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The most cited paper published by GEOPHYSICS, according to the ISI Web of Knowledge (operated by Thomson Reuters), is Leon Thomsen's 1986 article “Weak elastic anisotropy.” This paper, which introduced the now standard Thomsen anisotropic parameters, had been cited more than 780 times at the time this anniversary issue of GEOPHYSICS was going to press. A statistician looking at this number might reject it as an outlier because it is far more than any other paper published by GEOPHYSICS in its 75 year history. The paper with the second highest number of citations (628) was “Occam's inversion — a practical algorithm for generating smooth models from electromagnetic sounding data” by S. C. Constable, R. L. Parker, and C. G. Constable, published in 1987. The difference in number of references to the top two papers, more than 150, is striking as the two papers at numbers 49 and 50 had been cited 185 and 184 times, respectively. Thomsen's paper is also, of course, the most cited article published by GEOPHYSICS in the last 25 years and comparison with others in this category puts the importance of this work into even starker relief. It has been cited nearly 600 more times than the 16th paper on that list, “Velocity analysis for transversely isotropic media” by T. Alkhalifah and I. Tsvankin (which is an extension of Thomsen's work and, of course, cites it). This paper is also 47th on the “all years” list. Chris Liner, former editor of GEOPHYSICS (1999–2001), gave a concise analysis of the importance of Thomsen's breakthrough in World Oil in July 2010: A bit more about anisotropy is in order. The tendency of seismic waves to have directional velocity was well known 50 years ago, and the theory was worked out in detail 50 years before that. But anisotropy …

To: “The Best Papers Published in Geophysics (by the numbers),” GEOPHYSICS, 75, no. 5, 75A275–75A289.

Most authors of GEOPHYSICS papers are from universities or government research institutions. That does not mean no interesting research is being done by the oil or geophysical industry. In the current competitive age, it is apparently difficult for geophysicists from the industry to find time to write elaborate papers for GEOPHYSICS. Therefore, the GEOPHYSICS editors have decided to encourage authors from the oil and geophysical industry to submit high-quality papers. SEG Editor Gerard T. Schuster asked me to develop a shorter route for such papers that have at least one author from the industry.

In his important paper “Computing true amplitude reflections in a laterally inhomogeneous earth” (Hubral, 1983, this issue) the author derives the fundamental equation [Formula: see text] [Hubral (25)] Here [Formula: see text] is a factor compensating the energy of a zero‐offset reflection for geometrical spreading and [Formula: see text] and [Formula: see text] are certain wavefront curvature matrices which will be explained later.

[Editor’s note: The paper by A. Ziolkowski which appeared in the February issue of Geophysics has generated a great deal of interest. For our readers’ convenience, we are reprinting here two letters that appeared in The Leading Edge (July 1991 TLE, p. 8), followed by three discussions on the paper and a reply to each by the author.] Dear Editors: Every once in a great while, a paper appears in Geophysics which is more significant than first meets the eye and mind. These papers, like too many others, are barely scanned and forgotten or brushed aside, or even criticized for incidental reasons (disagrees with our own ideas, isn’t written in an acceptable “tone,” etc.). I think Ziolkowski’s paper in the February 1991 issue (Why don’t we measure seismic signatures?) is possibly one of these.

We compare the distribution of authors of papers published in GEOPHYSICS during 1975-76 to SEC membership distribution in 10 employer classifications. Also, paper distribution is compared to membership distribution in 9 disciplines. A disproportionately large percentage (43.2) of authors are in academic institutions which employ a small percentage (5.6) of Society members. Percentage of authors in government agencies (20.6) and in service companies (5.8) also are larger than percentage of members in these two employer classifications (6.7 and 2.4, respectively). Percentage of authors in petroleum companies (19.2) and in contracting companies (2.3) are considerably less than percentage of members in these two employer classifications (50.8 and 14.6, respectively). Percentage of papers (55.6) in the four potential field disciplines (gravity, magnetic, electrical, and electromagnetic) far exceeds the percentage of SEG members (30.5) in these disciplines. By contrast, percentage of papers on the seismic method (30.6) is appreciably less than percentage of members (56.5) in this discipline.

Oral and written presentation of a scientific paper require dissimilar preparation. Properly planned figures carry the theme in oral presentation from introduction through conclusions. The accompanying comments by the speaker, using the slides as notes, explain and emphasize. The planning of figure sequence and practice of the running comments aid mutually in assuring an optimum organization. An integrated delivery results. The complete and permanent disclosure in the published paper utilizes figures and tables primarily for the display of data. The text describes the research and carries the argument. The abstract, tables, figures, and figure captions should provide a good synopsis of the paper. Complete disclosure requires clear writing which is attained by outside criticism and thoughtful and continued revision.

In an eloquent paper Grant (1954) has commented briefly on my paper, ‘Regional Correction of Gravity Data’ (Vajk, 1951), stating that I argue in favor of graphical methods in determining a regional gravity effect and objected strongly to my conclusions that ‘…the regional effect cannot be determined uniquely. t is an interpretation problem which cannot be solved by some mechanical mathematical methods but only by analysis of the gravity data. Such determination is unavoidably a subject of personal factors as is every gravity (or magnetic) interpretation’.

The experimental data presented in the above paper are of interest and value. Nevertheless, it is of some importance to note a basic claim made by the authors; namely, that they can measure the tortuosities of porous media experimentally. This claim, we believe, cannot be substantiated. We shall demonstrate below why we think the claim is unjustified. It is necessary first to point out that the paper under discussion is based on the reasoning presented originally by Winsauer, Shearin, Masson and Williams. Thus what is said of the present paper applies with equal strength to the earlier work.

In his paper, Tuman found that, surprisingly, in all cases studied the minimum travel time of acoustic waves was along a curved path in a formation surrounding a borehole. The curvature resulted from velocity variations around the borehole in formations which show a nonlinear stress‐strain relationship. However, the results of these calculations may be in error due to the use of incorrect stresses selected for the determination of the local acoustic wave velocity. In particular, the use of the radial stress distribution for this purpose is doubtful for the calculation of a curved travel path which in general does not deviate much from the vertical direction.

When J. N. Hummel published his first apparent resistivity curves some 30 years ago, he used coordinates with a linear scale. A short time later it was found that such master curves are universally usable only when plotted on logarithmic scales. The reason for this is that the shape of the curves does not depend upon the absolute electrode spacing and the absolute resistivity values but only on the relative values. This, naturally, also holds true for the examples shown by A. R. Clark. The curves as shown by him reveal a resistivity ratio of [Formula: see text]. In the same way, the “Distance as a fraction of the Semimajor Axis” is a quotient. Both coordinates should therefore be presented in a logarithmic scale. When so plotted, the characteristic properties of the curves are much more conspciuous and are very different from those when linear scales are used. The remarks made by the author relative to the shape of the curves may have to be revised.

Baranov’s pseudo‐gravimetric anomaly method is based on well‐known relationships and his development appears to be sound. Applications of his methods should be of very appreciable use in evaluating aeromagnetic surveys. The comments which follow should not be interpreted as criticisms. They are intended to emphasize the conditions and limitations under which Baranov’s techniques might be utilized.

The “Review Article” by L. V. Hawkins in the December 1961 issue of Geophysics is an excellent article on the method used by a certain small group for the interpretation of shallow refraction work. However, it does not seem to give an unbiased review of methods generally used for this purpose and it describes a method that is rather unnecessarily complicated.

As this commentator pointed out originally in 1938, and at various times subsequently (Hubbert, 1938, 1946), the teaching of geophysics in the departments of geology as these were constituted up until 15 or 20 years ago was an almost impossible task. This was because it was then the custom, with few exceptions, for geology students to terminate their mathematical training at about trigonometry or college algebra, their physics either with no college physics at all or at most one year, and their chemistry after qualitative or quantitative analysis.

Bulletin No. 442 summarizes the results of investigations performed by the Bureau of Mines since 1930 relative to damage to buildings from quarry blasts, a study which was undertaken to supply basic data in settlement of damage claims.

I am herewith sending a list of typographical errors and omissions of several of my papers in Geophysics: “Transient Electromagnetic Propagation in a Conducting Medium” Vol. 16, pp. 213-222, 1951.

On page 240 of this very useful and stimulating paper, there appears to be an error in equation (14). The multiplier representing the number of different permutations of the ray‐path segments for a given j, k, n is given as (1) [Formula: see text], and this formula has apparently been used to compute the curves in Figures 7, 8, and 9. The number of permutations is actually larger and is given by the multiplier (2) [Formula: see text]. Since these multipliers are identical for k=0 and k=j−1, the examples in Figure 6 and the curves in Figures 7, 8, and 9 for j=0, 1, and 2 are correct. For j⩾3, sizable differences do occur; however, the qualitatively important features of the curves given do not change.

Papers such as “Statistical Evaluation of Deep Crustal Reflections in Germany,” by Dohr and Fuchs may seem unusual to the many readers of Geophysics who are likely to be involved in seismic exploration for oil. This is because geophysicists using seismic techniques in oil exploration have an enormous advantage

An extensive density study based on gamma‐gamma (or density) logs from 435 wells in western Canada was undertaken in an area extending from the Rocky Mountains in the west to longitude 100°W in the east and from the international boundary in the south to latitude 56°N in the north. The logs, with, total footage of about 814,000 ft, were subdivided into nearly 34,000 intervals for computer input. In this paper density is studied without separation of measurements according to lithology. Uncompensated density logs yield an average density for the whole basin which is lower by [Formula: see text] than that from compensated density logs. The weighted average densities in the Western Canada Basin established from compensated density logs are as follows: [Formula: see text] for the section above sea level, [Formula: see text] below sea level, and [Formula: see text] without regard to depth. Large density variations both horizontally and vertically are demonstrated on several contour density maps. The prevailing northwesterly contour trends indicated on maps of density and by some statistics coincide with the strike of the strata. Generally, density above sea level increases toward the Rocky Mountains, whereas below sea level no general rule is apparent. The linear correlation coefficient between density and depth based on all compensated density logs is 0.46, and the regression line of density D (in [Formula: see text]) on depth below sea level d (in feet) has the equation D = 2.372 + 0.000052d ± 0.21. The mean value of the correlation coefficient between density and depth calculated independently in single wells is 0.45, and a similarly established mean for density increments with depth is [Formula: see text] per 10,000 ft. However, both local (in single wells) and regional density sample distributions are most often skewed to the left which suggests that, in general, the vertical density gradient is higher at smaller depths than at larger depths.

Records of several types of ground motion are obtained with two vertical mechanical seismographs of widely different characteristics, mounted on the same base and recorded on the same moving photographic paper. Companion records obtained are shown in one case to yield substantially the same calculated ground motion although the original records are very dissimilar.

The propagation of seismic waves in fractured rocks is greatly influenced by the fracture system and fluid content. Seismic anisotropy varies with frequency and fluid saturation. Previous theories on frequency-dependent anisotropy (FDA) are mostly limited to the assumption of single-phase fluid, whereas almost all reservoirs are usually partially or fully saturated with one or more fluids. The inelasticity, heterogeneity, and anisotropy exhibited by real earth media seriously challenge the traditional theory of uniform, fully elastic media. Therefore, based on the Chapman elastic theory, this paper considers the viscoelastic model, the relative mobility of saturated fluids, and the coupled effects of commonly independently considered squirt flow and patch effects on the frequency-dependent anisotropic seismic wave propagation in viscoelastic media. By calculating the frequency-dependent anisotropic elastic coefficients of two-phase immiscible fluid-saturated fractured rocks, a new viscoelastic Chapman extension model for FDA in partially saturated rocks, which includes the unified seismic wave propagation effects of squirt flow and patch effects, is constructed. The effect of relative permeability is significant, and compared to the case of complete saturation, the effective fluid mobility in partially saturated rocks may be lower, which may lead to nonmonotonic changes in elastic modulus and water saturation. Numerical experiments are conducted on the proposed viscoelastic Chapman extension model to discuss the coupling effects of squirt flow and patch effects on the FDA of viscoelastic media in cracked rocks with partially saturated reservoirs, under the conditions of no fractures and the existence of fractures. The simulation results of the P-wave modulus, P-wave velocity, and anisotropy parameters confirm the validity of the proposed method and model. This paper links the anisotropy of viscoelastic media with fluid flow parameters in fractures, which is conducive to improving the understanding of frequency-dependent seismic anisotropy in partially saturated rocks with fractures and the combination of seismology and reservoir engineering.

High-resolution and high-fidelity seismic inversion imaging are one of the core issues of lithologic reservoir exploration. As a linearization subproblem of full waveform inversion (FWI), least-squares migration (LSM) is the basic theoretical framework of high-resolution and high-fidelity inversion imaging that can be solved in either the data domain or image domain. For data domain LSM (DD-LSM), the calculation of the data domain iteration can be very compute-intensive. In practical situations, the convexity of the cost function of LSM could be poor, resulting in the slow or even non-convergence iteration, so the ideal inversion imaging results cannot be reached. The image domain LSM (ID-LSM) follows the logic of image deblurring, which realizes the effects of LSM from another way. The key problem of ID-LSM is to calculate a reliable Hessian matrix that can be effectively replaced by a set of point-spread-functions (PSFs). Affected by the unknown source wavelet, the accuracy of the background velocity and the accuracy of the forward/migration operator, the calculation results of the Hessian/PSF cannot be accurate. In this paper, we first illustrate the impact of incorrect Hessian/PSF on ID-LSM through numerical experiments. To eliminate the influence of inaccuracy of PSF, this paper proposes the ID-LSM problem to a high-dimensional image deconvolution problem. An alternate update strategy of PSF and imaging results is given under the framework of the Expectation-Maximization (EM) algorithm by additionally introducing prior information about PSF and inversion result. Numerical examples on both synthetic data and field data verify the proposed method significantly improves the image quality.

The old technology [Formula: see text]-[Formula: see text] deconvolution stands for [Formula: see text]-[Formula: see text] domain prediction filtering. Early versions of it are known to create signal leakage during their application. There have been recent papers in geophysical publications comparing [Formula: see text]-[Formula: see text] deconvolution results with the new technologies being proposed. These comparisons will be most effective if the best existing [Formula: see text]-[Formula: see text] deconvolution algorithms are used. This paper describes common [Formula: see text]-[Formula: see text] deconvolution algorithms and studies signal leakage occurring during their application on simple models, which will hopefully provide a benchmark for the readers in choosing [Formula: see text]-[Formula: see text] algorithms for comparison. The [Formula: see text]-[Formula: see text] deconvolution algorithms can be classified by their use of data which lead to transient or transient-free matrices and hence windowed or nonwindowed autocorrelations, respectively. They can also be classified by the direction they are predicting: forward design and apply; forward design and apply followed by backward design and apply; forward design and apply followed by application of a conjugated forward filter in the backward direction; and simultaneously forward and backward design and apply, which is known as noncausal filter design. All of the algorithm types mentioned above are tested, and the results of their analysis are provided in this paper on noise free and noisy synthetic data sets: a single dipping event, a single dipping event with a simple amplitude variation with offset, and three dipping events. Finally, the results of applying the selected algorithms on field data are provided.

Considering all types of pure-mode and converted waves, we derive the azimuthally dependent, fourth-order normal moveout (NMO) velocity functions, and hence the corresponding effective anellipticity functions, for horizontally layered orthorhombic media. We emphasize that this paper does not suggest a new nonhyperbolic traveltime approximation; rather, it provides exact expressions of the NMO series coefficients, computed for normal-incidence rays, which can then be further used within known azimuthally dependent traveltime approximations for short to moderate offsets. We do not assume weak anisotropy or acoustic approximation for P-waves. At each layer, the elastic parameters, thickness, and azimuth of the orthorhombic vertical symmetry planes are considered to be different. We distinguish between two different azimuths: slowness azimuth (part 1 of this paper) and offset azimuth (part 2 of this paper). In part 1, the slowness-azimuth domain NMO is approximated as a series of either infinitesimal horizontal slowness (slowness-azimuth/slowness domain) or infinitesimal offsets (slowness-azimuth/offset domain). Similarly, in part 2, we distinguish between two offset-azimuth domains: offset-azimuth/slowness and offset-azimuth/offset. Note that the azimuthally dependent NMO velocity functions of each of the four cases are different. The validity of the method is tested by introducing our derived azimuthally dependent, fourth-order effective anellipticity, into the well-known azimuthally dependent, asymptotic nonhyperbolic traveltime approximation, in which we compare the traveltime approximation versus exact numerical ray tracing for short to moderate offsets. It is clearly shown that for these types of azimuthally anisotropic layered models, the fourth-order terms are essential even for relatively small horizontal-slowness values or short offsets.

We have developed a new tomographic inversion method that is able to determine the properties of complex surface waves, which are multimodal and heterogeneous. These properties can be used to generate a detailed near-surface earth model or to predict and remove the surface waves, while protecting reflection signals even with aliased data. The inversion assumes plane-wave physics and generates surface-consistent model parameters as a function of frequency. In this paper, we validate our method with 2D models and data. In a companion paper, we demonstrate its application to 3D data. Inversion for a single mode is linear, but the linearity does not hold at higher frequencies, where multiple modes interfere. However, single-mode inversion results can be used to create a starting model for the subsequent nonlinear multimode tomography. The resulting velocity-frequency grid has greater resolution compared with a beam-forming method. The dispersion curves can be used as input to a subsequent standard 1D surface-wave inversion to generate a velocity-depth model. The tomographic method also determines a grid of attenuation quality factors and variations in the source amplitude and bandwidth, which correlate with the near-surface elevation changes. The amplitude and phase properties can be used together to predict the surface-wave waveforms, which can then be adaptively subtracted from the data on a trace-to-trace basis.

Three-dimensional survey design for PS data is more complex than for P-wave data; therefore, I was particularly interested in this paper to see how the authors solved their specific problem. In the following, I make a few suggestions for improvement of the PS design process and I explain how some of the analysis results given in the paper can be better understood. In the paper’s abstract, the objectives of the design are described as “acceptable fold balance between bins and relatively smooth distribution of offset and azimuth within bins.” (“Smooth” is a somewhat strange property when describing the distribution of discrete shot-receiver pairs in bins, but the authors apply a smoothing filter during their bin analysis). The authors also aim for “even” (P58l [Pxxl, Pxxr refer to page number Pxx, left column, right column, respectively]) or “regular” (P58r) distributions of offset and azimuth. Certainly, the bin attributes do say something about the quality of the design, but judgment of this quality is not straightforward. Consider “Although offset-azimuth distribution is not as smooth as for the higher density designs, it is acceptable,” (P66r); the authors do not clarify why it is judged as acceptable. Of course, all survey design requires some judgmental reasoning at the end, open to change, but the differences between the PS results shown in Figures 8 and 11 are so large that the conclusion “acceptable” for the Figure 11 design would deserve a more clear explanation. Another problem of focusing the design process on only bin attributes is that there is no attention for the choice of bin size or station interval and corresponding ability to deal with noise. Also, the suitability for prestack migration needs attention for bin size and for sparsity of the geometry. How to go about this? Usually, in “conventional survey design” (Vermeer, 2012), dense …

As an alternative method for the compensated neutron porosity measurement method, the neutron-gamma porosity measurement method is widely used in cased holes. However, the neutron-gamma porosity measurement method has some problems, such as the lack of detailed theoretical analysis and low sensitivity in high-porosity formations. The purpose of this paper is to clarify the theory of neutron-gamma porosity measurement, improve the measurement sensitivity, and eliminate the effects of environmental factors. Based on the neutron diffusion theory and the gamma transport theory, the distribution of capture gamma rays is described. A new neutron-gamma porosity measurement method is developed based on inelastic and capture gamma-ray distribution. The applicability of the new method in different environments is analyzed using the Monte Carlo method, and the effectiveness of this method is verified using the synthetic model. The results indicate that the capture gamma-ray ratio is only related to the source-detector distance, gamma-ray attenuation length, and neutron migration length. By combining density, different neutron cross sections, inelastic gamma-ray count ratio, and capture gamma-ray count ratio, the parameter secondary gamma-ray hydrogen index (SGH) related to hydrogen index can be extracted. The dynamic range of SGH is much higher than thermal neutron count ratio and the capture gamma-ray count ratio. The errors in porosity calculation by this method under different borehole and lithologic conditions are generally less than 2 pu. The calculation error of this method is close to that of the compensated neutron porosity measurement method. In addition, the applicability of the new method is analyzed without density data, and the results indicate that the calculation results are basically consistent with the results of calculation with density data. The new method has great potential for extensive applications in cased holes or open holes as an alternative for the compensated neutron porosity logging measurement method.

Least-squares reverse time migration (LSRTM) has shown great potential to improve the amplitude-fidelity and spatial resolution of reverse time migration (RTM) image. However, the main disadvantage is that it requires significant computational resources for the iterative solution. To ameliorate this problem, the image-domain least-squares reverse time migration (IDLSRTM) approach through point-spread functions (PSFs) has been proven to be a viable and alternative technique to deconvolve the standard RTM image. In this paper, we present a tutorial for the numerical implementation of IDLSRTM through PSFs. The Hessian matrix in the standard IDLSRTM approach is estimated through the spatial interpolation of precomputed PSFs on the fly, where the PSFs are computed by one-round forward modeling and migration. However, the resulting IDLSRTM scheme is highly ill-conditioned, because of the incomplete acquisition condition, irregular subsurface illumination, and band-limited data. To stabilize inversion and improve the inverted image, we suggest that the PSFs and RTM image should be deblurred by applying a deblurring filter. The deblurring PSFs can reduce the condition number of the standard Hessian matrix and make the inverse problem more well-conditioned, thus improving imaging quality and accelerating convergence. Furthermore, the regularization operators should be imposed to produce a reasonable inverted image and avoid the overfitting of the image-matching term. Based on several examples with synthetic and field data, we can conclude two significant points. The first point is that the standard IDLSRTM approach through the conventional PSFs can only recover a similar reflectivity image to the deblurring RTM and non-stationary matching filter (NMF) approaches. The second point is that the deblurring IDLSRTM approach through the deblurring PSFs can retrieve the reflectivity image with higher resolution and better amplitude-fidelity than the standard IDLSRTM approach and the standard RTM approach with the deblurring filter or NMF.

In this paper, we derive a new poroelastic wave equation in triple-porosity media and develop a weighted Runge-Kutta (RK) discontinuous Galerkin method (DGM) for solving it. Based on Biot’s theory and Lagrangian formulas, we obtain 3D Biot’s equations in a heterogeneous anisotropic triple-porosity medium. We also summarize poroelastic wave equations in single- and double-porosity media. The traditional two-phase theory is a special case of the porous theory. Compared with single- or dual-porosity wave equations, our triple-porosity wave equation generates more accurate wavefield information. The isotropic and anisotropic cases are considered. Subsequently, we formulate the new poroelastic equation into a first-order hyperbolic conservation system, which is suitable to be solved by DGM. An optimized local Lax-Friedrichs flux and an implicit-weighted RK time discretization scheme are used for this computation. We use two types of mesh elements — quadrilateral and unstructured triangular elements. We find that there are two kinds of slow P waves, P1 and P2 waves, in double-porosity media, whereas three kinds of slow P waves, P1, P2, and P3 waves, exist in three-porosity media. We also study the analytical and numerical solutions of propagation velocities for different waves in isotropic media without dissipation using the Jacobian matrix of DGM and provide a comparison of field variables about three types of wave equations. Finally, we conduct a series of examples to quantitatively investigate the propagation properties of seismic waves in isotropic and anisotropic multiporosity media computed by DGM. The slow P wave in multiporosity media with dissipation decays rapidly, which also will lead to phase distortion. Numerical results verify the correctness and applicability of our proposed new equation and indicate that the weighted RK DGM is a stable and accurate algorithm to simulate wave propagation in poroelastic media.

A great number of high-quality fractured-vuggy reservoirs (FVRs) are buried in the ultradeep carbonate strata in the Tarim Basin, Western China. Drilling confirms that some FVRs with strong beaded reflections are partially or completely filled with solids, resulting in oil and gas exploration failures. In this paper, we propose a well data (the drilling information and the well-logging data) constrained seismic waveform component decomposition and reconstruction method for ultradeep FVR characteristic identification (WSFI). WSFI contains the well data (the drilling information and the well-logging data) constrained seismic waveform component linear discriminant analysis and reconstruction and seismic attribute (i.e., root-mean-square amplitude)-based FVR characteristic identification. A forward-modeling example indicates that WSFI can effectively identify the FVR characteristics. Field data example in the ZG block in the Tarim Basin demonstrates that WSFI can be widely used for FVR characteristic identification.