1
GEOP 315
Fall 2000
Midterm Exam
Exam time: 2 hours 15/11/2000
Student Name: Student ID#:
Instructions:
· This is a closed book & notes exam.
· Answer all the questions.
· Use figures and equations whenever appropriate.
· Define all your symbols.
Question 1 [30 points]:
Define the following briefly [5 points each]:
(a) Hooke’s law.
(b) Huygen’s principle.
(c) NMO.
(d) DMO.
(e) Porosity.
(f) Stacking velocity.
Question 2 [15 points]:
Are the following statements true (T) or false (F) [3 points each]?
(a) sxz is a strain that is caused by a force parallel to the x-axis acting upon a surface perpendicular to the z-axis.
(b) The P-wave velocity (a) in a fluid is given by: a = (l/r)1/2; where l and r are the Lame’s constant and density of the fluid.
(c) T0 is defined as the minimum time in the T-X curve for any layer.
(d) When fitting a hyperbola to the T-X curve of multiple layers, the fit is only good at Z/X<1, where Z is the depth and X is the offset.
(e) The most commonly used method for determining velocity in seismic exploration is the best-fit method.
Question 3 [30 points]:
(a) Verify that the following is a solution of the wave equation: A(x,t)=(x+V t)2, where x, V, and t are the offset, velocity, and time respectively [10 points].
(b) The velocity along the north-south direction was measured in an area and was found to be 3500 m/s. When the velocity was measured along the east-west direction, it was found to be 3000 m/s. Compute the velocity anisotropy (g). What is the most probable cause of this anisotropy? What is the direction of the symmetry axis? [10 points]
(c) Use the time-average equation to compute the porosity in a water-saturated limestone with a rock velocity (Vr) of 4.0 km/s [10 points].
Question 4 [25 points]:
Given the attached velocity model, compute the following:
(a) The interval zero-offset traveltime Dti of each reflector [5 points].
(b) The zero-offset traveltime to each reflector ti [3 points].
(c) The RMS velocity VRMS to each reflector [5 points].
(d) Compute the depth to each reflector using the RMS velocities and zero-offset traveltimes [5 points].
(e) Compare the depths you computed in (e) with the real depths by computing the error in depth to each reflector [5 points].
(f) Is it justified, in this case, to use the RMS velocities and zero-offset traveltimes to compute the depths [2 points]?
Layer / Velocity (m/s) / Thickness (m) / Depth (m)1 / 2000 / 200 / 200
2 / 3500 / 300 / 500
3 / 5000 / 500 / 1000