Source Radiation Pattern Research Articles

Estimating and correcting the amplitude radiation pattern of a virtual source

In the virtual source (VS) method we crosscorrelate seismic recordings at two receivers to create a new data set as if one of these receivers were a virtual source and the other a receiver. We focus on the amplitudes and kinematics of VS data, generated by an array of active sources at the surface and recorded by an array of receivers in a borehole. The quality of the VS data depends on the radiation pattern of the virtual source, which in turn is controlled by the spatial aperture of the surface source distribution. Theory suggests that when the receivers are surrounded by multi-component sources completely filling a closed surface, then the virtual source has an isotropic radiation pattern and VS data possess true amplitudes. In practical applications, limited sourceaperture and deployment of a single source type create an anisotropic radiation pattern of the virtual source, leading to distorted amplitudes. This pattern can be estimated by autocorrelating the spatial Fourier transform of the downgoing wavefield in the special case of a laterally invariant medium. The VS data can be improved by deconvolving the VS data with the estimated amplitude radiation pattern in the frequency-wavenumber domain. This operation alters the amplitude spectrum but not the phase of the data. We can also steer the virtual source by assigning it a new desired amplitude radiation pattern, given sufficient illumination exists in the desired directions. Alternatively, time-gating the downgoing wavefield before crosscorrelation, already common practice in implementing the VS method, can improve the radiation characteristics of a virtual source.

Formulation of the multiple anisotropic scattering process in two dimensions for anisotropic source radiation

SUMMARY The radiative transfer theory (RTT) describes the energy transport through a random heterogeneous medium, neglecting phase information. It provides an adequate framework for modelling high-frequency seismogram envelopes. For isotropic scattering and sources, the radiative transfer equation (RTE) has been formulated analytically and numerically simulated using Monte Carlo methods for acoustic and elastic media. Here, we derive an exact analytical solution of the RTE in 2-D space for the acoustic case, including anisotropic scattering for a anisotropic point-like impulsive source. For this purpose, we generalize the path integral method, which has been used before in the isotropic case, to take into account the anisotropy of both the source radiation pattern and scattering processes, simultaneously. Then we obtain a general solution, which is written in a closed form in the Fourier space. To illustrate the theoretical results, we compute the full space and time evolution of the specific intensity for an arbitrary case. We also compare the time traces computed from our general solution with cases in which the source and/or the scattering process are isotropic. The importance of taking into account both anisotropies simultaneously becomes obvious in our examples. We also show that at long lapse time, our example approaches the solution of the diffusion equation.

SU-GG-T-186: Simulation of Room Distortion On Measurements of RF Noise Due to a Medical Linac

Purpose: The goal of radiotherapy is to sculpt radiation dose to tumor shape. The integration of an MRI with a linac for real time image-guided radiotherapy (IGRT) would allow clinicians to reduce treatment margins beyond current technological limits. A problem with the integration of an MRI and a linac is the radio frequency (RF) noise produced by a linac. Our measurements indicate this noise exists in the MHz range with wavelengths on the order of 10s of meters. The purpose of this project is to investigate the effects an enclosed room has on the electric (E) and magnetic (H) field measurements on this type of RF source. Purpose: A software programming environment (MultiStripes, version 7.5 Flomerics) has been utilized to investigate the E and H fields produced from a small dipole in free space and an enclosed room, by solving Maxwell's equations using the transmission line matrix method. The results from these simulations elucidate the effects of room structure and contents on the radiation pattern of an RF source. Results: Our free space simulation demonstrates the theoretically expected falloff, of the E and H fields, as a function of distance from the dipole. When modeling the dipole confined in the laboratory, our results show perturbations from the free space solution. Our measurements also contain these perturbations. These results were found to depend strongly on the material properties used. Conclusion: Measurement of RF noise for MRI-linac integration is dependant on the configuration of the laboratory. Simulation of electromagnetic wave propagation can determine the wave perturbation due to room effects. Such simulations allow determination of a “room factor” which can be applied to laboratory measurements to determine the true strength of the RF emissions. More work is needed to validate the model.

한반도 지진의 지진원 상수

Source parameters for forty four earthquakes which occurred in and around the Korean Peninsula were determined and the relations between them were studied. Snoke`s method (Snoke, 1987) was applied in determining the corner frequencies and seismic moments. In general, the source parameters estimated at different stations for an earthquake show different values. These disagreements have been interpreted as originating, in principle, from an inadequate consideration of the source radiation pattern and direction dependent attenuation and amplification. The comer frequencies and seismic moments were averaged to exclude the such directional effects. Other source parameters were estimated from the mean corner frequency and seismic moment. The static stress drops, determined in this study, tend to be independent of seismic moment for events greater than a specific magnitude. For earthquakes with a size less than about dyne-cm (nearly same as $M_L

Radiation from a Line Source Placed in Two-dimensional Photonic Crystals

A novel formulation of radiation from a localized line source placed in two-dimensional photonic crystals consisting of layered periodic arrays of parallel circular cylinders is presented. The method employs the spectral domain approach. The spectral response of the photonic crystals to the line source excitation is calculated using the lattice sums, the T-matrix of a circular cylinder, and the generalized reflection and transmission matrices of the layered system. The far-zone radiated field is obtained using the conventional asymptotic method to the spectral response. The radiation patterns of the localized line source sandwiched by two photonic crystals are numerically studied.

Effects of source radiation patterns on the phase S670P beneath the Tonga subduction zone

SUMMARY Observations of short-period S-P converted phases from the 670 km discontinuity (S670P) provide unique constraints on the nature of the discontinuity and the seismic structure of deep subducted slabs. Because this is a subtle phase in the P codas from deep earthquakes, great care is necessary in its identification. In past work we identified S670P phases from a large number of deep events beneath Tonga primarily by showing that the arrival times for S670P had the correct dependence upon hypocentral depth. Here we offer further confirmation of our interpretation of this S-P converted phase by showing that the occurrence of the phase is a predictable consequence of the earthquake source mechanism. We show this in two ways: (1) independently determined moment tensor solutions for the earthquakes generally predict relatively high-amplitude S-P conversions where they are observed; and (2) the observed amplitudes of S670P, ScP, PP, and P arrivals vary systematically in a way which confirms that S670P, is generated with large amplitude when the S-wave energy pattern is optimal. Comparison of ScP observations with moment tensor solutions also suggests that much of the S-wave energy results from the non-double-couple or, for CMT solutions, linear vector dipole (LVD) part of the source mechanism for the northern part of the Tonga subduction zone, where we observe the strongest S670P, phases. Because these LVD components tend to be directed along fault planes inferred from deep seismicity patterns, we suggest that they may be caused by rupture propagation directivity. We conclude that the occurrence of S670P, is primarily controlled by the source radiation pattern in a way that is consistent with our previous interpretation, thus confirming that S670P, is an S-P conversion from an almost undeformed phase change boundary at about 670 km depth.

Green's tensor and radiation patterns of point sources in general anisotropic inhomogeneous elastic media

SUMMARY i (Marshall McLuhan, 1958) The elastodynamic ‘ray-theoretical’ Green's tensor for general anisotropic and inhomogeneous media (GANIMED) is derived in the far-field high-frequency approximation. This allows the quantification of the amplitude and phase charac-teristics of arbitrary point sources. The displacement field is controlled by the phase velocity and the Gaussian curvature of the wave surface. Exploiting the already existing computer codes for dynamic ray tracing in GANIMED, we demonstrate how one may couple it to source theory in order to calculate displacement-radiation patterns for unipolar and dipolar sources in various earth crustal materials, such as shales, sandstones, and olivine. The existence of a velocity gradient at the source causes asymmetry in the radiation patterns. In contradistinction, anisotropy at the source tends to distort the lobes and in some cases can beam excessive energy in specific directions. Our calculated radiation patterns for shear waves are similar to those observed from some explosions in soil.

An experimental study of phase angle fluctuation in seismic waves in random heterogeneous media: time-series analysis based on multivariate AR model

SUMMARY Effects of small-scale heterogeneities on seismic waveform fluctuations were studied by physical model experiments. Using a laser Doppler vibrometer, we recorded elastic waves propagating through a granite block at 180 observation points that were arranged as an equally spaced circular array. A disc-shaped PZT source was attached on the other side surface of the circular array for realizing equivalent positions with respect to both source radiation pattern and travel distances of waves. Waveform pairs were selected out from the 180 waveforms, and cross spectra of time-windowed partial waveforms were calculated by applying the multivariate AR model. By comparing waveforms of two observation points, the cross-spectral amplitudes and phases are obtained with respect to the lapse time by moving the time window, or to the spatial distance by changing the pairs of observation points. We obtain distributions of cross-spectral phase values for frequency and the lapse time of waveforms. The distributions indicate phase fluctuation of waves in random media with respect to frequency and lapse time. Heterogeneity of the rock sample is expressed as a 1-D exponential autocorrelation functions (ACF); e2 exp(−|r|/a), where r is the distance, and a and e are the correlation length (0.22 mm) and the strength of heterogeneity (8.5 per cent), respectively. The distributions are plotted against ka; the product of wavenumber and correlation length. For small ka, the distributions of phase are close to the Gaussian distributions with small variances, but the variances quickly become large above ka≈ 0.2–0.3. Then the distributions become uniform between −π and π. This suggests that the incoherent scattered waves become dominant above a critical ka value (or a critical frequency for a medium), and phase information in later portions of waveforms will be lost. This may be important for extracting reflection, refraction or converted waves that are assigned as signals from geologic discontinuities because those signals may be strongly distorted by scattered waves produced from the small-scale heterogeneities of earth's media.

Grating micro-dot patterned light guide plates for LED backlights

A novel LED backlight unit implementing a light guide plate (LGP) with a two-dimensional array of grating micro-dots is proposed. By optimizing grating-vector orientations of local gratings and applying suitable grating-depth modulation in the array, taking into consideration of the radiation pattern of the LED source, uniform out-coupled light distribution within a narrow luminance angle was achieved without recognizable hot spots. Such a light guide plate was fabricated using a dot-matrix holographic interferometer setup and a UV embossing replication. Fabricated polycarbonate LGP showed ~62% intensity uniformity within ~8 degrees and ~20 degrees luminance angles in two main directions.

A break in self‐similarity in the Lunigiana‐Garfagnana region (northern Apennines)

In this study, stable source parameters are determined for small earthquakes in the Lunigiana‐Garfagnana region using an empirical methodology based on coda envelope measurements that are significantly less affected by the source radiation pattern, directivity, and heterogeneous path variation, than traditional direct wave measurements. We find evidence that the scaled energy (=ER/M0) increases with moment and source spectra are not self‐similar for 3.0 ≤ Mw ≤ 4.6. The calibration procedure allows for an independent check of three important features: (1) that the empirical path corrections provide consistent amplitude measurements for the same event at different stations, distances, and azimuths; (2) that the long‐period levels of the source spectra are consistent with independent M0 derived from long‐period waveform modeling; (3) that small event spectra are flat below a conservative estimate of the corner frequency and thereby effectively accounting for near‐site attenuation.

Linearized 2.5-dimensional parameter imaging inversion in anisotropic elastic media

SUMMARY In this paper we derive 2.5-D short-period seismic modelling and imaging-inversion formulae in the Born approximation for anisotropic elastic media. The 2.5-D approach encompasses 3-D wave scattering measured in a common-azimuth acquisition geometry subject to 2-D computations under appropriate assumptions. The lowest possible symmetry of the medium in this approach, in principle, is monoclinic, while the medium must be translationally invariant in the normal direction to the associated symmetry plane. In the presence of caustics, artefacts may be generated by the imaging-inversion procedures. We show that in the 2.5-D approach the analysis of artefacts in the 2-D symmetry plane implies the corresponding analysis in 3-D in the framework of the common-azimuth acquisition geometry. An interesting aspect of our results is the occurrence of out-of-plane geometrical spreading in the least-squares removal of the contrast source radiation patterns on the data. We finally introduce the 2.5-D generalized Radon transform that generates common-image-point gathers. The reconsideration of 2.5-D scattering theory is motivated by the increase in use of ocean-bottom acquisition technology. It is not uncommon for ocean bottom cable (OBC) seismic data to be collected along a single line, and the question arises of how to make optimal use of these data. We show the effect of the factors making up the amplitude in the 2.5-D generalized Radon transform on OBC field data from the North Sea.

Elimination of the overburden response from multicomponent source and receiver seismic data, with source designature and decomposition into PP-, PS-, SP-, and SS-wave responses

This paper shows that Betti's reciprocity theorem gives an integral equation procedure to eliminate from the physical multicomponent-source, multicomponent-receiver seismic measurements the effect of the physical source radiation pattern and the response of the physical overburden (that is, the medium above the receiver plane). The physical multicomponent sources are assumed to be orthogonally aligned anywhere above the multicomponent-receiver depth level. Other than the position of the sources, no source characteristics are required. The method, denoted the Betti designature/elastic demultiple, has the following additional characteristics: it preserves primary amplitudes while eliminating all waves scattered from the overburden; it requires no knowledge of the medium below the receiver level; it requires no knowledge of the medium above the receiver level; it requires information only of the local density and elastic wave propagation velocities at the receiver level to decompose the physical seismic measurements into upgoing and downgoing waves. Following the Betti designature/elastic demultiple step is an elastic wavefield decomposition step that decomposes the data into PP-, PS-, SP-, and SS-wave responses that would be recorded from idealized compressional-wave and shear-wave sources and receivers. The combined elastic wavefield decomposition on the source and receiver side gives data equivalent to data from a hypothetical survey with overburden absent, with single-component compressional and shear-wave sources, and single-component compressional and shear-wave receivers. When the medium is horizontally layered, the Betti designature/elastic demultiple scheme followed by the elastic source-receiver decomposition scheme greatly simplifies and is conveniently implemented as deterministic multidimensional deconvolution and elastic source-receiver wavefield decomposition of common-source gathers (or common-receiver gathers when source array variations are negligible). Betti designature/elastic demultiple followed by source-receiver wavefield decomposition applies to three different seismic experiments: a 9-component (9C) land seismic experiment, a 12-component (12C) ocean-bottom seismic experiment, and an 18-component (18C) borehole seismic experiment. For the land and ocean-bottom seismic experiments, an additional geophone should be deployed below the zero-offset geophone to predict the source-induced vertical traction vector at the source location. A numerical example for the 12C ocean-bottom seismic experiment over a horizontally layered medium validates the Betti designature/elastic demultiple scheme.

Dipole emission into rectangular metallic gratings with subwavelength slits

We derive analytical expressions for the spontaneous emission rate as well as for the radiation pattern of a dipole source near a metallic grating with subwavelength slits. The theory is based on an extension of a surface impedance model used to explain the enhanced transmission in such systems [J. A. Porto et al., Phys. Rev. Lett. 83, 2845 (1999)]. Our results show how the coupling to the photonic resonances of the grating, which are responsible for its enhanced transmission, can be exploited to control effectively the dipole emission dynamics as well as its radiative efficiency and directivity.

Estimating Absolute Site Effects

The authors use previously determined direct-wave attenuation functions as well as stable, coda-derived source excitation spectra to isolate the absolute S-wave site effect for the horizontal and vertical components of weak ground motion. They used selected stations in the seismic network of the eastern Alps, and find the following: (1) all ''hard rock'' sites exhibited deamplification phenomena due to absorption at frequencies ranging between 0.5 and 12 Hz (the available bandwidth), on both the horizontal and vertical components; (2) ''hard rock'' site transfer functions showed large variability at high-frequency; (3) vertical-motion site transfer functions show strong frequency-dependence, and (4) H/V spectral ratios do not reproduce the characteristics of the true horizontal site transfer functions; (5) traditional, relative site terms obtained by using reference ''rock sites'' can be misleading in inferring the behaviors of true site transfer functions, since most rock sites have non-flat responses due to shallow heterogeneities resulting from varying degrees of weathering. They also use their stable source spectra to estimate total radiated seismic energy and compare against previous results. they find that the earthquakes in this region exhibit non-constant dynamic stress drop scaling which gives further support for a fundamental difference in rupture dynamics between small and large earthquakes. To correct the vertical and horizontal S-wave spectra for attenuation, they used detailed regional attenuation functions derived by Malagnini et al. (2002) who determined frequency-dependent geometrical spreading and Q for the region. These corrections account for the gross path effects (i.e., all distance-dependent effects), although the source and site effects are still present in the distance-corrected spectra. The main goal of this study is to isolate the absolute site effect (as a function of frequency) by removing the source spectrum (moment-rate spectrum) from the distance-corrected S-wave spectra. Typically, removing the S-wave source spectrum is difficult because of inadequate corrections for the source radiation pattern, directivity and random interference. In addition to complexities near the source, 2-D and 3-D structure beneath the recording site will result in an azimuth-dependent site effect. Since the direct wave only samples a narrow range in take-off and back-azimuth angles, multi-station averaging is needed to minimize the inherent scatter. To minimize these complicating effects, they apply the coda methodology outlined by Mayeda et al., (2003) to obtain stable moment-rate spectra. This methodology provides source amplitude and derived source spectra that are a factor of 3-to-4 times more stable than those derived from direct waves. Since the coda is commonly thought of as scattered energy that samples all ray parameters and back-azimuths, it is not very sensitive to the source radiation pattern and 3-D structure. This property makes it an excellent choice for use in obtaining average properties of the source, site and path effects in a region. Due to the characteristics of the techniques used in this study, all the inverted quantities are azimuthally averaged, since the aximuthal information is lost in the processing.

Seismic hazard of Romania due to Vrancea earthquakes - How asymmetric is the strong ground motion distribution

We present a short review of the most recent results coming from the numerical modeling of seismic hazard and interpretation of the new observations provided by the recently installed seismic stations in Romania. There are still controversial questions related to the asymmetric distribution of the ground motion radiated by the Vrancea intermediate-depth earthquakes and which is the main factor responsible for this particular distribution: seismic source, structural model, site effects or vulnerability. Our main goal is to provide a solution to this key problem, with direct implications upon the seismic hazard assessment. NE-SW elongation of the isoseismals and the maximum values in the Romanian Plain are well explained by the source radiation pattern and the average structural model. The attenuation toward NW is shown to be a frequency-dependent effect, much more important in the high frequency range (≯1 Hz). We conclude that the present seismic hazard of Romania, computed by the deterministic approach, fits well, as a first approximation, the ground motion distribution for the low-frequency band, and the apparent contradiction with the historically-based intensity maps arises mainly from a systematic difference in the vulnerability of the buildings in the intra- and extra-Carpathians regions.

Empirical path and station corrections for surface-wave magnitude,Ms, using a global network

SUMMARY One of the most commonly used methods of estimating the size of shallow earthquakes is the surface-wave magnitude scale, Ms. It has been known since the inception of the scale that the Ms of a seismic disturbance recorded at different stations can vary due to path propagation and station terms, but it has been difficult to quantify these variations on a global basis because, until recently, there has been no attempt to record Ms in a uniform way on a worldwide network. Here we use Ms measurements within the Reviewed Event Bulletin (REB) of the International Data Centre (IDC) which is produced to help monitor compliance with the Comprehensive Nuclear Test Ban Treaty (CTBT). The IDC collects waveforms from the as yet incomplete seismological network of the International Monitoring System (IMS) and Ms is then measured using an automatic algorithm, providing a unique set of surface-wave observations. In this paper we show that the Ms values reported in the REB show distinct geographic variations. We present preliminary attempts to model these observations in terms of a set of station corrections and a 2-D model which can be used to predict path corrections for Ms. The model shows a striking correlation with the known tectonic regions of the Earth, suggesting that this type of data set may provide a valuable tool for investigating shallow Earth structure. After modelling, the residuals show some systematic patterns which cannot be explained using the model basis we have used. These residuals are presumably due either to source radiation patterns or to complicated propagation effects not allowed for in the model, such as refraction at ocean-continent boundaries. From the CTBT monitoring viewpoint, Ms station and path corrections are valuable because they should improve the effectiveness of event screening using mb: Ms. However, we recommend that implementation of such corrections should wait until the full seismological network of the IMS is in place, and until a fuller understanding of path effects on Ms is available. In particular, it is vital that path propagation effects do not distort station corrections, and that earthquake radiation patterns should not influence corrections which may be applied to surface-waves from suspected explosions.

Near‐fault spatial variation in strong ground motion due to rupture directivity and hanging wall effects from the Chi‐Chi, Taiwan earthquake

AbstractDamaging earthquakes feature large variations in the spatial ground motion distribution mainly due to source complexity, radiation pattern, and site conditions. In this study, we tried to capture the hanging wall and rupture directivity effects from the 1999 Chi‐Chi, Taiwan earthquake (Mw=7.6), which provides the largest acceleration data set since the strong‐motion seismology studies began. First, the event‐specific attenuation relations of strong‐motion parameters for the near‐field, hanging wall and footwall sites were developed. Then an empirical hanging wall model for peak ground acceleration (PGA) was introduced to get the residuals from the obtained attenuation relationships. The new empirical model for the PGA on the hanging wall indicates 46% to 50% higher values than the predicted means over the near‐field distance ranges. Finally, a period‐dependent empirical spectral amplitude factor model representing the directivity effects for the dip‐slip faulting system was developed using the Somerville et al. directivity model. The proposed model shows a larger spectral amplification factor than the result of the previous study. During the Chi‐Chi earthquake, the maximum spectral directivity factors have been registered in the up‐dip region, located around the surface exposure of the Chelungpu fault, in the range of 1.1 to 1.3 for the structural periods from 0.6s to 5.0s. Since the proposed spectral directivity factor was derived from the residual function of the single event without any influence of inter‐event variability, the model is magnitude‐ and distance‐independent. Hence the result can be easily implemented into attenuation relations, seismic hazard assessment, and building code revision studies for the regions with a dip‐slip faulting. Copyright 2003 © John Wiley & Sons, Ltd.

Efficient integral equation formulation of diffraction at the edge of a truncated dielectric structure based on PO solutions: Application to the case of arbitrarily polarized line sources

The radiation patterns of electric and magnetic line sources placed near the truncation of a semi‐infinite grounded dielectric layer structure have been investigated. Two polarizations (parallel and normal to the edge) have been considered for both sources. In order to perform the analysis a new formulation is proposed for the aperture integral equations derived from the principle of equivalence. The novelty of this formulation is that it involves only the fringe components of the magnetic current. The total magnetic current flowing on the aperture is expressed in terms of the physical optics (PO) current and the fringe current. Although the PO current is not known analytically, we can calculate the field excited by this current using the relationship between the surface magnetic PO current on the aperture and the electric polarization PO current in the grounded dielectric slab. The latter PO current is approximated analytically by the expansion wave concept. This step opens a simple and effective way to calculate the right part of the integral equations and as a consequence the radiation pattern of the line sources. For comparison reasons the problem is solved also by using the method of Physical Optics and the Uniform Theory of Diffraction.

Design and analysis of spatially variant microlens-array diffuser with uniform illumination for short-range infrared wireless communications using photometric approach

A microlens-array was designed to transform the Gaussian radiation pattern of a point source to the uniform illumination in the far field, which can be used as an optical diffuser of short-range infrared wireless communication systems, allowing a transmitter to use more optical power safely. This paper describes how to design such a microlens-array diffuser and investigates the property of the light distribution generated thereby.

Stable and Transportable Regional Magnitudes Based on Coda-Derived Moment-Rate Spectra

We describe an empirical calibration method for obtaining stable seismic source moment-rate spectra derived from regional coda envelopes using broadband stations. The results of applying this method yield source spectra that are more stable than any other direct-phase measure to date. The procedure accounts for all propagation, site, and S -to-coda transfer function effects. The resultant coda-derived moment-rate spectra are then used to provide traditional band-limited magnitudes (e.g., M L , m b ), as well as an unbiased, unsaturated magnitude (moment magnitude, M w ) that is tied to a physical measure of earthquake size (i.e., seismic moment). We validate our results by comparing our coda-derived moment estimates with those obtained from long-period waveform modeling. Most importantly, we demonstrate that the interstation magnitude scatter is significantly reduced when using long-window-length coda (i.e., M w (coda) and m b (coda)). However, when we use short-window coda measurements of 5 sec in length taken after twice the direct-wave travel time, the scatter remains large, comparable to direct waves. Once calibrated, the coda-derived source spectra provide stable, unbiased magnitude estimates for events that are too small either to be reliably waveform modeled or to be seen at far-regional and teleseismic distances. This property is ideal for sparse local or regional networks. We found that our source amplitude estimates were nearly insensitive to the expected source radiation pattern and exhibited roughly a factor of 3-5 less interstation scatter when compared against coda duration and conventional direct-phase measurements (e.g., P g , L g ). We also found that the coda stability, as measured by the interstation scatter for common events, reached a minimum value beyond a certain critical measurement window length. For example, at 6-8 Hz, the interstation standard deviation was less than 0.08 provided the coda measurement was at least ∼80 sec in duration, whereas at 1.5-2.0 Hz, the critical window length was ∼100 sec. For all frequency bands, as the coda window becomes shorter, the standard deviation increases, asymptotically approaching the direct-wave scatter. In this article we describe in detail the calibration methodology and address concerns related to choosing optimal measurement window lengths, estimating error, testing empirical path corrections, and tying coda amplitudes to an absolute scale. In order to demonstrate the usefulness and transportability of our method, we chose the Dead Sea Rift as our study area.