Interpretation theory in applied geophysics: Grant, F S ... Interpretation theory in applied geophysics Unknown Binding – January 1, 1965 5.0 out of 5 stars 1 rating. See all formats and editions Hide other formats and editions. The Amazon Book Review Book recommendations, author interviews, editors' picks, and more. Read it now. Enter your mobile number or email address below and we'll send you a ...

Interpretation Theory in Applied Geophysics Grant (McGraw-Hill, 140s.)

In this paper, I present a modification of the Beylkin inversion operator. This modification accounts for the band-limited nature of the data and makes the role of discontinuities in the sound speed more precise. The inversion presented here partially dispenses with the small-parameter constraint of the Born approximation. This is shown by applying the proposed inversion operator to upward scattered data represented by the Kirchhoff approximation, using the angularly dependent geometrical-optics reflection coefficient. A fully nonlinear estimate of the jump in sound speed may be extracted from the output of this algorithm interpreted in the context of these Kirchhoff-approximate data for the forward problem. The inversion of these data involves integration over the source-receiver surface, the reflecting surface, and frequency. The spatial integrals are computed by the method of stationary phase. The output is asymptotically a scaled singular function of the reflecting surface. The singular function of a surface is a Dirac delta function whose support is on the surface. Thus, knowledge of the singular functions is equivalent to mathematical imaging of the reflector. The scale factor multiplying the singular function is proportional to the geometrical-optics reflection coefficient. In addition to its dependence on the variations in sound speed, this reflection coefficient depends on an opening angle between rays from a source and receiver pair to the reflector. I show how to determine this unknown angle. With the angle determined, the reflection coefficient contains only the sound speed below the reflector as an unknown, and it can be determined. A recursive application of the inversion formalism is possible. That is, starting from the upper surface, each time a major reflector is imaged, the background sound speed is updated to account for the new information and data are processed deeper into the section until a new major reflector is imaged. Hence, the present inversion formalism lends itself to this type of recursive implementation. The inversion proposed here takes the form of a Kirchhoff migration of filtered data traces, with the space-domain amplitude and frequency-domain filter deduced from the inversion theory. Thus, one could view this type of inversion and parameter estimation as a Kirchhoff migration with careful attention to amplitude.

On the imaging of reflectors in the earth

SUMMARY

A migration algorithm based on the least-squares formulation will find the correct reflector amplitudes if proper migration weights are applied. The migration weights can be viewed as a pre-conditioner for a gradient-based optimization problem. The pre-conditioner should approximate the pseudo-inverse of the Hessian of the least-squares functional. Usually, an infinite receiver coverage is assumed to derive this approximation, but this may lead to poor amplitude estimates for deep reflectors.



To avoid the assumption of infinite coverage, new amplitude-preserving migration weights are proposed based on a Born approximation of the Hessian. The expressions are tested in the context of frequency-domain finite-difference two-way migration and show improved amplitudes for the deeper reflectors.

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Frequency-domain finite-difference amplitude-preserving migration

A process may include providing heat from one or more heaters to at least a portion of a subsurface formation. Heat may transfer from one or more heaters to a part of a formation. In some embodiments, heat from the one or more heat sources may pyrolyze at least some hydrocarbons in a part of a subsurface formation. Hydrocarbons and/or other products may be produced from a subsurface formation. Certain embodiments describe apparatus, methods, and/or processes used in treating a subsurface or hydrocarbon containing formation.

Thermal processes for subsurface formations

You must turn in your code as well as output files. Please generate a report that contains the code and ouput in a single readable format. Getting Started  You may want to download Irfanview image viewing software. It handles pretty much any image type, lets you convert, and provides batch processing.  Download the sample images from the class website. The following question operates on the city.jpg image. (a) Perform image smoothing using a 7×7 averaging filter and a Gaussian filter with σ = 0.5 and 3. Compare the outputs. (b) Perform edge enhancement using the Sobel operator (Matlab's default parameters). Repeat using the Laplacian and Laplacian of Guassian operators. Compare the outputs 2. Frequency Domain Filtering The following question operates on the city.jpg image. (a) Find the Fourier transform of the image. Be sure to center the frequencies. (b) Perform image smoothing in the frequency domain using the filters defined in the previous problem. Compare the output images from the two methods (spatial and frequency) and the time for operation. (c) Perform edge enhancement using the filters defined in the previous problem. (d) Define a lowpass filter in the frequency domain with radius of 1/4 the height. Show the result. Repeat with a similar sized Guassian and compare the results. Give the σ parameter you used and show the output transform image. (e) Repeat with a rectangular filter with the same dimension as the ideal lowpass. Compare the results between the ideal filter and the rectangular approximation. 3. Canny Edge Detection (a) Give the convolution kernels for determining the gradient. You may examine the function gradient.m to help with the explanation. (It may be easiest to apply the gradient to an impulse and inspect the results. (b) Implement the simplified version of the Canny edge detector (single scale). The syntax of the function should be where E contains the detected edges, M the smoothed gradient magnitude, A contains the gradient angle, I is the input image, sig is the σ parameter for the smoothing filter, and tau= [τ h , τ l ] is the two element vector containing the hysteresis thresholds. See Algorithm 6.4 for non-maximal suppression and Algorithm 6.5 for hysteresis thresh-olding. (It may be more efficient to implement the hysteresis as edge tracking)

http://ieeexplore.ieee.org/iel5/5/31355/01457626.pdf

Multidimensional digital signal processing

Downgoing waves in multicomponent VSP experiments are used to obtain seismic P- and S-wave velocities as a function of depth and angle of incidence. If P and SV waveforms do not overlap in time at the depth of interest, local velocities of the medium are obtained by separate analysis of these events. The apparent velocity of the event (P or SV) is computed from the moveout across several neighboring depth locations. The angle of incidence of the same event is computed from the particle‐motion hodogram within an appropriately chosen time window. Then, the local medium velocity (P wave or S wave depending on the chosen event) is given by the apparent velocity multiplied by the cosine of the angle of incidence. Layer interfaces with reasonably sharp velocity contrasts are efficient P-wave to SV-wave converters, even at moderate angles of incidence. In offset VSP experiments, converted SV waves are generated with varying strengths at practically all depths. Consequently, the converted SV waveforms partially o...

Inversion of P and SV waves from multicomponent offset vertical seismic profiles

The scattered wave field propagated backward in time into an arbitrary background medium is related via a volume integral to perturbations in velocity about the background, which are expressed as a scattering potential. In general, there is no closed-form expression for the kernel of this integral representation, although it can be expressed asymptotically as a superposition of plane waves backpropagated from the receiver array. When the receiver array completely surrounds the scatterer, the kernel reduces to the imaginary part of the Green's function for the background medium.This integral representation is used to relate the images obtained by imaging algorithms to the actual scattering potential. Two such relations are given: (1) for the migrated image, obtained by deconvolving the extrapolated field with the incident field; and (2) for the reconstructed image, obtained by applying a one-way wave operator to the extrapolated field and then deconvolving by the incident field. The migrated image high-lights rapid changes in the scattering potential (interfaces), whereas the reconstructed image can, under ideal conditions, be a perfect reconstruction of the scattering potential. 'Ideal' conditions correspond to (1) weak scattering about a smoothly varying background medium, (2) a receiver array with full angular aperture, and (3) data of infinite bandwidth.Images obtained from a multioffset vertical seismic profile (VSP) illustrate some of the practical differences between the two imaging algorithms. The reconstructed image shows a much clearer picture of the target (a reef structure), in part because the one-way imaging operator eliminates artifacts caused by the limited aperture of the receiver array.

Reverse-time wave-field extrapolation, imaging, and inversion

Recent advances in well‐placement technology now allow a borehole to be steered with considerable precision inside the reservoir. With modern completion technology, the subsequent flow of hydrocarbons within the reservoir can be controlled to a greater extent than ever before. These developments have further emphasized the need for an improved ability to image structures such as caprock, stringers, faults, fractures, and pore‐fluid contacts, on the reservoir scale.

Acoustic imaging of reservoir structure from a horizontal well

A system and method for performing an adaptive drilling operation is provided. The method involves obtaining data prior to drilling, constructing a base model with a base model unit from data obtained prior to drilling, constructing an overburden posterior model with an overburden model unit using the base model and data obtained from overburden drilling, constructing a reservoir posterior model with a reservoir model unit using the overburden posterior model and the data obtained from reservoir drilling and updating drilling operation based on the models.

System and method for performing an adaptive drilling operation

Crossed dipole acoustic logs represent a new class of measurement of subsurface formations which can provide detailed information on anisotropy not previously available. As with any new class of data, departures from previous conceptions may occur. In this case, the detail inherent in sonic-scale measurements provide information on anisotropy at sub-formation scale whereas seismic investigations of anisotropy are normally restricted to sequence-scale. When borehole conditions allow formation properties to be measured, the tool provides detailed information interpretable in terms of fracturing. Crossed dipole acoustic logs were acquired using the multisource/multireceiver technique, and Alford rotation (Alford, 1986; Thomsen, 1988 and Esmersoy, 1994) was employed to resolve observed flexural or shear-wave mode splitting. The data show indications of sensitivity to natural fracturing and, secondarily, to borehole ovality. The azimuth of the leading shear-wave polarization, qS1, compare favorably with independent data on fracture azimuth. Thomsen anisotropy parameter {gamma} as high as 10--20% is observed in certain anisotropic intervals. Such intensities, and their spatial occurrence on log data, are new information on anisotropy.

Cengiz Esmersoy

Papers

Inversion of P and SV waves from multicomponent offset vertical seismic profiles

Reverse-time wave-field extrapolation, imaging, and inversion

Acoustic imaging of reservoir structure from a horizontal well

System and method for performing an adaptive drilling operation

Case Studies of the Dipole Shear Anisotropy Log