Geologic and geophysics data integration for isosist line interpretation with interpolation process and tectonic implications for southern Mexico.

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1 1 Geologic and geophysics data integration for isosist line interpretation with interpolation process and tectonic implications for southern Mexico. Carlos Francisco Yáñez Mondragón y Jesús Uribe Luna Consejo de Recursos Minerales Boulevard Felipe Angeles s/n, km. 93.5, Col. Venta Prieta, Pachuca, Hidalgo, México, C.P Abstract. Using 2207 data points of seismic epicentres from southern Mexico, a data base map was built with geographic information system tools, and its attributes were latitude, longitude, depth, and seismic magnitude in the Richter scale. To estimate the seismic intensity in the Mercalli scale, the magnitude and the depth data set attributes were used, the values of intensity were also stored in a new data field. Spatial distribution of the seismic intensity was processed in an interpolation model, using Kriging procedure, the result was a estimated surface from which was extracted contour lines with Mercalli degree values. The spatial variations of the intensity values were measured using the semi-variogram that is a graphical plot of semi-variance. The contour lines were displayed like a new information layer map named isosist. It was compared with the inverse distance weighted (IDW) interpolation process. The results were displayed with the geological province boundaries, geological map of Oaxaca and magnetic field image of the Oaxaca, 250,000-scale map sheet. The analysis of the geological and geophysical data models shows a homogeneous distribution of isosist for the Palaeozoic metamorphic Mixteco Terrane and a heterogeneous distribution for Precambrian metamorphic Zapoteco Terrane. The boundary between those terranes could be interpreted as a regional NW-SE fault basement trend. Introduction. The current plate tectonic model (Dobson, 1981) in its configuration of the south of Mexico shows the convergent margin between the boundaries of Cocos and North America plates, which has been active since the Mesozoic times (Urrutia, 1986). In this margin (Padilla y Sánchez, 1986) is possible that the seismic activity has been present for several million years ago. Actually the cost line area of Guerrero and Michoacan states is the most active region (Mota, et al., 1986), and has been documented as the most dangerous (Ferraes, 1971; Herrera, et al., 1985) in earthquake risk for whole Mexico. In this work a model of seismic intensity is presented for the region of the southern Mexico, and analyze the available data

2 2 and used modeling process of the seismicity and its relationship with the geological provinces (Ortega, et al., 1992). Source of data. For this work we used the available data of the National Seismological Service (S.S.N., ) of a 10 year-old period. The data of X and Y coordinates were ordered mainly in a text file that contains 2207 records of seismic events of the south of Mexico, for the Oaxaca state located in southern Mexico. By means of the tools of a Geographical Information System, a map of points was build it represents seismic epicentres according to the methodology proven (Bonham, 1991; ESRI, 1992). Finally the system of geographic coordinates has been changed to the Lambert Conical Projection (Figure 1) to integrate other reference maps as the state limits (INEGI, 1982) and the geological provinces of Mexico. Database. With the same text file a small database was build that it is related with each point of the epicentres on map. The attribute table contains the longitude, latitude and depth of the focus (seismic hipocenter), the magnitude in degrees of Richter s scale, the date and the hour of the event according to the following definition. Item Type Width Decimal Number Integer 4 Longitude Numeric 9 4 Latitude Numeric 7 4 Magnitude Number 3 1 Focus Integer 3 Date Character 8 Hour Character 8 The values of longitude are between to degrees of west longitude; the values of latitude are between to degrees of north latitude; the values of depth are between 2 to 288 kilometers of depth; the values of magnitude are between 3 to 7.4 degrees in the Richter s scale. For each seismic event the value of magnitude is a quantitative variable that represents the space distribution

3 3 of the energy liberated in a region or rupture area and it can not be interpolated appropriately since the energy liberated in a hipocenter is unique and particular. The concept of seismic intensity is referred as a perception of the energy of an earthquake and the damages, so we can consider it like a qualitative variable that can be used in an interpolation process like those used in others authors in natural resources evaluations (Webster and Oliver, 1990). The algorithm for the calculation of the seismic intensity (Esteva and Rosenbleuth, 1964) has been used to store the data in a new field in the database according to the following definition. Item Type Width Decimal Intensity Integer 2 0 The used algorithm is: I = * M log10 (F) Where I is the intensity calculated in the scale of Mercalli, M is the magnitude and F it is the focus depth or hipocenter (Lomnitz, 1974). The obtained values are between 4 and 13 degrees of Mercalli s scale that which is interesting because it considers the threshold values and it only allows to consider the interval of interest from 5 to 12 degrees. Model of seismic Intensity. The sense of the space modeling is to build a model that represents an interpolated variable. The seismic intensity is based on the process of interpolation kriging (Le krigeage) that is a lineal estimator of the sum of variations for the average of the z value of the points considered from 1 until " n " (Matheron, 1963). Z = a i x i The model is simple and relatively easy to generate and it is based on the modeling of the available information of a natural phenomenon. The modeling is the procedure in which we take the values of an attribute of the database of a map and a new layer of information is generate by means of an algorithm or a program with tools of a Geographical Information System (ESRI, 1991). The obtained values of the intensity are calculated with an algorithm and therefore they are

4 4 discreet values of a qualitative variable represented as values " z " those that are interpolated by means of the well-known method as kriging. Since the value of the intensity calculated considers the seismic magnitude and the depth in kilometers, the result represents an anisotropic distribution that is interesting to consider for the regional interpolation and its interpretation in the space distribution of the variable of intensity (Figure 2). The interpolation process generates a graph of the interpolation variations that is known as semi-variogram and that it contains a group of interpolated points compared with a curved line of the pattern of used mathematical equation. The semi-variogram equation is: (h) = ½ n [f (x i ) - f (x i + h) ] 2 Where h is the space vector among the point x i and the point candidate to interpolate in the distance x i + h while the mathematical function of the used spherical pattern is: (h) = C O + C (3/2 h/a - ½ (h/a) 3 ) Where C O are a constant value of increment in each well-known iteration step as the effect "nugget " and the heat of C O + C is the sill or threshold (David, 1977) and a is the range. When using the program Kriging the following values were obtained: C O = C = a = sill = The obtained variogram (Figures 3) shows the variance values in the Y-axis and the values of iteration distance among points in the X-axis. The regular line in the graph is the equation of the used spherical pattern. In the analysis of the graph the values of the irregular line are distributed regarding the regular line that is shown in the graph quite consistent it supposes the values of intensity have been interpolated correctly, that the space values are consistent and they have an appropriate space relationship. Visually, the result can be described like a cell structure (lattice) with a distance size among cells of 30 seconds of arch that

5 5 correspond to 900 meters in the ground (Figures 4). This cell size is the best to have a regional model and this analysis window allows obtaining a large-scale resolution. One of the interesting aspects of the modeling is that we can obtain a new topic or information layer in vector format with values of an attribute " z " (Royle, et al., 1981; Ostman, 1986; Ross, 1986). The cell structure is a surface of continuous data that represents the regionalized variable of intensity, interpolated homogeneously among the discreet values. Finally, it was obtained a new topic of isolines of same value of intensity or isosist (Figure 5). This layer of information is superimposed to other layers that came from other sources and the mean problem is to try to interpret the result and to correlate it with the large tectonic elements of the earth s surface and the geological provinces of Mexico. When compared the model made with inverse distance weighted (IDW) interpolation process (Figure 6), we can see that the intensity values has a local distribution around the highest values of data points and not have enough values among the points. This means that the model made with radial distance estimation is almost a geometric model rather than the kriging model that doesn t give enough interpolated information. Geological significance. The purpose of the spatial modeling is to build an improved model and process capable for changing the data in order to make the best model next time. But the model must be also compared with others earth science data to prove how to real is it. So, it is very important to have a data with a relationship with the model and then we use geological provinces map to overlay with the model and the effort that we need to do it to have an interpretation of the relationship between the obtained model and the geological available data. One of the most significant challenges is the correlation of the seismicity and the interpolated models with the big characteristic geological of the terrestrial surface. The pattern of seismic intensity represents the values of calculated and interpolated intensity and its relationship to their space distribution with the geological provinces of Mexico (Ortega, et al., 1992) which geological characteristic of lithology, structures and geological evolution is particular. The model represents a regional variable qualitative

6 6 homogeneously obtained by means of the interpolation kriging process of and it is represented finally as isolines that have a singular and significant distribution pattern and it seems to be in agreement with the current pattern of the plate tectonic boundaries (Dobson, 1981), specially for the south region of Mexico (Nikson, 1982). The spatial distribution of the isolines is homogeneous inside the continental region of southern Mexico where the highest value group is in the area of the coastline of Oaxaca in the boundary of the Xolapa metamorphic Complex. In the oceanic region, the highest values concentrate inside the area of tectonic decrease of the Meso America subduction zone and the area of accretion of the continental platform. The distribution of the isolines in the continental region it is related to the seismic activity intraplate (Sing, et al., 1980) whose lower values varies from 4 to 6 degrees in the Mercalli scale. They are distributed in wide and very defined areas inside the Zapoteca Province in the central area of the state of Oaxaca that has a compound tectonic complex of Precambrian age. The intermediate values from 6 to 8 degrees are presented in wide and very defined areas in the boundaries of Guerrero and Oaxaca states, inside the Mixteca Province that has a complex tectonic origin and Palaeozoic age (Figure 7). The obtained model is useful in the tectonic boundaries interpretation of Oaxaqueño and Acatlan metamorphic complexes, which are not easy to understand just to see lithology and structures in geological maps. Between Asuncion Nochixtlan and Tepelmeme towns there is not a superficial extension of faults zone because sedimentary Mesozoic and volcanic Cainozoic age lithologic units cover the complexes. The analysis of the isosist values within the metamorphic complexes show that there are a gentle change in the fault zone and strong change of magnetic field values so it can meaning a bearing like intrusive igneous rock response which could be Cozahuico Granite. The geologic significance is that the fault zone is extended to the north of Tepelmeme, to the Caltepec Fault zone (Elias and Ortega, 2000). The greatest intensity values are concentrate in the south of Oaxaca State, from Santiago Pinotepa Nacional to Salina Cruz. This is a great shear zone of Juchatengo Colotepec Chacalapa strike slip faults relate to the boundaries between Xolapa and Oaxaqueño metamorphic complexes as well as

7 7 igneous intrusive rocks of Miocene Pliocene age (Figure 8). The shallow seismic epicentres with values between 4.5 and 4.7 Richter s degree are near by Colotepec and Chacalapa fault zones and suggest that those faults do not extend deep into the continental crust, that they are into the same tectonic block and have lateral displacement into gneiss and schist rocks of Oaxaqueño Metamorphic Complex while few epicentres are near by Juchatengo fault zone which affect the rocks of Xolapa Metamorphic Complex of Pre Cambrian to Palaeocene age. The analysis of the epicentres distribution suggest that Colotepec and Chacalapa faults are the most active and the distribution of the isosist values show that the greatest values are near of Juchatengo fault zone which accumulate seismic energy. The Chacalapa fault is extended to the east where has high isosist values and affect volcanic and sedimentary rocks of Jurassic age intruded by granodioritic rocks of Miocene age that suggest a intersection fault zone to the west of Salina Cruz, western Oaxaca State. Other considered data comprises the evidences of geological field works from other authors (Elias and Ortega, op. Cit.) and with the interpretation of remote sensing image (Uribe, 2000) in the fault zone of the north boundaries of the Zapoteca and Mixteca Provinces as well as a digital model of total magnetic field (COREMI, 2001), which demonstrated that the interpretation of this tectonic features are appropriate and it extends in a pattern of lateral faults of regular expression toward the south in a NW - SE trend (Figure 9). A similar distribution of the intensity values in the Cuicateca Province in the oriental region of the state of Oaxaca that has a tectonic origin of submarine volcanic sedimentary arch Mesozoic age. Finally, the biggest values of intensity varies from 8 to 11 degrees which are concentrated in an irregular and heterogeneous arrangement on the region of the coast line of Guerrero and Oaxaca states. The interpretation of such a distribution responds to the characteristics of the Chatina Province, a tectonic arch root of plutonic origin of Mesozoic age.

8 8 Bibliography Bonham,C,G.F.,1991. Integration of geoscientific data using GIS, Geographical Information Systems, Principles and applications. Ed. Longman scientific and technical, pp Consejo de Recursos Minerales, Mapa de campo magnético total en relieve. Carta E14-9, Oaxaca, escala 1:250,000. David M., Geostatistical ore reserve estimation. Ed. Elsevier Scientific Publishing Co., pp Dobson, G., Plate tectonic of circumpacific and caribbean region. American Association of Petroleum Geologist. 1:2,000,000 scale. Elias, H. M., Ortega, G. F., Roots of the Caltepec Fault zone, Southern Mexico: early permian epidote bearing anatexitic granitoids. Segunda Reunión Nacional de Ciencias de la Tierra, Resúmenes en Revista Geos, Vol. 20, N. 3. pp ESRI, 1991.Cell-based modeling with grid. Arc/info user s guide, Environmental System Research Institute. pp ESRI, Understanding GIS, the arc-info method. Environmental System Research Institute. Ferraes, S., 1971.Probabilidad de ocurrencia de temblores sucesivos de magnitud en la ciudad de México. Revista Geofísica Internacional, Instituto de Geofísica. Vol. 2, No. 4, pp Herrera,R.I., Ponce,L.,Jiménez,Z., Espíndola,J.M., Lomnitz,C., El sismo del 19 de septiembre de 1985, informe geofísico y evaluación preliminar. Revista Ingeniería. N. 3, pp Instituto Nacional de Estadística, Geografía e Informática, (INEGI), Carta topográfica escala 1:4,000,000. Lomnitz, C., Global tectonics and earthquakes risk, Developments in geotectonics 5, Elsevier scientifc Pub. Co. 1974, pp Morán-Zenteno,D.J.,1986.Breve revisión sobre la evolución tectónica de México. Revista Geofísica Internacional, Instituto de Geofísica. Vol. 25, N. 1, pp.9-38.

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11 11 Figure 1. Seismic epicentres and geological provinces in Oaxaca State. Figure 2. Digital model of intensity values in the Mercalli scale, epicentres and its attributes.

12 12 Figure 3. Semi-variogram from the digital model of intensity. Figure 4. Digital model of intensity and epicentres from Oaxaca State.

13 13 Figure 5. Epicentres and intensity polygons overlayer. Note the dark areas of highest intensity values concentrated at the coas-line of Oaxaca State. Figure 6. Digital model of intensity with the IDW interpolation process. Note the white area concentrations of highest intensity values.

14 14 Figure 7. Digital model of intensity whit the geological provinces. Note the white areas to the south of Oaxaqueño (Zapoteca) and Acatlan (Mixteca) complexes. Figure 8. Digital model of relief, lithological units and geological structures. Note the strike-slip fault system and the dark areas of higest intensity values.

15 15 Figure 9. Geological provinces over the digital model of magnetic field relief and the polygons of intensity. Note the homogeneous distribution of the magnetic intensity within the geological provinces and the agreement with the dark areas of highest intensity values polygons.