Lý thuyết Fractal và những ứng dụng của nó trong Thu thập, Xử lý và Giải thích (API) trong Nghiên cứu Địa vật lý: Một Bài Tổng Quan

Bansal, A.R., Gabriel, G., Dimri, V.P., and Krawczyk, C.M. (2011) Estimation of depth to the bottom of magnetic sources by a modified centroid method for fractal distribution of sources: an application to aeromagnetic data in Germany. Geophysics, v.76, pp.L11–L22. Bansal, A.R., Anand, S.P., Rajaram, M., Rao, V.K., and Dimri V.P. (2013) Depth to the bottom of magnetic sources (DBMS) from aeromagnetic data of Central India using modified centroid method for fractal distribution of sources. Tectonophysics, v.603, pp.155–161. Bansal, A.R., and Dimri, V.P. (2013) Modelling of magnetic data for scaling geology. Geophy. Prosp., v.62, pp.385–396. Barnsley, M.F. (1986) Fractal functions and interpolation. Constr. Approx., v.2, pp.303–329. Barnsley, M.F., Elton, J., Hardin, D., and Massopust, P.R. (1986) Hidden variable fractal interpolation functions. SIAM Jour. Math. Anal., v.20, pp.1218–1242. Block, A., Von Bloh, W., Klenke, T., and Schellnhuber, H.J. (1991) Multifractal analysis of the microdistribution of elements in sedimentary structures using images from scanning electron microscopy and energy dispersive X ray spectrometry. Jour. Geophys. Res., v.96, pp.223–230. Boschetti, F., Dentith, M.D., and List, R.D. (1996) A fractal–based algorithm for detecting first arrivals on seismic traces. Geophysics, v.61, pp.1095–1102. Browaeys, T.J., and Fomel, S. (2009) Fractal heterogeneities in sonic logs and low–frequency scattering attenuation. Geophysics, v.74(2), pp.WA77–WA92. Chand, A.K.B., and Kapoor, G.P. (2003) Hidden variable bivariate fractal interpolation surfaces. Fractals, v.11, pp.277–288. Chand, A.K.B., and Kapoor, G.P. (2006) Generalized cubic spline fractal interpolation functions. SIAM Jour. Numer. Anal., v.44, pp.655–676. Chen, G., Cheng, Q., Zuo, R., Liu, T., and Xi, Y. (2015) Identifying gravity anomalies caused by granitic intrusions in Nanling mineral district, China: a multifractal perspective. Geophys. Prosp., v.63, pp.256–270. Chen, G., Cheng, Q., and Zhang, H. (2016) Matched filtering method for separating magnetic anomaly using fractal model. Comp. & Geosc., v.90, pp.179–188. Chen, G., and Cheng, Q. (2017) Fractal density modeling of crustal heterogeneity from the KTB deep hole. Jour. Geophys. Res. Solid Earth, v.122, pp.1919–1933. Cheng, Q. (2015) Multifractal interpolation method for spatial data with singularities. The Jour. of the South. Afric. Instt. of Min. & Metall., v.115, pp.235–240. Christensen, K., Danon, L., Scanlon, T., and Bak, P. (2002) Unified scaling law for earthquakes. Proc. Natl. Acad. Sci. USA, v.99, pp.2509–2513. Corral, A. (2004) Long–Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes. Phys. Rev. Lett.,v.92, pp.108501. Cortis, A., Puente, C.E., Huang, H., Maskey, M.L., Sivakumar, B., and Obregon, N. (2014) A physical interpretation of the deterministic fractal–multifractal method as a realization of a generalized multiplicative cascade. Stoch. Environ. Res. Risk. Assess., v.28, pp.1421–1429. Dalla, L. (2002) Bivariate fractal interpolation functions on grids. Fractals, v.10, pp.53–58. De Boever, E., Foubert, A., Oligschlaeger, D., Claes, S., Soete, J., Bertier, P., Ozkul, M., Virgone, A., and Swennen, R. (2016) Multiscale approach to (micro) porosity quantification in continental spring carbonate facies: Case study from the Cakmak quarry (Denizli, Turkey). Geochem. Geophys. Geosyst., v.17, pp.2922–2939. Dimri, V.P. (1992) Deconvolution and Inverse theory. Elsevier Science Publ., Amsterdam. Dimri, V.P. (1998) Fractal behavior and detectibility limits of geophysical surveys. Geophysics, v.63, pp.1943–1946. Dimri, V.P. (2000) Application of Fractals in Earth Sciences. A.A. Balkema, USA/Oxford and IBH Pub. Co., New Delhi, p.238. Dimri, V.P. (2005) Fractal Behavior of the Earth System. Springer, New York. Dimri, V.P., Srivastava, R.P., and Vedanti N. (2012) Fractal Models in Exploration Geophysics. Elsevier Science Publishers, Amsterdam, p.165. Dimri, V.P. (2016) Fractal Solutions for Understanding Complex Systems in Earth Sciences. Springer, New York. Doin, M.P., and Fleitout, L. (1996) Thermal evolution of the oceanic lithosphere: an alternative view. Earth. Planet. Sci. Lett., v.142, pp.121–136. Featherstone, W.E., and Kirby, J.F. (2000) The reduction of aliasing in gravity anomalies and geoid heights using digital terrain data. Geophy. Jour. Int., v.141, pp.204–212. Fedi, M., Quarta, T., and Santis, A.D. (1997) Inherent power law behavior of magnetic field power spectra from a Spector and Grant ensemble. Geophys., v.62, pp.1143–1150. Fedi, M. (2003) Global and local multiscale analysis of magnetic susceptibility data. Pure Appld. Geophys., v.160, pp.2399–2417. Fedi, M. (2016) Scaling laws in geophysics: Application to potential fields of methods based on the laws of self–similarity and homogeneity. In: Dimri V.P. (Ed.), Fractal Solutions for Understanding Complex Systems in Earth Sciences, Springer International, Cham, Switzerland, pp. 1–18. Florio, G., Fedi, M., and Rapolla, A. (2009) Interpretation of regional aeromagnetic data by the scaling function method: the case of Southern Apennines (Italy). Geophys. Prospect., v.57, pp.479–489. Ganguli, S.S., and Dimri, V.P. (2013) Interpretation of gravity data using eigenimage with Indian case study: A SVD approach. Jour. Appld. Geophys., v.95, pp.23–35. Ganguli, S.S., Nayak, G.K., Vedanti, N., and Dimri, V.P. (2016) A regularized Wiener–Hopf filter for inverting models with magnetic susceptibility. Geophys. Prospect., v.64, pp.456–468. Gettings, M.E. (2005) Multifractal magnetic susceptibility distribution models of hydrothermally altered rocks in the Needle Creek Igneous Center of the Absaroka Mountains, Wyoming. Nonlin. Processes Geophys., v.12, pp.587–601. Gholamy, S., Javaherian, A., and Ghods, A. (2008) Automatic detection of interfering seismic wavelets using fractal methods. Jour. Geophys. Engg., v.5, pp.338–347. Gibowicz, S.J. (1997) An Anatomy of a seismic sequence in a deep gold mine. Pure Appld. Geophys., v.150, pp.393–414. Goebel, T.H.W., Sammis, C.G., Becker, T.W., Dresen, G., and Schorlemmer, D. (2015) A Comparison of Seismicity Characteristics and Fault Structure Between Stick–Slip Experiments and Nature. Pure Appld. Geophys., v.172, pp.2247–2264. Grout, H., Tarquis, A.M., and Wiesner, M.R. (1998) Multifractal analysis of particle size distributions in soil. Environ. Sci. Tech., v.32, pp.1176–1182. Hahn, A., Kind, E.G., and Mishra D.C. (1976) Depth estimation of magnetic sources by means of fourier amplitude spectra. Geophys. Prosp., v.24, pp.287–308. Hasterok, D., Chapman, D., and Davis, E. (2011) Oceanic heat flow: Implications for global heat loss. Earth. Planet. Sci. Lett., v.311, pp.386–395. Hasterok, D. (2013) A heat flow based cooling model for tectonic plates. Earth. Planet. Sci. Lett., v.361, pp.34–4. Henderson, J.R., Barton, D.J., and Foulger, G.R. (1999) Fractal clustering of induced seismicity in The Geysers geothermal area, California. Geophy. Jour. Internat., v.139, pp.317–324. Hirabayashi, T., Ito, K., and Yoshii, T. (1992) Multifractal analysis of earthquakes. Pure Appld. Geophys., v.138, pp.591–610. Hirata, T., and Imoto, M. (1991) Multifractal analysis of spatial distribution of micro earthquakes in the Kanto region. Geophys. Jour. Internat., v.107, pp.155–162. Huang, Y., Geng, J., and Guo, T. (2015) New seismic attribute: Fractal scaling exponent based on gray detrended fluctuation analysis. Appld. Geophys., v.12, pp.343–352. Jouini, M.S., Vega, S., and Mokhtar, E.A. (2011) Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates. Nonlin. Processes Geophys., v.18, pp.941–953. Kagan, Y.Y., and Knopoff, L. (1980) Spatial distribution of earthquakes: The two point correlation function. Geophys. Jour. Internat., v.62(2), pp.303–320. Katsumata, K. (2011) A long–term seismic quiescence started 23 years before the 2011 off the Pacific coast of Tohoku Earthquake (M = 9.0). Earth, Planets and Space, v.63, p.36. Keating, P. (1993) The fractal dimension of gravity data sets and its implication for gridding. Geophys. Prospect., v.41, pp.983–993. Lovejoy, S., Schertzer, D., and Ladoy, P. (1986) Outlook brighter on weather forecasts. Nature, v.320, p.401. Lovejoy, S., Pecknold, S., and Schertzer, D. (2001) Stratified multifractal magnetization and surface geomagnetic fields–I, Spectral analysis and modelling. Geophys. Jour. Internat., v.145, pp.112–126. Lovejoy, S., and Schertzer, D. (2007) Scaling and multifractal fields in the solid earth and topography. Nonlin. Processes Geophys., v.14, pp.465–502. Lozada–Zumaeta, M., Arizabalo, R.D., Ronquillo–Jarillo, G., Coconi–Morales, E., Rivera–Recillas, D., and Castrejón–Vácio, F. (2012) Distribution of petrophysical properties for sandy–clayey reservoirs by fractal interpolation. Nonlinear Processes Geophys., v.19, pp.239–250. Lyubushin, A.A., and Sobolev G.A. (2006) Multifractal Measures of Synchronization of Microseismic Oscillations in a Minute Range of Periods. Physics of the Solid Earth, v.42, pp.734–744. Mandelbrot, B.B. (1982) The Fractal Geometry of Nature. W. H. Freeman and Company, San Francisco, Calif. Maus, S., and Dimri, V.P. (1994) Scaling properties of potential fields due to scaling sources. Geophysical Res. Lett., v.21, pp.891–894. Maus, S., and Dimri V.P. (1995) Potential field power spectrum inversion for scaling geology. Jour. Geophys. Res., v.100, pp.12605–12616. Maus, S., and Dimri V.P. (1996) Depth estimation from the scaling power spectrum of potential field? Geophys. Jour. Internat., v.124, pp.113–120. Muller, J. (1996) Characterization of pore space in chalk by multifractal analysis. Jour. Hydrol., v.187, pp.215–222. Naidu, P. (1968) Spectrum of the potential field due to randomly distributed sources. Geophysics, v.33, pp.337–345. Nath, K., and Dewangan, P. (2002) Detection of seismic reflections from seismic attributes through fractal analysis. Geophysical Prospect., v.50, pp.341–360. Navascués, M.A., and Sebastián, M.V. (2004) Generalization of Hermite functions by fractal interpolation. Jour. Approx. Theory, v.131, pp.19–29. Negi, J.G., Dimri, V.P., and Garde S.C. (1973) Ambiguity assessment of gravity interpretation for inhomogeneous multi–layer sedimentary basin. Jour. Geophys. Res., v.78, pp.3281–3286. Ogata, Y. (1999) Seismicity Analysis through Point–process Modeling: A Review. Pure Appld. Geophys., v.155, pp.471–507. Okubo, Y., Graf, R.J., Hansen, R.O., Ogawa, K., and Tsu, H. (1985) Curie point depths of the island of Kyushu and surrounding area, Japan. Geophysics, v.50, pp.481–489. Omori (1894) On aftershocks (in Japanese). Rep. Imp. Earthq. Investig. Comm., v.2, pp.103–139. Oxburgh, E.R., and Turcotte D.L. (1969) Increased estimate for heat flow at oceanic ridges. Nature, v.223, pp.1354–1355. Padhy, S., Mishra, O.P., Subhadra, N., Dimri, V.P., Singh, O.P., and Chakrabortty G.K. (2015) Effects of errors and biases on the scaling of earthquake spatial pattern: application to the 2004 Sumatra–Andaman sequence. Natural Hazards, v.77, pp.75–96. Parsons, B., and Sclater, J.G. (1977) An analysis of the variation of ocean floor bathymetry and heat flow with age. Jour. Geophys. Res., v.82, pp.803–827. Parsons, B., and McKenzie, D. (1978) Mantel convection and the thermal structure of the plates. J. Geophys. Res., v.83, pp.4485–4496. Pilkington, M., and Todoeschuck, J.P. (1993) Fractal magnetization of continental crust. Geophys. Res. Lett., v.20, pp.627–630. Pilkington, M., and Keating, P. (2012) Grid preparation for magnetic and gravity data using fractal fields. Nonlin. Processes Geophys., v.19, pp.291–296. Qiuming, C. (2016) Fractal density and singularity analysis of heat flow over ocean ridges. Scientific Reports, v.6, p.19167. Ouadfeul, S., and Aliouane, L. (2011) Multifractal analysis revisited by the continuous wavelet transform applied in lithofacies segmentation from well–logs data. Internat. Jour. Appld. Phys. Math., v.1, pp.10–18. Ramana, D.V., Pavan Kumar, J., Chelani, A., Chadha, R.K., Shekar, M., and Singh, R.N. (2015) Complexity in hydro–seismicity of the Koyna–Warna region, India. Nat. Hazards, v.77, pp.109–116. Ravat, D., Pignatelli, A., Nicolosi, I., and Chiappini, M. (2007) A study of spectral methods of estimating the depth to the bottom of magnetic sources from near–surface magnetic anomaly data. Geophys. Jour. Internat., v.169, pp.421–434. Ravi Prakash, M., and Dimri, V.P. (2000) Distribution of the aftershock sequence of the Latur earthquake in time and space by fractal approach. Jour. Geol. Soc. of India, v.55, pp.167–174. Richardson, S.W., and Oxburgh, E.R. (1979) The heat flow field in mainland UK. Nature, v.282, pp.565–567. Roy, A. (1962) Ambiguity in geophysical interpretation. Geophys., v.27, pp.90–99. Rykunov, L.N., Smirnov, V.B., Starovoyt, Y.O., and Chubarova, O.S. (1987) Self–similarity of Seismic Emition on Time. Dokl. AN SSSR., v.297, pp.1337–1341 (In Russian). San José Martínez, F., Caniego, F.J., García–Gutiérrez, C., and Espejo, R. (2007) Representative elementary area for multifractal analysis of soil porosity using entropy dimension. Nonlin. Processes Geophys., v.14, pp.503–511. Santis, A.D. (1997) A Direct Divider Method for Self–Affine Fractal Profiles and Surfaces. Geophys. Res. Lett., v.24, pp.2099–2102. Schertzer, D., and Lovejoy, S. (1985) Generalised scale invariance in turbulent phenomena. Physico Chem. Hydrodyn., v.6, pp.623–635. Silberschmidt, V.V. (1996) Fractal approach in modelling of earthquakes. Geologische Rundschau, v.85, pp.116–123. Smirnov, B.V. (1995) Recurrence of Earthquakes and Parameters of Seismic Regime. Vulkanologia and seismologia., v.3, pp.59–70 (In Russian). Smirnov, V.B., Cherepantsev, A.S., and Mirzoev, V.K. (1994) Fractal Properties of Induced Seismicity in the Region of the Dam Nurekskoe. Induced Seismicity. Ì.: Nauka, pp.138–147 (In Russian). Srivastava, R.P., Vedanti, N., and Dimri, V.P. (2007) Optimum Design of a Gravity Survey Network and its Application to delineate the Jabera–Damoh Structure in the Vindhyan Basin, Central India. Pure Appld. Geophys., v.164, pp.1–14. Srivastava, R.P., and Sen M.K. (2009) Stochastic inversion of prestack seismic data using fractal–based initial models. Geophys., v.75, pp.R47–R59. Stein, C.A., and Stein, S. (1992) A model for the global variation in oceanic depth and heat flow with lithospheric age. Nature, v.359, pp.123–129. Stein, C.A., and Stein, S. (1994) Constraints on hydrothermal heat flux through the oceanic lithosphere from global heat flow. Jour. Geophys. Res., v.99, pp.3081–3095. Tarquis, A.M., McInnes, K., Keys, J., Saa, A., Garcia, M.R., and Diaz, M.C. (2006) Multiscaling analysis in a structured clay soil using 2D images. Jour. Hydrology, v.322, pp.236–246. Telesca, L., Lovallob, M., Hsu, H.L., and Chen, C.C. (2012) Analysis of site effects in magnetotelluric data by using the multifractal detrended fluctuation analysis. Jour. Asian Earth Sci., v.54–55, pp.72–77. Telesca, L., and Toth, L. (2016) Multifractal detrended fluctuation analysis of Pannonian earthquake magnitude series. Physica A: Stat. Mech. and its Appl., v.448, pp.21–29. Teotia, S.S., and Kumar, D. (2011) Role of multifractal analysis in understanding the preparation zone for large size earthquake in the North–Western Himalaya region. Nonlin. Processes Geophys., v.18, pp.111–118. Todoeschuck, J.P., and Jensen O.G. (1988) Joseph geology and scaling deconvolution. Geophysics, v.53, pp.1410–1411. Toledo, B.A., Chian, A.C.L., Rempel, E.L., Miranda, R.A., Munoz, P.R., and Valdivia, J.A. (2013) Wavelet–based multifractal analysis of nonlinear time series: The earthquake–driven tsunami of 27 february 2010 in chile. Physical Review E, v.87, p.022821. Toverud, T., Dimri, V.P., and Ursin, B. (2001) Comparison of deconvolution methods for scaling reflectivity. Jour. Geophys., v.22, pp.117–123. Turcotte, D.L. (1992) Fractal and chaos in geology and geophysics. Cambridge Univ. Press. Turcotte D.L. (1997) Fractal and chaos in geology and geophysics, 2nd edition, Cambridge Univ. Press. Yikilmaz, M.B., Heien, E.M., Turcotte, D.L., Rundle, J.B., and Kellogg, L.H. (2011) A fault and seismicity based composite simulation in northern California. Nonlinear Process. Geophys., v.18, pp.955–966. Walden, A.T., and Hosken, J.W.J. (1985) An investigation of the spectral properties Ilf primary reflection coefficients. Geophys. Prosp., v.33, pp.400–435. Wang, H.Y., and Yu, J.S. (2013) Fractal interpolation functions with variable parameters and their analytical properties. Jour. Approx. Theory, v.175, pp.1–18. Wu, R.S., and Aki, K. (1985) Scattering characteristics of elastic waves by an elastic heterogeneity. Geophysics, v.50, pp.582–595.