Pure and Applied Geophysics

Schütt, H.; Spetzler, H.

doi: 10.1007/PL00001197pmid: N/A

 — We study the filling of horizontal cracks with constant aperture driven by capillary forces. The physical model of the crack consists of a narrow gap between two flat glass plates (Hele-Shaw cell). The liquid enters the gap through a hole in the bottom plate. The flow is driven purely by the force acting on the contact lines between solid, liquid, and gas. We developed a theoretical model for this type of flow on the basis of Darcy's law; it allows for the consideration of different surface conditions.¶We run the experiment for two surface conditions: Surfaces boiled in hydrogen peroxide to remove initial contamination, and surfaces contaminated with 2-propanol after boiling in hydrogen peroxide. The flow rate depends on the gap aperture and on the interaction of the liquid with the air and the solid surfaces: The smaller the aperture, the lower the flow rate due to viscous resistance of the liquid. The flow rate is also reduced when the glass surfaces are contaminated with 2-propanol. The contact line force per unit length is approximately 60% higher on clean glass surfaces than it is on glass surfaces with the 2-propanol contamination. These experimental results are in agreement with our theoretical model and are confirmed by independent measurements of the liquid-solid interaction in capillary rise experiments under static conditions with the same Hele-Shaw cell.¶Another aspect of this study is the distribution of the liquid for the different surface conditions. The overall shape is a circular disk, as assumed in the theoretical model. However, a pronounced contact line roughness develops in case of the surfaces contaminated with 2-propanol, and air bubbles are trapped behind the contact line. A further analysis of the flow regime using the capillary number and the ratio of the viscosities of the involved fluids (water and air) reveals that the experiments take place in the transition zone between stable displacement and capillary fingering, i.e., neither viscous nor capillary fingers develop under the conditions of the experiment. The contact line roughness and the trapped air bubbles in the contaminated cell reflect local inhomogeneities of the surface wettability.

Zahradník, J.; Janský, J.; Papatsimpa, K.

doi: 10.1007/PL00001198pmid: N/A

 — The ASPO method (Amplitude Spectra and POlarities) for the focal-mechanism retrieval from relatively weak events is based on a widely available instrumental setup: A few broadband stations within a denser short-period network. Collectively all stations provide the epicenter location. Complete records are taken from three-component broadband stations, without selecting a particular wave type, or picking amplitudes. It makes the method suitable for automated data processing, and enables studies of the interference crustal phases. Only the amplitude spectra are inverted. This is a robust feature which makes the method insensitive to any timing problems (such as those due to uncertain origin time, or due to technical failures). The first-motion polarities serve as an additional constraint of the amplitude-spectra inversion; only few (clear) polarities are taken from the nearest stations, wher e they mostly belong to direct P waves. The method seeks five parameters: The focal depth, scalar moment, strike, dip, and rake. Green's function, automatically including possible near-field effects and interference (e.g., surface) waves, is calculated by the discrete wavenumber method. ASPO works below the corner frequency, and the time function is not being retrieved. This feature not only minimizes the number of the inverted parameters, but also speeds up the calculation, because the lower the frequency, the faster the discrete wavenumber run. Instead of an exceedingly slow 5-parameter grid search, the inversion is organized in two steps: (i) the depth and moment determination with a coarse grid search of the strike, dip and rake, and (ii) a fine grid search of the three source angles. Uncertainty of the best-fitting solution is assessed from the minimum error value and from the scatter of the nodal lines (and/or P and T axes) between min and min + 10%. The method was tested on the clustered M ≈ 3.5 earthquakes recorded by a temporary network of three CMG3-T broadband stations in western Corinth Gulf. A fundamental problem is that the broadband stations suffer systematically from event-induced instabilities at horizontal components if earthquakes of the studied magnitudes occur at short distances, 10–30 km. Therefore, the ASPO method could not be applied below 0.1 Hz. As such, the results are sensitive with respect to unknown crustal structure details, and the focal mechanisms remain rather uncertain (minimum error higher than 0.34). Compared to synthetic tests with perturbed data, in which the error is lower than 0.2, it is concluded that the crustal model needs further improvement.

Růžek, B.; Kvasnička, M.

doi: 10.1007/PL00001199pmid: N/A

 — A novel global optimizing algorithm — Differential Evolution (DE) — has appeared recently. This method is easy and advantageous when used for kinematic location of the earthquake hypocenter. The motivation for implementing a robust (i.e., global and nonlinear) optimizing algorithm for the location problem is to obtain better results than those from the classical (i.e., linearized) approach (such as the FASTHYPO, HYPOELLIPSE, HYPOCENTER solutions, among others). Better solutions have lower final misfits expressed as the common L2 norm. The features of the DE algorithm are studied on a set of synthetic location problems. The DE procedure is controlled by 3 internal parameters, which are easy to adjust, and the convergence properties are very good. Location results using DE are compared with the HYPO71 solutions for real earthquake data from the Gulf of Corinth region, Greece. The DE results are significantly better. The DE optimizing algorithm seems to be very promising both for the location problem as well as for other problems in geophysics.

Parolai, S.; Bindi, D.; Trojani, L.

doi: 10.1007/PL00001200pmid: N/A

 — Thirty-three earthquakes which occurred in the Central Apennines (Italy) with Ml ranging from 2.4 to 3.7 have been spectrally analysed using digital recordings from twelve stations of the Rete Sismometrica Marchigiana (RSM) network. Data corrected for geometrical spreading and quality factor Q have been inverted by means of the Generalised Inversion Technique. Site responses have been compared with those obtained by H/V ratio. Site amplifications have been observed both at stations placed on Pleistocene sediments and at one station located at 1800 m altitude. Source parameters have been calculated by fitting the spectra with an automatic procedure adopting the ω2 source model. The seismic moments range from 9.23 × 1019 to 4.28 × 1021 dyne-cm with an average M 0 (S) to M 0 (P) ratio of 1.13 ± 0.38. The stress drops are generally low and they vary between 1.1 and 10.2 bar when estimated by using S source spectra, and between 0.5 and 7.1 bar when the P-source spectra are fitted. For the considered range of seismic moments we observe that the stress drop does not have significant dependence on event size.

Funahashi, F.; Yoshioka, N.

doi: 10.1007/PL00001201pmid: N/A

 — In order to clarify the effects of contact geometry of faults on transmission waves, we have performed a series of experiments in which P and S waves with known wavelength were transmitted through an artificial fault. A pair of piezo-electric transducers (PZT) with various resonant frequency were used for the transmitter and the receiver. Parallel grooves were cut on disk surfaces and two disks were placed face to face with the grooves on one disk being perpendicular to those on the other disk. This yields evenly spaced square contacts on the fault. We regard the square contacts as asperity contacts, the size and the height of which were controlled by changing the width and the depth of the grooves. We found that the transmissivity of the waves is solely determined by the ratio of the groove depth/width to wavelength. The shallower and the narrower the groove depth and width are, the larger the amplitude of first arrival is for both P and S waves. When the groove depth is shallower than a quarter of wavelength, the effect of groove depth is negligible; deeper grooves significantly reduce the amplitude. We have made a mathematical model based on the stiffness of fault. By comparing the model calculations with the observation we found that the model has a limit at which the prediction by the model deviates from the data. The deviation occurs when the ratio of the groove depth/width to wavelength becomes 0.25. We refer to the wavelength as the critical wavelength. When the wavelength is larger than the critical wavelength, the observed data can be well explained by the model. Above this threshold, the model no longer fits the data. In this range, the amplitude of transmitted waves is found to be proportional to the real contact area. Although it is a kind of paradox that the amplitude, not the energy, is proportional to the real contact area, it is possibly explained by taking a non-uniform distribution of stress on the surface of the receiver PZT into account.

Burroughs, S.M.; Tebbens, S.F.

doi: 10.1007/PL00001202pmid: N/A

 — When a cumulative number-size distribution of data follows a power law, the data set is often considered fractal since both power laws and fractals are scale invariant. Cumulative number-size distributions for data sets of many natural phenomena exhibit a “fall-off ” from a power law as the measured object size increases. We demonstrate that this fall-off is expected when a cumulative data set is truncated at large object size. We provide a generalized equation, herein called the General Fitting Function (GFF), that describes an upper-truncated cumulative number-size distribution based on a power law. Fitting the GFF to a cumulative number-size distribution yields the coefficient and exponent of the underlying power law and a parameter that characterizes the upper truncation. Possible causes of upper truncation include data sampling limitations (spatial or temporal) and changes in the physics controlling the object sizes. We use the GFF method to analyze four natural systems that have been studied by other approaches: forest fire area in the Australian Capital Territory; fault offsets in the Vernejoul coal field; hydrocarbon volumes in the Frio Strand Plain exploration play; and fault lengths on Venus. We demonstrate that a traditional approach of fitting a power law directly to the cumulative number-size distribution estimates too negative an exponent for the power law and overestimates the fractal dimension of the data set. The four systems we consider are well fit by the GFF method, suggesting they have properties characterized by upper-truncated power laws.

Tinti, S.; Bortolucci, E.; Chiavettieri, C.

doi: 10.1007/PL00001203pmid: N/A

— Landslide-induced tsunamis are receiving increased attention since there is evidence that recent large devastating events have been caused by underwater mass failures. Normally, numerical models are used to simulate tsunami excitation, most of which are based on shallow water, known also as long wave, approximation to the full equations of hydrodynamics. Analytical studies may handle only simplified problems, but help understand the basic features of physical processes. This paper is an analytical investigation of long-water waves excited by rigid bodies sliding on the sea bottom, based on the shallow-water approximation, which is here derived by properly scaling Euler equations for an inviscid, incompressible and irrotational ocean. In one-dimensional (1-D) cases (where motion depends only on one horizontal coordinate), under the further assumptions of small-height slide, which permits the recourse to linear theory, and of flat ocean floor, a solution for arbitrary body shape and velocity is deduced by applying the Duhamel theorem. It is also shown that this theorem can be advantageously used to obtain a general solution in case of a non-flat ocean floor, when the sea bottom follows a special power law, that can be adapted to study reasonable bottom profiles. The characteristics of the excited tsunamis are then evaluated by computing solutions in numerous examples, with special focus on wave pattern and wave evolution. The energy of the wave system is shown to depend on time: it grows expectedly in the initial phase of tsunami generation, when the moving body transfers energy to the water, but it may also diminish later, implying that a certain amount of energy may pass back from water waves to the slide.

Bansal, A.R.; Dimri, V.P.

doi: 10.1007/PL00001204pmid: N/A

— A technique to estimate the depth to anomalous sources from the scaling power spectra of long nonstationary gravity profiles is presented. The nonstationary profile is divided into piecewise stationary segments based on the criterion of optimum gate length in which the time-varying and time-invariant autocorrelation functions are similar. The division of a nonstationary into piecewise stationary allows identification of the portion of the crust with different geological histories, and using the stationary portion of the gravity profiles, more consistent depths to the anomalous sources have been obtained. The technique is tested with the synthetic gravity profile and applied along the Jaipur-Raipur geotransect in western and central India. The geotransect has been divided into four stationary parts: Vindhyan low, Bundelkhand low, Narmada rift and Chhattisgarh basin; each section corresponding to a different geological formation. Forward modeling of gravity data using results of each stationary section is carried out to propose the subsurface structure along the Jaipur-Raipur transect.

Sarma, V.S.; Srinivas, G.S.; Joshi, M.S.

doi: 10.1007/PL00001205pmid: N/A

— This work extends the results that Apparao et al. (1997a) obtained for a vertical resistive sheet to the case of inclined resistive sheet models for different electrode arrays. It is found that the depth of investigation (DI) remains the same as that for the vertical target. Using this DI, modified pseudo-depth sections have been constructed over sheet models at different inclinations. It is noted that, for the Wenner array, the maximum anomaly contours fall directly over the target cross section. For dipole-dipole and three-electrode arrays, these contours fall on the up-dip side of the dipping target, with the maximum anomaly contour matching the depth level of the top of the target. It is also observed that the target cross section is at a distance of about 0.33L (L/3) from the maximum anomaly value/contour position for the three-electrode array and 0.25L (L/4) for the dipole-dipole system. These features are identifiable in the individual profiles and may help field geophysicists in the recognition and location of dipping target bodies.

Kambezidis, H.D.; Adamopoulos, A.D.; Zevgolis, D.

doi: 10.1007/PL00001206pmid: N/A

 — This work estimates the Ångström coefficients, assuming a linear behavior of the natural logarithm of aerosol optical thickness, ln δα(λ), versus the natural logarithm of wavelength, ln λ, in the urban environment of Athens for a period of one year. The calculation of the coefficients α, β, was carried out using records of spectral beam irradiance in the 320–575 nm spectral range. The seasonal and diurnal variation of the coefficients shows different features with generally higher values of β and lower values of α in summertime. The Ångström coefficients are investigated with respect to various wind regimes and the results are discussed with a view to air pollution sources, climatic and topographic characteristics of the Athens basin. A similar study is also carried out for the Schüepp's turbidity parameter.