[ { "id": "authors:s654f-zzp17", "collection": "authors", "collection_id": "s654f-zzp17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140813-135154513", "type": "article", "title": "Shear-wave velocity at the base of the mantle from profiles of diffracted SH waves", "author": [ { "family_name": "Okal", "given_name": "Emile A.", "clpid": "Okal-E-A" }, { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" } ], "abstract": "Profiles of SH waves diffracted around the core (Sd) for three deep events at stations across North America and the Atlantic (\u0394 = 92\u00b0 to 152\u00b0) are used to determine the properties of the lower mantle in the vicinity of the core-mantle boundary (CMB). The S-wave velocity above the CMB is found to be \u03b2_c = 7.22 \u00b1 0.1 km/sec, in agreement with gross earth models, but higher than previously reported values from direct measurements of Sd. The frequency imdependence of the Sd ray parameter argues strongly against the possibility of a low-velocity zone immediately above the core mantle boundary.\n\nWe compute synthetic seismograms for Sd by summing normal modes. A comparison of the present data with a synthetic profile for earth model 1066A gives excellent agreement at periods greater than 45 seconds. Synthetics for other models are used to substantially constrain the possibility of significant rigidity of the uppermost layer of the core.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1979-08", "series_number": "4", "volume": "69", "issue": "4", "pages": "1039-1053" }, { "id": "authors:gjdqf-m8s85", "collection": "authors", "collection_id": "gjdqf-m8s85", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140916-083402219", "type": "article", "title": "Attenuation measurements of split normal modes for the 1960 Chilean and 1964 Alaskan earthquakes", "author": [ { "family_name": "Stein", "given_name": "Seth", "clpid": "Stein-S" }, { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" } ], "abstract": "Measurements of attenuation for the Earth's longest period modes can be significantly biased by the effects of frequency splitting. Using our previously developed methods of time domain synthesis of split normal modes, we measure Q without such a bias. We also conduct numerical experiments to confirm the errors in Q measurements which result from neglecting the effects of splitting. In contrast to frequency domain this time domain technique allows us to reject data below the ambient noise level for each mode. The Q's of the longest period spheroidal (_0S_(2\u20130)S_5) and torsional (_0T_(3\u20130)T_4) modes are determined using long (500 hr) records from the Chilean and Alaskan earthquakes.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1978-12", "series_number": "6", "volume": "68", "issue": "6", "pages": "1595-1611" }, { "id": "authors:c8bhk-m7747", "collection": "authors", "collection_id": "c8bhk-m7747", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141008-145455612", "type": "article", "title": "Addenda and corrections to \"Magnitude of great shallow earthquakes from 1904 to 1952\"", "author": [ { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" }, { "family_name": "Kanamori", "given_name": "Hiroo", "orcid": "0000-0001-8219-9428", "clpid": "Kanamori-H" }, { "family_name": "Abe", "given_name": "Katsuyuki", "clpid": "Abe-K" } ], "abstract": "Since the paper by Geller and Kanamori (1977) was published, we have found\nadditional data which enabled us to fill the blank columns left in Table 1 of Geller\nand Kanamori (1977). Table 1 of this paper lists the values obtained since then, and\nalso two corrections (footnote b). The quantities in this table are described in the\noriginal paper.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1978-12", "series_number": "6", "volume": "68", "issue": "6", "pages": "1763-1764" }, { "id": "authors:5zm9y-2xa96", "collection": "authors", "collection_id": "5zm9y-2xa96", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140812-142518798", "type": "article", "title": "Time-domain observation and synthesis of split spheroidal and torsional free oscillations of the 1960 chilean earthquake: Preliminary results", "author": [ { "family_name": "Stein", "given_name": "Seth", "clpid": "Stein-S" }, { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" } ], "abstract": "The rotationally and elliptically split normal modes of the earth are observed for the 1960 Chilean earthquake by analysis in the time domain. One hundred and fifty hours of the Isabella, California, strain record are narrow band filtered about the central frequency of each split multiplet to isolate the complex wave form resulting from the interference of the different singlets. We compute synthetic seismograms using our previous theoretical results, which show the dependence of the amplitude and phase of the singlets on source location, depth, mechanism, and the position of the receiver. By comparing these synthetics to the filtered record, we conclusively demonstrate the splitting of modes whose splitting had not been definitely resolved: torsional modes (_0T_3, _0T_4) and spheroidal modes (_0S_4, _0S_5). The splitting of _0S_2 and _0S_3 is reconfirmed. We obtain good agreement between the synthetics and the filtered data for a source mechanism (previously determined from long-period surface waves) of thrust motion on a shallow dipping fault.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1978-04", "series_number": "2", "volume": "68", "issue": "2", "pages": "325-332" }, { "id": "authors:qzfxh-fwn77", "collection": "authors", "collection_id": "qzfxh-fwn77", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140812-120433750", "type": "article", "title": "Normal modes of a laterally heterogeneous body: A one-dimensional example", "author": [ { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" }, { "family_name": "Stein", "given_name": "Seth", "clpid": "Stein-S" } ], "abstract": "Various methods, including first- and second-order perturbation theory and variational methods have been proposed for calculating the normal modes of a laterally heterogeneous earth. In this paper, we test all three of these methods for a simple one-dimensional example for which the exact solution is available: an initially homogeneous \"string\" in which the density and stiffness are increased in one half and decreased in the other by equal amounts. It is found that first-order perturbation theory (as commonly applied in seismology) yields only the eigenvalues and eigenfunctions for a string with the average elastic properties; second-order perturbation theory is worse, because the eigenfunction is assumed to be the original eigenfunction plus small correction terms, but actually may be almost completely different.\n\nThe variational method (Rayleigh-Ritz), using the unperturbed modes as trial functions, succeeds in giving correct eigenvalues and eigenfunctions even for modes of high-order number. For the example problem only the variational solution correctly yields the transient solution for excitation by a point force, including correct amplitudes for waves reflected by and transmitted through the discontinuity. Our result suggests but does not demonstrate, that the variational method may be the most appropriate method for finding the normal modes of a laterally heterogeneous earth model, particularly if the transient solution is desired.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1978-02", "series_number": "1", "volume": "68", "issue": "1", "pages": "103-116" }, { "id": "authors:gaxrn-zfe22", "collection": "authors", "collection_id": "gaxrn-zfe22", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140812-163520389", "type": "article", "title": "Split free oscillation amplitudes for the 1960 Chilean and 1964 Alaskan earthquakes", "author": [ { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" }, { "family_name": "Stein", "given_name": "Seth", "clpid": "Stein-S" } ], "abstract": "Splitting of the Earth's normal modes was observed for both the 1960 Chilean and 1964 Alaskan earthquakes. The strong peaks in the observed spectrum of each split multiplet correspond to singlets with much higher amplitudes than the others. Using theoretical results we have derived elsewhere (Stein and Geller, 1977a), we are able to predict this pattern. We show that the source mechanisms inferred for these earthquakes from surface waves are consistent with the observed pattern of relative spectral amplitudes of the split modes. However other mechanisms, such as a slow isotropic volume change, are also consistent with the split-mode amplitudes and are excluded only by additional data.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1977-06", "series_number": "3", "volume": "67", "issue": "3", "pages": "651-660" }, { "id": "authors:vdgds-d4558", "collection": "authors", "collection_id": "vdgds-d4558", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140812-160833446", "type": "article", "title": "Magnitudes of great shallow earthquakes from 1904 to 1952", "author": [ { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" }, { "family_name": "Kanamori", "given_name": "Hiroo", "orcid": "0000-0001-8219-9428", "clpid": "Kanamori-H" } ], "abstract": "The \"revised magnitudes\", M, converted from Gutenberg's unified magnitude, m, and listed by Richter (1958) and Duda (1965) are systematically higher than the magnitudes listed by Gutenberg and Richter (1954) in Seismicity of the Earth. This difference is examined on the basis of Gutenberg and Richter's unpublished original worksheets for Seismicity of the Earth. It is concluded that (1) the magnitudes of most shallow \"class a\" earthquakes in Seismicity of the Earth are essentially equivalent to the 20-sec surface-wave magnitude, M_s; (2) the revised magnitudes, M, of most great shallow (less than 40 km) earthquakes listed in Richter (1958) (also used in Duda, 1965) heavily emphasize body-wave magnitudes, m_b, and are given by M = 1/4 M_s + 3/4 (1.59 m_b - 3.97). For earthquakes at depths of 40 to 60 km, M is given by M = (1.59 m_b \u2212 3.97). M and M_s are thus distinct and should not be confused. Because of the saturation of the surface-wave magnitude scale at M_s \u2243 8.0, use of empirical moment versus magnitude relations for estimating the seismic moment results in large errors. Use of the fault area, S, is suggested for estimating the moment.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1977-06", "series_number": "3", "volume": "67", "issue": "3", "pages": "587-598" }, { "id": "authors:veeyx-vd717", "collection": "authors", "collection_id": "veeyx-vd717", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140915-144757818", "type": "article", "title": "Body force equivalents for stress-drop seismic sources", "author": [ { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" } ], "abstract": "The equivalent body forces for a stress-drop seismic source are found. When the isotropic stress drop and one of the three principal stress drops are zero, then the equivalent body forces are the same double couple without moment which would result from a shear dislocation. In general however, all six stress-drop components must be specified as independent functions of time.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1976-12", "series_number": "6", "volume": "66", "issue": "6", "pages": "1801-1804" }, { "id": "authors:7e14q-dh164", "collection": "authors", "collection_id": "7e14q-dh164", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140917-130821652", "type": "article", "title": "Scaling relations for earthquake source parameters and magnitudes", "author": [ { "family_name": "Geller", "given_name": "Robert J.", "clpid": "Geller-R-J" } ], "abstract": "A data set of 41 moderate and large earthquakes has been used to derive scaling rules for kinematic fault parameters. If effective stress and static stress drop are equal, then fault rise time, \u03c4, and fault area, S, are related by \u03c4 = 16S^(1/2)/(7\u03c0^(3/2)\u03b2), where \u03b2 is shear velocity. Fault length (parallel to strike) and width (parallel to dip) are empirically related by L=2W. Scatter for both scaling rules is about a factor of two. These scaling laws combine to give width and rise time in terms of fault length. Length is then used as the sole free parameter in a Haskell type fault model to derive scaling laws relating seismic moment to M_S (20-sec surface-wave magnitude), M_S to S and m_b (1-sec body-wave magnitude) to M_S. Observed data agree well with the predicted scaling relation. The \"source spectrum\" depends on both azimuth and apparent velocity of the phase or mode, so there is a different \"source spectrum\" for each mode, rather than a single spectrum for all modes. Furthermore, fault width (i.e., the two dimensionality of faults) must not be neglected. Inclusion of width leads to different average source spectra for surface waves and body waves. These spectra in turn imply that m_b and M_S reach maximum values regardless of further increases in L and seismic moment. The m_b versus M_S relation from this study differs significantly from the Gutenberg-Richter (G-R) relation, because the G-R equation was derived for body waves with a predominant period of about 5 sec and thus does not apply to modern 1-sec m_b determinations. Previous investigators who assumed that the G-R relation was derived from 1-sec data were in error. Finally, averaging reported rupture velocities yields the relation v_R = 0.72\u03b2.", "issn": "0037-1106", "publisher": "Seismological Society of America", "publication": "Bulletin of the Seismological Society of America", "publication_date": "1976-10", "series_number": "5", "volume": "66", "issue": "5", "pages": "1501-1523" } ]