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GATE Questions Radioactivity Method

on December 28, 2020 in GATE questions

GATE 2020

GATE 2019

GATE 2018

GATE 2017

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE 2016

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE 2015

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE 2014

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE 2013

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE 2012

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE 2011

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE 2010

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE 2009

1. The ratio of the number of daughter nuclides to the number of parent nuclides after a decay period of 3 half-lives is .

GATE Questions Electrical

on December 18, 2020 in GATE questions

GATE 2020

1. Ten equisplaced metal electrodes are arranged along a profile for multi-electrode 2D resistivity imaginary survey. If Wenner array is used for data recording, the maximum number of observations will be

(a) 7 (b) 11 (c) 12 (d) 13

2. Current and potential electrodes in resistivity survey over an inhomogeneous ground is shown in the shown in the figure below. If 100mA current flow between C1 and C2 generates 50mV potential difference between P1 and P2 , then the apparent resistivity of the medium will be ____ohm-m. (Round off to 2 decimal places) (Use \(\pi=3.14\))

3. The means the resistivity of a horizontally stratified cuboid rock sample is 100 oohm- m and coefficient of electrical anisotropy is 1.15. The transverse resistivity of the rock sample_____ohm-m. (Round off 2 decimal places)

4. The ‘Geometrical factor’ for the electrode configuration given below will be _______ m. (Round off to 2 decimal places) (Use \(\pi = 3.14\)) (C1 and C2 are current electrodes; P1 and P2 are potential electrodes)

GATE 2019

1. The difference in the mobility of ions in the electrolyte and electrons in metallic conductors in the sub-surface due to applied external electric field gives rise to _________ .

(a) electrode polarization (b) membrane polarization

2. A massive sulphide body in the subsurface is partially above the water table. According to the pH variation hypothesis for the origin of Self Potential, which one of the following statements is CORRECT for such a body?

(a) Acidic above and basic below the water table.

(b) Basic above and acidic below the water table.

(d) Basic above and below the water table.

3. A pair of current electrodes C1 (+I) and C2 (–I) is placed 50m apart (shown in the figure below) over a homogeneous structure of resistivity 100 ohm-m and 1 Ampere current flows through the subsurface. Which one of the following is CORRECT for the potential (Vp ) and horizontal component of electric field (Ex) at a point P located exactly below the midpoint between Cl and C2 at a depth of 10 m?

(a) Vp = 0 and Ex = 0 (b) Vp = 0 and Ex \(\neq\) 0

4. A Two-electrode array is placed over a vertical contact (2-D) as shown in the given figure (strike of contact is perpendicular to the plane of paper). If 1 Amp current flows through the subsurface, then the potential at the potential electrode PI will be ____ millivolts. (round off to the nearest integer). (Consider structures with resistivity \(\rho_1\) and \(\rho_2\) to be laterally extending to infinity on both sides of the contact and also in the downward direction, C2 and P2 are grounded at infinity) (Use \(\pi\) = 3.14)

3. In an electrical resistivity imaging survey, Axial Dipole-dipole array is placed over an inhomogeneous structure. The centers of current and potential dipoles are separated by a distance of 100 m. The length of each dipole is 10 m. If 5 Amp current flows through the subsurface and 50 mV potential difference is measured across the potential dipole then apparent resistivity will be ________ ohm-metres, (round off to the nearest integer) (Use \(\pi\) = 3.14)

GATE 2018

1. Multi-electrode resistivity survey is carried out by placing 10 equispaced electrodes (denoted by arrows in the figure below) on the surface of the earth. The points of observations in the distanceapparent depth plane are marked as solid dots in the figure shown below. Considering the mid-point of the 4-electrode array as the point of observation in the lateral direction, identify the CORRECT electrode configuration used for the survey.

(a) Multi-electrode Wenner array. (b) Multi-electrode Axial Dipole-dipole array.

2. A student interpreted a four layer Schlumberger resistivity sounding data and obtained the resistivities (ohm) and thicknesses (h) as follows: p1 = 100 ohm-m, p2 = 20 ohm-m, p3 = 1500 ohm-m and p4 = 50 ohm-m; h1 = 50 m, h2 =10 m and h3 =20 m. The same data is interpreted by another student who obtains p3 = 2000 ohm-m. Then, according to the principle of equivalence, the value of h3 interpreted by the second student is ________m. (All other model parameters estimated by both the students are the same.)

3. The apparent resistivities obtained at 0.1 Hz and 10 Hz in the frequency domain I.P. measurement are 100 ohm-m and 80 ohm-m, respectively. The Percentage Frequency Effect is _________.

GATE 2017

2. The apparent resistivity for Wenner and Schlumberger configurations in an electrical sounding experiment is the same for a certain electrode spacing ‘a’ (Wenner configuration). Given the current electrode spacing of 18 m and the potential electrode spacing of 2 m for a Schlumberger configuration, the value of ‘a’ is ________m.

3. In a time-domain (TD) induced polarization experiment with a steady voltage of 10 mV during the current flow interval, the voltage decay after the current cut-off is given by \(v(t) = 4.0 \ e^-{0.3t}\) mV. The chargeability after current cut-off between t1 = 1 s and t2 = 4 s is __________ ms.

GATE 2016

GATE 2015

1. In which one of the following configurations the electrodes are uniformly spaced?

(a) Schlumberger array

(b) Pole-dipole array

(d) Pole-pole array

2. Which type of VES curve is obtained for a three layered earth model consisting of wet shale (top layer), poorly water saturated sandstone (middle layer) and impermeable granite (bottom layer)?

(a) K (b) Q (c) H (d) A

3. In frequency domain IP, which one of the following frequency ranges (in Hz) is used to measure apparent resistivity at DC and AC limits?

(a) 0.01 – 0.1

(b) 0.1 – 1

(d) 10 – 100

GATE 2014

1. The reflection coefficient at the interface between two layers of resistivities 9 ohm-m and 1 ohm-m respectively is

(a) 0.6 (b) 0.7 (c) 0.8 (d) 0.9

2. Compute the coefficient of anisotropy from the following parameters estimated from a Vertical Electric Sounding (VES) survey.

Resistivity of first layer, p1 = 15 ohm-m

Resistivity of second layer, p2 = 4 ohm-m

Resistivity of lower half-space, p3 = 50 ohm-m

Thickness of first layer, h1 =3m

Thickness of second layer, h2 =16m

(a) 1.43 (b) 1.28 (c) 1.19 (d) 1.13

3. Arrange the following electrode configurations in the ascending order of their depth of investigation (P) Dipole-Dipole (Q) Schlumberger (R) Wenner (S) Pole-Pole

(a) R – S – Q – P (b) P – Q – S – R (c) R – Q – P – S (d) R – Q – S – P

GATE 2013

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GATE 2010

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GATE 2018

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

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GATE 2011

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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

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

GATE questions Gravity method

on September 30, 2020 in GATE questions

GATE 2009

1. Which of the following parameters is uniquely resolved by residual gravity anomaly data

(a) lateral density contrast

(b) excess/deficit mass

(d) geometric dimensions of geophysical model

2. The presence of crustal root beneath a mountain chain can be best explained by

(a) Pratt's model (b) Airy's model

3. For under water gravity measurements, the following correction is needed:

(a) Prey correction (b) Free-air correction

Common Data for Questions 4 and 5:

The peak gravity anomaly over a 2-D line mass of circular cross-section (horizontal cylinder) of density contrast 500 kg/m3 is 1.674 mGal. The anomaly decreases to 0.837 mGal at a distance of 500 m along a principal profile. The universal gravitation constant, \(G = 6.6667 \times 10^{-11}\ \ m^3sec^{-2}kg^{-1}\).

4. The depth (m) to center of line mass and radius (m) of the horizontal cylinder are =

(a) 500, 199.80

(b) 200, 150.93

(d) 100, 60.37 56.

5. Hence compute the excess mass per unit length (kg/m) of the line mass

(a) \(11.0 \times 10^{7}\), (b)\(9.0 \times 10^{7}\)

GATE 2010

1. If the average crustal thickness is 35 km and the height of a mountain is 5 km above mean sea level the crustal thickness based on Airy's model beneath the mountain will he approximately

(a) 35 km (b) 40 km (c) 50 km (d) 70 km

2. The equipotential sur face over which the gravitational field has equal value is known as

(a) geoid (b) spheroid (c) ellipsoid (d) mean sea level

3. Among the following, the best reconnaissance method for determining basement configuration of sedimentary basins is

(a) gravity method (b) self potential method

4. The gravity value measured at the base of a 10 m tall building is 40 mGal. The value at the top of the bullding ignoring its mass is close to

(a) 20 mGal (b) 37 mGal (c) 40 mGal (d) 43 mGal

5. Upward continuation technique filters ________ wavelength anomalies and ____ their amplitudes.

(a) short, reduces (b) long, enhances (c) long, reduces (d) short, enhances

Common Data (or Questions)

The terrain correction in gravity method accounts for topographic relief in the vicinity of the observation point. The Bouguer slab assumes the topography around the observation point to be flat. In the figure below, the Bouguer slab thickness is h and the hollow portion P lies within the Bouguer slab. Q and Rare parts of the topography

6. In the region P, the terrain correction is

(a) half of that in R (b) negative (c) zero (d) positive

7. In the region Q, the terrain correction is required to account for

(a) hollow portion P

(b) reduced gravity due to excess mass in portion Q

(d) over-correction of Bouguer slab

GATE 2011

1. The acceleration due to gravity (g) and universal gravitational constant (G) are related by the expression (Me and Re are the mass and radius of the earth, respectively)

2. Gravity measurement is made on a ship sailing at the speed of 6 knots in the direction N65°E at 20°N latitude. The Eotvos correction (in mGal) is

(a) +38.5 (b) +24.5 (c) – 35.5 (d) – 39.5

Statement for Linked Answer Questions

A gravity survey is conducted over a highly compact ore deposit (spherical shape). Bouguer anomaly values reduced along a profile are given below.

3. What is the depth to the center of the ore deposit?

(a) 3100 m (b) 1820 m (c) 1560 m (d) 1450 m

4. What is the excess mass (in metric tons) by the deposit?

(a) 1.615 × 10^8 (b) 2.165 × 10^8 (c) 1.312 × 10^9 (d) 1.825 × 10^9

GATE 2012

1. Bouguer correction is applied to correct for the gravity anomaly due to mass between station location and

(a) mean sea level (b) local datum plane

2. The change in gravity caused by Earth’s tides on the land surface in a complete tidal cycle is in the range of (in milligal)

(a) 0.1 to 0.2 (b) 0.2 to 0.3 (c) 0.3 to 0.4 (d) 0.4to 0.5

GATE 2013

1. The acceleration due to gravity, 'g' is maximum at

(a) equator (b) poles (c) mid-latitudes (d) sub-tropical regions

2. Which of the following is useful to estimate the depth to the centre of a spherical body from a gravity anomaly curve?

(a) Surface integration (b) low-pass filtering Volume integration (c) Twice the absolute maximum (d) Half-width of the anomaly

3. If L, B, F and T respectively stand for Latitude correction, Bouguer correction, Free-air correction and Terrain correction, then the order in which they will have to be applied for gravity data analysis is

(a) LFBT (b) LBTF (c) FLBT (d) TBLF

GATE 2014

1. The International Gravity Formula predicts the theoretical gravity value at a given point assuming a

(a) non-rotating homogeneous spherical earth model

(b) decreases rotating inhomogeneous spherical earth model

(d) rotating inhomogeneous oblate spheroidal earth model

2. Compute the maximum value of gravity anomaly in µGal over a buried sphere from the following data:

Radius of a sphere = 5 m

Depth to centre of sphere =11 m

Density contrast = 0.1 gm/cc

G = 6.673 × 10– 8 dyne-cm2 /gm2

(a) 2887.58 (b) 288.76 (c) 28.88 (d) 2.89

GATE 2015

1. The shape of the earth is best described as

(a) spheroid (b) prolate ellipsoid (c) ellipsoid (d) oblate spheroid

2. Considering the Airy isostatic compensation for a mountain having elevation of 2.0 km above the mean sea level at a point P, the thickness of its root below P would be _________km. (consider densities of crustal rocks and upper mantle as 2.7 g/cc and 3.3 g/cc respectively).

3. . The Bouguer anomaly obtained after applying all necessary corrections is due to

(a) topographic undulations above the datum

(b) increase in densities of crustal rocks with depth

(d) vertical density contrast across Moho

GATE 2016

1. According to Airy’s model, gravity anomalies for fully isostatically compensated topography are characterized by

(a) negative Bouguer anomaly and positive free-air anomaly.

(b) positive Bouguer anomaly and negative free-air anomaly.

(d) positive Bouguer anomaly and zero free-air anomaly.

2. The value of free-air correction (assuming sea level as datum plane) at an elevation of 150 m is _________ mGal.

3. A spherical cavity of radius 8 m has its centre 15 m below the surface. If the cavity is full of sediments of density \(1.5 \times 10^3 kg/m3\) and is in a rock body of density \(2.4 \times 10^3 kg/m3\), the maximum value of its gravity anomaly is __________ mGal.

4. Match the items (listed in Group I) with the corresponding corrections applied for reduction of marine gravity data (listed in Group II).

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

GATE 2017

1. The normal gravity formula (for e.g. GRS80) is a function of

(a) geocentric latitude (b) geodetic latitude (c) longitude (d) altitude

2. Given the Bouguer density of 2.8 g/cc, the Bouguer correction for a gravity station at an elevation of 30 m above the datum is ____ mGals. (Use \(\pi\) = 3.14)

GATE 2018

1. The geoid can be best defined as

(a) an oblate spheroid that best approximates the shape of the earth.

(b) a surface over which the value of gravity is constant.

(d) an equipotential surface of gravity of the earth.

2. Which one of the following corrections is always added during reduction of the observed gravity data?

(a) Latitude (b) Free-air (c) Bouguer (d) Terrain

3. In the figure below, Z denotes the depth to the center of a buried sphere from the surface and \(X_{1/2}\) denotes the half-width of the profile at half the maximum value of gravity. Then, the ratio \(\frac{Z}{X_{1/2}}\) is ________.

4. Two survey vessels with shipborne gravimeters are cruising towards each other at a speed of 6 knots each along an east -west course. The difference in gravity readings of the two gravimeters is 63.5 mGal at the point at which the survey vessels cross each other. The latitude along which the survey vessels are cruising is ______ °N.

5. A gravity reading is taken in a stationary helicopter hovering 1 km above mean-sea level at a particular location. The difference in the value of g measured in the helicopter and at mean sea level vertically beneath the helicopter is ____________ mGals.

GATE 2019

1. Which one of the following is only a correction and not a reduction in the computation of gravity anomalies with respect to a datum?

(a) Free air (b) Bouguer (c) Terrain (d) Isostatic

2. Assuming Airy isostatic compensation, the depth to the Moho from a point located 2 km above the mean sea level is _____ km. (round off to 1 decimal place). (The depth of compensation T for the crust at mean sea level is 30 km, the density of crust and upper mantle are 2.67 gm/cc and 3.30 gm/cc, respectively).

3. In gravity anomalies, the ‘Indirect effect’ mainly arises from__________.

(a) the sources outside the area of investigation

(b) improper instrument drift

(d) short-wavelength uncompensated masses in the subsurface

4. Which one of the following statements about the gravity anomalies on land is CORRECT?

(a) Free-air and Bouguer anomalies are always positively correlated with elevation

(b) Isostatic anomalies are not useful to understand the crustal heterogeneities

(d) X-horizontal gradient \(dg/dx\) map enhances/sharpens anomalies of bodies trending N-S (X-East, Y-North, Z-downward).

5. In an abandoned mine-site, three hollow spherical cavities are located below the surface centered at depths of 50, 100 and 150 metres. Assuming that residual gravity is low due to each one of these cavities are small (~ 0.05 mGal), do not interfere and can be detected by the gravimeter, the most ideal (largest) grid spacing for carrying out the gravity surveys in order to correctly delineate these cavities is __________ metres, (round off to the nearest integer).

GATE 2020

1. A 4 km-high plateau is isostatically compensated as shown in the figure. Assuming Pratt’s hypothesis of isostasy, the calculated density of the plateau is _____ kg/m3.

2. International gravity formula is based on which one of the following models?

(a) Non-rotating homogeneous spherical Earth model

(b) Non-rotating homogeneous oblate spheroidal Earth model

(d) Rotating inhomogeneous spherical Earth model

3. A micro-gravity survey with appropriate station spacing is performed to detect a subsurface spherical cavity in a bedrock of density 2500 kg/m3. The depth to the center of the cavity is 4 m from the surface and the elevation measurement accuracy of the surveying instrument is 0.1 m. The smallest cavity that can be detected by the survey must have a radius greater than _______ m. (Round off to 1 decimal place) (Assume \(G = 6.673 \times 10^{-11} m^3kg^{–1}s^{–2}\)).

4. The gravity anomaly over a spherical ore body is shown in the figure below. The calculated excess mass due to the ore body will be _______ × 1010 kg. (Round off to 1 decimal place) (Assume \(z = 1.3 \times x_{1/2}\); \(G = 6.673 \times 10^{-11} m^3kg^{–1}s^{–2}\)).

GATE questions Signal Processing

on September 26, 2020 in GATE questions

GATE - 2009

1. Which of the following is a minimum-phase wavelet? The first value in each case is at time zero.

(a) {– 2, 5, – 2} (b) {– 2, 5, 2}
(c) {6, – 1, – 2} (d) {3, 4, – 4}

2. The output of a linear and invariant system for a unit input is { 3, 1}. Then what would be the output for an input {– 2, 1} ?

(a) {– 6, 1, 1}
(c) {– 1, 6, 1}

(b) {– 1, 1, 6}
(d) {1, – 1, 6}

Statement for Linked Answer Questions 3 and 4:

Given the wavelets, a = {3, – 2} and b = { 1, – 2}

3. The cross-correlation, \(\phi_{ab}\) is given by

(a) {– 6, 7, – 2} (b) {– 6, 10, – 12}
(c) {– 4, – 11, – 6} (d) {– 6, 11, – 4}

4. The inverse of wavelet ‘a', \(W_a^{– t}\) is given by

(a) {4/3, 16/9, 17/7, 64/81}
(b) { 1/3, 2/9, 4/27, 8/81}
(c) {4/9, 1/3, 64/81, 16/27}
(d) {16/27, 64/81, 4/9, 1/3}

5. Match the following functions in time-domain with their fourier spectra:

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

GATE 2010

1. An input signal {– 1, 1, 0.2}, after passing through a delay operator z, will be

(a) \(- z^2 + z^3 + 2z^5\) (b) {0, – 1, 1, 0, 2}

2. The Hilbert transform of a function f (t) is denoted by H {f (t)}. If f (t) = sin t, then H{H(f (t))} is

(a) – sin t (b) – cost t
(c) sin t (d) cos t

3. The rectangular function \(\pi(t)\) is defined as

\(\pi(t) =1 for \ |t|\le1/2\)

\(= 0 for \ |t|>1/2\)

The convolution of \(\pi(t)\) with itself will be

(a) a triangular function \(\Lambda(t)\) (b) \(\pi(t)\) again

4. Given \(A= e^{-y}(cos x \ a_x – sin x \ a_y )\), where \(a_x\) and \(a_y\) denote the unit vectors in x- and y-directions, respectively. Then \(\nabla.(\nabla \times A)\) is equal to

(a) \(e^{-y}\) (b) 0

5. Match the items in Group I with those in Group II.

Group I Group II

P. Convolution in 1. \(\frac{1}{2\Delta}\)

time domain

Q. Nyquist frequency 2. Flat spectrum

R. Aliasing 3. Multiplication in frequency domain

S. White noise 4. Frequency folding

5. Autocorrelation function

(a) P - 3, Q - 1, R - 4, S - 2
(b) P - 2, Q - 1, R - 5, S - 4
(c) P - 3, Q - 1, R - 2, S - 1
(d) P - 2, Q - 4, R - 1, S - 5

GATE 2011

1. The frequency of a signal sampled at 200 samples per second appears as 75 Hz. If the signal was under sampled, the frequency (in Hz) of the original signal would be

(a) 100
(c) 150

(b) 125
(d) 175

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

Group I Group II

P. correlation in 1. reciprocal of total signal

frequency domain duration

Q. phase spectrum 2. aliasing

R. frequency interval 3. product of Fourier transform and its conjugate

S. undersampling 4. autocorrelation

5. Hilbert transform

(a) P - 3, Q - 5, R - 1, S - 2
(b) P - 3, Q - 4, R - 2, S - 1
(c) P - 3, Q - 4, R - 1, S - 2
(d) P - 2, Q - 3, R - 4, S - 5

3. The derivative of the following boxcar function is

Common Data Questions
Common Data for Questions 4 and 5:

Time series P and Q are given by
P = {1, – 1, – 2, 0, 1}
Q = {1, 0, – 1}

4. The convolution of P and Q is

(a) {– 1, 0, 3, 1, – 3, – 1, 1}
(b) {1, – 1, – 3, 1, 3, 0, – 1}
(c) {1, – 1, – 3, – 1, 3, 1, – 1}
(d) {1, 0, 3, 1, – 3, – 1, 1}

5. P is similar and most out of phase to Q at a lag of
(a) 0 (b) 1
(c) 2 (d) 3

GATE 2012

Common Data Questions
Common Data for Questions 1 and 2

A signal having duration of 10 seconds is sampled at a rate of 1000 samples per second. The maximum frequency of the sampled signal is 475 Hz.

1. If t he signal has been under -sampled, the maximum frequency (in Hz) of the original signal would have been

(a) 475
(c) 525

(b) 500
(d) 550

2. What is the frequency interval (in Hz) at which the spectrum of the above signal is evaluated?

(a) 0.08 (b) 0.10

GATE 2013

1. Given a scalar function, f (x, y) = xy . The curl of gradient of f (x, y) is

(a) \(2x\hat{i}\) (b) \(-2y\hat{j}\)

Common Data Questions

Common Data for Questions 2 and 3:

A recursive filter yn is given by \(y_n = 2x_n - x_{n-1} + y_{n-2}\).

2. The order of \(y_n\) is_________.

3. The transfer function of \(y_n\) in z-domain is

a) \(\frac{1-1.5z}{2-z^2}\) b) \(\frac{1-z^2}{2-1.5z}\)

c) \(\frac{2+z^2}{1+1.5z}\) d) \(\frac{1-1.5z}{2-z^2}\)

GATE 2014

1. The convolution of two finite length sequences xn = [1, 0, - 2] and yn = [1, - 1] is

(a) [-1, 1, 2, -2]
(b) [1, -1, -2, 2]
(c) [1, 0, -2, 2]
(d) [1, -2, -1, 2]

2. An 80 Hz seismic signal is sampled at a rate of 100 samples/s. What will be its aliased period (in seconds) in the sampled signal?

(a) 30 (b) 10
(c) 0.1 (d) 0.05

3. The Fourier transform and integral of the Dirac delta function respectively are

(a) 1 and 1 (b) 0 and 0

4. A signal \(x_n\) = [2, 1] is input to a system whose impulse response is \(h_n\) = [8, 4, 2, 1]. The z-transform of the output is

GATE 2015

1. In any given signal, removal of all periods shorter than Nyquist period is achieved by

(a) high-pass filtering (b) band-pass filtering
(c) low-pass filtering (d) band-reject filtering

2. The analytic signal for the function \(f(t)= sin \omega t\) is

(a) \(- cos \omega t\) (b) \(- sin \omega t\)

3. The minimum frequency at which a signal comprising of 30 Hz, 50 Hz and 70 Hz frequencies should be sampled to avoid aliasing is _______ Hz.

GATE 2016

1. Given a seismic wavelet w = { 6, – 4, – 2 } and reflectivity series r = { 0, 1, 0 }, the corresponding seismic trace is ___________.

(a) {0, – 4, 0, 0, 0} (b) {0, – 2, – 4, 6, 0}

2. The time period of the signal \(s(t)= sin(\frac{\pi}{3}t) cos(\frac{\pi}{2}t) \), is ______ seconds.

3. Assertion (a): The inverse of a minimum phase wavelet is causal and stable.

Reason (r): The Z-transform of a minimum phase wavelet has all its zeros outside the unit circle.

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

(b) (a) is false but (r) is true

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

GATE 2017

1. Convolution of two box car functions of different widths yields a

(a) step function

(b) trapezoidal function

(d) sinc function 45.

2. Assuming the Z-transform to be defined with Z as the unit delay operator, the pole of the infinite sequence \([1,\frac{1}{2}, \frac{1}{4},\frac {1}{8}]\) is at Z = _________.

GATE 2018

1. The formula for the ‘forward’ Fourier transform is \(F(\omega)=\int_{-\infty}^{\infty}f(t) dt\) and that for the ‘inverse’ Fourier transform is \(f(t)=\int_{-\infty}^{\infty}F(\omega) d\omega\) . Then, the forward Fourier transform of the function \(𝐹(\omega) = e^{-2i\omega}\) is

(a) \(2\delta(t)\) (b) \(\delta(2t)\)

GATE 2019

1. If \(G(\omega)\) is the Fourier transform of \(g(t)\), then the Fourier transform of \(g(t + ln 2)\) will be

a)\(e^{-2j\omega}G(\omega)\)

b)\(e^{2j\omega}G(\omega)\)

c)\(2e^{j\omega}G(\omega)\)

d)\(2e^{-j\omega}G(\omega)\)

GATE 2020

1. The convolution of A(4, 2, –1, 2) with B (1, 0, –1) gives

(a) {– 4, 2, –5, 0, 1, 2 }

(b) { 4, 2, –5, 0, 1, –2 }

(d) { 4, 2, 5, 0, –1, 2 }