Focal mechanisms of recent earthquakes in the Southern Korean Peninsula

We evaluate the stress field in and around the southern Korean Peninsula with focal mechanism solutions, using the data collected from 71 earthquakes ( M_L = 1.9–5.2) between 1999 and 2004. For this, the hypocentres were relocated and well-constrained fault plane solutions were obtained from the data set of 1270 clear P -wave polarities and 46 SH / P amplitude ratios. The focal mechanism solutions indicate that the prevailing faulting types in South Korea are strike-slip-dominant-oblique-slip faultings with minor reverse-slip component. The maximum principal stresses (σ₁) estimated from fault-slip inversion analysis of the focal mechanism solutions show a similar orientation with E–W trend (269°–275°) and low-angle plunge (10°–25°) for all tectonic provinces in South Korea, consistent with the E–W trending maximum horizontal stress (σ_Hmax) of the Amurian microplate reported from in situ stress measurements and earthquake focal mechanisms. The directions of the intermediate (σ₂) and minimum (σ₃) principal stresses of the Gyeongsang Basin are, however, about 90 deg off from those of the other tectonic provinces on a common σ₂–σ₃ plane, suggesting a permutation of σ₂ and σ₃. Our results incorporated with those from the kinematic studies of the Quaternary faults imply that NNW- to NE-striking faults (dextral strike-slip or oblique-slip with a reverse-slip component) are highly likely to generate earthquakes in South Korea.     

Estimate of the stress field in Kilauea's South Flank, Hawaii

We estimated stress and seismic strain tensors for the Kilauea volcano's south flank. the stress orientation inversion and the seismic strain calculation were performed using fault-plane solutions. the principal stress and seismic strain directions are approximately uniformly distributed in space and time during the interval covered by the data. However, the σ1, σ3 plane is approximately orthogonal to the 1, 3 plane. Therefore, a weak layer may exist beneath the south flank. σ1 has a plunge of 59° and an azimuth of 152°, with a 10° 95 per cent confidence range. We also developed a stress magnitude inversion to estimate magnitudes of boundary and interior stresses. In this inversion, the principal stress directions were taken as constraints in the seismic volume, and surface geodetic observations were used as data. the maximum magmatic pressure in Kilauea's rift zone is about 160 MPa. the direction of σ1 can be interpreted as the superposition of hydrostatic stress ( pgh ) and magmatic pressure. Without the constraint imposed by the direction of σ1, the estimated pressure is only 60MPa, the distribution of magmatic pressure may be similar to that of pgh . In contrast, the upper rift zone may be in tension. the shear stress in the rift zone is about one order of magnitude smaller than the maximum compressive stress, supporting the interpretation of magmatic flow as fluid in dikes or channels. the combination of stress orientation inversion, seismic strain calculation, and stress magnitude inversion performed in this study provides a means by which to estimate the stress state in seismic areas.     

Calculating horizontal stress orientations with full or partial knowledge of the tectonic stress tensor

Earthquakes potentially serve as abundant and cost-effective gauges of tectonic stress provided that reliable means exist of extracting robust stress parameters. Several algorithms have been developed for this task, each of which typically provides information on the orientations of the three principal stresses and a single stress magnitude parameter. A convenient way of displaying tectonic stress results is to map the azimuth of maximum horizontal compressive stress, which is usually approximated using the azimuth of the larger subhorizontal principal stress. This approximation introduces avoidable errors that depend not only on the principal stress axes' plunges but also on the value of the stress magnitude parameter. Here we outline a method of computing the true direction of maximum horizontal compressive stress ( S _H) and show that this computation can be performed using only the four stress parameters obtained in routine focal mechanism stress estimation. Using theoretical examples and new stress inversion results obtained with focal mechanism data from the central Grímsey lineament, northern Iceland, we show that the S _H axis may differ by tens of degrees from its commonly adopted proxy. In order to most appropriately compare tectonic stress estimates with other geophysical parameters, such as seismic fast directions or geodetically measured strain rate tensors, or to investigate spatiotemporal variations in stress, we recommend that full use be made of the routinely estimated stress parameters and that a formal axis of maximum horizontal compression be calculated.     

A Bayesian approach to estimating tectonic stress from seismological data

Earthquakes are conspicuous manifestations of tectonic stress, but the non-linear relationships between the stresses acting on a fault plane, its frictional slip, and the ensuing seismic radiation are such that a single earthquake by itself provides little information about the ambient state of stress. Moreover, observational uncertainties and inherent ambiguities in the nodal planes of earthquake focal mechanisms preclude straightforward inferences about stress being drawn on the basis of individual focal mechanism observations. However, by assuming that each earthquake in a small volume of the crust represents a single, uniform state of stress, the combined constraints imposed on that stress by a suite of focal mechanism observations can be estimated. Here, we outline a probabilistic (Bayesian) technique for estimating tectonic stress directions from primary seismological observations. The Bayesian formulation combines a geologically motivated prior model of the state of stress with an observation model that implements the physical relationship between the stresses acting on a fault and the resultant seismological observation. We show our Bayesian formulation to be equivalent to a well-known analytical solution for a single, errorless focal mechanism observation. The new approach has the distinct advantage, however, of including (1) multiple earthquakes, (2) fault plane ambiguities, (3) observational errors and (4) any prior knowledge of the stress field. Our approach, while computationally demanding in some cases, is intended to yield reliable tectonic stress estimates that can be confidently compared with other tectonic parameters, such as seismic anisotropy and geodetic strain rate observations, and used to investigate spatial and temporal variations in stress associated with major faults and coseismic stress perturbations.     

A resampling approach to test stress-field uniformity from fault data

Several methods have been proposed to constrain the stress field from fault plane orientations and slip directions within a crustal volume characterized by brittle deformation. All the methods are based on the assumption that the stress field is uniform in the volume considered. If this hypothesis is not checked in advance, however, the methodology may lead to misleading conclusions. In this work, a procedure is defined to check stress-field uniformity by a statistical analysis of the available fault data. Since, in most cases, the statistical features of the uncertainties that affect such data are not well known, a distribution-free approach is proposed. It is based on a simple search algorithm, devoted to selecting stress configurations compatible with available data, combined with a bootstrap resampling approach. The test results are more conservative than the ones so far proposed in the literature. When the test allows stress heterogeneities to be safely excluded, approximate confidence intervals for the principal stress directions can be obtained; otherwise, the level of stress heterogeneity present in the volume under study can be assessed. An application of the proposed procedure to a sample of fault data deduced from seismological data is presented.     

Modelling the effect of atmospheric pressure variations on gravity

Summary. The 1973 Hawaii earthquake occurred north of Hilo, at a depth of 40 to 50km. The location was beneath the east flank of Mauna Kea, a volcano dormant historically, but active within the last 4000 yr. Aftershocks were restricted to a depth of 55–35km. The event and its aftershock sequence are located in an area not normally associated with the seismicity of the Mauna Loa and Kilauea calderas. The earthquake was a double event, the epicentres trending NE-SW. The events were of similar size and faulting mechanism. The fault plane solutions obtained by seismic waveform analysis are a strike-slip fault striking EW and dipping 55° S, the auxiliary plane a NS vertical plane with a faulting plunge of 35°. The axis of maximum compressive stress is aligned with the direction of the gravity gradient associated with the island of Hawaii. The fault plane striking EW parallels a surface feature, the Mauna Kea east rift zone. The earthquakes were clearly not associated with volcanic activity normally associated with Mauna Loa and Kilauea and may indicate a deep seated prelude to a resumption of activity at Mauna Kea.     

A detailed analysis of the February 1996 aftershock sequence in the eastern Pyrenees, France

Following the 1996 February 18 M _L = 5.2 earthquake in the Agly massif in the eastern French Pyrenees, we installed a temporary network of seismometers around the epicentre. In this paper, we analyse 336 well-located aftershocks recorded from February 19 to February 23 by 18 temporary stations and two permanent stations located less than 35  km from the epicentre. Most aftershocks have been located with an accuracy better than 1.5  km in both horizontal and vertical positions. Their spatial distribution suggests the reactivation of a known fault system. We determined 39 fault-plane solutions using P -wave first motions. Despite their diversity, the focal mechanisms yield an E–W subhorizontal T-axis. We also determined fault-plane solutions and principal stress axes using the method developed by Rivera & Cisternas (1990 ) for the 15 best-recorded events. We obtain a pure-shear-rupture tectonic regime under N–S subhorizontal compression and E–W subhorizontal extension. These principal stress axes, which explain the focal mechanisms for at least 75 per cent of the 39 aftershocks, are different from the axes deduced from the main shock. The post-earthquake stress field caused by the main-shock rupture, modelled as sinistral strike slip on three vertical fault segments, is computed for various orientations and magnitudes of the regional stress field, assumed to be horizontal. The aftershock distribution is best explained for a compressive stress field oriented N30°E. Most aftershocks concentrate where the Coulomb failure stress change increases by more than 0.2  MPa. The diversity of aftershock focal mechanisms, poorly explained by this model, may reflect the great diversity in the orientations of pre-existing fractures in the Agly massif.     

Focal Mechanism of the Koyna, India Earthquake of 1967, December 10

One of the two alternate fault plane solutions determined in this study for the Koyna earthquake of 1967 December 10 shows a component of normal faulting. This possibility remained unnoticed in previous focal mechanism studies. Both solutions show left lateral motion along the nodal plane striking towards north-north-east. The origin of the tectonic stress causing the earthquake is believed to be related to the collision of Indian and Eurasian continents, following which the entire Indian Peninsula may be under a state of left lateral shear.     

A method for the near-source anisotropy by the pair-event inversion of Rayleigh-wave radiation patterns

Summary. A novel method is proposed for retrieving the 3-D orientation of axes of symmetry of near-source anisotropy by a non-linear inversion of observed radiation patterns of seismic displacement spectra of Rayleigh waves.
If faulting is generated within an anisotropic source region, body force equivalents for the faulting are in general not a double couple but the sum of three orthogonal dipole forces (Kosevich; Kawasaki & Tanimoto). As a result of the third dipole force, radiation patterns of Rayleigh waves are deformed, the deformation amounting to several per cent of those for an isotropic source medium. The non-linear inversion is carried out to find the optimum fault plane solutions giving the minimum square residual between observed and theoretical radiation patterns in some period range. In order to remove effects of heterogeneity along propagation paths, a pair-event scheme is involved in the inversion, which denotes taking spectral amplitude ratios and differential phases of the seismic displacement spectra of the pair-events having close hypocentres and different fault plane solutions. The uniqueness of the fault plane solutions of the non-linear inversion is afforded a proof by the Monte-Carlo experiment.
The non-linear inversion is repeated for some possible types of symmetry of the near-source orthotropic anisotropy due to the preferred orientation of olivine crystals as mantle materials. Square residuals thus obtained are compared with each other to see which orientation gives the minimum.
The method is applied to pair-events which occurred in the anomalous mantle beneath the Mid-Atlantic Ridge. This leads to a discovery that one type of symmetry of the preferred orientations with a -, b - and c-axes aligned vertical, parallel to and perpendicular to the trend (N11E) of the ridge axis, respectively, is most likely existing in the anomalous mantle.     

Present-day deformation of the Dauphine Alpine and Subalpine massifs (SE France)

The positions of 20 geodetic points surveyed in 1946-1952 by the Institut Géographique National in the Grenoble area (western Alps) were remeasured in 1993-1994 using GPS. We evaluate the displacements of the common points of the networks between the two surveys, and calculate the strain-rate tensors for different sets of three adjacent points. The significant N70° shortening direction observed at the boundary of the Belledonne and Taillefer massifs suggests that the dextral strike-slip motion between the External Crystalline Massifs (ECM) and the Subalpine domain is still active. Geological evidence suggests that this deformation, which is compatible with the few focal mechanisms available for the area, occurred throughout the late Neogene. Our data also suggest a roughly 3-5 mm yr⁻¹ active shortening concentrated at the external front of the Subalpine chains. This thrust motion results in a principal axis of compression orientated N130°, oblique to the direction of shortening observed in the ECM. This change in direction is also seen in in situ stress measurements. This motion may mark the southward continuation of the active fault observed in the Jura mountains by Jouanne, Ménard & Darmendrail (1995).     

Source investigation of a small event using empirical Green's functions and simulated annealing

We propose a two-step inversion of three-component seismograms that (1) recovers the far-field source time function at each station and (2) estimates the distribution of co-seismic slip on the fault plane for small earthquakes (magnitude 3 to 4). The empirical Green's function (EGF) method consists of finding a small earthquake located near the one we wish to study and then performing a deconvolution to remove the path, site, and instrumental effects from the main-event signal.
The deconvolution between the two earthquakes is an unstable procedure: we have therefore developed a simulated annealing technique to recover a stable and positive source time function (STF) in the time domain at each station with an estimation of uncertainties. Given a good azimuthal coverage, we can obtain information on the directivity effect as well as on the rupture process. We propose an inversion method by simulated annealing using the STF to recover the distribution of slip on the fault plane with a constant rupture-velocity model. This method permits estimation of physical quantities on the fault plane, as well as possible identification of the real fault plane.
We apply this two-step procedure for an event of magnitude 3 recorded in the Gulf of Corinth in August 1991. A nearby event of magnitude 2 provides us with empirical Green's functions for each station. We estimate an active fault area of 0.02 to 0.15 km² and deduce a stress-drop value of 1 to 30 bar and an average slip of 0.1 to 1.6 cm. The selected fault of the main event is in good agreement with the existence of a detachment surface inferred from the tectonics of this half-graben.     

2001 August earthquake swarm at Shadwan Island, Gulf of Suez, Egypt

The earthquake swarm that struck Shadwan Island at the entrance of the Gulf of Suez in 2001 August included 408 events. Almost all of these events (94 per cent) were microearthquakes and only 6 per cent had small measurable magnitudes  (5.0 > M _L≥ 3.0)  . Most of the earthquakes were weak and followed each other so closely in time that they could not be identified at more distant stations. The fault plane solutions of the strongest events of the swarm show almost identical focal mechanisms, predominately normal faulting with a significant sinistral strike-slip component for nodal planes trending NW–SE. A comparison with the mechanisms of the 1969 and 1972 events which took place 20 km north of the swarm epicentral region shows similarities in faulting type and orientation of nodal planes. The azimuths of T -axes determined from focal mechanisms in this study are oriented in the NNE–SSW direction. This direction is consistent with the present-day stress field derived from borehole breakouts in the southern Gulf of Suez and the last phase of stress field changes in the Late Pleistocene, as well as with recent GPS results.
The source parameters of the largest  ( M _L≥ 3.0)  events of the 2001 August Shadwan swarm have been estimated from the P -wave spectra of the Egyptian National Seismograph Network (ENSN). Averaging of the values obtained at different stations shows relatively similar source parameters, including a fault length of  0.65 ≤ L ≤ 2 km  , a seismic moment of  7.1 × 10¹²≤ Mo ≤ 3.0 × 10¹⁴ N m  and a stress drop of  0.4 ≤Δσ≤ 10  bar.     

Groups, algebras, and the non-linearity of geophysical inverse problems

Mathematical methods from the theory of continuous groups are used to determine whether a non-linear inverse problem, in the form of a functional, can be transformed into a linear inverse problem. If such transformations exist they can be constructed from the solutions of a linear system of differential equations. An illustration of the methodology is given by the linearization of the functional relating basement topography to observed surface gravity. The linearized inversion of gravity data for basement topography is applied to observations from Yucca Mountain, Nevada. A 2.0 km step in the basement to the west of Yucca Mountain, corresponding to the Bare Mountain fault, matches the Bouguer gravity anomaly. The resolution and uncertainty associated with the estimates of basement topography indicate that the structure directly beneath the gravity line is well constrained.     

New techniques for the analysis of earthquake sources from local array data with an application to the 1993 Scotts Mills, Oregon, aftershock sequence

We analysed aftershocks recorded by a temporary digital seismic network following the moderate M _w = 5.5 1993, Scotts Mills, Oregon, earthquake. A technique to retrieve source moment tensors from local waveforms was developed, tested, and applied to 41 small earthquakes ( M _w ranging from 1.6 to 3.2). The derived focal mechanisms, although well resolved, are highly variable and do not share a common nodal plane. In contrast, the majority of the events, relocated with a joint hypocentre determination algorithm, collapse to a well-focused plane. The incompatibility of the nodal planes of most events with the plane defined by their locations suggests that the aftershocks did not occur on the fault plane, but tightly around it, outlining the rupture area rather than defining it. Furthermore, the moment tensors reveal stable P -axes, whereas T  -axes plunges are highly dispersed. We detect a rotation of average T  -axis plunge with depth, indicating a change from shallower, predominantly dip-slip mechanisms to deeper strike-slip mechanisms. These characteristics are difficult to explain by remnant stress concentrations on the main-shock rupture plane or asperity- and barrier-type models. We suggest that the aftershocks occurred under the ambient regional stress, triggered by a sudden weakening of the region surrounding the main-shock slip, rather than from a shear stress increase due to the main shock.     

Aseismic fault movement before the 1995 Kobe earthquake detected by a GPS survey: implication for preseismic stress localization?

By inversion analysis of the baseline changes and horizontal displacements observed with GPS (Global Positioning System) during 1990–1994, a high-angle reverse fault was detected in the Shikoku-Kinki region, southwest Japan. The active blind fault is characterized by reverse dip-slip (0.7±0.2  m yr⁻¹ within a layer 17–26  km deep) with a length of 208±5  km, a (down-dip) width of 9±2  km, a dip-angle of 51°±2° and a strike direction of 40°±2° (NE). Evidence from the geological investigation of subfaults close to the southwestern portion of the fault, two historical earthquakes ( M _L=7.0, 1789 and 6.4, 1955) near the centre of the fault, and an additional inversion analysis of the baseline changes recorded by the nationwide permanent GPS array from 18 January to 31 December 1995 partially demonstrates the existence of the fault, and suggests that it might be a reactivation of a pre-existing fault in this region. The fact that hardly any earthquakes ( M _L>2.0) occurred at depth on the inferred fault plane suggests that the fault activity was largely aseismic. Based on the parameters of the blind fault estimated in this study, we evaluated stress changes in this region. It is found that shear stress concentrated and increased by up to 2.1 bar yr⁻¹ at a depth of about 20  km around the epicentral area of the 1995 January 17  Kobe earthquake ( M _L=7.2, Japan), and that the earthquake hypocentre received a Coulomb failure stress of about 5.6 bar yr⁻¹ during 1990–1994. The results suggest that the 1995  Kobe earthquake could have been induced or triggered by aseismic fault movement.     

CMT data inversion using a Bayesian information criterion to estimate seismogenic stress fields

We developed an inversion method to estimate the stress fields related to earthquake generation (seismogenic stress fields) from the centroid moment tensors (CMT) of seismic events by using Akaike's Bayesian information criterion (ABIC). On the idea that the occurrence of an earthquake releases some part of the seismogenic stress field around its hypocentre, we define the CMT of a seismic event by a weighted volume integral of the true but unknown seismogenic stress field. Representing each component of the seismogenic stress field by the superposition of a finite number of 3-D basis functions (tri-cubic B-splines), we obtain a set of linear observation equations to be solved for the expansion coefficients (model parameters). We introduce prior constraint on the roughness of the seismogenic stress field and combine it with observed data to construct a Bayesian model with hierarchic, highly flexible structure controlled by hyper-parameters. The optimum values of the hyper-parameters are objectively determined form observed data by using ABIC. Given the optimum values of the hyper-parameters, we can obtain the best estimates of model parameters by using a maximum likelihood algorithm. We tested the validity of the inversion method through numerical experiments on two synthetic CMT data sets, assuming the distribution of fault orientations to be aligned with the maximum shear stress plane in one case and to be random in the other case. Then we applied the inversion method to actual CMT data in northeast Japan, and obtained the pattern of the seismogenic stress field consistent with geophysical and geological observations.     

AN ASSESSMENT OF CLAST MACROFABRICS IN GLACIGENIC SEDIMENTS BASED ON A/B PLANE DATA

Previous studies of clast macrofabrics in glacigenic deposits have concentrated on A‐axis orientations and dips, and a variety of control samples are available based upon such measurements. Like clast A‐axes, A/B planes will also tend to rotate to parallelism with the direction of shear and therefore should also provide meaningful data on the direction and cumulative impact of shear by the depositing/deforming medium (i.e. glacier ice). The measurement of A/B plane dip and orientation avoids the potential problem of the transverse orientations observed for clast A‐axes and provides poles‐to‐plane data, thereby strengthening the modality of samples and providing clear visual impressions of stress directions. Such data also enable more significant inter‐sample comparisons of fabric strength and clast dip angles, which are significant when assessing the impact of shearing in sediment genesis. We present data on clast A/B plane dip directions and angles from subglacial tills, glacitectonite continuums, subglacially lodged clasts and glacimarine/glacilacustrine deposits using traditional methods of statistical and graphical macrofabric analysis. These sample sets will serve as control data for future macrofabric analyses that utilize A/B planes. The separation of the unequivocally lodged clast component from subglacial till samples allows us to demonstrate the influence of deformation and ploughing in the relative weakening of till fabrics as proposed by some researchers. High angles of A/B plane dip in glacigenic subaqueous deposits appear to be well developed in the glacilacustrine setting investigated here, confirming previous studies based on A‐axis dips, but less convincing in the glacimarine sediments of the Canadian Arctic, thereby widening the range of fabric strengths in subaqueous glacigenic deposits. Significant overlaps of A/B plane fabric shape envelopes reflect the strain history of subglacial and subaqueous depositional environments, which is unsurprising given the hybrid nature of glacigenic deposits, but the statistical isolation of the lodgement component from subglacial traction tills strongly suggests that the continuum of sample plots on modality/isotropy graphs reflects the range of strain histories in glacitectonites and subglacial traction till.     

Piezomagnetic potentials due to an inclined rectangular fault in a semi-infinite medium

Analytical solutions for the piezomagnetic potentials are derived for strike-slip, dip-slip and tensile-opening fault motions with arbitrary dip and strike angles, so as to be applicable in various types of earthquakes. These solutions are expressed as the composition of elementary functions which are identical to the magnetic potentials produced by magnetic dipoles, quadrupoles and octupoles distributed on the fault plane and other planes. Therefore, the geomagnetic field changes due to the piezomagnetic effect are expressed by the superposition of the fields produced by these equivalent sources.
Examples of calculated results show characteristic features for various types of fault motions as follows: (1) the pattern of the geomagnetic field changes becomes significantly different depending on the strike direction, although the maximum amplitude is almost the same for all directions; (2) the geomagnetic field change reaches a maximum at a dip angle of 90° for strike-slip and tensile-opening fault motions and at 45° for dip-slip fault motion.     

Seismotectonic implications of relocated aftershock sequences in Iran and Turkey

Summary. Six aftershock sequences in Iran and Turkey are relocated using existing teleseismic data. Two of these are in the Zagros mountains where local fieldwork has failed to detect subcrustal seismicity but published teleseismic locations show depths greater than 100 km. All apparently deep events are shown to be small and badly recorded with poor depth resolution. There is thus no evidence for active lithospheric subduction in the Zagros.
Relocations of other sequences in Iran and Turkey are used with fault plane solutions, satellite photographs and surface faulting to provide new insight on the geometry of faulting and crustal deformation of those regions. Linear seismic trends from these sequences are shown to cut older geological structures and do not always bear a simple relation to surface faulting. In such cases aftershock activity may be on primary buried faults whose behaviour is not simply revealed in surface structure and deformation.
A linearized inversion scheme is used to investigate the trade-off between resolution and uncertainty in the hypocentral parameters. The ultimate resolution of teleseismic locations is shown to be limited by the quality of arrival time data.     

Sensitivities of seismic traveltimes and amplitudes in reflection tomography

Seismic traveltimes and amplitudes in reflection-seismic data show different dependences on the geometry of reflection interfaces, and on the variation of interval velocities. These dependences are revealed by eigenanalysis of the Hessian matrix, defined in terms of the Fréchet matrix and its adjoint associated with different norms chosen in the model space. The eigenvectors and eigenvalues of the Hessian clearly show that for reflection tomographic inversion, traveltime and amplitude data contain complementary information. Both for reflector-geometry and for interval-velocity variations, the traveltimes are sensitive to the model components with small wavenumbers, whereas the amplitudes are more sensitive to the components with high wavenumbers. The model resolution matrices, after the rejection of eigenvectors corresponding to small eigenvalues, give us some insight into how the addition of amplitude information could potentially contribute to the recovery of physical parameters.
In order to cooperatively invert seismic traveltimes and amplitudes simultaneously, we propose an empirical definition of the data covariance matrix which balances the relative sensitivities of different types of data. We investigate the cooperative use of both data types for, separately, interface-geometry and 2-D interval-velocity variations. In both cases we find that cooperative inversions can provide better solutions than those using traveltimes alone. The potential benefit of including amplitude-data constraints in seismic-reflection traveltime tomography is therefore that it may be possible to resolve the known ambiguity between the reflector-depth uncertainty and the interval-velocity uncertainty better.