GATE Questions Well Logging

on December 11, 2020 in GATE questions

GATE 2009

GATE 2010

GATE 2011

GATE 2012

GATE 2013

1. Which of the following logging techniques is best suited to estimate the shaliness of hydrocarbon reservoirs?

(a) Resistivity (b) Sonic (c) Induction (d) Gamma ray

2. Match the items of Group I with those of Group II

Group I Group II

P) Caliper log 1) Permeability

Q) NMR log 2) Resistivity

R) Neutron log 3) Diameter

S) SP log 4) Velocity

5) Porosity

(a) P – 3, Q – 4, R – 2, S – 5 (b) P – 3, Q – 1, R – 5, S – 2

GATE 2014

1. The following gamma r ay (GR) log data are recorded in a borehole: GR log value against a formation = 30 API units, Maximum GR log value = 45 API units, Minimum GR log value = 20 API units. What is the fraction of shale in the formation?

(a) 0.33 (b) 0.40 (c) 0.66 (d) 0.75

2. Match the type of well logs (listed in Group I) with the characteristics of measurement (listed in Group II).

(a) P – 3; Q – 1; R – 5; S – 2 (b) P – 4; Q – 1; R – 5; S – 3 (c) P – 3; Q – 4; R – 5; S – 2 (d) P – 3; Q – 1; R – 4; S – 2

GATE 2015

1. Which one of the following logging methods is NOT used to determine porosity?

(a) Sonic (b) SP (c) Neutron (d) Gamma-gamma

2. A clean, thick and hydrocarbon bearing sandstone bed can be identified through a combination of

(a) low SP and high resistivity (b) large SP and high resistivity

3. I n a consolidated sandstone formation, the interval transit times of the formation, matrix and fluid are 70 µs, 55 µs and 190 µs respectively. The porosity of the formation is ______.

GATE 2016

1. In resistivity logging using a ‘Normal device’, the distance between electrodes A and M is 0.40 m. If 20 mA current generates 10 mV potential, the apparent resistivity of the layer between the electrodes is _________ ohm-m. (Use $\pi$ = 3.14)

2. A cylindrical sandstone core sample of diameter 0.02 m and length 0.04 m is fully saturated with brine solution of resistivity 0.5 ohm-m. The resistance of the saturated sample measured in the laboratory is 500 ohm. The formation factor of the sample is __________. (Use $\pi$ = 3.14)

GATE 2017

1. Which one amongst the following logging tools has the largest depth of investigation?

(a) Density (b) Laterolog 3 (c) Laterolog 8 (d) Neutron

2. The most abundant radioactive isotope in the continental crust is

(a) $_{40}K$ (b) $_{232}Th$ (c) $_{235}U$ (d) $_{238}U$

3. The characteristic log response of a thick coal seam are

(a) low transit time, low resistivity and high gamma ray count.

(b) low transit time, high resistivity and low gamma ray count.

(d) high transit time, low resistivity and high gamma ray count.

4. The SP response of a thick, clean sandstone bed is – 54V. Given the mud filtrate resistivity to be 0.45 ohm-m at a formation temperature ($T_f$) of 130°F and the coefficient, K = 77.29, the formation water resistivity is _________ohm-m.

5. Which one of the following log responses is TRUE for a porous and permeable sandstone bed, when the resistivity of the mud filtrate used in equal to the resistivity of the formation water?

(a) A large negative SP is observed.

(b) A large positive SP is observed.

(d) LLm and LLd logs overlap with each other.

GATE 2018

1. If the total porosity of a soil is 20%, its void ratio (%) is _________.

2. Assertion (a) : The Static Self-Potential for a thick , clean freshwater bearing sandstone formation is positive.

Reason (r) : Resistivity of the formation water is less than the resistivity of salt water mudfiltrate.

(a) Both (a) and (r) are true and (r) is the correct reason for (a).

(b) Both (a) and (r) are true and (r) is not the correct reason for (a)

(d) (a) is true but (r) is false.

3. Which one of the following well log responses characterizes an over pressured zone in the subsurface?

(a) High velocity and high resistivity.

(b) Low velocity and low density.

(d) Low velocity and high density.

GATE 2019

1. Which one of the following clay minerals contain potassium (K)?

(a) Illite (b) Kaolinite

2. A high frequency acoustic wave propagating in a gas saturated sandstone formation exhibits an increase in __________ .

(a) frequency (b) velocity (c) wavelength (d) wave number

3. Which one of the following logging methods uses a radioactive source in the sonde?

(a) Natural Gamma ray

(b) Gamma-Gamma

(d) Nuclear Magnetic Resonance (NMR)

4. Which one of the following is CORRECT for the density porosity ($\phi_D$) and neutron porosity ($\phi_N$) estimated for a finely interbedded organic-rich, shaly sandstone formation relative to those for a shale-free sandstone formation at shallow depths?

(a) $\phi_N$ decreases and $\phi_D$ increases.

(b) $\phi_N$ increases and $\phi_D$ decreases.

(d) Both $\phi_N$ and $\phi_D$ increase.

5. Which one of the following statements is INCORRECT with regard to Nuclear Magnetic Resonance (NMR) logging? ($\phi_{NMR}$ - NMR derived total porosity, $\phi_N$ - Density porosity)

(a) The relaxation time (T2) decreases with decrease in pore size.

(b) The $\phi_{NMR}$ is greater than $\phi_N$ in a water saturated sandstone formation.

(d) The $\phi_{NMR}$ is less than $\phi_D$ in a gas saturated shaly sandstone formation

6. The bulk resistivity of a carbonate formation having 10% porosity which is 75% saturated with hydrocarbons is 500 ohm-m. The bulk resistivity of the formation when the porosity is doubled and 100% saturated with water is ______ ohm-metres, (round off to 1 decimal place).

(Assume the tortuosity, cementation factor and saturation exponent to be 1, 2 and 2, respectively).

GATE 2020

1. During ‘K - capture’ nuclear transmutation process

(a) both atomic number and atomic mass increase

(b) atomic number decreases but atomic mass remain same

(d) both atomic number and atomic mass decreases

2. Which one amongst the following logs has the maximum depth of investigation?

(a) Neutron log (b) Natural Gamma - ray log

3. Which one of the following does NOT contribute to the supression of SP log response for a thin, shaly, gas bearing sandstone formation? (Resistivity of mud filtrate > resistivity of formation water)

(a) Increase in shale content

(b) Increase in hydrocarbon content

(d) Increase in the salinity of formation water

4. The crossover observed for a hydrocarbon-bearing sandstone formation in the plot Neutron and Density porosity logs ($\phi_n$ – Neutron porosity and $\phi_d$ –Density porosity) is due to

(a) increase in $\phi_d$ and decrease in $\phi_n$

(b) decrease in $\phi_d$ and increase in $\phi_n$

(d) decrease in both $\phi_d$ and $\phi_n$

GATE Questions Seismic Method

on December 09, 2020 in GATE questions

GATE 2009

GATE 2010

GATE 2011

GATE 2012

GATE 2013

GATE 2014

GATE 2015

GATE 2016

1. Depth migration is applied to a stacked seismic section. Compared to the stacked section, dipping events in the migrated section

(a) have a steeper slope and move updip.

(b) remain unchanged.

(d) have a steeper slope and move downdip.

2. A monochromatic elastic wave of frequency 20 Hz propagates in a medium with average velocity 3 km/s. For zero offset reflection from horizontal reflectors, the thickness of the vertical first Fresnel zone is ________ m.

3. The following figure shows a seismic reflection experiment above a reflector that dips 45° . The P-wave velocity in the medium is constant and equal to 2 km/s. The source is kept at location ‘S’ and the receiver is kept at location ‘G’. The midpoint between S and G is denoted by ‘M’ and the depth to the reflector from ‘M’ is 1 km. The traveltime of the primary reflected arrival recorded at the receiver is equal to____ seconds.

4. For land seismic data acquisition, the following figure is a schematic plot of arrival times of seismic waves recorded at several detectors placed along the x-axis. The shot is placed at the origin (x = 0).

Match the events labeled in the figure (listed in Group I ) with their corresponding types (listed in Group I I)

GATE 2017

1. A seismic reflection survey was carried out over a subsurface consisting of a stack of horizontal isotropic layers. In the common midpoint (CMP) domain, the moveout (travel time v/s offset) curve for any primary reflection event is best approximated by

(a) an ellipse (b) a parabola (c) a circle (d) a hyperbola

2. Normal movement (NMO) correction was applied to seismic data in the common midpoint (CMP) domain. The frequency distortion due to “NMO stretch” is highest for

(a) larger offsets of deeper reflections.

(b) smaller offsets of shallower reflections.

(d) smaller offsets of deeper reflections.

3. Consider a hypothetical zero-offset seismic reflection survey acquired over a reflector whose dip is 30°. The velocity of the medium above the reflector is 2 km/s and the trace spacing is 25 m. The maximum unaliased frequency in the data is _________ Hz.

4. In statistical wavelet deconvalution, the reflectivity series is assumed to be a random sequence. Then, the autocorrelation of the wavelet is

(a) a scaled version of the autocorrelation of the seismic trace.

(b) a random sequence.

(d) dirac-delta function.

5. In the figure shown below, a ray corresponding to a P-wave is incident on the interface between layer 1 and layer 2 at an angle of 30°. The P-wave velocity is 1 km/s, 1.2 km/s and 1.5 km/s in layer 1, layer 2 and the half space, respectively. The emergence angle of the ray into the half space is _________ degrees.

6. How do the P-wave velocity (VP). S-wave velocity (V S), and Poisson’s ratio ($\sigma$) change fr om water saturated sandstone to a gas saturated sandstone?

(a) Vp increases, Vs decreases and $\sigma$ increases.

(b) Vp decreases, Vs remains the same and $\sigma$ decreases.

(d) Vp, Vs and $\sigma$ all remain constant.

7. Consider a Vertical Seismic Profiling (VSP) data acquisition experiment as shown in the figure below. The subsurface consists of a horizontal layer of 2 km thickness underlain by a semi-infinite half-space. The P-wave velocities (VP) in the first layer and the half-space are 2.0 km/s and 2.5 km/ s, respectively. The vertical well has a string of receivers (denoted by inverted triangles) spaced 10 m apart, with the shallowest receiver at a depth of 0.5 km and the deepest receiver at a depth of 1.5 km. The source (denoted by star) is placed 0.5 km from the well head. The traveltime of the primary reflection event at the deepest receiver is ________s.

GATE 2018

1. The impulse response of the Kirchhoff pre-stack time migration operator for non-zero offsets in a homogeneous and isotropic medium is _______.

(a) a circle (b) a parabola (c) a hyperbola (d) an ellipse

2. Figure 1 is a schematic diagram of four seismic events in t-x (time-offset) domain and Figure 2 is the result of transformation from t-x domain to fkx (frequency-horizontal wavenumber) domain. Match the events in t-x domain in Figure 1 with their counterparts in f-kx domain in Figure 2.

(a) P-1; Q-2; R-3; S-4 (b) P-1; Q-3; R-2; S-4 (c) P-4; Q-3; R-2; S-1 (d) P-4; Q-2; R-3; S-1

3. A horizontally travelling surface wave with a wavelength of 20 m is attenuated by a linear and uniform receiver array consisting of 4 receivers if the minimum receiver spacing is ________ m.

4. An end-on marine survey is carried out with equal and uniform shot and receiver spacing. If the total number of shots fired is 50 and a total of 10000 traces are recorded, the maximum fold for the survey is _______.

5. Consider a laterally homogeneous and isotropic ear t h model wi t h a fl at hor i zont al sur face and three hor izontal layers under lain by a halfspace. A seismic reflection survey was simulated on this model with the sources and receivers placed on the surface. The table below lists the root mean square (rms) velocities, V rms, and zero-offset two-way traveltimes t0 for the three reflection events from the bottom of each of the three layers observed in a pre-stack CDP (CMP) gather. The interval velocity of the second layer is _______ m/s.

GATE 2019

1. A reversed refraction survey was done over a two layered medium with the interface between them dipping at an angle of 15°. The velocities in the upper and lower medium are V1 and V2 respectively, with V2 > V1. If the critical angle is 45°, then, which one of the following isCORRECT? (V u and V d are updip and downdip velocities).

(a) V 1 = Vd = Vu (b) Vu > Vd > V1

2. In a migrated seismic time section _______ .

(a) both synclines and anticlines appear tighter

(b) both synclines and anticlines appear broader

(d) synclines appear broader and anticlines appear tighter.

3. A 3-D seismic tomography experiment was carried out with an inter-station spacing of ‘X’ km. The subsurface velocity perturbations in three dimensional blocks were estimated with block size of ‘2X’km and ‘0.5X’km in case 1 and case 2, respectively. Which one of the following statements is CORRECT?

(a) The spatial resolution is poor and variance is small for case 1.

(b) The spatial resolution is good and variance is small for case 2.

(d) The spatial resolution is poor and variance is large for case 2.

4. A split-spread reflection survey is carried out along a profile in the direction of the dipping interface. The difference in arrival times of the reflected waves from the interface at two geophones with an offset distance of 1000 m from the shot-point on both sides is 20 msec. If the velocity of the layer above the dipping interface is 3000 m/s, then the dip of the bed is _______ degrees, (round off to 1 decimal place). (Assumption 2d >> X, where ‘d’ is depth below the shot-point normal to the interface and X is the source-geophone spacing)

5. A vibroseis source sweeps acoustic signal in the frequency range 10 Hz – 100 Hz. The maximum sampling interval to correctly recover the recorded signal will be _________ milliseconds.

GATE 2020

1. The transmission coefficient for the vertically incident seismic wave at the interface between Layer 1 and Layer 2 given in the figure is______. (Round off to 2 decimal places)

2. Assuming uncorrelated noise, the improvement in the signal to noise ratio in a reflection seismic survey with ‘n’ geophones spaced equally along the profile is proportional to

(a) $n$ (b) $\frac{1}{n}$ (c) $\sqrt{n}$ (d) $\frac{1}{\sqrt{n}}$

3. A waveform with amplitude spectrum A ($\omega$) and phase spectrum $\phi(\omega)$ is autocorrelated. Which one of the option given below correctly represents the information about the original waveform that can be retrieved from the autocorrelated waveform?

(a) A($\omega$) can be retrieved but not $\phi(\omega)$

(b) $\phi(\omega)$ can be retrieved but not A($\omega$)

(d) Both $\phi(\omega)$ and A($\omega$) cannot be retrieved

4. In a 3D seismic survey, there are 512 groups of receivers in one line of a patch. Eight groups are moved per line from one patch to the next along the swath. What is the inline fold?

(a) 32 (b) 16 (c) 8 (d) 4

5. A sample of granite is observed to have a P-wave velocity of 5km/s and density of 2600kg/m3. The bulk modulus of the granite, assuming it to be a Poisson’s solid, is ______kilo-Pascal(kPa). (Round off to 2 decimal places)

6. A seismic reflection survey is carried out over a 1500m thick horizontal layer with a P-wave velocity of 2000m/s. The travel time of reflected wave at a surface detector placed 1000m from a surface source is ______ milliseconds.

7. A seismic reflection survey is carried out using a 10 milliseconds seismic wavelet over a subsurface medium having an average P-wave velocity of 1600m/s. The best resolution which is obtained on the basis of Rayleigh criteria is ______ m (Assume seismic wavelet contains one cycle)

8. A 10 Hz seismic wave propagates for 40 km through a material with a P-wave velocity of 5 km/s and quality factor (Q) of 100. The percentage of the initial amplitude retained in the attenuated wave is ________. (Round off to 1 decimal place) (Use $\pi$ = 3.14)

GATE Questions Seismology

on December 06, 2020 in GATE questions

GATE 2009

1. The Gutenberg discontinuity is located at a depth of around

(a) 35 km (b) 150 km (c) 2900 km (d) 5000 km

2. A vast majority of earthquake sources are often linked to

(a) inner core (b) outer core

3. The teleseismic rays are those that arrive at a seismometer for a distance greater than

(a) 18° (b) 28° (c) 38° (d) 48°

4. Which is the parameter for measuring the size of the earthquake that does not need an instrumental record?

(a) Richter Magnitude (b) Intensity (c) Moment (d) Mw

5. The standard form of wave equation for propagation of cubical dilatation ($\theta$) is

The compressional wave velocity is given by

6. PKI KP is a seismic body wave which travels through

(a) upper mantle (b) upper and lower mantle

GATE 2010

1. Cooling of basaltic lava under water will lead to the formation of

(a) lava tunnel (b) pillow structure (c) columnar jointing (d) cumulus texture

2. What rock would you expect to find at the base of a typical oceanic plate?

(a) Basalt (b) Diorite (c) Gabbro (d) Peridotite

3. The compressional wave velocity V p , within a wild with adiabatic bulk modulus K f, rigidity modulus G and density $\rho$ is given by

4. The number of independent elements of the 4th order stiffness tensor required to characterize general elastic media is

(a) 2 (b) 21 (c) 36 (d) 81

5. The seismic energy released in an earthquake of magnitude Ms = 7.0 is about ________ times that released in an earthquake of Ms = 6.0.

(a) 10 (b) 32 (c) 64 (d) 100

6. In the figure given below "– " represents dilatation and "+" represents compression. The fault plane solution of an earthquake with strike-slip mechanism is represented by

7. The anelastic attenuation of seismic energy depends on

(a) quality factor (b) particle acceleration (c) stress drop (d) particle velocity

8. The seismic wave travelling in low velocity layer and critically incident at the discontinuity between low and high velocity layers

(a) will be diffracted (b) will be reflected

GATE 2011

1. The P-wave velocity of the earth’s mantle at the Mohorovicic discontinuity is

(a) 5.5 km/s (b) 6.0 km/s (c) 7.0 km/s (d) 8.0 km/s

2. Tsunamis are

(a) gravity waves (b) acoustic waves (c) capillary waves (d) internal waves

3. In a formation, if the density increases and elastic constants remain unchanged, then

(a) both P and S wave velocities increase

(b) P wave velocity increases and S wave velocity decreases

(d) P wave velocity decreases and S wave velocity increases

4. The Poisson ratio ($\sigma$) for rocks in terms of Lame’s constants $\lambda$ and $\mu$ is

5. Shadow zones for direct P- and S-waves lies between

(a) 102° to 142° for both direct P- and S-waves

(b) 102° to 180° for direct P- wave and 102° to 142° for direct S-wave

(d) 102° to 142° for direct P- wave and 102° to 180° for direct S-wave

6. Snell’s law of refraction deals with which of the following properties of refracted waves?

(a) amplitude (b) direction (c) energy (d) phase

GATE 2012

1. Depth range of the ‘transition zone’ associated with phase changes in the Earth’s mantle is (in km)

(a) 35 to 150 (b) 150 to 410 (c) 410 to 660 (d) 660 to 800

2. The S-wave velocity in the lower continental crust is 6800 m/s and its density is 3380 kg/m3. Find its rigidity in GPa. (Give answer up to 2 decimal places)

(a) 156.29 (b) 160.21 (c) 162.34 (d) 500

Statement for Linked Answer Questions 3 and 4:

The seismic slip of a fault after an earthquake is measured to be 0.5 m and the fault area is estimated to be 250 km2 . The rigidity of the medium surrounding the fault is 30 GPa.

3. The seismic moment (in Nm) of the earthquake is

(a) $3.75 \times 10^{18}$ (b) $3.75 \times 10^{16}$ (c) $3.75 \times 10^{14}$ (d) 3.75 \times 10^{121}\)

4. . Based on the above, the moment magnitude of the earthquake is

(a) 5.15 (b) 5.36 (c) 6.35 (d) 7.25

GATE 2013

1. Both strength and plasticity of a rock increase with the

(A) increase in temperature (B) decrease in strain rate

2. Amongst the following options, the acceptable value of the Poisson’s ratio of a rock is

(a) 0.55 (b) 1.00 (c) 0.25 (d) -1.00

3. The type of wave that arrives first at a station from an earthquake hypocenter is

(a) P-wave (b) S-wave (c) Rayleigh wave (d) Love wave

4. Which of the following is NOT an inverse square law?

(a) Newton’s law of gravitation (b) Coulomb’s law of electrostatics

5. For seismic S-wave velocity, V, the rigidity modulus, µ, is proportional to

(a) $\sqrt{V}$ (b) $V$ (c) $V^2$ (d) $V^3$

6. In a homogeneous anisotropic medium, the physical property varies

(a) with position but not with direction

(b) with both position and direction

(d) neither with position nor with direction

7. Which of the following ways of measuring the size of an earthquake does not require instrumental recording?

(a) Richter magnitude (b) Moment (c) Mw (d) Intensity

8. Wadati diagram is a plot of the difference in P and S- wave arrival times against the arrival time of P-wave. It helps in estimating the

(a) velocity of P-wave. (b) velocity of S-wave.

GATE 2014

1. From the surface to the Earth’s interior, the velocity of P-wave decreases and the material density increases at the boundary between

(a) Outer core and inner core (b) Mantle and outer core

2. As compared to large earthquakes, small earthquakes are

(a) more frequent and caused by short fault slip and long rupture lengths

(b) more frequent and caused by long fault slip and short rupture lengths

(d) more frequent and caused by short fault slip and short rupture lengths

3. For earthquakes of magnitudes 6 and 7, the seismic wave amplitudes are A 6 and A 7 and the radiated energies are E 6 and E 7 respectively. Which one of the following is true?

(a) $A_7\approx \frac{7}{6} A_6 \ and \ E_{7}\approx10E_6$

(b) $A_7\approx 10 A_6 \ and \ E_{7}\approx100E_6$

(d) $A_7\approx 10 A_6 \ and \ E_{7}\approx32E_6$

4. The velocity discontinuity between the upper crust and the lower crust is known as __________ discontinuity.

(a) Lehmann (b) Gütenber (c) Mohorovicic (d) Conrad

5. The S-wave veloci t y of a medium havi ng a Poisson’s ratio and a P-wave velocity of 0.5 and 3 km/s respectively is _________km/s.

6. The PKiKP phase denotes the passage of a seismic wave in the Earth as

(a) P in mantle, S in outer core, reflected as P from inner-outer core boundary, S in outer core, P in mantle and crust

(b) P in crust, P in mantle, reflected as P from core-mantle boundary, P in mantle, P in crust

(d) P in mantle, P in outer core, reflected as P from inner-outer core boundary, P in outer core, P in mantle and crust

GATE 2015

1. PcP and ScS phases are reflected from

(a) crust - mantle boundary

(b) core - mantle boundary

(d) lithosphere - asthenosphere boundary

2. Gardner’s formula relates the seismic P-wave velocity (VP ) to

(a) density (b) porosity (c) permeability (d) lithology

3. Analysis of data from a 3-component broadband seismological station yields seismic velocities, Vp = 7.0 km/s and Vs = 3.87 km/s for the lower crust. The resulting Poisson’s ratio of the lower crustal rocks (rounded to two decimal places) is

(a) 0.24 (b) 0.26 (c) 0.28 (d) 0.30

GATE 2016

1. Which one of the following layers of the Earth has the largest volume?

(a) Upper Mantle (b) Lower Mantle (c) Outer core (d) Inner Core

2. The S-wave shadow zone of the Earth ranges from ________.

(a) 103° to 180° (b) 103° to 160° (c) 103° to 153° (d) 103° to 143°

3. Which one of the following is the ray path for the P-wave that converts to S-wave while passing through the solid inner core?

(a) PKiKP (b) PKIKP (c) pPcP (d) PKJKP

4. Which one of the following statements is CORRECT for the stress drop ($Delta \sigma$) of an earthquake?

(a) Large slip on a small fault will cause more stress drop.

(b) Small slip on a large fault will cause more stress drop.

(d) Stress is directly proportional to the rupture dimension.

5. The energy released by an earthquake of magnitude 7 is ________ times the energy released by an earthquake of magnitude 4 (use Kanamori’s formula).

GATE 2017

1. A seismic gap refers to a

(a) time gap between two great earthquakes.

(b) distance gap between the epicenters of two great earthquakes.

(d) wide gap in the earth created by a great earthquake

2. The travel time difference between the arrival times of a shear wave (S) and primary wave (P) observed on a seismogram recorded at an epicentral distance of 100 km from a near surface earthquake is _________s.

(Assume the average P and S wave velocities to be 6.0 km/s and 3.5 km/s, respectively).

3. The percentage increase in P-wave velocity (km/ s) across the Mohorovicic discontinuity from the lower crust to the upper mantle beneath craton is approximately ___________(%).

4. Which one of the following seismic phases is observable in the P-wave shadow zone?

(a) P (b) PmP (c) PcS (d) PKiKP

5. Which one of the following statements is TRUE for near surface earthquake occurring in a homogeneous, isotropic Earth?

(a) Rayleigh wave are generated (b) Love waves are generated.

6. A dynamic range of 60 dB in power corresponds to an increases in amplitude by a factor of ______.

7. The slope of the Wadati plot obtained using the P and S arrival times of a local earthquake is 1.0 The corresponding Vp/Vs ratio of the subsurface medium is _________.

8. The beach ball figure given below depicts the focal mechanism of an earthquake. The shades and unshaded portions indicate compressional and dilatational quadrants, respectively. FP1 is the fault plane solution. The focal mechanism and FP1 represent

(a) a thrust fault with strike 45° and 30° with the tension axis in the compression quadrant. (b) a normal fault with strike 45° and 30° with the tension axis in the compression quadrant. (c) a thrust fault with strike 225° and 60° with the tension axis in the compression quadrant. (d) a normal fault with strike 225° and 60° with the tension axis in the compression quadrant.

9. Match the items listed in Group I with their respective analytical expressions in Group II.

(a) P-2; Q-3; R-4; S-1 (b) P-2; Q-4; R-1; S-3

GATE 2018

1. For a layered isotropic medium with a flat horizontal free surface, match the wave types listed in Group-I with their corresponding polarizations listed in Group II

(a) P-1; Q-3; R-4; S-2 (b) P-3; Q-1; R-4; S-2 (c) P-3; Q-1; R-2; S-4 (d) P-2; Q-3; R-1; S-4

2. The unit of shear modulus (rigidity modulus) is

(a) kg m– 1 s– 2 (b) m2 s– 2 (c) kg m– 2 s– 2 (d) m– 1

3. Assume a flat earth with crustal thickness of 35 km and average crustal and upper mantle P-wave velocities of 6.4 km.s– 1 and 8.1 km.s– 1, respectively. The minimum distance from the epicenter of a near surface earthquake at which Pn -waves are observed is _______ km.

4. A solution to the eikonal equation $|\nabla \tau|=\frac{1}{V_0}$ for homogeneous and isotropic medium in cartesion coordinates is

5. There is a change in t he values of t he bulk modulus and density across the Gutenberg discontinuity (from mantle to outer core). Which one of the following statements is CORRECT?

(a) Both bulk modulus and density increase.

(b) Both bulk modulus and density decrease.

(d) Bulk modulus increases and density decreases.

6. Using t he Gutenberg-Richter recurrence relationship, the mean annual rate of exceedance of earthquake occurrence in a seismic belt is 0.3 per year for an earthquake of magnitude 6.0. The return period for an earthquake of magnitude 6.0 in this belt is ______ years.

7. The P-wave velocity and the Poisson’s ratio for a homogeneous and isotropic sedimentary rock are 2500 m/s and 0.3, respectively. The S-wave velocity for the rock is ________m/s.

GATE 2019

1. Body waves __________ .

(a) can travel through vacuum (b) have cylindrical wavefronts

2. The acceleration due to gravity (g) begins to fall sharply towards the centre of the Earth from the __________ discontinuity.

(a) Conrad (b) Mohorovicic (c) Gutenberg (d) Lehmann

3. Which one of the following lists ONLY kinematic parameters?

(a) Force, translation, rotation.

(b) Translation, rotation, distortion.

(d) Force, stress, strain.

4. The Young’s modulus ‘E’ is related to the Lame’s parameter ‘A,’ for a Poisson solid as

(a) E = 2.5$\lambda$, (b) E = 1.5$\lambda$ (c) E = $\lambda$ (d) E = 0.5$\lambda$.

5. Which one of the following seismic phases is the earliest arrival in the P shadow zone?

(a) PKiKP (b) PPP (c) P diff (d) PKIKP

6. A shallow focus, Great earthquake with seismic moment of 2.5 × 1040 dyne-cm is recorded at an epicentral distance of 50°. The body wave magnitude (mb), surface wave magnitude (Ms) and moment magnitude (Mw) were estimated. Which one of the following is CORRECT?

(a) mb > Ms > Mw (b) mb = Ms = Mw

7. In a seismogram of a shallow focus (h = 5 km) earthquake, the difference between the arrival times of the S and P phases is 1.34 s. Assuming the average P wave velocity of the crust to be 6.0 km/s and the Poisson’s ratio to be 0.27, the epicentral distance is _____ kilometres, (round off to 1 decimal place).

GATE 2020

1. The given stereoplot of the axial plane and the axis of a fold represents an/a

(a) upright fold (b) vertical fold (c) reclined fold (d) recumbent fold.

2. Which of the following options shows the internal structure units of the Earth arranged in the CORRECT sequence of increasing volume?

(a) Outer core < Inner core < Upper mantle < Lower mantle

(b) Outer core < Inner core < Lower mantle < Upper mantle

(d) Inner core < Outer core < Lower mantle < Upper mantle

3. Which one of the following is NOT an earthquake intensity scale?

(a) Richter scale (b) JMA scale (c) Modified Mercalli scale (d) Rossi-Forel scale

4. Assuming the inner core of the Earth to be one-third of its present size, which one of the following satement is CORRECT ? (Radius of the Earth and outer core remain unchanged)

(a) Shadow zone of P-wave increases but that of S-wave decreases

(b) Shadow zone of P-wave increases but that of S-wave remains unchanged

(d) Shadow zone of P-wave decreases but that of S-wave remains unchanged

GATE Questions Magnetic Method

on December 02, 2020 in GATE questions

2011

1. The Larmor precession frequency (in Hz) measured by proton precession magnetometer for a total field of 50,000 nT is (gyromagnetic ratio of proton $\gamma_p = 0.267513 \ nT^{-1}S^{-1}$ )

(a) 1890 (b) 2020 (c) 2130 (d) 2420

Structural Geology

on October 17, 2020 in Geology

When the sedimentary rock beds are found to have been deposited without interruption the age difference(s) between adjacent beds are negligible (geologically). We refer such contacts formed between layers and within such sequences as conformable depositional contacts. Conformable depositional contacts are usually planar to slightly irregular in form.

Unconformities

An unconformity is a depositional contact between two rocks of measurably different ages.

Where conformable deposition was interrupted, or where erosion during long intervals removed a part of the rock record an unconformity is formed. The unconformity in places will separate young horizontal sedimentary rocks from older, tilted, deformed sedimentary rocks. In other places the young horizontal sedimentary rocks may rest directly on an erosionally carved surface on old granite or schist. Again, the unconformity marks a gap in the rock record. Time is missing.

Unconformities are divided into three major classes: nonconformities, angular unconformities, and disconformities.

Nonconformity: A geological surface that separates younger overlying sedimentary strata from eroded igneous or metamorphic rocks and represents a large gap in the geologic record.

Nonconformity = top of basement rocks

Angular unconformity: An angular unconformity is an unconformity that separates layers above and below that are not parallel. Classical angular unconformities are horizontal depositional surfaces separating relatively young horizontal strata above from older steeply dipping strata below.

Angular unconformity = hiatus, erosion, and tilt

Disconformity: A disconformity is an unconformity separating strata that are parallel to each other. Some disconformities are highly irregular whereas others have no relief and can be difficult to distinguish within a series of parallel strata. Recognition may require complete knowledge of the ages of beds within the sequence of strata that contains the disconformity.

Disconformity = hiatus + erosion

For all three types of unconformity, the surface marking the unconformity itself is parallel to the bedding or layering of the rocks above the unconformity. The bed directly above an unconformity commonly contains a basal conglomerate, normally composed of clasts of the rock directly beneath the unconformity. Basal conglomerates itself declares erosional intervals. The basal conglomerate may range in coarseness from a thin fine granule conglomerate to a thick coarse boulder conglomerate. Surfaces of unconformity may locally possess topographic relief that can be recognized as the product of ancient erosion, perhaps even including the preservation of the cross-section of an old stream channel. Under ideal conditions, fossil soil profiles, called paleosols, are preserved in rocks directly beneath the old erosion surface. These may be baked where overlain by lava flows.

Paraconformity

A paraconformity is a type of unconformity in which strata are parallel; no apparent erosion is discernable and the surface of the unconformity resembles a simple bedding plane. It is also called pseudoconformity or nondepositional unconformity. Short paraconformities are called diastems.

Paraconformity = hiatus ± erosion (no discernable erosion)

Diastem

A relatively short interruption in sedimentation, involving only a brief interval of time, with little or no erosion before deposition is resumed; a depositional break of lesser magnitude than a paraconformity, or a paraconformity of very small time value.

Diastem = short hiatus ± erosion (a minor paraconformity)

Traps

on October 13, 2020 in Geology

NOMENCLATURE OF A TRAP

The highest point of the trap is the crest, or culmination.

The lowest point at which hydrocarbons may be contained in the trap is the spill point; this lies on a horizontal contour, the spill plane.

The vertical distance from crest to spill plane is the closure of the trap.

The zone immediately beneath the petroleum is referred to as the bottom water, and the zone of the reservoir laterally adjacent to the trap as the edge zone.

Fig1: Cross section through a simple anticlinal trap

Within the trap the productive reservoir is termed the pay.

The vertical distance from the top of the reservoir to the petroleum/water contact is termed gross pay.

All of the gross pay does not necessarily consist of productive reservoir, so gross pay is usually differentiated from net pay.

The net pay is the cumulative vertical thickness of a reservoir from which petroleum may be produced. Development of a reservoir necessitates mapping the gross : net pay ratio across the field.

Within the geographic limits of an oil or gas field there may be one or more pools, each with its own fluid contact.

This field contains two pools, with different oil : water contacts (OWC). In the upper pool the net pay is much less than the gross pay because of non-productive shale layers. In the lower pool the net pay is equal to the gross pay.

DISTRIBUTION OF PETROLEUM WITHIN A TRAP

A trap may contain oil, gas, or both. The oil : water contact (OWC) is the deepest level of producible oil. Similarly, the gas : oil contact (GOC) or gas : water contact is the lower limit of producible gas.

Where oil and gas occur together in the same trap, the gas overlies the oil because the gas has a lower density.

Whether a trap contains oil and/or gas depends both on the chemistry and level of maturation of the source rock and on the pressure and temperature of the reservoir itself.

Fields with thick oil columns may show a more subtle gravity variation through the pay zone. Boundaries between oil, gas, and water may be sharp or transitional. Abrupt fluid contacts indicate a permeable reservoir; gradational ones indicate a low permeability with a high capillary pressure. Not only does a gross gravity separation of gas and oil occur within a reservoir, but more subtle chemical variations may also exist.

Tar Mats

Some oil fields have a layer of heavy oil, termed a tar mat, immediately above the bottom water. Tar mats are very important to identify and understand because they impede the flow of water into a reservoir when the petroleum is produced.

Fluid Contacts

Fluid contacts in a trap are generally planar, but are by no means always horizontal. Correct identification of the cause of the tilt is necessary for the efficient production of the field. There are several causes of tilted fluid contacts.

They may occur where a hydrodynamic flow of the bottom waters leads to a displacement of the hydrocarbons from a crestal to a flank position. This displacement can happen with varying degrees of severity.

In some fields the OWC has tilted as a result of production, presumably because of fluid movement initiated by the production of oil from an adjacent field.

An alternative explanation for a sloping fluid contact is that a trap has been tilted after hydrocarbon invasion, and the contact has not moved.

A third possible cause of a tilted OWC may be a change in facies.

SEALS AND CAP ROCKS

For a trap to have integrity it must be overlain by an effective seal. Any rock may act as a seal as long as it is impermeable. Seals will commonly be porous, and may in fact be petroleum saturated, but they must not permit the vertical migration of petroleum from the trap. Shales are the commonest seals, but evaporites are the most effective. Shales are commonly porous, but because of their fine grain size have very high capillary forces that prevent fluid flow.

Shales may selectively trap oil, while permitting the upward migration of gas. Gas chimneys may sometimes be identified on seismic lines either by a velocity pull-down of the reflector on top of the reservoir, and/or by a loss in seismic character in the overlying reflectors. Indeed some petroleum accumulations are sometimes identified because of their gas-induced seismic anomalies.

CLASSIFICATION OF TRAPS

Wavelet

on October 09, 2020 in Signal processing

Practical seismic waveforms are finite and have limited bandwidth. They are the summation of discrete sinusoids, each with its own amplitude, frequency, and phase characteristics.

A band-limited wavelet and its component sinusoids is shown below,

A bandlimited signal cannot be also timelimited. More precisely, a function and its Fourier transform cannot both have finite support unless it is identically zero.

Zero phase

When the wavelet is symmetric about t = 0, it is referred to as a zero-phase wavelet, each of its component sinusoids is zero phase, and each is uniquely defined by its own amplitude and frequency.

Constrained Least Square Inversion

on October 05, 2020 in Inversion

In many geophysical problems it is possible to generate a set of completely different solutions that adequately explain the experimental data, especially where measurement errors are present. Ultimately, one solution has to be selected as the 'best' or most feasible answer to the problem. To do this we have to add to the problem some information not contained in the original equation d=Gm. This extra information is referred to as a priori information and serves to constrain our solutions so as to satisfy any of our quantified expectations of the model parameters. A priori information can take several forms. It may represent previously obtained geophysical, borehole or geological data or may simply be dictated by the physics of the problem. Consequently, constrained inversion takes many forms.

Inversion with prior information

We can incorporate previously obtained information about the sought model parameters in our problem formulation. This external information could be in the form of results from previous experiments or quantified expectations dictated by the physics of the problem. Generally, these external data help to single out unique solution from among all equivalent ones. The solution process is said to be constrained. The procedure is simple. The constraining equations (data) are arranged to form an expression of the form$$Dm=h$$where, D is a matrix (with all the off-diagonal elements equal to zero) that operates on the model parameters m to yield or preserve the the a priori values of m that are contained in the vector h. The equation $Dm = h$ means that we are employing linear equality constraints that are to be satisfied exactly. The mathematical development is straightforward. We wish to bias $m_j$ towards $h_j$.

We simply minimize,

GATE questions Inversion

on October 02, 2020 in GATE questions

GATE 2009

1. Geophysical inverse problems are described by

(a) Fredholm's integral equation of first kind

(b) Fredholm's integral equation of second kind

(d) Legendre equation

2. Spot the ANN method from the following:

(a) Singular value decomposition

(b) monte-car lo technique

(d) Back propagation technique

3. The concept of resolving kernel is used in

(a) Tikhonov's regularization method

(b) Ridge regression method

(d) Simulated annealing method

GATE 2010

1. Unguided random-walk inversion technique signifies

(a) Genetic algorithm

(b) Simulated annealing

(d) Metropolis algorithm

2. If m represents the number of model parameters, d the number of data points and p the rank of matrix to be inverted, then which of the following defines an under determined system?

(a) m < d and p = d

(b) m > d and p = d

(d) m < d and $p \neq d$

GATE 2011

1. The least squares generalized inver se of an overdetermined problem is expressed as

(a) $(GTTG)^{-1}G^T$ (b) $(G^T G)^{-1}$

GATE 2012

1. The solution to the purely under-determined problem Gm = d is given by

(a) $(G^TG)^{-1} G^Td$

(b) $(G^TG)^{-1} Gd^T$

(d) $G^Td(GG^T)^{-1}$

2. Given the following matrix equation: $A_{m\times n} X_{x\times1} = b_{m\times1}$ the nature of this system of equation is

(a) over-determined if m > n

(b) under-determined if m < n

(d) determined by the rank of the matrix A

GATE 2013

1. A singular value of an $m \times n$ matrix, A, is defined as

(a) positive square root of eigenvalue of $AA^T$

(b) modulus of eigenvalue of A

(d) square of eigenvalue of A

2. In an ill-posed geophysical inverse problem, stated as non-singular matrix equation, the magnitude of determinant of the coefficient matrix is

(a) large (b) zero (c) near zero (d) very large

GATE 2014

1. Consider the four systems of algebraic equations (listed in Group I). The systems (Q), (R) and (S) are obtained from (P) by restricting the accuracy of data or coefficients or both respectively, to two decimal places.

Match these systems to their characteristics (listed in Group II)

Group I Group I I

P. x+ 1.0000y = 2.0000 1. instability

x+1.0001y = 2.0001

Q. x+ 1.0000y = 2.00 2. inconsistency

x+1.0001y = 2.00

R. x+ 1.00y = 2.0000 3. non-uniqueness

x+1.00y = 2.0001

S. x+ 1.00y = 2.00 4. exact

x+1.00y = 2.00

(a) P-1; Q-4; R-3; S-2

(b) P-4; Q-1; R-2; S-3

(d) P-1; Q-4; R-2; S-3 50.

2. The eigenvalue (\(Lambda) and eigenvector (U) matrices for singular value decomposition of the matrix

respectively are

GATE 2015

GATE 2016

GATE 2017

GATE 2018

GATE 2019

GATE 2020

Null space

on October 01, 2020 in Inversion

If the seismic velocity in the earth depends only on depth, the velocity can be constructed exactly from the measurement of the arrival time as a function of distance.

Fig1: The traditional definition of the forward and inverse problems

Despite the mathematical elegance of the exact nonlinear inversion schemes, they are of limited applicability. There are a number of reasons for this.

First, the exact inversion techniques are usually only applicable for idealistic situations that may not hold in practice.

Second, the exact inversion techniques often are very unstable.

Third reason is the most fundamental. In many inverse problems the model that one aims to determine is a continuous function of the space variables. This means that the model has infinitely many degrees of freedom. However, in a realistic experiment the amount of data that can be used for the determination of the model is usually finite. A simple count of variables shows that the data cannot carry sufficient information to determine the model uniquely.

The fact that in realistic experiments a finite amount of data is available to reconstruct a model with infinitely many degrees of freedom necessarily means that the inverse problem is not unique in the sense that there are many models that explain the data equally well. The model obtained from the inversion of the data is therefore not necessarily equal to the true model that one seeks. This implies that the view of inverse problems as shown in fig1 is too simplistic. For realistic problems, inversion really consists of two steps.

Fig2: Inverse problem as a combination of

an estimation problem and an appraisal problem.

Let the true model be denoted by m and the data by d. From the data d one reconstructs an estimated model $m^{est}$, this is called the estimation problem (Fig2). Apart from estimating a model $m^{est}$ that is consistent with the data, one also needs to investigate what relation the estimated model $m^{est}$ bears to the true model m.

In the appraisal problem one determines what properties of the true model are recovered by the estimated model and what errors are attached to it. Thus, $$inversion = estimation + appraisal$$In general there are two reasons why the estimated model differs from the true model. The first reason is the non-uniqueness of the inverse problem that causes several (usually infinitely many) models to fit the data. Technically, this model null-space exits due to inadequate sampling of the model space. The second reason is that real data are always contaminated with errors and the estimated model is therefore affected by these errors as well.

Therefore model appraisal has two aspects, non-uniqueness and error propagation.

Model estimation and model appraisal are fundamentally different for discrete models with a finite number of degrees of freedom and for continuous models with infinitely many degrees of freedom. Also, the problem of model appraisal is only well-solved for linear inverse problems. For this reason the inversion of discrete models and continuous models is treated separately, and the case of linear inversion and nonlinear inversion is also treated independently.

Despite the mathematical elegance of the exact nonlinear inversion schemes, they are of limited applicability. There are a number of reasons for this.

Null space

The vector d of the realisations can be related by a linear function to the vector of model parameters as:$$d=Gm \tag{1}$$where, G is an M x N matrix, and m and b are vectors of dimension N and M respectively. Equation (1) defines G as a linear mapping from an N-dimensional vector space to (generally) an M-dimensional one. But the map might be able to reach only a lesser-dimensional subspace of the full M-dimensional one. That subspace is called the range of G. The dimension of the range is called the rank of G. Sometimes there are nonzero vectors $m_0$ that are mapped to zero by G, that is, $Gm_0=0$. The space of such vectors (a subspace of the N-dimensional space that $m_0$ lives in) is called the nullspace of G, and its dimension is called G’s nullity. The nullity can have any value from zero to N.

System (1) is usually either under- or over-determined, and a least squares solution is sought; unfortunately, we rarely get a unique and reliable solution because it is rank deficient. In fact, the so-called null space exists, constituted by vectors $m_0$ being solution of the associated homogeneous system:$$Gm_0=0\tag{2}$$
Any linear combination of vectors $m_0$ with a solution of (1) still satisfies system (1), and therefore the number of possible solutions is infinite in this case.

Singular value decomposition (SVD) allows to express matrix G by the following product:$$A = USV^T$$where: $U^TU = I$, $V^TV = VV^T = I$ , and I is the identity matrix.

The elements $s_{ij}$ of the diagonal matrix S are the singular values of G. The columns of the matrix V corresponding to null singular values constitute an orthonormal basis of the nullspace, whilst the columns of U corresponding to non-null singular values are an orthonormal base of the range.

Null space Example:

The vector of realizations d can be related by a linear function to the vector of model parameters m as z: $$d=Gm$$ Let us suppose that the inverse problem has two distinct solutions m1 and m2.

So, $$Gm1=d$$
and $$Gm2=d$$
Subtracting these two equations yields
$$G(m1-m2)=0$$
Since, the two solutions are by assumptions distinct, their difference $$m_0=m_1-m_2$$ is non-zero.

The converse is also true, any linear inverse problem that has null vectors then it has non-unique solution. If $m_{par}$ (particular) is an non-null solution to $Gm=d$, for instance minimum length solution, then $m_{par}+\alpha m_0$, is also a solution any choice of $\alpha$.

Note that since $\alpha m_0$ is a null vector for any non-zero $\alpha$, null vectors are only distinct if they are linearly independent.

If a given inverse problem has a q distinct null solutions, then most general solution $$m_{gen}=m_{par}+\sum_{i=1}^{q} \alpha_i m_0$$

The data null space

Linear combinations of data that cannot be predicted by any possible model vector m. For example, no simple linear theory could predict different values for a repeated measurement, but real repeated measurements will usually differ due to measurement error. If there is a data null space, and if the data have a component in this null space, then it will be impossible to fit them exactly.

The model null space

A model null vector is any solution to the homogenous problem $$Gm_{0}=0$$This means we can add in an arbitrary constant times any model null vector and not affect the data misfit. So, the existence of a model null space implies non-uniqueness of any inverse solution.

Both a Model and a Data Null Space

In the case of a data null space, we saw that the generalized inverse solution minimized the least squares mis-fit of data and model response. While in the case of a model null space, the generalized inverse solution minimized the length of the solution itself. If there are both model and data null spaces, then the generalized inverse simultaneously optimizes these goals.

Null space from SVD

Column vectors of U associated with 0 (or very near-zero) singular values are in the data null space.

Column vectors of V associated with 0 singular values are in the model null space.

Minimum length solution never contains any null vectors. But if we use other solution simply(flatness/roughness), those solutions will contain null vectors.