Prediction of ground motion in the Osaka sedimentary basin associated with the hypothetical Nankai earthquake

We studied the long-period ground motions in the Osaka sedimentary basin, Japan, which contains a 1- to 3-km thickness of sediments and is the site of many buildings or construction structures with long-natural period. We simulated the broadband ground motions likely to be produced by the hypothetical Nankai earthquake: the earthquake expected to give rise to the most severe long-period ground motion within the basin. For the simulation, we constructed multiscale heterogeneous source models based on the Central Disaster Management Council of Japan (CDMC) source model and adopted a hybrid computation method in which long-period motion and short-period motion are computed using a 3-D finite difference method and the stochastic Green’s function method, respectively. In computing long-period motions, we used a 3-D structure model of the crust and the Osaka sedimentary basin. The ground motions are estimated to have peak velocities of 50–90 cm/s, prolonged durations exceeding 300 s, and long predominant periods of 5–10 s in the area with great thickness of sediments. The predominant periods are in agreement with an approximate evaluation by 4 H/V _s where H and V _s are the thickness of the sediment and the average S wave velocity, respectively.     

大兴安岭造山带及两侧邻区莫霍面深度与泊松比分布特征

利用2009～2016年内蒙古自治区数字地震台网宽频带固定地震台站的远震波形数据,采用接收函数H-k算法获得23个基岩台站下方的莫霍面深度和泊松比,同时,收集并筛选出277个已有探测台阵和流动台站的接收函数研究结果,综合分析给出大兴安岭造山带及两侧邻区莫霍面深度、泊松比的分布特征。研究表明,研究区域的莫霍面在整体上呈现自东向西逐渐加深的特征,莫霍面深度为25.0～42.3km,平均约为33.5km。莫霍面最浅的区域为松辽盆地(深度为27.0～35.0km),最深的区域为大兴安岭重力梯级带以西地区(深度为41.0～42.3km)。研究区域泊松比为0.19～0.33,平均值为0.26,大于全球大陆地壳的平均值。泊松比高值异常区集中在火山岩区及具有较厚沉积层的盆地。台站所处位置的海拔与莫霍面深度之间具有较强的正相关性,艾里补偿模式在研究区成立,莫霍面起伏与区域地形地貌特征间具有显著的镜像关系。大兴安岭地区的莫霍面深度与泊松比间存在显著的反相关关系,而在松辽盆地及周缘地区未发现明显的规律性,这也意味着松辽盆地在构造演化过程中经历了更为复杂的地壳改造过程。     

Simulating the Taipei basin response by numerical modeling of wave propagation

Taipei, the capital of Taiwan, suffered from destructive earthquakes four times during the 20th century (M _L = 7.3 on April 15, 1909; M _L = 6.8 on November 15, 1986; the Chi–Chi M _L = 7.3 earthquake on September 21, 1999; and M _L = 6.8 on March 31, 2002). Analysis of recorded data shows a strong dependence of spectral amplification in the Taipei Basin on earthquake depth and azimuth. At low frequencies (f < 3 Hz) significant larger amplifications are observed for shallow earthquakes as compared to intermediate depth events. The former ones also display strong azimuthal dependence. As structures with large response periods such as bridges and tall buildings are sensitive to these low frequencies the understanding of the associated wave effects within the basin and their role for site effect amplification is critical. The tool we employ is 3D finite-difference modeling of wave propagation of incident wave fronts. The available detailed model of the basin allows studying the wave effects. Modeling clearly reveals that basin edge effects as observed in data are related to surface wave generation at the basin edges with a high degree of azimuthal dependency. The reproduced site amplification effects are in qualitative agreement with the observations from strong motion data.     

Modelling shear waves in OBS data from the Vøring basin (Northern Norway) by 2-D ray-tracing

Three component recordings from an array of five ocean bottom seismographs in the northwestern part of the Vøring basin have been used to obtain a 2-D shear-wave (S-wave) velocity-depth model. The shear waves are identified by means of travel-time differences compared to the compressional (P) waves, and by analyzing their particle motions. The model has been obtained by kinematic (travel-time) ray-tracing modelling of the OBS horizontal components.The shear-wave modelling indicates that mode conversions occur at several high velocity interfaces (sills) in the 4–10 km depth range, previously defined by a compressional-wave velocity-depth model using the same data set.An averageV _p /V _s ratio of 2.1 is inferred for the layers above the uppermost sill, indicative of both poorly consolidated sediments and a low sand/shale ratio. A significant decrease in theV _p /V _s ratio (1.7) below the first sill may in part be atributed to well consolidated sediments, and to a change in lithology to more sandy sediments. This layer is interpreted to lie within the lower Cretaceous sequence. At 5–10 km depthV _p /V _s ratios of 1.85 indicate a lower sand/shale ratio consistent with the expected lithologies. The averageV _p /V _s ratio inferred for the crust is 1.75, which is consistent with values obtained north of Vøring, in the Lofoten area. An eastward thinning of the crystalline basement is supported by the shear-wave modelling.     

Geophysical Images of the North Anatolian Fault Zone in the Erzincan Basin, Eastern Turkey, and their Tectonic Implications

The collision between the Arabian and Eurasian plates in eastern Turkey causes the Anatolian block to move westward. The North Anatolian Fault (NAF) is a major strike-slip fault that forms the northern boundary of the Anatolian block, and the Erzincan Basin is the largest sedimentary basin on the NAF. In the last century, two large earthquakes have ruptured the NAF within the Erzincan Basin and caused major damage (M _s = 8.0 in 1939 and M _s = 6.8 in 1992). The seismic hazard in Erzincan from future earthquakes on the NAF is significant because the unconsolidated sedimentary basin can amplify the ground motion during an earthquake. The amount of amplification depends on the thickness and geometry of the basin. Geophysical constraints can be used to image basin depth and predict the amount of seismic amplification. In this study, the basin geometry and fault zone structure were investigated using broadband magnetotelluric (MT) data collected on two profiles crossing the Erzincan Basin. A total of 24 broadband MT stations were acquired with 1–2 km spacing in 2005. Inversion of the MT data with 1D, 2D and 3D algorithms showed that the maximum thickness of the unconsolidated sediments is ~3 km in the Erzincan Basin. The MT resistivity models show that the northern flanks of the basin have a steeper dip than the southern flanks, and the basin deepens towards the east where it has a depth of 3.5 km. The MT models also show that the structure of the NAF may vary from east to west along the Erzincan Basin.     

Site Effect Study in Urban Area: Experimental Results in Grenoble (France)

—?Three methods are used to determine the site effect in the town of Grenoble, located in the Western Alps. First we use the classical spectral ratio method in 14 sites to calculate the transfer function of the basin. We find an amplification of 10 in the frequency range of 0.25 to 10?Hz. Second, we compare these results with the H over V spectral ratio method, and propose a map of resonance frequency of the basin. We find a lower resonance frequency in the center of the basin than on the edge, that is consistent with the structure deduced from a gravity Bouguer anomaly map. Finally we use the empirical Green's function method to simulate a M _w 5.5 earthquake at a distance of 20?km from the town. The simulated acceleration reaches the level of 2?m/s² in the center of the basin compared to 0.2?m/s² on the edges. The simulated ground motion we compute is smaller than the French seismic codes on the edge of the valley but significantly larger in the center.     

Characteristics of the seismic attenuation in two tectonically active zones of Southern Europe

The seismic energy attenuation in the frequency range of 1–18 Hz was studied in the two tectonically active zones of Irno Valley (Southern Italy) and Granada Basin (South-East Spain). Data were recorded by short period vertical components seismographs for low-magnitude local earthquakes. The method of coda waves, assuming singleS toS scattering approximation, was used to calculate the quality factorQ from the two data set. Results show a quality factor increasing with frequency, following the empirical lawQ=Q _o f ⁿ .Q _o andn are lower for the Irno Valley than for Granada. This result is interpreted in terms of different scattering environments present in the two investigated areas.     

Validation of 3-D basin structure models for long-period ground motion simulation in the Osaka basin, western Japan

We studied the applicability of two types of existing three-dimensional (3-D) basin velocity structure models of the Osaka basin, western Japan for long-period ground motion simulations. We synthesized long-period (3–20 s) ground motions in the Osaka basin during a M6.5 earthquake that occurred near the hypothetical Tonankai earthquake source area, approximately 200 km from Osaka. The simulations were performed using a 3-D finite-difference method with nonuniform staggered grids using the two basin velocity structure models. To study the ground motion characteristics inside the basin, we evaluated the wave field inside the basin using the transfer functions derived from the synthetics at the basin and a reference rock site outside the basin. The synthetic waveforms at the basin site were obtained by a convolution of the calculated transfer function and the observed waveform at the reference rock site. First, we estimated the appropriate Q values for the sediment layers. Assuming that the Q value depends on the S wave velocity V _S and period T, it was set to Q = (1/3V _S)(T ₀/T) where V _S is in m/s and the reference period T ₀ is 3.0 s. Second, we compared the synthetics and the observations using waveforms and pseudovelocity response spectra, together with a comparison of the velocity structures of the two basin models. We also introduced a goodness-of-fit factor to the pseudovelocity response spectra as an objective index. The synthetics of both the models reproduced the observations reasonably well at most of the stations in the central part the basin. At some stations, however, especially where the bedrock depth varies sharply, there were noticeable discrepancies in the simulation results of the models, and the synthetics did not accurately reproduce the observation. Our results indicate that the superiority of one model over the other cannot be determined and that an improvement in the basin velocity structure models based on simulation studies is required, especially along the basin edges. We also conclude that our transfer function method can be used to examine the applicability of the basin velocity structure models for long-period ground motion simulations.     

Ambient noise H/V spectral ratio in site effects estimation in Fateh jang area,Pakistan

Local geology or local site effect is a crucial component while conducting seismic risk assessment studies. Investigations made by utilization of ambient noise are an effective tool for local site estimation. The present study is conducted to perform site response analysis at 13 different sites within urban settlements of Fateh jang area(Pakistan). The aim of this study was achieved by utilizing Nakamura method or H/V spectral ratio method. Some important local site parameters, e.g., the fundamental frequencies f0 of soft sediments, amplitudes A0 of corresponding H/V spectral ratios, and alluvium thicknesses over 13 sites within the study area, were measured and analyzed. The results show that the study area reflects low fundamental frequency f0. The fundamental frequencies of the sediments are highly variable and lie in a range of 0.6–13.0 Hz. Similarly, amplification factors at these sites are in the range of 2.0–4.0.     

IMPROVED PHASE-ELLIPSE METHOD FOR IN SITU GEOPHONE CALIBRATION*

For amplitude and phase response calibration of moving-coil electromagnetic geophones two parameters are needed, namely, the geophone natural frequency, f₀, and the geophone upper resonance frequency f_u. The phase-ellipse method is commonly used for the in situ determination of these parameters. For a given signal-to-noise ratio, the precision of the measurement off₀ andf_u depends on the phase sensitivity, f(δφ/δf) For some commercial geophones f(δφ/δf) atf_u can be an order of magnitude less than the sensitivity atf₀. In this paper we present an improved phase-ellipse method with increased precision. Compared to measurements made with the existing phase-ellipse methods, our method shows a 6- and 3-fold improvement in the precision, respectively, on measurements of f₀ andf_u on a commercial geophone.     

Effective medium theory and multiple linear regression-based velocity estimation in syn-rift clastic sequence of the Krishna–Godavari basin,India

An inclusion model, based on the Kuster–Toksöz effective medium theory along with Gassmann theory, is tested to forward model velocities for fluid-saturated rocks. A simulated annealing algorithm, along with the inclusion model, effectively inverts measured compressional velocity (V_P) to achieve an effective pore aspect ratio at each depth in a depth variant manner, continuously along with depth. Early Cretaceous syn-rift clastic sediments at two different depth intervals from two wells [well A (2160–2274 m) and well B (5222–5303 m)], in the Krishna–Godavari basin, India, are used for this study. Shear velocity (V_S) estimated using modelled pore aspect ratio offers a high correlation coefficient (>0.95 for both the wells) with measured data. The modelled pore aspect ratio distribution suggests the decrease in pore aspect ratio for the deeper interval, mainly due to increased effective vertical stress. The pore aspect ratio analysis in relation to total porosity and volume of clay reveals that the clay volume has insignificant influence in shaping the pore geometry in the studied intervals. An approach based on multiple linear regression method effectively predicts velocity as a linear function of total porosity, the volume of clay and the modelled pore-space aspect ratio of the rock. We achieved a significant match between measured and predicted velocities. The correlation coefficients between measured and modelled velocities are considerably high (approximately 0.85 and 0.8, for V_P and V_S, respectively). This process indicates the possible influence of pore geometry along with total porosity and volume of clay on velocity.     

Vitrinite reflectance and consolidation characteristics of the post‐middle Miocene Forearc Basin in central and eastern Boso Peninsula,central Japan: Implications for basin subsidence

To understand the sedimentary development of the Boso Forearc Basin, central Japan, since ~ 3 Ma, we investigated paleothermal structure and consolidation trends in the central and eastern parts of the forearc basin through vitrinite reflectance measurements and consolidation tests. Vitrinite reflectance (R_m) was in the range 0.33 % to 0.61 % for the Miura Group in the central part of the forearc basin and 0.34 % to 0.41 % for the Miura and Kazusa Groups in the eastern. These values suggest a roughly uniform vitrinite reflectance for the Miura Group from the central to eastern parts. No significant vitrinite reflectance difference is observed across the ~ 3 Ma Kurotaki Unconformity in the eastern part of the basin. The consolidation yield stress (p_c) was calculated as 27.5 MPa and 32.2 MPa for the Kiyosumi and Amatsu Formations of the Miura Group in the eastern part, respectively. Both the p_c values are consistent quantitatively with represent the trend of the maximum overburden pressure estimated from the thickness and density of overlying sediments, and the difference in p_c is expected by the maximum burial depths of the strata at the sampling localities. Values of p_c in the eastern part of the basin increase with thickness of overlying sediment, showing no break across the Kurotaki Unconformity. Considering the eroded thickness of the Miura Group, the continuous trends in vitrinite reflectance and consolidation between the Miura and Kazusa Groups in the eastern part reflect the greater deposition of the eastern part of the Boso Forearc Basin since ~ 2.3 Ma.     

Coda wave attenuation in the Parecis Basin,Amazon Craton,Brazil: sensitivity to basement depth

Small local earthquakes from two aftershock sequences in Porto dos Gaúchos, Amazon craton—Brazil, were used to estimate the coda wave attenuation in the frequency band of 1 to 24 Hz. The time-domain coda-decay method of a single backscattering model is employed to estimate frequency dependence of the quality factor (Q _c) of coda waves modeled using Q_c = Q₀ f^hQ_{\rm c} =Q_{\rm 0} f^\eta , where Q ₀ is the coda quality factor at frequency of 1 Hz and η is the frequency parameter. We also used the independent frequency model approach (Morozov, Geophys J Int, 175:239–252, 2008), based in the temporal attenuation coefficient, χ(f) instead of Q(f), given by the equation c(f)=g+\fracpfQ_e \chi (f)\!=\!\gamma \!+\!\frac{\pi f}{Q_{\rm e} }, for the calculation of the geometrical attenuation (γ) and effective attenuation (Q_e^-1 )(Q_{\rm e}^{-1} ). Q _c values have been computed at central frequencies (and band) of 1.5 (1–2), 3.0 (2–4), 6.0 (4–8), 9.0 (6–12), 12 (8–16), and 18 (12–24) Hz for five different datasets selected according to the geotectonic environment as well as the ability to sample shallow or deeper structures, particularly the sediments of the Parecis basin and the crystalline basement of the Amazon craton. For the Parecis basin Q_c = (98±12)f^(1.14±0.08)Q_{\rm c} =(98\pm 12)f^{(1.14\pm 0.08)}, for the surrounding shield Q_c = (167±46)f^(1.03±0.04)Q_{\rm c} =(167\pm 46)f^{(1.03\pm 0.04)}, and for the whole region of Porto dos Gaúchos Q_c = (99±19)f^(1.17±0.02)Q_{\rm c} =(99\pm 19)f^{(1.17\pm 0.02)}. Using the independent frequency model, we found: for the cratonic zone, γ = 0.014 s^− 1, Q_e^-1 = 0.0001Q_{\rm e}^{-1} =0.0001, ν ≈ 1.12; for the basin zone with sediments of ~500 m, γ = 0.031 s^− 1, Q_e^-1 = 0.0003Q_{\rm e}^{-1} =0.0003, ν ≈ 1.27; and for the Parecis basin with sediments of ~1,000 m, γ = 0.047 s^− 1, Q_e^-1 = 0.0005Q_{\rm e}^{-1} =0.0005, ν ≈ 1.42. Analysis of the attenuation factor (Q _c) for different values of the geometrical spreading parameter (ν) indicated that an increase of ν generally causes an increase in Q _c, both in the basin as well as in the craton. But the differences in the attenuation between different geological environments are maintained for different models of geometrical spreading. It was shown that the energy of coda waves is attenuated more strongly in the sediments, Q_c = (78±23)f^(1.17±0.14)Q_{\rm c} =(78\pm 23)f^{(1.17\pm 0.14)} (in the deepest part of the basin), than in the basement, Q_c = (167±46)f^(1.03±0.04)Q_{\rm c} =(167\pm 46)f^{(1.03\pm 0.04)} (in the craton). Thus, the coda wave analysis can contribute to studies of geological structures in the upper crust, as the average coda quality factor is dependent on the thickness of sedimentary layer.     

基于谱元法的三维盆地－子盆地共振初步研究

本文基于谱元法,模拟三种深度的点震源下,四种倾角的三维单一小盆地模型和盆地－子盆地模型的地震动,通过盆地模型和基岩半空间模型的傅氏谱比分析三维盆地－子盆地模型的共振频率和放大特性。结果表明:（1）盆地－子盆地模型下,外部大盆地的存在导致子盆地共振频率下降约5%,盆地倾角的增大导致子盆地的共振频率略微减小。三维子盆地的共振频率约为二维模型的1.5倍左右。（2）子盆地模型相对于基岩半空间的放大倍数随着盆地形状比降低而增加。形状比由0.88降低至0.5,子盆地的放大系数增大1.3－1.8倍左右。（3）盆地－子盆地模型相对于单一小盆地模型的放大随震源深度的增加而降低,震源深度由2 km增加到18 km,由2.3降至1.3。     

Interpretation of the microtremor spectra at the Zafarraya basin, southern Spain

The microtremor spectra observed at the sediment-filled basin of Zafarraya show a peak near 2·8 Hz, independent of the local basin depth. Based on geoelectric and geologic data we constructed a tentative model of the site. The seismic response for vertically incident plane waves, both SH and P-SV, was computed by the finite-difference method. The observed spectral peak was found to be due to a combined effect of the 2-D basin bottom shape and the horizontally layered basin fill. Neither of the two effects explain the spectra when treated separately. Synthetic seismo-grams indicate a transitional basin behaviour, little investigated so far, between that typical of local basin-induced surface waves and a global 2-D resonance. A practical conclusion is that the site effects cannot be simply assessed by means of the basin shape ratio (thickness to half-width ratio) and the velocity contrast at the bottom.     

Mapping the thickness of sediments in the Ljubljana Moor basin (Slovenia) using microtremors

The Ljubljana Moor basin is characterized by moderate bedrock topography and thicknesses of Quaternary lacustrine and fluvial sediments ranging from 0 to 200 m. More than 65 boreholes which reached the bedrock were drilled in the area, but their distribution in the basin is very uneven and some data from the boreholes uncertain. There are also no data on S-velocity distribution within the basin, but seismic refraction measurements pointed out a rather uniform increase of P-velocity with depth, great impedance contrast with the bedrock and relatively small lateral velocity variations. The microtremor horizontal-to-vertical spectral ratio (HVSR) method was therefore applied as a complementary tool to seismic refraction survey to map the thickness of sediments. First, microtremors were measured at the locations of boreholes which reached the bedrock and the resonance frequencies determined. The inverse power relationship between the resonance frequency and the thickness of sediments was then determined from 53 data pairs. The quality of the correlation is moderate due to possible heterogeneities in sediments and possible 3D effects in some minor areas, but the obtained parameters correspond well to the values obtained in six other European basins. Secondly, a 16 km-long discontinuous seismic refraction profile was measured across the whole basin, leaving uncovered some larger segments where active seismic measurements were not possible. Microtremors were then measured at 64 locations along the same profile, using 250 m point spacing, without leaving any gaps. The frequency–thickness relationship was used to invert resonance frequencies to depths. These were first validated using the results of the seismic refraction survey, which showed good agreement, and finally used for interpolation in the segments of missing refraction data to obtain a continuous depth profile of the bedrock. The study has shown that the microtremor method can be used as a complementary tool for mapping the thickness of unconsolidated sediments also in areas characterized by moderate bedrock topography. As the input data are always to some extent uncertain, it is important to have a sufficiently large number of borehole data to establish a frequency–thickness relationship, as well as some additional independent geophysical information for its validation.     

Simulation of near source ground motion and its characteristics

It is fact that the severe ground motions of shear waves have a strong effect on the dynamic behavior of buildings and civil structures. We simulate near source strong motions of a pure shear wave and synthesize small motions, using the parameters based on the recorded accelerograms at the site that is regarded as a base rock in the Osaka basin, Japan. By making use of a stochastic technique, we can easily introduce higher frequency contents in the motions and apply the technique to the synthesis of small waves regarding as a green function. We also introduce to the analysis the useful relationships among the time duration T_d, the seismic moment M₀, the corner frequency f_c and the high cutoff frequency f_max which were regressed by a simple representation scheme. Considering two active faults that may affect severe damage on buildings and civil structures, we try to predict strong ground motions in Osaka basin and show the characteristics of them.     

A model for attenuation and scattering in the Earth's crust

The mechanisms contributing to the attenuation of earthquake ground motion in the distance range of 10 to 200 km are studied with the aid of laboratory data, coda wavesRg attenuation, strong motion attenuation measurements in the northeast United States and Canada, and theoretical models. The frequency range 1–10 Hz has been studied. The relative contributions to attenuation of anelasticity of crustal rocks (constantQ), fluid flow and scattering are evaluated. Scattering is found to be strong with an albedoB ₀=0.8–0.9 and a scattering extinction length of 17–32 km. The albedo is defined as the ratio of the total extinction length to the scattering extinction length. TheRg results indicate thatQ increases with depth in the upper kilometer or two of the crust, at least in New England. CodaQ appears to be equivalent to intrinsic (anelastic)Q and indicates that thisQ increases with frequency asQ=Q _o f ⁿ , wheren is in the range of 0.2–0.9. The intrinsic attenuation in the crust can be explained by a high constantQ (500Q _o2000) and a frequency dependent mechanism most likely due to fluid effects in rocks and cracks. A fluid-flow attenuation model gives a frequency dependence (QQ _o f ^0.5) similar to those determined from the analysis of coda waves of regional seismograms.Q is low near the surface and high in the body of the crust.     

Turbidity as a control on phytoplankton biomass and productivity in estuaries

In many coastal plain estuaries light attenuation by suspended sediments confines the photic zone to a small fraction of the water column, such that light limitation is a major control on phytoplankon production and turnover rate. For a variety of estuarine systems (e.g. San Francisco Bay, Puget Sound, Delaware Bay, Hudson River plume), photic-zone productivity can be estimated as a function of phytoplankton biomass times mean irradiance of the photic zone. Net water column productivity also varies with light availability, and in San Francisco Bay net productivity is zero (estimated respiratory loss of phytoplankton balances photosynthesis) when the ratio of photic depth (Z_p) to mixed depth (Z_m) is less than about 0.2. Thus whenever Z_p: Z_m < 0.2, the water column is a sink for phytoplankton production.Much of the spatial and temporal variability of phytoplankton biomass or productivity in estuaries is explained by variations in the ratio of photic depth to mixed depth. For example, phytoplankton blooms often coincide with stratification events that reduce the depth of the surface mixed layer (increase Z_p: Z_m). Shallow estuarine embayments (high Z_p: Z_m) are often characterized by high phytoplankton biomass relative to adjacent channels (low Z_p: Z_m). Many estuaries have longitudinal gradients in productivity that mirror the distribution of suspended sediments: productivity is low near the riverine source of sediments (low Z_p: Z_m) and increases toward the estuary mouth where turbidity decreases. Some of these generalizations are qualitative in nature, and detailed understanding of the interaction between turbidity and estuarine phytoplankton dynamics requires improved understanding of vertical mixing rates and phytoplankton respiration.     

Determination of the maximum-depth to potential field sources by a maximum structural index method

A simple and fast determination of the limiting depth to the sources may represent a significant help to the data interpretation. To this end we explore the possibility of determining those source parameters shared by all the classes of models fitting the data. One approach is to determine the maximum depth-to-source compatible with the measured data, by using for example the well-known Bott–Smith rules. These rules involve only the knowledge of the field and its horizontal gradient maxima, and are independent from the density contrast.Thanks to the direct relationship between structural index and depth to sources we work out a simple and fast strategy to obtain the maximum depth by using the semi-automated methods, such as Euler deconvolution or depth-from-extreme-points method (DEXP).The proposed method consists in estimating the maximum depth as the one obtained for the highest allowable value of the structural index (N_max). N_max may be easily determined, since it depends only on the dimensionality of the problem (2D/3D) and on the nature of the analyzed field (e.g., gravity field or magnetic field). We tested our approach on synthetic models against the results obtained by the classical Bott–Smith formulas and the results are in fact very similar, confirming the validity of this method. However, while Bott–Smith formulas are restricted to the gravity field only, our method is applicable also to the magnetic field and to any derivative of the gravity and magnetic field. Our method yields a useful criterion to assess the source model based on the (∂f/∂x)_max/f_max ratio.The usefulness of the method in real cases is demonstrated for a salt wall in the Mississippi basin, where the estimation of the maximum depth agrees with the seismic information.