of the time airguns
  • receivers are called hydrophones, measure the pressure changes
  • shooting and receiving take place concurrently so several lines are acquired. Boat time is very expensive.
  • large explosives may be used for deep surveys
  • Can have 2 ships out for reversals
  • Sonobouys may be left out to record
  • OBS sit at the bottom like land surveying. can get 3-component data this way.

Undulating interfaces delay times

• Some surfaces may undulate
  • topography
  • basin/bedrock contacts
  • moho
• Delay times:
  
• The deplay time is easiest calculated at the receiver:
  
  
  can get t_f,t_r, and t_total from the travel time plot.
• The depth can be deduced:
  
  Have to find V₁ and V₂ than you can determine the intercept time.

Plus-Minus Method

• plot 2 additional lines on the travel time curve t_f + t_r
  t_f - t_r
• slope is 2/V₂ for t_f - t_r; so can get V₂
• calculate V₁ from the direct arrivals
• So t_total for each receiver is subtracted from t_f + t_r and then halfed (equation 6.11)
• then use eq. 6.12 to get depth of interface
• only used for part of the the profiles, has to be long, typically only used for the first interface, not so good is the dip >10^o

Ray tracing and synthetics

• have previously described inverse methods for interpretating refraction data
• forward modelling or ray tracing
  • Using Snell's law
  • can vary velocities
  • point to fit the observed and calculated arrvials
• Can calculate amplitude
  comparing synthetic with original data
• Can detect faults if the travel times are offset

Fan shooting - simple tomography

• shooting in a fan of receivers
• increases coverage area

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