Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2025 / Paper 3 / 1 / b

For incidence from cap rock (1) into reservoir (2), use the conventional normal-incidence stress-amplitude reflection coefficient

R_{j} = \frac{Z _{j 2} - Z _{j 1}}{Z _{j 2} + Z _{j 1}}, Z_{p j} = ρ_{j} V_{p j}, Z_{s j} = ρ_{j} V_{s j} .

(1)

Here acoustic impedance is the P wave impedance;

ρ V_{s}

is the corresponding shear-wave impedance. Positive

R

preserves the chosen stress-wave seismic reflection polarity; negative

R

reverses it. These are amplitude coefficients, not reflected energy fractions. At normal incidence in the ideal isotropic model there is no P-to-S mode conversion. The cap-rock impedances are

Z_{p 1} = 2.25 \times 1 0^{6}, Z_{s 1} = 0.900 \times 1 0^{6} kg m^{- 2} s^{- 1} .

(2)

The following are approximate readings of the supplied Figure 1 PNG, checked against the matching source PDF, rather than exact tabulated parameters. At zero gas, use

ρ ≃ 1.75 g c m^{- 3}

V_{p} ≃ 1.75 km s^{- 1}

, and

V_{s} ≃ 0.60 km s^{- 1}

; at full gas use

ρ ≃ 1.25 g c m^{- 3}

V_{p} ≃ 1.15 km s^{- 1}

, and

V_{s} ≃ 0.65 km s^{- 1}

. The left-hand

V_{p}

endpoint is crowded against the axis and the density curve; readings differing by roughly

0.05

in the plotted units are reasonable. The resulting coefficients deserve about two significant figures, not the apparent precision of the intermediate arithmetic.

Both end members change seismic reflection polarity, but the P wave change is much larger: approximately

+ 0.15

- 0.22

, compared with

+ 0.08

- 0.05

for S waves. Thus a calibrated P wave survey is better for distinguishing these two saturation end members and should give a stronger reflection from the fully gas-filled reservoir. A negative P wave reflection relative to the water-filled prediction is a useful gas indicator in this stipulated model. In a real seismic reflection survey, lithology, porosity, effective pressure, and seismic wavelet phase also affect the response, so a bright or reversed reflection alone does not prove the presence of gas.

Table of contents
- i b
  - Solution i
- ii b
  - Solution ii

i

 0  0

Solution

 0  0

For the fully water-filled reservoir, the approximate densities and wave speeds give

Z_{p 2} ≃ 3.06 \times 1 0^{6}, Z_{s 2} ≃ 1.05 \times 1 0^{6} kg m^{- 2} s^{- 1},

(1)

and hence

R_{p} ≃ \frac{3.0625 - 2.25}{3.0625 + 2.25} ≃ + 0.15, R_{s} ≃ \frac{1.05 - 0.900}{1.05 + 0.900} ≃ + 0.08.

(2)

Both are positive: the reservoir has larger P wave and shear-wave impedances than the cap rock, and neither reflection reverses the chosen stress-wave seismic reflection polarity.

ii

 0  0

Solution

 0  0

For the fully gas-filled reservoir,

Z_{p 2} ≃ 1.44 \times 1 0^{6}, Z_{s 2} ≃ 0.81 \times 1 0^{6} kg m^{- 2} s^{- 1},

(1)

R_{p} ≃ \frac{1.4375 - 2.25}{1.4375 + 2.25} ≃ - 0.22, R_{s} ≃ \frac{0.8125 - 0.900}{0.8125 + 0.900} ≃ - 0.05.

(2)

Both impedances are now smaller than those of the cap rock. Both reflections reverse seismic reflection polarity, with a substantially larger amplitude for the P wave reflection. Reading the right-hand